**Meet the editors**

Professor Magd Abdel Wahab is a full-time professor of applied mechanics in the Faculty of Engineering and Architecture at Ghent University, Belgium, and an adjunct professor of computational mechanics at Ton Duc Thang University, Vietnam. He received his B.Sc., 1988, in Civil Engineering and his M.Sc., 1991, in Structural Mechanics, both from Cairo University. Professor Wahab complet-

ed his Ph.D. in Fracture Mechanics in 1995 at KU Leuven, Belgium. He was awarded the degree of Doctor of Science from the University of Surrey in 2008. He has published more than 350 scientific papers in solid mechanics and dynamics of structures, and edited more than 12 books and proceedings. His research interests include fracture mechanics, damage mechanics, fatigue of materials, durability, structural health monitoring, and dynamics and vibration of structures.

Dr. Yun Lai Zhou is a research fellow in the Department of Civil and Environmental Engineering at the National University of Singapore, Singapore. He received his B.Sc., 2010, in Mechanical Engineering from Northwestern Polytechnical University, China, and completed his M.Sc. in 2011 and PhD in 2015, both in Civil Engineering, from the Technical University of Madrid (UPM), Spain. He was awarded the

honor of International Ph.D. from UPM in 2015. He has published more than 40 scientific papers, conference proceedings, and technical reports in structural health monitoring, transmissibility-based damage identification, machine learning, and structural dynamics. His current research interests include structural health monitoring, sensing techniques, data processing, fracture mechanics, damage mechanics, coupling, and structural vibrations.

Professor Nuno Manuel Mendes Maia had his habilitation in Mechanical Engineering in 2001 from Instituto Superior Tecnico (IST), University of Lisbon. Professor Maia has authored and co-authored two textbooks and about 200 scientific publications in international journals and conference proceedings on the subject of modal analysis and structural dynamics. He obtained his first degree in

1978 and his master's degree in 1985, both in Mechanical Engineering, from Instituto Superior Tecnico IST, University of Lisbon. He received his Ph.D. in Mechanical Vibrations (1989) from Imperial College London, UK. His current research interests are modal analysis and modal testing, updating of finite element models, coupling and structural modification, damage detection in structures, modeling of damping, transmissibility in multiple degree-of-freedom systems, and force identification.

Contents

**Preface VII**

**Technique 23**

Tomasz Gałka

Md. Tawhidul Islam Khan

**Diagnosis and Prognosis 39**

Zenghua Liu and Honglei Chen

Zenghua Liu and Honglei Chen

Francesc Pozo and Yolanda Vidal

**Applications 117**

Chapter 1 **Failure Assessment of Piezoelectric Actuators and Sensors for**

**Increased Reliability of SHM Systems 1** Inka Mueller and Claus-Peter Fritzen

Chapter 2 **Structural Health Monitoring by Acoustic Emission**

Chapter 3 **Evaluation of Diagnostic Symptoms for Object Condition**

Chapter 4 **Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part A-Lamb Waves Signals Emitting and Optimization Techniques 61**

Chapter 5 **Application and Challenges of Signal Processing Techniques for**

**Imaging and Recognition Techniques 87**

Chapter 6 **Qualification of PWAS-Based SHM Technology for Space**

Chapter 7 **Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing 137**

Ioan Ursu, Mihai Tudose and Daniela Enciu

**Lamb Waves Structural Integrity Evaluation: Part B-Defects**

## Contents

## **Preface XI**


## Chapter 8 **Structural Health Monitoring of Bolted Joints Using Guided Waves: A Review 163**

Preface

Structural health monitoring (SHM) has attracted more attention during the last few decades in many engineering fields with the main aim of avoiding structural disastrous events. This aim is achieved by using advanced sensing techniques and further data processing. SHM is a multidisciplinary technique that has undergone decades of development. It has experienced booming advancements during recent years due to the developments in sensing techniques such as wireless sensing systems, embedded sensing systems, fiber optical sensing systems, etc. The reliable operation in current sophisticated man-made structures, e.g. dams, bridges, and wind turbines in civil engineering applications, and vehicles, trains, and aircraft in me‐ chanical and aerospace applications, drives the development of incipient reliable damage di‐ agnosis and assessment. This book aims to illustrate the background and applications of SHM from both sensing and processing approaches. Its main objective is to summarize the advan‐ tages and disadvantages of SHM methodologies and their applications, which may provide a

new perspective in understanding SHM for readers from diverse engineering fields.

this book for their invaluable contributions.

This book contains eight chapters that cover SHM methodologies and applications. The chap‐ ters concerned with methodologies include topics on aspects of reliability of piezoelectric ac‐ tuators and sensors, the acoustic emission technique for SHM, and selection of diagnostic symptoms for condition assessment and prognosis. The chapters concerned with applica‐ tions include topics on applications and challenges of signal processing techniques for Lamb wave structural integrity, the use of piezoelectric wafer active sensor technology in SHM for space applications, application of SHM to wind turbine structures using univariate and mul‐ tivariate hypothesis testing, and application of SHM to bolted joints using guided waves. The editors would like to express their thanks to the authors of the chapters presented in

**Professor Magd Abdel Wahab**

Department of Civil and Environmental Engineering

National University of Singapore, Singapore

**Prof. Nuno Manuel Mendes Maia**

Ghent University Ghent, Belgium

**Dr. Yun Lai Zhou**

University of Lisbon Lisbon, Portugal

Fei Du, Chao Xu, Huaiyu Ren and Changhai Yan

## Preface

Chapter 8 **Structural Health Monitoring of Bolted Joints Using Guided**

Fei Du, Chao Xu, Huaiyu Ren and Changhai Yan

**Waves: A Review 163**

**VI** Contents

Structural health monitoring (SHM) has attracted more attention during the last few decades in many engineering fields with the main aim of avoiding structural disastrous events. This aim is achieved by using advanced sensing techniques and further data processing. SHM is a multidisciplinary technique that has undergone decades of development. It has experienced booming advancements during recent years due to the developments in sensing techniques such as wireless sensing systems, embedded sensing systems, fiber optical sensing systems, etc. The reliable operation in current sophisticated man-made structures, e.g. dams, bridges, and wind turbines in civil engineering applications, and vehicles, trains, and aircraft in me‐ chanical and aerospace applications, drives the development of incipient reliable damage di‐ agnosis and assessment. This book aims to illustrate the background and applications of SHM from both sensing and processing approaches. Its main objective is to summarize the advan‐ tages and disadvantages of SHM methodologies and their applications, which may provide a new perspective in understanding SHM for readers from diverse engineering fields.

This book contains eight chapters that cover SHM methodologies and applications. The chap‐ ters concerned with methodologies include topics on aspects of reliability of piezoelectric ac‐ tuators and sensors, the acoustic emission technique for SHM, and selection of diagnostic symptoms for condition assessment and prognosis. The chapters concerned with applica‐ tions include topics on applications and challenges of signal processing techniques for Lamb wave structural integrity, the use of piezoelectric wafer active sensor technology in SHM for space applications, application of SHM to wind turbine structures using univariate and mul‐ tivariate hypothesis testing, and application of SHM to bolted joints using guided waves.

The editors would like to express their thanks to the authors of the chapters presented in this book for their invaluable contributions.

> **Professor Magd Abdel Wahab** Ghent University Ghent, Belgium

**Dr. Yun Lai Zhou** Department of Civil and Environmental Engineering National University of Singapore, Singapore

> **Prof. Nuno Manuel Mendes Maia** University of Lisbon Lisbon, Portugal

**Chapter 1**

Provisional chapter

**Failure Assessment of Piezoelectric Actuators and**

DOI: 10.5772/intechopen.77298

Failure Assessment of Piezoelectric Actuators and

**Sensors for Increased Reliability of SHM Systems**

In the chain from sensing to information extraction, there are many traps where errors can occur, which might lead to false alarms and therefore leave us with the impression of an unreliable system. In this chapter, we deal with the important first element of the chain, the sensor, which can undergo various faults and defects during its lifetime. Especially for the use of acousto-ultrasonic (AU)-based methods or the electro-mechanical impedance (EMI) method, piezoelectric transducers are frequently used. Subsequent steps within the chain of SHM rely on the quality and reliability of these measurements. An overview is given on the usage of piezoelectric transducers within SHM systems, their electromechanical coupling and its modeling as well as frequent faults of these devices and methods on how to inspect them and diagnose defects. The authors show the effects of different transducer faults on the excited wave field, used for AU. It is shown how a sensor fault can be detected before the SHM system indicates a (false) alarm. With the help of application scenarios—including temperature variations—the advantages and disadvantages of the introduced methods of transducer inspection are presented, enabling

Keywords: piezoelectric transducers, piezoelectric wafer active sensors, faults, defects, electro-mechanical impedance, acousto-ultrasonics, guided waves, lamb waves, structural

Aspects of reliability play a major role for the development of structural health monitoring (SHM) systems in working industrial applications. This reliability has to be ensured for all

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Sensors for Increased Reliability of SHM Systems

Inka Mueller and Claus-Peter Fritzen

Inka Mueller and Claus-Peter Fritzen

http://dx.doi.org/10.5772/intechopen.77298

Abstract

1. Introduction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

an increased reliability of SHM systems.

health monitoring, system reliability

#### **Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems** Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

DOI: 10.5772/intechopen.77298

Inka Mueller and Claus-Peter Fritzen Inka Mueller and Claus-Peter Fritzen

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77298

#### Abstract

In the chain from sensing to information extraction, there are many traps where errors can occur, which might lead to false alarms and therefore leave us with the impression of an unreliable system. In this chapter, we deal with the important first element of the chain, the sensor, which can undergo various faults and defects during its lifetime. Especially for the use of acousto-ultrasonic (AU)-based methods or the electro-mechanical impedance (EMI) method, piezoelectric transducers are frequently used. Subsequent steps within the chain of SHM rely on the quality and reliability of these measurements. An overview is given on the usage of piezoelectric transducers within SHM systems, their electromechanical coupling and its modeling as well as frequent faults of these devices and methods on how to inspect them and diagnose defects. The authors show the effects of different transducer faults on the excited wave field, used for AU. It is shown how a sensor fault can be detected before the SHM system indicates a (false) alarm. With the help of application scenarios—including temperature variations—the advantages and disadvantages of the introduced methods of transducer inspection are presented, enabling an increased reliability of SHM systems.

Keywords: piezoelectric transducers, piezoelectric wafer active sensors, faults, defects, electro-mechanical impedance, acousto-ultrasonics, guided waves, lamb waves, structural health monitoring, system reliability

## 1. Introduction

Aspects of reliability play a major role for the development of structural health monitoring (SHM) systems in working industrial applications. This reliability has to be ensured for all

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

steps of the SHM process, which are, according to Farrar and Worden, (1) operational evaluation, (2) data acquisition, (3) feature selection and (4) statistical modeling for feature discrimination [1]. Within this chapter, the second step "data acquisition" is focused. It is closely linked to the third step, which aims at extracting the damage relevant information from the measured data via data analysis. Within the toolbox of methods used for SHM, the two groups vibrationbased methods and wave-based methods have emerged. Vibration-based methods are based on the fact that modal parameters like eigenfrequencies, mode shapes and modal damping are functions of physical properties like the distribution of stiffness or of mass. In case of damage, physical properties are changed, leading to a change of the modal parameters, which are monitored by vibration-based SHM systems. Moreover, we can go to the higher frequency range and evaluate the time data directly. For their monitoring, excitation is necessary, which is often achieved by using ambient excitation, e.g., cars crossing a bridge to be monitored. Wavebased SHM methods either use the fact that a damage, e.g., cracks or breaking fibers within a composite component, will result in an emitted acoustic signal or use the fact that a wave will interfere with a possible damage. For the first, the acoustic signal will travel through the component and be detected by members within a net of listening sensors. Data evaluation will identify these single events and might locate the crack's position via triangulation. While this method is a passive method, the wave-based acousto-ultrasonics method is characterized as an active method. A well-defined excitation is used, creating a wave, which travels through the structure, interferes with specific geometric features of the structure, like edges, thickness, changes but also damages and is sensed after these interferences, e.g., at a different point of the structure. When traveling through thin-walled plates or rods, waves often appear as guided waves. They are reflected, can convert into different modes or the transmitted part is changed by discontinuities, like damages. Therefore, a change of the evaluated signal is interpreted as an indicator for damage.

vibration-based SHM systems use statistical damage classification [6, 7] including, e.g., fuzzy

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

http://dx.doi.org/10.5772/intechopen.77298

3

For vibration-based SHM systems, the used sensors are often based on well-approved measurement sensors, which have been used in the past for different purposes, measuring strain, acceleration or displacement. The special requirements of SHM systems regarding the continuous monitoring on-site over long periods are achievable and the measurement systems might include a self-check and transducer electronic data sheets (TEDS) to increase the reliability, e.g., ICP compatible accelerometers. Wave-based methods often use a distributed sensor network and the included sensors are just starting to enter more into commercial products, e.g., PICeramic P-876.SP1 and Acellent SMART Layer [11, 12]. This chapter focuses on the wave-based methods, which use

Using guided waves, an SHM system identifies damages via comparing signals from different states. While the current state which should be evaluated is always based on measurements, the reference state, often taken from the pristine structure, can either be based on measurement data or set up by physics-based models. Occasionally, the comparison is also based on assumptions like the linear material behavior of the system in pristine state. The different methods of feature selection and feature discrimination are not within the focus of this chapter, as there are a multitude of possibilities. Nevertheless, the consideration of reliability on these steps is highly important and is a major research area to enable certification processes, necessary for

Focusing the inspection of sensors and its self-test, different approaches can be found. Simple systems check, if the sensor signal is different from zero. More advanced data-driven methods are based on hardware redundancy [13]. Typical faults are bias, complete failure, drifting and precision degradation, see [14], as well as gain, noise and constant with noise [13]. For networks of wireless sensor nodes, these methods are used to find faulty nodes to be able to either replace those nodes or simply remove them from the network, which is only possible with sufficient redundancy, see e.g., [15]. The use of hardware redundancy, which tests if the sensor signal fits the assumed signal, when only using all other sensors, has been used for SHM systems, too. In [16], a modal filtering approach is used, and [17] uses a PCA-model to represent the signal in a lower-dimensional space and compare it with the original signal. The effect of temperature change and structural damage is considered in [18] using the mutual information concept. All these methods use the measurement data for a mathematical procedure not based on physical quantities. While it is an advantage that no additional measurements are needed, this also leads to difficulties in distinguishing between structural damage and sensor fault, especially for the case of small defects and in widespread sensor network. Depending on the type of sensor, physics-based methods of self-diagnosis using additional measurements can be found. Ref. [19] describes the use of electrical impedance spectroscopy measurement to enable self-monitoring of semiconductor gas sensor systems. In [20], methods to enable a validation of the sensor functions under operational conditions are suggested, which include the use of a magnetostrictive coated fiber. For piezoelectric wafer active sensors (PWAS), self-diagnosis capabilities exist, which are mainly based on the transducers physics.

classification [8], the use of neural networks [9] and self-organizing maps [10].

piezoelectric transducers for data acquisition, including actuation and sensing purposes.

the use of SHM systems in industrial applications.

For all SHM systems, it has been shown that the influence of environmental and operational conditions cannot be neglected. If we ignore a change of temperature, it might be interpreted as damage or a temperature change might decrease or even reverse the effect of damage. Depending on the SHM method, different approaches to tackle especially temperature changes have been proposed. For methods using acousto-ultrasonics, in [2] an overview of different methods for the compensation of temperature changes is given and the use of the local temporal coherence to cope with the changes of temperature and effects of surface wetting is detailed. Similar to this approach, for methods based on the signature of the electromechanical impedance (EMI) spectrum, in [3], a correlation coefficient-based method is used, which compensates frequency and magnitude shifts, caused by temperature changes, while changes of the shape, caused by damages within the structure, are identified. This method is applicable if the effects of damage can be clearly separated from effects of temperature variation. This is not the case for all applications. Therefore, in [4, 5], a physics-based compensation of the influences of temperature changes is used for EMI and acousto-ultrasonics (AU)-based methods. The effort for this method is large, as the temperature dependence of all significant parameters has to be included within the model. Other efforts to compensate for varying environmental and operational conditions for signal-based techniques within wave- and vibration-based SHM systems use statistical damage classification [6, 7] including, e.g., fuzzy classification [8], the use of neural networks [9] and self-organizing maps [10].

steps of the SHM process, which are, according to Farrar and Worden, (1) operational evaluation, (2) data acquisition, (3) feature selection and (4) statistical modeling for feature discrimination [1]. Within this chapter, the second step "data acquisition" is focused. It is closely linked to the third step, which aims at extracting the damage relevant information from the measured data via data analysis. Within the toolbox of methods used for SHM, the two groups vibrationbased methods and wave-based methods have emerged. Vibration-based methods are based on the fact that modal parameters like eigenfrequencies, mode shapes and modal damping are functions of physical properties like the distribution of stiffness or of mass. In case of damage, physical properties are changed, leading to a change of the modal parameters, which are monitored by vibration-based SHM systems. Moreover, we can go to the higher frequency range and evaluate the time data directly. For their monitoring, excitation is necessary, which is often achieved by using ambient excitation, e.g., cars crossing a bridge to be monitored. Wavebased SHM methods either use the fact that a damage, e.g., cracks or breaking fibers within a composite component, will result in an emitted acoustic signal or use the fact that a wave will interfere with a possible damage. For the first, the acoustic signal will travel through the component and be detected by members within a net of listening sensors. Data evaluation will identify these single events and might locate the crack's position via triangulation. While this method is a passive method, the wave-based acousto-ultrasonics method is characterized as an active method. A well-defined excitation is used, creating a wave, which travels through the structure, interferes with specific geometric features of the structure, like edges, thickness, changes but also damages and is sensed after these interferences, e.g., at a different point of the structure. When traveling through thin-walled plates or rods, waves often appear as guided waves. They are reflected, can convert into different modes or the transmitted part is changed by discontinuities, like damages. Therefore, a change of the evaluated signal is

For all SHM systems, it has been shown that the influence of environmental and operational conditions cannot be neglected. If we ignore a change of temperature, it might be interpreted as damage or a temperature change might decrease or even reverse the effect of damage. Depending on the SHM method, different approaches to tackle especially temperature changes have been proposed. For methods using acousto-ultrasonics, in [2] an overview of different methods for the compensation of temperature changes is given and the use of the local temporal coherence to cope with the changes of temperature and effects of surface wetting is detailed. Similar to this approach, for methods based on the signature of the electromechanical impedance (EMI) spectrum, in [3], a correlation coefficient-based method is used, which compensates frequency and magnitude shifts, caused by temperature changes, while changes of the shape, caused by damages within the structure, are identified. This method is applicable if the effects of damage can be clearly separated from effects of temperature variation. This is not the case for all applications. Therefore, in [4, 5], a physics-based compensation of the influences of temperature changes is used for EMI and acousto-ultrasonics (AU)-based methods. The effort for this method is large, as the temperature dependence of all significant parameters has to be included within the model. Other efforts to compensate for varying environmental and operational conditions for signal-based techniques within wave- and

interpreted as an indicator for damage.

2 Structural Health Monitoring from Sensing to Processing

For vibration-based SHM systems, the used sensors are often based on well-approved measurement sensors, which have been used in the past for different purposes, measuring strain, acceleration or displacement. The special requirements of SHM systems regarding the continuous monitoring on-site over long periods are achievable and the measurement systems might include a self-check and transducer electronic data sheets (TEDS) to increase the reliability, e.g., ICP compatible accelerometers. Wave-based methods often use a distributed sensor network and the included sensors are just starting to enter more into commercial products, e.g., PICeramic P-876.SP1 and Acellent SMART Layer [11, 12]. This chapter focuses on the wave-based methods, which use piezoelectric transducers for data acquisition, including actuation and sensing purposes.

Using guided waves, an SHM system identifies damages via comparing signals from different states. While the current state which should be evaluated is always based on measurements, the reference state, often taken from the pristine structure, can either be based on measurement data or set up by physics-based models. Occasionally, the comparison is also based on assumptions like the linear material behavior of the system in pristine state. The different methods of feature selection and feature discrimination are not within the focus of this chapter, as there are a multitude of possibilities. Nevertheless, the consideration of reliability on these steps is highly important and is a major research area to enable certification processes, necessary for the use of SHM systems in industrial applications.

Focusing the inspection of sensors and its self-test, different approaches can be found. Simple systems check, if the sensor signal is different from zero. More advanced data-driven methods are based on hardware redundancy [13]. Typical faults are bias, complete failure, drifting and precision degradation, see [14], as well as gain, noise and constant with noise [13]. For networks of wireless sensor nodes, these methods are used to find faulty nodes to be able to either replace those nodes or simply remove them from the network, which is only possible with sufficient redundancy, see e.g., [15]. The use of hardware redundancy, which tests if the sensor signal fits the assumed signal, when only using all other sensors, has been used for SHM systems, too. In [16], a modal filtering approach is used, and [17] uses a PCA-model to represent the signal in a lower-dimensional space and compare it with the original signal. The effect of temperature change and structural damage is considered in [18] using the mutual information concept. All these methods use the measurement data for a mathematical procedure not based on physical quantities. While it is an advantage that no additional measurements are needed, this also leads to difficulties in distinguishing between structural damage and sensor fault, especially for the case of small defects and in widespread sensor network. Depending on the type of sensor, physics-based methods of self-diagnosis using additional measurements can be found. Ref. [19] describes the use of electrical impedance spectroscopy measurement to enable self-monitoring of semiconductor gas sensor systems. In [20], methods to enable a validation of the sensor functions under operational conditions are suggested, which include the use of a magnetostrictive coated fiber. For piezoelectric wafer active sensors (PWAS), self-diagnosis capabilities exist, which are mainly based on the transducers physics. For these transducers, the typical classification into gain, drifting, and so on does not represent the effects of faulty PWAS. The importance of reliable sensor data cannot be overestimated to achieve a reliable output of an SHM system over long monitoring periods.

Within this chapter, a short overview on the usage of piezoelectric transducers within AUbased SHM systems, their electro-mechanical structure and its modeling is given in Section 2. The effects of different transducer faults on the generated wave field, used for AU, as well as on the electro-mechanical impedance spectrum are described in Section 3. Section 4 shows a variety of methods for transducer inspection including model-based and data-based methods with different requirements on the available knowledge about the system and material parameters. Using application scenarios—also including temperature variations—the advantages and disadvantages of the introduced methods of transducer inspection, enabling an increased reliability of SHM systems, are presented in Section 5.

## 2. Tasks of piezoelectric transducers

In many applications, piezoelectric material is used purely for actuating or sensing purposes. The use of PWAS for SHM purposes is mostly including both, the inverse and the direct piezoelectric effect. In general, the piezoelectric effect is not linear. Nevertheless, the effect can be modeled linearly in a certain strain range for most piezoelectric materials. Moreover, the temperature needs to stay well below the Curie point. The actuation (inverse piezoelectric effect) can be described by

$$D\_i = d\_{ikl} T\_{kl} + \varepsilon\_{ik}^T E\_k \tag{1}$$

D<sup>1</sup> D<sup>2</sup> D<sup>3</sup>

SE SE

SE SE

SE SE

 

SE

SE

SE

SE

SE

0 0 0 0 02 S<sup>E</sup>

 d<sup>15</sup> 0 d<sup>15</sup> 0 0 d<sup>31</sup> d<sup>31</sup> d<sup>33</sup> 0 00

00 0

00 0

00 0

0 0

showing small strain magnitudes and a relatively high Curie point (TC ≈ 250�

0

 � <sup>S</sup><sup>E</sup> <sup>12</sup> � �

A huge variety of piezoelectric materials exist—well known are barium titanate BaTiO ð Þ<sup>3</sup> and lead zirconate titanate (Pb Zr ð Þ ; Ti O3Þ, known as PZT, as well as more flexible materials like polyvinylidene fluoride (PVDF). Most common are PWAS, made of PZT. They are separated into hard and soft PZTs by their coercive field. Hard PZTs exhibit a large linear drive region,

exhibit larger induced strain, while having a smaller linear region. Most soft PZTs have a Curie

—Navy Type II, PIC151, PIC155, PZT5A-3195STD and PSI-5H4E Navy Type VI; examples for hard PZTs are PIC 181 and PIC 300, depending on the manufacturers naming (e.g., PICeramic, Piezo systems Inc.). In [21], a threshold of Ec ¼1 kV/mm to divide those two groups is

For AU-based SHM systems, the use of PZT discs has proven to be useful. Different types of transducers exist. The simple form is a piezoceramic disc with a wrap-around electrode, which enables the soldering of both contacts on the top surface of the transducer, see Figure 1a. Alternatively, one might use PZT discs, which are already capsulated in embedding material. Depending on the application, the connecting cables are also embedded as conducting paths within a layer of embedding material. Examples are Acellent SMART layer© and DuraAct

Figure 1. Types of transducers, (a) single transducer with wrap-around electrode from PICeramic, (b) embedded trans-

C, but below those of hard PZTs. Examples of soft PZTs are PIC255, PSI 5A4E

 

T<sup>11</sup> T<sup>22</sup> T<sup>33</sup> T<sup>23</sup> T<sup>13</sup> T<sup>12</sup>

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

þ

T<sup>11</sup> T<sup>22</sup> T<sup>33</sup> T<sup>23</sup> T<sup>13</sup> T<sup>12</sup>

þ

εT

 

 0 0 ε<sup>T</sup>

 0 0 0 ε<sup>T</sup>

 

http://dx.doi.org/10.5772/intechopen.77298

 

E1 E2 E3  

E1 E2 E3

C); soft PZTs

 

(5)

 

S<sup>11</sup> S<sup>22</sup> S<sup>33</sup> S<sup>23</sup> S<sup>13</sup> S<sup>12</sup>

point above 150�

ducer, Acellent SMART layer©.

mentioned.

$$S\_{i\circ} = s\_{i\circ k\circ}^E T\_{kl} + d\_{k\circ} E\_k \tag{2}$$

with stress T, strain S, elastic compliance s, dielectric constant ε, electric field E, dielectric displacement D, defined by charge Q per unit area A at given stress T, and piezoelectric constants d, linking dielectric displacement with stress as well as strain with electric field.

Although these equations already fully describe the direct and inverse piezoelectric effect, for sensing purposes (direct piezoelectric effect) the most familiar description uses g as piezoelectric voltage coefficient to connect stress with electric field.

$$E\_i = -g\_{ikl}T\_{kl} + \beta\_{ik}^T D\_k \tag{3}$$

$$\mathcal{S}\_{i\circ} = \mathcal{s}\_{i\circ kl}^{D} T\_{kl} + \mathcal{g}\_{k\circ} D\_k \tag{4}$$

These equations can be simplified especially in their dimension, when using Voigt notation and assuming multiple symmetry in the piezoelectric materials as well as in the strain and stress tensors.

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems http://dx.doi.org/10.5772/intechopen.77298 

$$
\begin{bmatrix} D\_1 \\ D\_2 \\ D\_3 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 & 0 & d\_{15} & 0 \\ 0 & 0 & 0 & d\_{15} & 0 & 0 \\ d\_{31} & d\_{31} & d\_{33} & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} T\_{11} \\ T\_{22} \\ T\_{33} \\ T\_{23} \\ T\_{13} \\ T\_{12} \end{bmatrix} + \begin{bmatrix} \varepsilon\_{11}^T & 0 & 0 \\ 0 & \varepsilon\_{11}^T & 0 \\ 0 & 0 & \varepsilon\_{33}^T \end{bmatrix} \begin{bmatrix} E\_1 \\ E\_2 \\ E\_3 \end{bmatrix} \tag{5}
$$

$$
\begin{bmatrix} \varepsilon\_{11}^T & S\_{12}^E & S\_{13}^E & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} T\_{11} \end{bmatrix} \qquad \begin{bmatrix} \tau\_{11} \end{bmatrix} \qquad \begin{bmatrix} 0 & 0 & d\_{31} \end{bmatrix}
$$

For these transducers, the typical classification into gain, drifting, and so on does not represent the effects of faulty PWAS. The importance of reliable sensor data cannot be overestimated to

Within this chapter, a short overview on the usage of piezoelectric transducers within AUbased SHM systems, their electro-mechanical structure and its modeling is given in Section 2. The effects of different transducer faults on the generated wave field, used for AU, as well as on the electro-mechanical impedance spectrum are described in Section 3. Section 4 shows a variety of methods for transducer inspection including model-based and data-based methods with different requirements on the available knowledge about the system and material parameters. Using application scenarios—also including temperature variations—the advantages and disadvantages of the introduced methods of transducer inspection, enabling an increased

In many applications, piezoelectric material is used purely for actuating or sensing purposes. The use of PWAS for SHM purposes is mostly including both, the inverse and the direct piezoelectric effect. In general, the piezoelectric effect is not linear. Nevertheless, the effect can be modeled linearly in a certain strain range for most piezoelectric materials. Moreover, the temperature needs to stay well below the Curie point. The actuation (inverse piezoelectric

Di <sup>¼</sup> diklTkl <sup>þ</sup> <sup>ε</sup><sup>T</sup>

with stress T, strain S, elastic compliance s, dielectric constant ε, electric field E, dielectric displacement D, defined by charge Q per unit area A at given stress T, and piezoelectric constants d, linking dielectric displacement with stress as well as strain with electric field.

Although these equations already fully describe the direct and inverse piezoelectric effect, for sensing purposes (direct piezoelectric effect) the most familiar description uses g as piezoelec-

Ei ¼ �giklTkl <sup>þ</sup> <sup>β</sup><sup>T</sup>

These equations can be simplified especially in their dimension, when using Voigt notation and assuming multiple symmetry in the piezoelectric materials as well as in the strain and

Sij ¼ s D

Sij ¼ s E ikEk (1)

ikDk (3)

ijklTkl þ gkijDk (4)

ijklTkl þ dkijEk (2)

achieve a reliable output of an SHM system over long monitoring periods.

reliability of SHM systems, are presented in Section 5.

tric voltage coefficient to connect stress with electric field.

2. Tasks of piezoelectric transducers

Structural Health Monitoring from Sensing to Processing

effect) can be described by

stress tensors.

S<sup>11</sup> S<sup>22</sup> S<sup>33</sup> S<sup>23</sup> S<sup>13</sup> S<sup>12</sup> SE SE 00 0 SE SE SE 00 0 SE SE SE 00 0 SE 0 0 SE 0 0 0 0 0 02 S<sup>E</sup> � <sup>S</sup><sup>E</sup> <sup>12</sup> � � T<sup>11</sup> T<sup>22</sup> T<sup>33</sup> T<sup>23</sup> T<sup>13</sup> T<sup>12</sup> þ 0 0 d<sup>31</sup> 0 0 d<sup>31</sup> 0 0 d<sup>33</sup> d<sup>15</sup> 0 d<sup>15</sup> 0 0 E1 E2 E3 (6)

A huge variety of piezoelectric materials exist—well known are barium titanate BaTiO ð Þ<sup>3</sup> and lead zirconate titanate (Pb Zr ð Þ ; Ti O3Þ, known as PZT, as well as more flexible materials like polyvinylidene fluoride (PVDF). Most common are PWAS, made of PZT. They are separated into hard and soft PZTs by their coercive field. Hard PZTs exhibit a large linear drive region, showing small strain magnitudes and a relatively high Curie point (TC ≈ 250� C); soft PZTs exhibit larger induced strain, while having a smaller linear region. Most soft PZTs have a Curie point above 150� C, but below those of hard PZTs. Examples of soft PZTs are PIC255, PSI 5A4E —Navy Type II, PIC151, PIC155, PZT5A-3195STD and PSI-5H4E Navy Type VI; examples for hard PZTs are PIC 181 and PIC 300, depending on the manufacturers naming (e.g., PICeramic, Piezo systems Inc.). In [21], a threshold of Ec ¼1 kV/mm to divide those two groups is mentioned.

For AU-based SHM systems, the use of PZT discs has proven to be useful. Different types of transducers exist. The simple form is a piezoceramic disc with a wrap-around electrode, which enables the soldering of both contacts on the top surface of the transducer, see Figure 1a. Alternatively, one might use PZT discs, which are already capsulated in embedding material. Depending on the application, the connecting cables are also embedded as conducting paths within a layer of embedding material. Examples are Acellent SMART layer© and DuraAct

Figure 1. Types of transducers, (a) single transducer with wrap-around electrode from PICeramic, (b) embedded transducer, Acellent SMART layer©.

from PICeramic (see Figure 1b). Within this chapter, the first type is named single transducer/ PWAS, while the second type is called embedded transducer/PWAS.

The generated wave field depends on the excitation frequency and the orientation of the transducer itself. In [22] it is shown that the orientation of the wrap-around electrode has significant influence on the generated wave field.

The use of PWAS for AU purposes has been described in a multitude of publications. An excellent overview is given in [21]. Herein, the interested reader will also find an extensive description of the governing equations for AU and EMI. In this chapter, only main results are cited.

For free disc-shaped transducers, the model is based on axial symmetry, leading to uniform radial and circumferential expansion. Using Eqs. (1) and (2) in cylindrical coordinates, the derivation of the induced strain and displacement—used for AU—as well as the electrical displacement, finally leading to the EMI spectrum, can be derived. As soon as the PWAS is attached to the structure, stress-free boundary conditions have to be replaced by a force equilibrium at the PWAS edges. Moreover, a shear layer coupling between PWAS and structure, achieved by the adhesive layer, needs to be considered. Based on [21, 23], in [4], a model was developed, which includes these effects and focuses on the PWAS signature, including resonances and antiresonances of the EMI spectrum Zð Þ ω .

$$Z(\omega) = \left( \mathrm{i}\omega \mathbb{C} \left( 1 - k\_p^2 \left( 1 - \frac{(1 + \nu\_a) I\_1 \left( \wp\_a \right)}{\wp\_a I\_0 \left( \wp\_a \right) - (1 - \nu\_a) I\_1 \left( \wp\_a \right) + \chi(\omega) (1 + \nu\_a) I\_1 \left( \wp\_a \right)} \right) \right) \right)^{-1} \tag{7}$$

It includes the Bessel functions of the first kind J, Poisson's ratio of the PWAS's material νa, the capacitance C, the coupling factor kp, the frequency dependent stiffness quotient χ ωð Þ and the abbreviation φ<sup>a</sup> which can be derived by

$$\mathcal{C} = \varepsilon\_{33} \frac{\pi r\_{p\text{uas}}^2}{h\_{p\text{uas}}} \tag{8}$$

kstr <sup>¼</sup> <sup>2</sup>hstrEstr rpwas <sup>1</sup> � <sup>ν</sup><sup>2</sup>

This includes the geometry parameters rPWAS, hPWAS, hstr, hadh, the material parameters elastic modulus Estr,Poisson's ratio νstr and the wave speed for axially symmetric radial motion in the

It must also be kept in mind that many of the parameters used have complex values as

<sup>11</sup> <sup>¼</sup> <sup>b</sup>s<sup>E</sup>

The frequency dependency of the characteristic structural stiffness was neglected. This model is therefore useful for analyzing the PWAS itself and its bonding condition, while it cannot be

From Eq. (7), the susceptance B as the imaginary part of the admittance which is the inversion

visible. The capacitance C describes the slope, when plotting B over ω. This line is interrupted by the effects of the PWAS eigenfrequencies and its coupling with the structure. As the model does not include the frequency dependency of the structures stiffness, the peaks of eigenfrequencies of the stiffness are not visible. Other models include this frequency dependency of the structures stiffness, see [21]. Due to the necessary simplicity of these models, the applicability for SHM based on the EMI spectrum is limited, but they lead to a better understanding of its

Different types of PWAS faults result from different causes. Due to the continuous or periodical monitoring with permanently installed sensors, PWAS used for SHM need to be tested against degradation issues. Nevertheless, early faults within the PWAS service life have to be taken into account. Production deficiencies can lead to an insufficient bonding quality between structure and PWAS before the PWAS can be used for the first time. Depending on the type of

fault, the effects on the generated wave field as well as on the EMI spectrum differ.

1

Yð Þ¼ ω

2

<sup>11</sup>ð Þ 1 � iη .

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

kadh <sup>¼</sup> Gadh 2

PWAS c.

ω <sup>c</sup> ffiffi α p � �<sup>2</sup> sinh <sup>ω</sup>hadh <sup>c</sup> ffiffi α p � �

0 @

damping has to be taken into account, e.g., s<sup>E</sup>

of the impedance can be calculated.

If neglecting the factor multiplied with k

3. Classification of transducer faults

characteristic features.

2 <sup>ω</sup> <sup>c</sup> ffiffi α p þhadh

used for the modeling of changes respecting damages within the structure.

1 A∙ 1 2 ω <sup>c</sup> rpwas J 2 0 ω <sup>c</sup> rpwas � �<sup>2</sup>

sinh<sup>2</sup> <sup>ω</sup>hadh <sup>c</sup> ffiffi α p � � str ð Þ (14)

http://dx.doi.org/10.5772/intechopen.77298

<sup>c</sup> rpwas � �J<sup>1</sup> <sup>ω</sup>

<sup>Z</sup>ð Þ <sup>ω</sup> (16)

Bð Þ¼ ω Im Yf g ð Þ ω (17)

<sup>p</sup>, the simple model of a PWAS as a capacitor gets

<sup>c</sup> rpwas � �<sup>þ</sup> <sup>J</sup>

2 1 ω <sup>c</sup> rpwas � �

(15)

7

�2J<sup>0</sup> <sup>ω</sup>

ω c J 2 1 ω <sup>c</sup> rpwas � �

$$k\_p^2 = \frac{2d\_{31}^2}{\varepsilon\_{33}s\_{11}^E(1-\nu\_a)}\tag{9}$$

$$
\varphi\_a = \frac{\omega}{c} r\_{\text{pous}} \tag{10}
$$

$$\chi(\omega) = \frac{k\_{\text{str\\$a}all\text{r}}}{k\_{\text{pwas}}} \tag{11}$$

When including the frequency dependent stiffness of the adhesive layer and a simple model for the stiffness of PWAS and structure, this can be included into χ ωð Þ.

$$k\_{\text{pous}} = \frac{h\_{\text{pous}}}{r\_{\text{pous}}s\_{11}^F(1 - \nu\_a)}\tag{12}$$

$$\mathbf{k}\_{\text{str\&adh}} = \frac{1}{\frac{1}{k\_{\text{str}}} + \frac{1}{k\_{\text{all}}}} \tag{13}$$

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems http://dx.doi.org/10.5772/intechopen.77298 7

$$k\_{str} = \frac{2h\_{str}E\_{str}}{r\_{p\text{meas}}(1 - \nu\_{str}^2)}\tag{14}$$

$$k\_{\rm add} = \frac{\mathbb{G}\_{\rm add}}{2} \frac{\left(\frac{\omega}{c\sqrt{a}}\right)^2}{\sinh^2\left(\frac{\omega b\_{\rm add}}{c\sqrt{a}}\right)} \left(\frac{\sinh\left(\frac{\omega b\_{\rm add}}{c\sqrt{a}}\right)}{2\frac{\omega}{c\sqrt{a}}} + h\_{\rm add}\right) \cdot \frac{1}{2} \frac{\frac{\omega}{c}r\_{\rm pass}\,l\_{0}^{2}\left(\frac{\omega}{c}\Big r\_{\rm pass}\right)^{2} - 2l\_{0}\left(\frac{\omega}{c}r\_{\rm pass}\right)l\_{1}\left(\frac{\omega}{c}r\_{\rm pass}\right) + l\_{1}^{2}\left(\frac{\omega}{c}r\_{\rm pass}\right)},\tag{15}$$

This includes the geometry parameters rPWAS, hPWAS, hstr, hadh, the material parameters elastic modulus Estr,Poisson's ratio νstr and the wave speed for axially symmetric radial motion in the PWAS c.

It must also be kept in mind that many of the parameters used have complex values as damping has to be taken into account, e.g., s<sup>E</sup> <sup>11</sup> <sup>¼</sup> <sup>b</sup>s<sup>E</sup> <sup>11</sup>ð Þ 1 � iη .

The frequency dependency of the characteristic structural stiffness was neglected. This model is therefore useful for analyzing the PWAS itself and its bonding condition, while it cannot be used for the modeling of changes respecting damages within the structure.

From Eq. (7), the susceptance B as the imaginary part of the admittance which is the inversion of the impedance can be calculated.

$$Y(\omega) = \frac{1}{Z(\omega)}\tag{16}$$

$$\mathcal{B}(\omega) = \mathrm{Im}\{\mathcal{Y}(\omega)\}\tag{17}$$

If neglecting the factor multiplied with k 2 <sup>p</sup>, the simple model of a PWAS as a capacitor gets visible. The capacitance C describes the slope, when plotting B over ω. This line is interrupted by the effects of the PWAS eigenfrequencies and its coupling with the structure. As the model does not include the frequency dependency of the structures stiffness, the peaks of eigenfrequencies of the stiffness are not visible. Other models include this frequency dependency of the structures stiffness, see [21]. Due to the necessary simplicity of these models, the applicability for SHM based on the EMI spectrum is limited, but they lead to a better understanding of its characteristic features.

## 3. Classification of transducer faults

from PICeramic (see Figure 1b). Within this chapter, the first type is named single transducer/

The generated wave field depends on the excitation frequency and the orientation of the transducer itself. In [22] it is shown that the orientation of the wrap-around electrode has

The use of PWAS for AU purposes has been described in a multitude of publications. An excellent overview is given in [21]. Herein, the interested reader will also find an extensive description of

For free disc-shaped transducers, the model is based on axial symmetry, leading to uniform radial and circumferential expansion. Using Eqs. (1) and (2) in cylindrical coordinates, the derivation of the induced strain and displacement—used for AU—as well as the electrical displacement, finally leading to the EMI spectrum, can be derived. As soon as the PWAS is attached to the structure, stress-free boundary conditions have to be replaced by a force equilibrium at the PWAS edges. Moreover, a shear layer coupling between PWAS and structure, achieved by the adhesive layer, needs to be considered. Based on [21, 23], in [4], a model was developed, which includes these effects and focuses on the PWAS signature, including

<sup>p</sup> <sup>1</sup> � ð Þ <sup>1</sup> <sup>þ</sup> <sup>ν</sup><sup>a</sup> <sup>J</sup><sup>1</sup> <sup>φ</sup><sup>a</sup>

C ¼ ε<sup>33</sup>

<sup>p</sup> <sup>¼</sup> <sup>2</sup>d<sup>2</sup>

<sup>φ</sup><sup>a</sup> <sup>¼</sup> <sup>ω</sup> c

χ ωð Þ¼ kstr&adh kpwas

When including the frequency dependent stiffness of the adhesive layer and a simple model

kpwas <sup>¼</sup> hpwas rpwass<sup>E</sup>

> kstr&adh <sup>¼</sup> <sup>1</sup> 1 kstr <sup>þ</sup> <sup>1</sup> kadh

ε33s<sup>E</sup>

� � � ð Þ <sup>1</sup> � <sup>ν</sup><sup>a</sup> <sup>J</sup><sup>1</sup> <sup>φ</sup><sup>a</sup>

It includes the Bessel functions of the first kind J, Poisson's ratio of the PWAS's material νa, the capacitance C, the coupling factor kp, the frequency dependent stiffness quotient χ ωð Þ and the

> πr<sup>2</sup> pwas hpwas

> > 31

<sup>11</sup>ð Þ 1 � ν<sup>a</sup>

<sup>11</sup>ð Þ 1 � ν<sup>a</sup>

! ! ! �<sup>1</sup>

φaJ<sup>0</sup> φ<sup>a</sup>

k 2

for the stiffness of PWAS and structure, this can be included into χ ωð Þ.

� �

� � <sup>þ</sup> χ ωð Þð Þ <sup>1</sup> <sup>þ</sup> <sup>ν</sup><sup>a</sup> <sup>J</sup><sup>1</sup> <sup>φ</sup><sup>a</sup>

rpwas (10)

� �

(7)

(8)

(9)

(11)

(12)

(13)

the governing equations for AU and EMI. In this chapter, only main results are cited.

PWAS, while the second type is called embedded transducer/PWAS.

significant influence on the generated wave field.

6 Structural Health Monitoring from Sensing to Processing

resonances and antiresonances of the EMI spectrum Zð Þ ω .

<sup>Z</sup>ð Þ¼ <sup>ω</sup> <sup>i</sup>ω<sup>C</sup> <sup>1</sup> � <sup>k</sup><sup>2</sup>

abbreviation φ<sup>a</sup> which can be derived by

Different types of PWAS faults result from different causes. Due to the continuous or periodical monitoring with permanently installed sensors, PWAS used for SHM need to be tested against degradation issues. Nevertheless, early faults within the PWAS service life have to be taken into account. Production deficiencies can lead to an insufficient bonding quality between structure and PWAS before the PWAS can be used for the first time. Depending on the type of fault, the effects on the generated wave field as well as on the EMI spectrum differ.

## 3.1. Cracks

When describing the fault type crack within this chapter, this refers to macro-size cracks. Different causes can lead to these cracks. During production or later use, falling objects, which hit the transducer itself, cause cracks and spalling. Two examples of single transducers impacted twice by falling mass (m = 53.5 g, h = 350 mm for (a), 450 mm for (b)) are shown in Figure 2.

Due to the nonsymmetric characteristic of the fault, the effects on the wave field are also nonsymmetric. Figure 3 shows the signal, recorded by two neighboring transducers (PWAS 1 and PWAS 3), generated by a cracked PWAS (PWAS 2). The two signals differ significantly, showing the nonsymmetric characteristic of the fault. Single transducers as well as embedded transducers show decreased output when being cracked. The effect of spalling is not present for embedded transducers, as the embedding material holds the separated parts together. If a PWAS inspection system does not indicate these faults, the SHM system is based on corrupted signals and will most likely give alarm, although not the structure but the PWAS is damaged.

decreased for the embedded transducers, where the embedding material leads to remaining stiffness between the cracked parts. A drop of capacitance, which will lead to a decreased susceptance slope is visible for the case of spalling. As the capacitance is proportional to the area, the reason for this drop is the missing piece of transducer, which is only the case for

Figure 4. Change of EMI spectra depending on PWAS type and type of fault, (a) single transducer with crack, (b) single

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

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9

Degradation of the piezoelectric transducer and its bonding to the structure is a major transducer fault especially for long-term monitoring, favored in structural health monitoring. It can be caused, e.g., by elevated temperatures. Depending on the selected adhesive (e.g., Hysol EA9394 by Henkel, Z70 by HBM) and the chosen PWAS material (e.g., PIC 255, PIC 151), either the adhesive or the piezoelectric material is prone to degrade. It has been shown in [24] that the pure exposure to outdoor conditions can also lead to minor degradation, which is visible in the generated wave field by a slightly decreased signal. Its level decreases uniformly. In Figure 5,

the degradation, caused by elevated temperature, is shown.

Figure 5. EMI spectra for 20 and 80C, (a) baseline and (b) degraded state.

transducer with crack and spalling, (c) embedded transducer with crack.

single transducers.

3.2. Degradation

The effects of this type of fault on the EMI spectrum differ significantly depending on the type of transducer, see Figure 4. Due to the changed stiffness of the cracked PWAS, the resonance frequency changes. These changes are larger for the single transducers, while the effect is

Figure 2. Micrographs of transducer fault type, (a) crack (b) crack and spalling.

Figure 3. Change of wave propagation depending on the orientation of damage, (a) PWAS2-PWAS1, (b) PWAS2-PWAS3.

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems http://dx.doi.org/10.5772/intechopen.77298 9

Figure 4. Change of EMI spectra depending on PWAS type and type of fault, (a) single transducer with crack, (b) single transducer with crack and spalling, (c) embedded transducer with crack.

decreased for the embedded transducers, where the embedding material leads to remaining stiffness between the cracked parts. A drop of capacitance, which will lead to a decreased susceptance slope is visible for the case of spalling. As the capacitance is proportional to the area, the reason for this drop is the missing piece of transducer, which is only the case for single transducers.

#### 3.2. Degradation

3.1. Cracks

8 Structural Health Monitoring from Sensing to Processing

When describing the fault type crack within this chapter, this refers to macro-size cracks. Different causes can lead to these cracks. During production or later use, falling objects, which hit the transducer itself, cause cracks and spalling. Two examples of single transducers impacted twice

Due to the nonsymmetric characteristic of the fault, the effects on the wave field are also nonsymmetric. Figure 3 shows the signal, recorded by two neighboring transducers (PWAS 1 and PWAS 3), generated by a cracked PWAS (PWAS 2). The two signals differ significantly, showing the nonsymmetric characteristic of the fault. Single transducers as well as embedded transducers show decreased output when being cracked. The effect of spalling is not present for embedded transducers, as the embedding material holds the separated parts together. If a PWAS inspection system does not indicate these faults, the SHM system is based on corrupted signals and will most likely give alarm, although not the structure but the PWAS is damaged. The effects of this type of fault on the EMI spectrum differ significantly depending on the type of transducer, see Figure 4. Due to the changed stiffness of the cracked PWAS, the resonance frequency changes. These changes are larger for the single transducers, while the effect is

Figure 3. Change of wave propagation depending on the orientation of damage, (a) PWAS2-PWAS1, (b) PWAS2-PWAS3.

by falling mass (m = 53.5 g, h = 350 mm for (a), 450 mm for (b)) are shown in Figure 2.

Figure 2. Micrographs of transducer fault type, (a) crack (b) crack and spalling.

Degradation of the piezoelectric transducer and its bonding to the structure is a major transducer fault especially for long-term monitoring, favored in structural health monitoring. It can be caused, e.g., by elevated temperatures. Depending on the selected adhesive (e.g., Hysol EA9394 by Henkel, Z70 by HBM) and the chosen PWAS material (e.g., PIC 255, PIC 151), either the adhesive or the piezoelectric material is prone to degrade. It has been shown in [24] that the pure exposure to outdoor conditions can also lead to minor degradation, which is visible in the generated wave field by a slightly decreased signal. Its level decreases uniformly. In Figure 5, the degradation, caused by elevated temperature, is shown.

Figure 5. EMI spectra for 20 and 80C, (a) baseline and (b) degraded state.

It led to a slight decrease of the susceptance slope, which is not caused by a change of the surface area but the degrading of the PWAS material and a change of its adhesive stiffness, see Eq. (15). If the temperature is unknown, degradation might be interpreted as temperature change.

## 3.3. Debonding

Debonding is a fault type, located at the adhesive zone between PWAS and structure. While a contaminated surface of the structure during the bonding process will lead to deficiencies of the bonding quality and debonding effects right from the beginning, fatigue of the bonding layer, e.g., under bending moments, might also lead to a debonding of the PWAS from the structure. The latter has a defined orientation of the fault, while a contamination might be local or evenly distributed over the bonding area. Figure 6 shows the maxima of the out-of-plane component of the velocity field of a perfectly bonded transducer compared to the fields, generated by two PWAS, which were bonded on an aluminum plate, being contaminated with wax before bonding.

The out-of-plane velocity has been measured on the structure, from the back-site of the plate using a Laser Doppler Vibrometer CLV1000 with CLV700 head. The generated wave field of the debonded transducers is far from being symmetric and the generated amplitudes are smaller, compared to the perfectly attached transducer.

The debonding due to bending has been modeled by partial bonding of a PWAS to an aluminum plate. Figure 7 shows the out-of-plane velocity, measured at the surface of the PWAS itself and from the back-site. A vibration of the debonded section is visible in Figure 7a. This energy is stored and transferred to the structure with a delay. The amplitude on the back is decreased in the debonded area.

The partial debonding also changes the frequency characteristic of a bonded PWAS. It has been shown that with some frequencies used as input frequency, the amplitudes, measured at a distance of 20 mm to the PWAS center, are larger for the debonded case; see Figure 8.

Figure 8. Maximum out-of-plane velocity at different angles for 30 kHz, 100 kHz and 170 kHz, measured at 20 mm

Figure 7. Out-of-plane velocity of a debonded PWAS, (a) measured at the top surface of the PWAS after the decay of the input signal, the radius of the circular measurement area is 4 mm, (b) measured at the back of the plate, the maxima of out-ofplane velocity are plotted, the dotted circle marks the PWAS location, the radius of the circular measurement area is 8 mm.

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

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11

Figure 9. Effects of 20% debonded area on the susceptance spectrum. Four completely bonded PWAS are compared with four partially debonded PWAS. The orientation of the bonding relative to the wrap-around electrode has been changed.

distance, (a) for the fully bonded PWAS, (b) for the partially debonded PWAS.

The debonding also leads to a changed EMI spectrum, the effects depend on the severity of debonding. Figure 9 shows the effect of a 20% debonded surface, with four different orientations of the debonded area, relative to the wrap-around electrode.

Figure 6. Maximum values of the out-of-plane velocity time signal, generated by the PWAS and transferred to the structure, measured by a laser vibrometer at the back of the structure, (a) perfectly attached PWAS, (b), (c) two PWAS attached on a plate with wax-contaminated surface.

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems http://dx.doi.org/10.5772/intechopen.77298 11

It led to a slight decrease of the susceptance slope, which is not caused by a change of the surface area but the degrading of the PWAS material and a change of its adhesive stiffness, see Eq. (15). If the temperature is unknown, degradation might be interpreted as temperature

Debonding is a fault type, located at the adhesive zone between PWAS and structure. While a contaminated surface of the structure during the bonding process will lead to deficiencies of the bonding quality and debonding effects right from the beginning, fatigue of the bonding layer, e.g., under bending moments, might also lead to a debonding of the PWAS from the structure. The latter has a defined orientation of the fault, while a contamination might be local or evenly distributed over the bonding area. Figure 6 shows the maxima of the out-of-plane component of the velocity field of a perfectly bonded transducer compared to the fields, generated by two PWAS, which were bonded on an aluminum plate, being contaminated with

The out-of-plane velocity has been measured on the structure, from the back-site of the plate using a Laser Doppler Vibrometer CLV1000 with CLV700 head. The generated wave field of the debonded transducers is far from being symmetric and the generated amplitudes are

The debonding due to bending has been modeled by partial bonding of a PWAS to an aluminum plate. Figure 7 shows the out-of-plane velocity, measured at the surface of the PWAS itself and from the back-site. A vibration of the debonded section is visible in Figure 7a. This energy is stored and transferred to the structure with a delay. The amplitude

The partial debonding also changes the frequency characteristic of a bonded PWAS. It has been shown that with some frequencies used as input frequency, the amplitudes, measured at a

The debonding also leads to a changed EMI spectrum, the effects depend on the severity of debonding. Figure 9 shows the effect of a 20% debonded surface, with four different orienta-

Figure 6. Maximum values of the out-of-plane velocity time signal, generated by the PWAS and transferred to the structure, measured by a laser vibrometer at the back of the structure, (a) perfectly attached PWAS, (b), (c) two PWAS

distance of 20 mm to the PWAS center, are larger for the debonded case; see Figure 8.

tions of the debonded area, relative to the wrap-around electrode.

change.

3.3. Debonding

10 Structural Health Monitoring from Sensing to Processing

wax before bonding.

smaller, compared to the perfectly attached transducer.

on the back is decreased in the debonded area.

attached on a plate with wax-contaminated surface.

Figure 7. Out-of-plane velocity of a debonded PWAS, (a) measured at the top surface of the PWAS after the decay of the input signal, the radius of the circular measurement area is 4 mm, (b) measured at the back of the plate, the maxima of out-ofplane velocity are plotted, the dotted circle marks the PWAS location, the radius of the circular measurement area is 8 mm.

Figure 8. Maximum out-of-plane velocity at different angles for 30 kHz, 100 kHz and 170 kHz, measured at 20 mm distance, (a) for the fully bonded PWAS, (b) for the partially debonded PWAS.

Figure 9. Effects of 20% debonded area on the susceptance spectrum. Four completely bonded PWAS are compared with four partially debonded PWAS. The orientation of the bonding relative to the wrap-around electrode has been changed.

## 4. Methods of transducer inspection

To achieve an increased reliability of SHM systems, a check of the systems' piezoelectric transducers and a good knowledge about the component itself is necessary. Refs. [24–28] pay attention to durability and long-term integrity as well as investigations on typical damage patterns. These investigations include stereomicroscopy [26], monitoring a possible change of the slope of electric charge over strain [26–28] and near-field scanning interferometry [24]. These methods are useful under laboratory conditions but cannot be transferred to the inspection of transducers during their employment and operation.

As already shown in Eqs. (7-17), the model itself includes a bunch of parameters. Although most of them cannot be changed due to damage (e.g., nominal radius of the PWAS), these parameters will have some variations resulting from different batches, different bonding procedures, and so on. Therefore, the model needs to be adapted to the experimental baseline first.

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

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13

The major disadvantage of this procedure is the high correlation of the different parameters on the influence on the susceptance spectrum. The adaptation of the parameters is based on optimization procedures, which do not necessarily result in physically meaningful parameters. Moreover, the user needs to know a multitude of parameters about the applied PWAS before

The avail of the EMI spectrum started from using the susceptance slope coefficient SC as the damage indicator [33, 37, 39]. As the capacitance is a linear factor for the susceptance, it can be seen as an advanced alternative to solely measure the PWAS capacitance. It is measured in a frequency range up to a small share of the eigenfrequency, which interrupts the constant slope. Although it has been shown that not all faults can be detected with this method, it is a simple method, which can be applied easily, and which detects severe damages like fracture of the PWAS. The employment of more information from the susceptance spectrum than only using the slope is also possible with data-based methods. In [48], 12 parameters, which can be extracted from the susceptance spectrum, have been listed. After extraction from the spectrum, they are used for PCA. The first principal component (PC) can be taken as damage indicator for degradation and breakage. While data-based models in general are less numerically expensive than model-based methods, one difficulty of this method is to extract the parameters,

The inclusion of more information of the spectrum is also possible by using the correlation coefficient and subtracting its absolute value from 1 to achieve a damage index. This way, no

DICC <sup>¼</sup> <sup>1</sup> � j j CC with CC <sup>¼</sup> <sup>V</sup><sup>12</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Vkl being the entries within the covariance matrix V. The correlation coefficient CC is 1 for two susceptance spectra, which only differ by a proportional change This way, the slope is an insensitive parameter for this method. Nevertheless, PWAS faults change the characteristic shape of the spectrum at resonance also for small faults. This is focused, when using the

The quality of the inspection methods has to be assured not only by checking if specific damaged can be found; Moreover, the combination of SHM system and transducer inspection

4.3. Transducer inspection in the context of the whole SHM system reliability

<sup>V</sup>11V<sup>22</sup> <sup>p</sup> , (18)

With this updated model, the model-based transducer inspection procedure can start.

being able to use this method.

depending on the data quality.

additional extraction of features is necessary.

damage index based on the correlation coefficient DICC.

4.2. Data-based methods

In [29], a method of transducer inspection based on a time reversal index, a symmetry index and a Lamb wave energy ratio index is suggested. Herein, the capacitance is used as a first indicator to finally separate structural damage, changes of environmental conditions and PWAS faults. The systems are partially based on analytical and hardware redundancy.

Using a second, independent measurement quantity, the EMI spectrum was discussed as a side issue in [30, 31] and later is focused in [32, 33]. They concentrate on the susceptance slope, which is increased by debonding and decreased if the PWAS breaks. As it can be seen in Figure 4, this is possible for some fault types and severe damages but does not detect, e.g., minor cracks and central debonding [34]. Further work in this regard can be found in [29, 35–39]. Using more information like the resonance behavior included in the EMI-spectrum enables the detection of minor PWAS faults and is especially valuable for the inspection of embedded transducers [40–42]. This is possible with the use of a physical model [4] or by utilizing purely datadriven approaches [43]. A simplified measurement of the EMI spectrum suggested in [44] and implemented, e.g., in [45] enables a quick measurement of the EMI spectrum with the same equipment as used for AU-based SHM systems. Based on the results of a PWAS inspection system, in [46, 47], signal correction factors are suggested to enable the exploitation of the signals in case of minor damage.

Within this section, the most used and elevated methods of transducer inspection based on the EMI spectrum, resp. the susceptance spectrum, are described. They are categorized into databased and model-based methods. If a method allows to waive the explicit use of the temperature information for temperature compensation, this will be highlighted.

## 4.1. Model-based methods

For the inspection of PWAS with model-based methods, the analytical model, introduced in Section 2 can be used. The idea is to adapt the model to the experimental data via fitting of the parameters. The fitted parameter vector is used to separate the healthy state. Using principal component analysis (PCA), they can be aggregated to a damage index DImodel. For details, the reader is referred to [4, 42].

An advantage of this method is the nonnecessity to include temperature information for the test in application, also if the influence of environmental conditions should be compensated. Nevertheless, during training, temperature information is necessary.

As already shown in Eqs. (7-17), the model itself includes a bunch of parameters. Although most of them cannot be changed due to damage (e.g., nominal radius of the PWAS), these parameters will have some variations resulting from different batches, different bonding procedures, and so on. Therefore, the model needs to be adapted to the experimental baseline first. With this updated model, the model-based transducer inspection procedure can start.

The major disadvantage of this procedure is the high correlation of the different parameters on the influence on the susceptance spectrum. The adaptation of the parameters is based on optimization procedures, which do not necessarily result in physically meaningful parameters. Moreover, the user needs to know a multitude of parameters about the applied PWAS before being able to use this method.

## 4.2. Data-based methods

4. Methods of transducer inspection

12 Structural Health Monitoring from Sensing to Processing

in case of minor damage.

4.1. Model-based methods

reader is referred to [4, 42].

tion of transducers during their employment and operation.

To achieve an increased reliability of SHM systems, a check of the systems' piezoelectric transducers and a good knowledge about the component itself is necessary. Refs. [24–28] pay attention to durability and long-term integrity as well as investigations on typical damage patterns. These investigations include stereomicroscopy [26], monitoring a possible change of the slope of electric charge over strain [26–28] and near-field scanning interferometry [24]. These methods are useful under laboratory conditions but cannot be transferred to the inspec-

In [29], a method of transducer inspection based on a time reversal index, a symmetry index and a Lamb wave energy ratio index is suggested. Herein, the capacitance is used as a first indicator to finally separate structural damage, changes of environmental conditions and

Using a second, independent measurement quantity, the EMI spectrum was discussed as a side issue in [30, 31] and later is focused in [32, 33]. They concentrate on the susceptance slope, which is increased by debonding and decreased if the PWAS breaks. As it can be seen in Figure 4, this is possible for some fault types and severe damages but does not detect, e.g., minor cracks and central debonding [34]. Further work in this regard can be found in [29, 35–39]. Using more information like the resonance behavior included in the EMI-spectrum enables the detection of minor PWAS faults and is especially valuable for the inspection of embedded transducers [40–42]. This is possible with the use of a physical model [4] or by utilizing purely datadriven approaches [43]. A simplified measurement of the EMI spectrum suggested in [44] and implemented, e.g., in [45] enables a quick measurement of the EMI spectrum with the same equipment as used for AU-based SHM systems. Based on the results of a PWAS inspection system, in [46, 47], signal correction factors are suggested to enable the exploitation of the signals

Within this section, the most used and elevated methods of transducer inspection based on the EMI spectrum, resp. the susceptance spectrum, are described. They are categorized into databased and model-based methods. If a method allows to waive the explicit use of the tempera-

For the inspection of PWAS with model-based methods, the analytical model, introduced in Section 2 can be used. The idea is to adapt the model to the experimental data via fitting of the parameters. The fitted parameter vector is used to separate the healthy state. Using principal component analysis (PCA), they can be aggregated to a damage index DImodel. For details, the

An advantage of this method is the nonnecessity to include temperature information for the test in application, also if the influence of environmental conditions should be compensated.

ture information for temperature compensation, this will be highlighted.

Nevertheless, during training, temperature information is necessary.

PWAS faults. The systems are partially based on analytical and hardware redundancy.

The avail of the EMI spectrum started from using the susceptance slope coefficient SC as the damage indicator [33, 37, 39]. As the capacitance is a linear factor for the susceptance, it can be seen as an advanced alternative to solely measure the PWAS capacitance. It is measured in a frequency range up to a small share of the eigenfrequency, which interrupts the constant slope. Although it has been shown that not all faults can be detected with this method, it is a simple method, which can be applied easily, and which detects severe damages like fracture of the PWAS.

The employment of more information from the susceptance spectrum than only using the slope is also possible with data-based methods. In [48], 12 parameters, which can be extracted from the susceptance spectrum, have been listed. After extraction from the spectrum, they are used for PCA. The first principal component (PC) can be taken as damage indicator for degradation and breakage. While data-based models in general are less numerically expensive than model-based methods, one difficulty of this method is to extract the parameters, depending on the data quality.

The inclusion of more information of the spectrum is also possible by using the correlation coefficient and subtracting its absolute value from 1 to achieve a damage index. This way, no additional extraction of features is necessary.

$$DI\_{\text{CC}} = 1 - |\text{CC}| \text{ with } \text{CC} = \frac{V\_{12}}{\sqrt{V\_{11} V\_{22}}},\tag{18}$$

Vkl being the entries within the covariance matrix V. The correlation coefficient CC is 1 for two susceptance spectra, which only differ by a proportional change This way, the slope is an insensitive parameter for this method. Nevertheless, PWAS faults change the characteristic shape of the spectrum at resonance also for small faults. This is focused, when using the damage index based on the correlation coefficient DICC.

## 4.3. Transducer inspection in the context of the whole SHM system reliability

The quality of the inspection methods has to be assured not only by checking if specific damaged can be found; Moreover, the combination of SHM system and transducer inspection needs to be checked. This is especially the case as most operators of SHM systems are not able to define specific types of transducer defects and its sizes to assess the quality of performance of a transducer inspection method. It therefore has to be ensured that the transducer inspection will find a faulty PWAS, before the signal deterioration will lead to a changed output of the SHM system. The authors emphasize that it is necessary to consider the algorithm of the SHM system as well as the PWAS inspection method to assess its performance. This way it is also possible to reconsider if data of a degraded transducer might still be used or has to be neglected.

A possible approach for this is described in [49, 42] and suggests using statistical methods, based on the probability of detection (POD) approach: it enables increased knowledge of the combination of transducer inspection and SHM system, including the value, which the structural damage detection indicator reaches, before a defective transducer can be detected with a probability of 90% at a confidence level of 95% (SDI\_90|95). A complete reliability analysis needs to incorporate the interaction of SHM system and transducer inspection system.

## 5. Application scenarios

In this section, several application scenarios, including a comparison of different methods of transducer inspection, as described in Sections 4.1 and 4.2, are presented. Moreover, the results of these methods have to be evaluated taking into account the effects of the different defects of the results of the SHM system, which is implemented, as discussed in Section 4.3.

## 5.1. Detection of cracks in and debonding of transducers

To detect cracks and debondings, two data-based methods are compared in the following application scenarios. The most proposed method to inspect piezoelectric transducers is the monitoring of the susceptance slope. This is compared with the correlation coefficient-based method.

As this procedure makes it difficult to have a baseline measurement of each sensor, four fully bonded transducers are used as a baseline. For all eight transducers, the EMI spectrum has been recorded five times within an interval of 10 m. Figure 12 shows the resulting damage

Figure 12. (a) Slope coefficient SC, (b) correlation coefficient-based damage indicator DICC for four fully bonded and four

Figure 11. Debonding scenario and orientation of debonded area relative to the wrap-around electrode.

Figure 10. (a) Experimental setup with a four-point-bending test and micrographs of the three different crack states of an embedded DuraAct transducer caused by different strain levels (0.5, 0.6 and 0.7%), (b) slope coefficient SC of the impedance spectrum, (c) correlation coefficient-based damage index DICC, evaluated for measurements of four uncracked

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indices.

partially debonded transducers.

and three cracked states.

Cracks in an embedded transducer, bonded in central position on a CFRP strip, have been caused by four-point-bending of the strip (see Figure 10a) left down. First cracks started on reaching a strain level of 0.5%.

The EMI spectrum was always measured at unloaded condition after deforming the specimen at the following strain levels: 0.15, 0.3, 0.45, 0.5, 0.6, and 0.7%. Figure 10b shows that the multiple cracks of the embedded transducer after 0.7% strain led to a slight decrease of the susceptance slope, while the first two fault levels exhibit similar behavior like the undamaged states. For the correlation coefficient-based method, all three stages of fault can be clearly identified and separated from the undamaged state (see Figure 10c). For detailed information about the experimental setup, see [43, 42].

The debonding scenario is achieved by preventing the contact between adhesive and PWAS at approximately 20% of the surface area. This area was covered with Teflon tape during the process of gluing. Four different orientations of the debonded area relative to the wrap-around electrode have been tested (Figure 11).

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems http://dx.doi.org/10.5772/intechopen.77298 15

needs to be checked. This is especially the case as most operators of SHM systems are not able to define specific types of transducer defects and its sizes to assess the quality of performance of a transducer inspection method. It therefore has to be ensured that the transducer inspection will find a faulty PWAS, before the signal deterioration will lead to a changed output of the SHM system. The authors emphasize that it is necessary to consider the algorithm of the SHM system as well as the PWAS inspection method to assess its performance. This way it is also possible to

A possible approach for this is described in [49, 42] and suggests using statistical methods, based on the probability of detection (POD) approach: it enables increased knowledge of the combination of transducer inspection and SHM system, including the value, which the structural damage detection indicator reaches, before a defective transducer can be detected with a probability of 90% at a confidence level of 95% (SDI\_90|95). A complete reliability analysis

In this section, several application scenarios, including a comparison of different methods of transducer inspection, as described in Sections 4.1 and 4.2, are presented. Moreover, the results of these methods have to be evaluated taking into account the effects of the different defects of

To detect cracks and debondings, two data-based methods are compared in the following application scenarios. The most proposed method to inspect piezoelectric transducers is the monitoring of the susceptance slope. This is compared with the correlation coefficient-based method.

Cracks in an embedded transducer, bonded in central position on a CFRP strip, have been caused by four-point-bending of the strip (see Figure 10a) left down. First cracks started on

The EMI spectrum was always measured at unloaded condition after deforming the specimen at the following strain levels: 0.15, 0.3, 0.45, 0.5, 0.6, and 0.7%. Figure 10b shows that the multiple cracks of the embedded transducer after 0.7% strain led to a slight decrease of the susceptance slope, while the first two fault levels exhibit similar behavior like the undamaged states. For the correlation coefficient-based method, all three stages of fault can be clearly identified and separated from the undamaged state (see Figure 10c). For detailed information

The debonding scenario is achieved by preventing the contact between adhesive and PWAS at approximately 20% of the surface area. This area was covered with Teflon tape during the process of gluing. Four different orientations of the debonded area relative to the wrap-around

reconsider if data of a degraded transducer might still be used or has to be neglected.

needs to incorporate the interaction of SHM system and transducer inspection system.

the results of the SHM system, which is implemented, as discussed in Section 4.3.

5.1. Detection of cracks in and debonding of transducers

5. Application scenarios

14 Structural Health Monitoring from Sensing to Processing

reaching a strain level of 0.5%.

about the experimental setup, see [43, 42].

electrode have been tested (Figure 11).

Figure 10. (a) Experimental setup with a four-point-bending test and micrographs of the three different crack states of an embedded DuraAct transducer caused by different strain levels (0.5, 0.6 and 0.7%), (b) slope coefficient SC of the impedance spectrum, (c) correlation coefficient-based damage index DICC, evaluated for measurements of four uncracked and three cracked states.

Figure 11. Debonding scenario and orientation of debonded area relative to the wrap-around electrode.

As this procedure makes it difficult to have a baseline measurement of each sensor, four fully bonded transducers are used as a baseline. For all eight transducers, the EMI spectrum has been recorded five times within an interval of 10 m. Figure 12 shows the resulting damage indices.

Figure 12. (a) Slope coefficient SC, (b) correlation coefficient-based damage indicator DICC for four fully bonded and four partially debonded transducers.

While the slope coefficient values are not normalized with a reference value, the reference for the correlation coefficient-based method is the first measurement of the first transducer. Using the slope coefficient, the difference between debonded and healthy state is small, especially for the debonding beneath the wrap-around electrode. For the correlation coefficient-based method, the debonding can be clearly separated from the fully bonded state. Moreover, the variation between the measurements of the same state is higher for the slope coefficient.

application scenario, a model-based and a purely data-based method are used for the detection

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As defect, a degradation of the adhesive as well as of the piezoelectric material was introduced to a PWAS by heat exposure for 32 h at 130C. Fourteen measurements, equally distributed over the whole temperature range, have been used as reference data for the data-based approach to train the model for the model-based approach. Twenty-six measurements distributed over the whole temperature range are used as test data and 42 measurements over the

Figure 14 shows the results for the model- and data-based methods in (b) and (c) as well as the

Both methods clearly distinguish between the degraded and the healthy state. The results show that the model fits best for medium temperatures, although the whole temperature range was used for training. The model-based approach allows to waive the explicit use of the

Figure 14. (a) Temperature, (b) DImodel and (c) DICC for several measurements of a single transducer before and after

degradation of adhesive and piezoelectric material.

of degradation faults within a temperature range of 20–85C.

whole temperature range have been recorded after degradation took place.

temperature present during the specific EMI measurement in (a).

An analysis of the resulting wave propagation for these debonded PWAS can be found in [50]. For detailed information about the experimental setup and other debonding levels, see [42].

## 5.2. Inspection of transducers after system setup

The difficulty of transducer inspection after system setup is the absence of a proper reference. In many cases, this can be overcome with the help of a model-based approach. Nevertheless, in this application, a whole batch of transducers as a reference within the batch is used. Building the mean correlation coefficient for all combinations of all transducers, except a single one, and subtracting the mean correlation coefficient of all transducers with the single one from this value, this can be used as an indicator for the similarity of the single one with the whole batch. Another procedure without using a reference is described in [37], the use of correlation blocks is suggested in [14].

In this application, 16 transducers have been mounted on a plate structure. The plate has been contaminated with wax at two positions so that PWAS 12 and 16 are insufficiently bonded. Using the correlation coefficients of all combinations, the two contaminated PWAS could be clearly identified, see Figure 13, showing significantly higher indicator values than the rest of the sensors.

#### 5.3. Inspection of transducers under changing temperature conditions

The influence of environmental and operational conditions is known to be nonnegligible for the automated continuous monitoring of structures in general. The effect on the inspection of piezoelectric transducers using the EMI spectrum therefore needs to be considered. In this

Figure 13. Damage indices, based on the comparison of correlation coefficients for all 16 PWAS after system setup. PWAS 12 and 16 are insufficiently bonded due to contamination with wax.

application scenario, a model-based and a purely data-based method are used for the detection of degradation faults within a temperature range of 20–85C.

While the slope coefficient values are not normalized with a reference value, the reference for the correlation coefficient-based method is the first measurement of the first transducer. Using the slope coefficient, the difference between debonded and healthy state is small, especially for the debonding beneath the wrap-around electrode. For the correlation coefficient-based method, the debonding can be clearly separated from the fully bonded state. Moreover, the variation between the measurements of the same state is higher for the slope coefficient.

An analysis of the resulting wave propagation for these debonded PWAS can be found in [50]. For detailed information about the experimental setup and other debonding levels, see [42].

The difficulty of transducer inspection after system setup is the absence of a proper reference. In many cases, this can be overcome with the help of a model-based approach. Nevertheless, in this application, a whole batch of transducers as a reference within the batch is used. Building the mean correlation coefficient for all combinations of all transducers, except a single one, and subtracting the mean correlation coefficient of all transducers with the single one from this value, this can be used as an indicator for the similarity of the single one with the whole batch. Another procedure without using a reference is described in [37], the use of correlation blocks

In this application, 16 transducers have been mounted on a plate structure. The plate has been contaminated with wax at two positions so that PWAS 12 and 16 are insufficiently bonded. Using the correlation coefficients of all combinations, the two contaminated PWAS could be clearly identified, see Figure 13, showing significantly higher indicator values than the rest of

The influence of environmental and operational conditions is known to be nonnegligible for the automated continuous monitoring of structures in general. The effect on the inspection of piezoelectric transducers using the EMI spectrum therefore needs to be considered. In this

Figure 13. Damage indices, based on the comparison of correlation coefficients for all 16 PWAS after system setup. PWAS

5.3. Inspection of transducers under changing temperature conditions

12 and 16 are insufficiently bonded due to contamination with wax.

5.2. Inspection of transducers after system setup

16 Structural Health Monitoring from Sensing to Processing

is suggested in [14].

the sensors.

As defect, a degradation of the adhesive as well as of the piezoelectric material was introduced to a PWAS by heat exposure for 32 h at 130C. Fourteen measurements, equally distributed over the whole temperature range, have been used as reference data for the data-based approach to train the model for the model-based approach. Twenty-six measurements distributed over the whole temperature range are used as test data and 42 measurements over the whole temperature range have been recorded after degradation took place.

Figure 14 shows the results for the model- and data-based methods in (b) and (c) as well as the temperature present during the specific EMI measurement in (a).

Both methods clearly distinguish between the degraded and the healthy state. The results show that the model fits best for medium temperatures, although the whole temperature range was used for training. The model-based approach allows to waive the explicit use of the

Figure 14. (a) Temperature, (b) DImodel and (c) DICC for several measurements of a single transducer before and after degradation of adhesive and piezoelectric material.

temperature information after the training is completed. The data-based approach employing the correlation coefficient needs the temperature information to select the correct baseline. For more information on the experimental setup and the estimated model parameters, see [4], on the data-based method, see [42].

Author details

\* and Claus-Peter Fritzen2

\*Address all correspondence to: inka.mueller@rub.de

Frequency Control. 2005;52:1769-1782

Monitoring. 2014;13:321-342

2002;13(9):561-574

95-104

1 Institute for Structural Engineering, Ruhr-Universität Bochum, Germany

2 Institute for Mechanics and Control Engineering—Mechatronics, University of Siegen,

Failure Assessment of Piezoelectric Actuators and Sensors for Increased Reliability of SHM Systems

http://dx.doi.org/10.5772/intechopen.77298

19

[1] Farrar CR, Worden K. Structural Health Monitoring: A Machine Learning Perspective.

[2] Michaels JE, Michaels TE. Detection of structural damage from the local temporal coherence of diffuse ultrasonic signals. IEEE Transactions on Ultrasonics, Ferroelectrics and

[3] Baptista FG, Vieira Filho J, Inman DJ. Real-time multi-sensors measurement system with temperature effects compensation for impedance-based structural health monitoring.

[4] Buethe I, Eckstein B, Fritzen CP. Model-based detection of sensor faults under changing

[5] Roy S, Lonkar K, Janapati V, Chang FK. A novel physics-based temperature compensation model for structural health monitoring using ultrasonic guided waves. Structural Health

[6] Sohn H, Worden K, Farrar CR. Statistical damage classification under changing environmental and operational conditions. Journal of Intelligent Material Systems and Structures.

[7] Figueiredo E, Park G, Farrar CR, Worden K, Figueiras J. Machine learning algorithms for damage detection under operational and environmental variability. Structural Health

[8] Fritzen C-P, Kraemer P, Buethe I. Vibration-based damage detection under changing environmental and operational conditions. Advances in Science and Technology. 2013;83:

[9] Sepehry N, Shamshirsaz M, Abdollahi F. Temperature variation effect compensation in impedance-based structural health monitoring using neural networks. Journal of Intelli-

[10] Buethe I, Kraemer P, Fritzen C-P. Applications of self-organizing maps in structural health

Chichester, West Sussex, United Kingdom: John Wiley & Sons Ltd; 2012

Structural Health Monitoring-an International Journal. 2012;11:173-186

temperature conditions. Structural Health Monitoring. 2014;13:109-119

Monitoring-an International Journal. 2011;10:559-572

gent Material Systems and Structures. 2011;22:1975-1982

monitoring. Key Engineering Materials. 2012;518:37-46

Inka Mueller<sup>1</sup>

Germany

References

## 6. Conclusion

Piezoelectric transducers are used within several SHM systems for a multitude of applications. For the system reliability, the proper functionality of the permanently installed transducers must be secured. This chapter proposes a system self-check, similar to other measurement equipment. For its realization, a detailed analysis of possible fault types and their effects on the generated wave field and the EMI spectrum is necessary. Moreover, it is tremendously important to incorporate the effects of possible PWAS faults on the SHM system to know if a faulty transducer will be identified before it will have an influence on the SHM system output and a false alarm will be produced. To enable the reader to increase the reliability of SHM systems, within this chapter several methods for transducer inspection have been presented. Their usage was demonstrated for different applications, showing disadvantages and advantages of the different methods. While model-based methods are linked to the necessity of an expert knowledge about the transducer and its bonding conditions, data-based approaches, using the correlation coefficient, need a temperature measurement to incorporate temperature changes. Especially for small cracks without spalling, using more aspects of the EMI than just the susceptance slope is advantageous.

## Acknowledgements

Most of this work has been conducted during 2012–2016 within the framework of national and international cooperation, leading to the PhD thesis [42]. The authors would like to acknowledge Maria Moix-Bonet (DLR) and Martin Bach (Airbus), who have been a great help in identifying the need of research within this area and supported the research with samples and fruitful discussions especially regarding the damage types of degradation and crack. Moreover, the authors would like to acknowledge Alisa Shpak and Mikhail Golub from Kuban State University, Krasnodar, Russia, with whom they have worked on the modeling of the debonding fault and its experimental validation within the last years and enjoyed fruitful discussions.

Parts of this work are based on research activities within the EU 7th framework project SARISTU under grant agreement No. 284562 which is thankfully acknowledged.

## Conflict of interest

The authors declare no conflict of interest. The founding sponsors and employers had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript and in the decision to publish the results.

## Author details

temperature information after the training is completed. The data-based approach employing the correlation coefficient needs the temperature information to select the correct baseline. For more information on the experimental setup and the estimated model parameters, see [4], on

Piezoelectric transducers are used within several SHM systems for a multitude of applications. For the system reliability, the proper functionality of the permanently installed transducers must be secured. This chapter proposes a system self-check, similar to other measurement equipment. For its realization, a detailed analysis of possible fault types and their effects on the generated wave field and the EMI spectrum is necessary. Moreover, it is tremendously important to incorporate the effects of possible PWAS faults on the SHM system to know if a faulty transducer will be identified before it will have an influence on the SHM system output and a false alarm will be produced. To enable the reader to increase the reliability of SHM systems, within this chapter several methods for transducer inspection have been presented. Their usage was demonstrated for different applications, showing disadvantages and advantages of the different methods. While model-based methods are linked to the necessity of an expert knowledge about the transducer and its bonding conditions, data-based approaches, using the correlation coefficient, need a temperature measurement to incorporate temperature changes. Especially for small cracks without spalling, using more aspects of the EMI than just

Most of this work has been conducted during 2012–2016 within the framework of national and international cooperation, leading to the PhD thesis [42]. The authors would like to acknowledge Maria Moix-Bonet (DLR) and Martin Bach (Airbus), who have been a great help in identifying the need of research within this area and supported the research with samples and fruitful discussions especially regarding the damage types of degradation and crack. Moreover, the authors would like to acknowledge Alisa Shpak and Mikhail Golub from Kuban State University, Krasnodar, Russia, with whom they have worked on the modeling of the debonding fault

Parts of this work are based on research activities within the EU 7th framework project

The authors declare no conflict of interest. The founding sponsors and employers had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of

and its experimental validation within the last years and enjoyed fruitful discussions.

SARISTU under grant agreement No. 284562 which is thankfully acknowledged.

the manuscript and in the decision to publish the results.

the data-based method, see [42].

18 Structural Health Monitoring from Sensing to Processing

the susceptance slope is advantageous.

Acknowledgements

Conflict of interest

6. Conclusion

Inka Mueller<sup>1</sup> \* and Claus-Peter Fritzen2

\*Address all correspondence to: inka.mueller@rub.de

1 Institute for Structural Engineering, Ruhr-Universität Bochum, Germany

2 Institute for Mechanics and Control Engineering—Mechatronics, University of Siegen, Germany

## References


[11] PI Ceramic GmbH. https://www.piceramic.com/en/products/piezoceramic-components/

[27] Gall M. Experimentelle und numerische Untersuchungen zur Lebensdauer von flächigen

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http://dx.doi.org/10.5772/intechopen.77298

21

[28] Bach M, Dobmann M, Eckstein B, Moix-Bonet M, Stolz M. Reliability of co-bonded piezoelectric sensors on CFRP structures. In: 9th International Workshop on Structural Health

[29] Lee SJ, Sohn H, Hong JW. Time reversal based piezoelectric transducer self-diagnosis under varying temperature. Journal of Nondestructive Evaluation. 2010;29:75-91

[30] Giurgiutiu V, Zagrai A, Bao JJ. Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring. Structural Health Monitoring. 2002;1:41-61

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**Chapter 2**

**Provisional chapter**

**Structural Health Monitoring by Acoustic Emission**

**Structural Health Monitoring by Acoustic Emission** 

Elastic wave, which is formed due to sudden rearrangement of stresses in a material, is called acoustic emission (AE). It is widely used in nondestructive testing (NDT) of materials and structures especially in health monitoring of structures for damage detection. When a body is subjected to an external force (in the form of changing pressure, load, or temperature), any micro fracture inside the body releases energy in the form of AE wave, which is received by sensor and later on is converted to electrical signal for inspection. In early stage, major importance was given on studying the AE characteristics during the deformation and fracture on various materials (by J. Kaiser in Germany in 1950 and B. H. Schofield in the USA in 1954). Nowadays, lots of research are conducting on formulating the theories behind AE formation, propagation, and inspection in various fields as an important health monitoring tool for NDT. In this chapter, I would like to elaborate a "feature outlook of AE" based on past, present, and future perspectives; "AE monitoring" procedure based on theoretical and experimental perspectives; and smart applications in structural health monitoring based on industrial and biostructural perspectives with related figures and tables. **Keywords:** structural health monitoring, nondestructive testing, acoustic emission

Structural health monitoring (SHM) refers to the theme of damage detection, evaluation, and characterization strategy of an engineering structure through time ranging feature extraction by sensors. Analytical and statistical representations, periodic forms in most cases, of damage-sensitive features of the structure focus on the monitoring system about the present

technique, industrial applications, biomedical engineering application

DOI: 10.5772/intechopen.79483

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Technique**

**Technique**

Md. Tawhidul Islam Khan

Md. Tawhidul Islam Khan

**Abstract**

**1. Introduction**

status of structural health condition.

http://dx.doi.org/10.5772/intechopen.79483

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


#### **Structural Health Monitoring by Acoustic Emission Technique Structural Health Monitoring by Acoustic Emission Technique**

DOI: 10.5772/intechopen.79483

Md. Tawhidul Islam Khan Md. Tawhidul Islam Khan

[41] Mueller I, Fritzen C-P. Inspection of piezoceramic transducers used for structural health

[42] Mueller I. Inspection of piezoelectric transducers used for structural health monitoring

[43] Buethe I, Moix-Bonet M, Wierach P, Fritzen CP. Check of piezoelectric transducers using the electro-mechanical impedance. In: EWSHM—7th European Workshop on Structural

[44] Overly TGS. Development and integration of hardware and software for active-sensors in

[45] Fritzen CP, Moll J, Chaaban R, Eckstein B, Kraemer P, Klinkov M, Dietrich G, Yang C, Xing KJ, Buethe I. A multifunctional device for multi-channel EMI and guided wave propagation measurements with PWAS. In: EWSHM—7th European Workshop on Struc-

[46] Mulligan KR, Quaegebeur N, Masson P, Brault L-P, Yang C. Compensation of piezoceramic bonding layer degradation for structural health monitoring. Structural Health Monitoring.

[47] Masson P, Quaegebeur N, Mulligan K, Ostiguy PC. Increasing the roburobust in damage

[48] Xing K. Experiments and simulation in structural health monitoring systems using the E/M

[49] Buethe I, Fritzen CP. Quality assessment for the EMI-based inspection of PWAS. In:

[50] Golub MV, Shpak AN, Buethe I, Fritzen CP, Jung H, Moll J. Continuous wavelet transform application in diagnostics of piezoelectric wafer active sensors in Days on Diffraction; 2013

imagin for SHM. In: International Symposium on SHM and NDT; 2013

International Workshop on Structural Health Monitoring, Stanford; 2015

impedance and cross transfer function methods [PhD thesis]; 2015

monitoring. Materials. 2017;10(1):17

22 Structural Health Monitoring from Sensing to Processing

Health Monitoring, Nantes; 2014

tural Health Monitoring, Nantes; 2014

2014;13:68-81

structural health monitoring [MSc thesis]; 2007

systems [PhD thesis]; 2016

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79483

#### **Abstract**

Elastic wave, which is formed due to sudden rearrangement of stresses in a material, is called acoustic emission (AE). It is widely used in nondestructive testing (NDT) of materials and structures especially in health monitoring of structures for damage detection. When a body is subjected to an external force (in the form of changing pressure, load, or temperature), any micro fracture inside the body releases energy in the form of AE wave, which is received by sensor and later on is converted to electrical signal for inspection. In early stage, major importance was given on studying the AE characteristics during the deformation and fracture on various materials (by J. Kaiser in Germany in 1950 and B. H. Schofield in the USA in 1954). Nowadays, lots of research are conducting on formulating the theories behind AE formation, propagation, and inspection in various fields as an important health monitoring tool for NDT. In this chapter, I would like to elaborate a "feature outlook of AE" based on past, present, and future perspectives; "AE monitoring" procedure based on theoretical and experimental perspectives; and smart applications in structural health monitoring based on industrial and biostructural perspectives with related figures and tables.

**Keywords:** structural health monitoring, nondestructive testing, acoustic emission technique, industrial applications, biomedical engineering application

## **1. Introduction**

Structural health monitoring (SHM) refers to the theme of damage detection, evaluation, and characterization strategy of an engineering structure through time ranging feature extraction by sensors. Analytical and statistical representations, periodic forms in most cases, of damage-sensitive features of the structure focus on the monitoring system about the present status of structural health condition.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **1.1. Acoustic emission (AE) in SHM**

Many conventional techniques are proposed by many engineers and scientists for health monitoring of structures, and maximum of them is nondestructive testing (NDT) type methods. Again, in many NDT systems, testing loadings are applied before or after the testing and are widely used as an active method, where signals or energy is delivered from the outside to the testing body. Contrary to active NDT, acoustic emission is widely used as passive NDT method in structural health monitoring, where external energy is not needed to supply the testing structure. The stimulated internal energy of the structure is received in this acoustic emission technique as health monitoring features. Due to this unique characteristic, acoustic emission technique has become very simple; however, accuracy or acquisition sensitivity is very high. Therefore, acoustic emission technique is becoming popular day by day in all types of structural monitoring fields [1–4].

**1.2. Onward features and prospective of present topic**

**2.1. History of AE**

**2.2. AE technique**

structural health monitoring applications.

According to the strategy of the present writing, acoustic emission technique will be elaborated perspective to its historical criteria in structural health monitoring statistics. Following to its historical elongation, theoretical and experimental applications will be strategically approached. Afterward, some classical applications will be discussed before an elaborate dis-

Structural Health Monitoring by Acoustic Emission Technique

http://dx.doi.org/10.5772/intechopen.79483

25

Historically, the application of AE to structural health monitoring is not so new; however, the challenges of this monitoring strategy are still facing and progressing on time. Technologically, AE was investigated in the middle of twentieth century. In early stage, AE phenomena were realized in Germany by Forester [14] in transforming mechanical vibration into electrical voltage by electrodynamic transmitter-receiver system. They measured tiny voltage change due to resistance variations caused by martensite transformations in metallurgical experiments. However, AE experiments were officially founded by Kaiser [15] through the publication of his historical irreversibility theory, known as the "Kaiser effect" in 1950. The terminology "AE" was first in history published by Kaiser's pioneering work "Acoustic Emission" in 1961. Later on, Obert, Schofield, Drouillard, Yokomichi, Ikeda, Matsuoka, and Kishinoue did enormous efforts to apply AE in various fields until the end of twentieth century [16–20]. Thus, the application of AE became familiar as a well-known nondestructive tool to different fields in

Acquisition of transient elastic wave generated due to the sudden change of material stress for any external stimulus locally or globally to the material generates acoustic emission waves. The generated waves propagate through the surface of the material, and therefore, acquisition of these elastic waves and conversion of these waves to electrical signals for visualization and analysis refer to the fundamentals of AE testing. In AE testing, a piezoelectric transducer, generally called as AE sensor, is placed on the surface of the material to be tested. The transducer responds to the dynamic motion generated by the elastic wave as mechanical motion and converts it to an electrical voltage signal, which is often called as AE signal. AE sensor is selected based on the operating frequency. Therefore, different types of AE sensors are com-

A fundamental AE testing system consists of a sensor (AE sensor), a preamplifier, main amplifier with appropriate filters, and data acquisition system along with display (oscilloscopes, personal computer with data acquisition software, and data transferring devices like AD conversion system). As AE signals are very small, it is boosted by preamplifier to gain at low signal-to-noise ratio. Later on, AE signals are amplified again and passed through band

mercially available based on their applicable frequencies and sensitivities [21–23].

cussion and conclusions of the technique to the structural health monitoring system.

**2. Fundamentals of AE technique to SHM applications**

A dominating attribute of acoustic emission technique is its application ability in its loading condition. Therefore, it provides instant damage information within a short period of time. Thus, acoustic emission monitoring tests are often performed in the operating conditions of the structure. As a result, adequate damage information even in minute state triggers the acoustic emission technique as a valuable health monitoring method. Dynamic characterization of any structural damage has become advantageous in this unique monitoring system. Furthermore, since acoustic emission technique is applied in dynamic feature, early stage of any damage can be characterized in this technique. Therefore, easy and adequate measures against any matured fracture or damage can be adopted in the presented fault detection technique [5–8].

Among many important features of acoustic emission technique, source location ability of involved damage inside the material attracts people in application of this technique as well. Following the traveling information of AE hits and applying to preferable algorithms, source location of AE event is performed. Based on the availability of sensors, dimension of source location is defined. For example, if two AE sensors are available, a single degree of source location is applicable; if three sensors are available, two-dimensional source location is applicable; if four or more sensors are available, three-dimensional source location is applicable. Since signal velocity influences the source location very much, velocity modes greatly affect the source location technique as well [9–12].

Present acoustic emission technique can quantify qualitative measure of the defects of a structure. For getting quantitative information of the damage, it often prefers to get supports of ultrasonic testing method. However, ultrasonic technique is necessary to apply in static condition, which is contradictory to the basic principle of acoustic emission. Therefore, pre- or postquantitative diagnosis is suitable for getting damage sizing inside the structure [13].

In addition to many advantages of AE applications in nondestructive testing environment, entire structural damage evaluation can be obtained under whole loading conditions by single or several sensors only. No replacement or cleaning of sensor placements is necessary for that purpose. Furthermore, a noisy environment except structural vibrations, and so on, does not influence to the data acquisition system too much. Therefore, acoustic emission technique in structural health monitoring system is widely applied as a preferable nondestructive tool in various fields of industrial to biomedical engineering fields.

## **1.2. Onward features and prospective of present topic**

According to the strategy of the present writing, acoustic emission technique will be elaborated perspective to its historical criteria in structural health monitoring statistics. Following to its historical elongation, theoretical and experimental applications will be strategically approached. Afterward, some classical applications will be discussed before an elaborate discussion and conclusions of the technique to the structural health monitoring system.

## **2. Fundamentals of AE technique to SHM applications**

## **2.1. History of AE**

**1.1. Acoustic emission (AE) in SHM**

24 Structural Health Monitoring from Sensing to Processing

the source location technique as well [9–12].

in various fields of industrial to biomedical engineering fields.

Many conventional techniques are proposed by many engineers and scientists for health monitoring of structures, and maximum of them is nondestructive testing (NDT) type methods. Again, in many NDT systems, testing loadings are applied before or after the testing and are widely used as an active method, where signals or energy is delivered from the outside to the testing body. Contrary to active NDT, acoustic emission is widely used as passive NDT method in structural health monitoring, where external energy is not needed to supply the testing structure. The stimulated internal energy of the structure is received in this acoustic emission technique as health monitoring features. Due to this unique characteristic, acoustic emission technique has become very simple; however, accuracy or acquisition sensitivity is very high. Therefore, acoustic emission technique is becoming popular day by day in all types of structural monitoring fields [1–4].

A dominating attribute of acoustic emission technique is its application ability in its loading condition. Therefore, it provides instant damage information within a short period of time. Thus, acoustic emission monitoring tests are often performed in the operating conditions of the structure. As a result, adequate damage information even in minute state triggers the acoustic emission technique as a valuable health monitoring method. Dynamic characterization of any structural damage has become advantageous in this unique monitoring system. Furthermore, since acoustic emission technique is applied in dynamic feature, early stage of any damage can be characterized in this technique. Therefore, easy and adequate measures against any matured fracture or damage can be adopted in the presented fault detection technique [5–8].

Among many important features of acoustic emission technique, source location ability of involved damage inside the material attracts people in application of this technique as well. Following the traveling information of AE hits and applying to preferable algorithms, source location of AE event is performed. Based on the availability of sensors, dimension of source location is defined. For example, if two AE sensors are available, a single degree of source location is applicable; if three sensors are available, two-dimensional source location is applicable; if four or more sensors are available, three-dimensional source location is applicable. Since signal velocity influences the source location very much, velocity modes greatly affect

Present acoustic emission technique can quantify qualitative measure of the defects of a structure. For getting quantitative information of the damage, it often prefers to get supports of ultrasonic testing method. However, ultrasonic technique is necessary to apply in static condition, which is contradictory to the basic principle of acoustic emission. Therefore, pre- or postquantitative diagnosis is suitable for getting damage sizing inside the structure [13].

In addition to many advantages of AE applications in nondestructive testing environment, entire structural damage evaluation can be obtained under whole loading conditions by single or several sensors only. No replacement or cleaning of sensor placements is necessary for that purpose. Furthermore, a noisy environment except structural vibrations, and so on, does not influence to the data acquisition system too much. Therefore, acoustic emission technique in structural health monitoring system is widely applied as a preferable nondestructive tool Historically, the application of AE to structural health monitoring is not so new; however, the challenges of this monitoring strategy are still facing and progressing on time. Technologically, AE was investigated in the middle of twentieth century. In early stage, AE phenomena were realized in Germany by Forester [14] in transforming mechanical vibration into electrical voltage by electrodynamic transmitter-receiver system. They measured tiny voltage change due to resistance variations caused by martensite transformations in metallurgical experiments. However, AE experiments were officially founded by Kaiser [15] through the publication of his historical irreversibility theory, known as the "Kaiser effect" in 1950. The terminology "AE" was first in history published by Kaiser's pioneering work "Acoustic Emission" in 1961. Later on, Obert, Schofield, Drouillard, Yokomichi, Ikeda, Matsuoka, and Kishinoue did enormous efforts to apply AE in various fields until the end of twentieth century [16–20]. Thus, the application of AE became familiar as a well-known nondestructive tool to different fields in structural health monitoring applications.

## **2.2. AE technique**

Acquisition of transient elastic wave generated due to the sudden change of material stress for any external stimulus locally or globally to the material generates acoustic emission waves. The generated waves propagate through the surface of the material, and therefore, acquisition of these elastic waves and conversion of these waves to electrical signals for visualization and analysis refer to the fundamentals of AE testing. In AE testing, a piezoelectric transducer, generally called as AE sensor, is placed on the surface of the material to be tested. The transducer responds to the dynamic motion generated by the elastic wave as mechanical motion and converts it to an electrical voltage signal, which is often called as AE signal. AE sensor is selected based on the operating frequency. Therefore, different types of AE sensors are commercially available based on their applicable frequencies and sensitivities [21–23].

A fundamental AE testing system consists of a sensor (AE sensor), a preamplifier, main amplifier with appropriate filters, and data acquisition system along with display (oscilloscopes, personal computer with data acquisition software, and data transferring devices like AD conversion system). As AE signals are very small, it is boosted by preamplifier to gain at low signal-to-noise ratio. Later on, AE signals are amplified again and passed through band

**AE event:** The time domain or frequency domain of acoustic emission signals represents parametric features due to the elastic wave generated inside the material. It is the total AE wave

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27

**AE hit:** It is represented as the AE signal from one channel and crosses the user-defined threshold. There can be multiple hits in an AE event or an AE test of multiple channels.

**Maximum amplitude:** Maximum amplitude (amplitude) is the greatest amplitude of an AE hit measured in voltage or in decibels (dB). AE signals with maximum amplitude below the

**Counts:** Counts are referred to the numbers of pulses of an AE hit, which cross the user-

**Rise time:** Rise time is defined as the time span of an AE hit from its first threshold crossing

**Duration:** Duration is defined as the time span of an AE hit from its first threshold crossing

**Peak frequency:** It is the frequency component (kHz) corresponding to the maximum ampli-

**Average frequency:** It is the average frequency in an AE hit. It is associated with duration and count and can be calculated from dividing "count" by "duration." It can roughly represent the signal frequency (when AE waveform is not possible to record). It represents complete

**Center frequency:** It is the frequency component (kHz) corresponding to the center of gravity

**Initial frequency:** It indicates the initial condition of an AE spectrum. It is calculated from

**Reverberation frequency:** It is calculated from the relation derived from total count to initial

**RA value:** It is calculated from rise time divided by maximum amplitude (amplitude). It is the reciprocal of gradient in AE signal waveform and represents the type of cracks in the unit of ms/V.

In a practical AE experiment, generally piezoelectric sensor is widely used as AE sensor. It is normally a contact-type sensor consisted of piezoelectric element protected by hard metal housing and connected by an electric connector for transmitting the generated electric effects. The sensing system is based on the piezoelectric effect out of lead zirconate titanate (PZT). This type of sensor is relatively cheap and highly sensitive and converts the mechanical move-

**Energy:** It is the area below the detection envelope within the duration of an AE hit.

representation during the AE testing.

amplitude to its maximum amplitude.

tude in an AE wave spectrum.

acoustic emission impact signal.

dividing "counts" until peak by "rise time."

**2.4. AE sensors and data acquisition**

count divided by the relation derived from duration to rise time.

ment to electrical voltage in AE experiments efficiently.

in an AE wave spectrum.

amplitude to its last threshold crossing amplitude.

defined threshold value.

user-defined threshold line are not recorded as AE signals.

**Figure 1.** Fundamentals of AE technique.

**Figure 2.** Common parametric features in an AE hit.

pass filters before storing to the mainframe of personal computer (PC) for analysis to any of desired features. The abovementioned AE technique is explained by the following schematic diagram as shown in **Figure 1** [24–26].

## **2.3. Important AE parametric features**

In AE testing, as shown in **Figure 1**, AE signals are received and visualized to the display of the acquisition device when AE sensor is attached to the material surface (object to be tested) by adhesives or tape and is excited by the generated stress wave at the material. AE waves are then saved to PC for further synthesis to characterize the damage inside the test object. Then, parametric features are widely used in analyzing or monitoring damage inside an object by AE NDT, as shown in **Figure 2** [13, 27].

**AE event:** The time domain or frequency domain of acoustic emission signals represents parametric features due to the elastic wave generated inside the material. It is the total AE wave representation during the AE testing.

**AE hit:** It is represented as the AE signal from one channel and crosses the user-defined threshold. There can be multiple hits in an AE event or an AE test of multiple channels.

**Maximum amplitude:** Maximum amplitude (amplitude) is the greatest amplitude of an AE hit measured in voltage or in decibels (dB). AE signals with maximum amplitude below the user-defined threshold line are not recorded as AE signals.

**Counts:** Counts are referred to the numbers of pulses of an AE hit, which cross the userdefined threshold value.

**Rise time:** Rise time is defined as the time span of an AE hit from its first threshold crossing amplitude to its maximum amplitude.

**Duration:** Duration is defined as the time span of an AE hit from its first threshold crossing amplitude to its last threshold crossing amplitude.

**Energy:** It is the area below the detection envelope within the duration of an AE hit.

**Peak frequency:** It is the frequency component (kHz) corresponding to the maximum amplitude in an AE wave spectrum.

**Average frequency:** It is the average frequency in an AE hit. It is associated with duration and count and can be calculated from dividing "count" by "duration." It can roughly represent the signal frequency (when AE waveform is not possible to record). It represents complete acoustic emission impact signal.

**Center frequency:** It is the frequency component (kHz) corresponding to the center of gravity in an AE wave spectrum.

**Initial frequency:** It indicates the initial condition of an AE spectrum. It is calculated from dividing "counts" until peak by "rise time."

**Reverberation frequency:** It is calculated from the relation derived from total count to initial count divided by the relation derived from duration to rise time.

**RA value:** It is calculated from rise time divided by maximum amplitude (amplitude). It is the reciprocal of gradient in AE signal waveform and represents the type of cracks in the unit of ms/V.

## **2.4. AE sensors and data acquisition**

**Figure 2.** Common parametric features in an AE hit.

**Figure 1.** Fundamentals of AE technique.

26 Structural Health Monitoring from Sensing to Processing

diagram as shown in **Figure 1** [24–26].

**2.3. Important AE parametric features**

AE NDT, as shown in **Figure 2** [13, 27].

pass filters before storing to the mainframe of personal computer (PC) for analysis to any of desired features. The abovementioned AE technique is explained by the following schematic

In AE testing, as shown in **Figure 1**, AE signals are received and visualized to the display of the acquisition device when AE sensor is attached to the material surface (object to be tested) by adhesives or tape and is excited by the generated stress wave at the material. AE waves are then saved to PC for further synthesis to characterize the damage inside the test object. Then, parametric features are widely used in analyzing or monitoring damage inside an object by In a practical AE experiment, generally piezoelectric sensor is widely used as AE sensor. It is normally a contact-type sensor consisted of piezoelectric element protected by hard metal housing and connected by an electric connector for transmitting the generated electric effects. The sensing system is based on the piezoelectric effect out of lead zirconate titanate (PZT). This type of sensor is relatively cheap and highly sensitive and converts the mechanical movement to electrical voltage in AE experiments efficiently.

source to each AE sensor is calculated. For simplicity, wave velocity for a particular material is assumed constant in general AE source location technique. However, considering different geometric or traveling effects, like wave reflection due to material inhomogeneity, various wave modes (p-mode, s-mode, etc.) precise velocity calculation is necessary for improving the accuracy of AE source location technique. Based on the number of AE sensors connected to the acquisition system, several source location techniques have been developed already.

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29

A fundamental and very commonly used technique is the linear type of AE source location technique. At least two AE sensors (minimum required number of AE sensors in AE source location technique) are necessary in this technique. Linear type of structures such as bridge and pipe is used for measurements by this technique. This technique is very simple and easy

In linear source location technique, two sensors are placed to an appropriate distance, and therefore, the time of arrivals from two sensors is collected. Based on the difference in signal arrival time, source location is defined. For example, if the source location is located at the middle point of two sensors, the difference between two arrival times is zero. Otherwise, the arrival time will be different. It is considered in this technique that shorter arrival time is the closer source to the receiving sensor. Thus, the source length is calculated by multiplying the arrival time with wave traveling velocity. The schematic of a linear source location

indicate as the AE sensor 1, AE sensor 2 and time of arrival to sensor 1, time of arrival to sensor

distance of AE source to sensor 1, and axial distance between AE source and the midpoint (*l*/2)

The mathematical relations of the linear source location algorithm are explained as the following equations, where Δ*t* indicates the time difference between two arrival times to sensor

indicate the distance between two sensors (s1

, s2 and t1 , t2

, s2

), axial

Several AE source location techniques are discussed later.

to apply. It is also called as one degree AE source location technique [13].

technique is shown in **Figure 4**, where AE source is mentioned by s. Similarly, s1

2, and *l* 1

1 and sensor 2 and v indicates the AE wave velocity [31].

**Figure 4.** Schematic of linear source location technique.

**3.1. Linear source location technique**

2, respectively. Furthermore, *l*, *l*

of two AE sensors, respectively.

**Figure 3.** A typical AE sensor with connecting cable.

Selection of an appropriate AE sensor depends on the demanded frequency in the experiment. As the propagation of elastic wave is heavily affected by the property of the propagation path and the propagation mechanism to the AE sensor, the frequency content of the propagating elastic wave plays a very important role in the selection of the suitable AE sensor in AE tests (**Figure 3**).

Appropriate sensors for AE testing to pressure vessels, storage tanks, heat exchangers, piping, reactors, aerial lift devices, nuclear power plants, and biomedical fields are well prepared based on their required frequency range. In general, based on the frequency range for AE tests, sensors are classified accordingly as low-frequency range sensor (20–100 kHz), middle or standard range sensor (100–400 kHz), and high-frequency range sensor (~400 kHz). Different companies such as Physical Acoustic Corporation (PAC), Vallen Systeme Company, and so on produce their sensors regarding the type of commercial AE sensor with high sensitivity [25, 28–30].

## **3. AE source location**

Source location plays a significant role in AE technique. It is an advantageous facility in AE technique when compared with many other NDTs. It makes the characterizing of damage propagation behavior and the overall damage monitoring system well understandable and well predictable.

It is already mentioned that many AE hits can be taken in one AE event by placing many AE sensors in AE testing. One channel (one AE sensor) can record one AE hit, and thus, multiple channels (multiple AE sensors) can record multiple AE hits. When AE sensors place at different places at a suitable sensor to sensor distance (sometimes carefulness in signal wavelength is necessary) according to the desired inspection area, all AE hits are recorded by the system with different signal traveling times based on the different distances of sensors to the signal source. This traveling time is termed as "arrival time" in AE source location. Knowing the traveling time or arrival time of each hit from the signal acquisition system and multiplying it with the AE signal traveling velocity in that material, signal traveling distance from the source to each AE sensor is calculated. For simplicity, wave velocity for a particular material is assumed constant in general AE source location technique. However, considering different geometric or traveling effects, like wave reflection due to material inhomogeneity, various wave modes (p-mode, s-mode, etc.) precise velocity calculation is necessary for improving the accuracy of AE source location technique. Based on the number of AE sensors connected to the acquisition system, several source location techniques have been developed already. Several AE source location techniques are discussed later.

## **3.1. Linear source location technique**

Selection of an appropriate AE sensor depends on the demanded frequency in the experiment. As the propagation of elastic wave is heavily affected by the property of the propagation path and the propagation mechanism to the AE sensor, the frequency content of the propagating elastic wave plays a very important role in the selection of the suitable AE sensor in AE tests (**Figure 3**). Appropriate sensors for AE testing to pressure vessels, storage tanks, heat exchangers, piping, reactors, aerial lift devices, nuclear power plants, and biomedical fields are well prepared based on their required frequency range. In general, based on the frequency range for AE tests, sensors are classified accordingly as low-frequency range sensor (20–100 kHz), middle or standard range sensor (100–400 kHz), and high-frequency range sensor (~400 kHz). Different companies such as Physical Acoustic Corporation (PAC), Vallen Systeme Company, and so on produce their sensors regarding the type of commercial AE sensor with high sensitivity [25, 28–30].

Source location plays a significant role in AE technique. It is an advantageous facility in AE technique when compared with many other NDTs. It makes the characterizing of damage propagation behavior and the overall damage monitoring system well understandable and

It is already mentioned that many AE hits can be taken in one AE event by placing many AE sensors in AE testing. One channel (one AE sensor) can record one AE hit, and thus, multiple channels (multiple AE sensors) can record multiple AE hits. When AE sensors place at different places at a suitable sensor to sensor distance (sometimes carefulness in signal wavelength is necessary) according to the desired inspection area, all AE hits are recorded by the system with different signal traveling times based on the different distances of sensors to the signal source. This traveling time is termed as "arrival time" in AE source location. Knowing the traveling time or arrival time of each hit from the signal acquisition system and multiplying it with the AE signal traveling velocity in that material, signal traveling distance from the

**3. AE source location**

**Figure 3.** A typical AE sensor with connecting cable.

28 Structural Health Monitoring from Sensing to Processing

well predictable.

A fundamental and very commonly used technique is the linear type of AE source location technique. At least two AE sensors (minimum required number of AE sensors in AE source location technique) are necessary in this technique. Linear type of structures such as bridge and pipe is used for measurements by this technique. This technique is very simple and easy to apply. It is also called as one degree AE source location technique [13].

In linear source location technique, two sensors are placed to an appropriate distance, and therefore, the time of arrivals from two sensors is collected. Based on the difference in signal arrival time, source location is defined. For example, if the source location is located at the middle point of two sensors, the difference between two arrival times is zero. Otherwise, the arrival time will be different. It is considered in this technique that shorter arrival time is the closer source to the receiving sensor. Thus, the source length is calculated by multiplying the arrival time with wave traveling velocity. The schematic of a linear source location technique is shown in **Figure 4**, where AE source is mentioned by s. Similarly, s1 , s2 and t1 , t2 indicate as the AE sensor 1, AE sensor 2 and time of arrival to sensor 1, time of arrival to sensor 2, respectively. Furthermore, *l*, *l* 2, and *l* 1 indicate the distance between two sensors (s1 , s2 ), axial distance of AE source to sensor 1, and axial distance between AE source and the midpoint (*l*/2) of two AE sensors, respectively.

The mathematical relations of the linear source location algorithm are explained as the following equations, where Δ*t* indicates the time difference between two arrival times to sensor 1 and sensor 2 and v indicates the AE wave velocity [31].

**Figure 4.** Schematic of linear source location technique.

$$l\_1 = \frac{1}{2}(t\_1 - t\_2).v = \frac{1}{2}\,\Delta t.v\tag{1}$$

$$I\_2 = \frac{1}{2}l - l\_1 = \frac{1}{2}(l - \Delta t.\nu) \tag{2}$$

#### **3.2. Two-dimensional source location technique**

Planner or two-dimensional source location technique requires three or more AE sensors to be placed on a plane for identifying AE source. Three sensors generate three hyperbolae, which intersect each other on the monitoring plane at a common interceding point or cross-sectional point, and the point is termed as the AE source. Theoretically, three sensors are sufficient for identifying the source in two-dimensional technique; however, another extra sensor, which is called as reference sensor, improves the accuracy of the source location technique. Therefore, the placement of four sensors in a rectangular sensor array generates six sensor pairs. Calculating time of arrival from each sensor pair and correlating according to the following relations planner or two-dimensional AE source location are done.

The simple algorithm for calculating two-dimensional AE source location is based on the following relations [32].

$$\left|\mathbf{x}\_s\right|^2 + \left|y\_s\right|^2 = \left|r\_s\right|^2\tag{3}$$

Similarly, the source angle (*θ*) can be calculated as follows:

**Figure 5.** Geometrical representation of two-dimensional source location algorithm.

two-dimensional source location can be found.

**4. Smart applications of AE technique**

AE applications are mentioned later.

**4.1. Industrial applications in SHM**

over the world.

*θ* = ϕ + *ψ* (11)

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31

In Eq. (11), the parameters ϕ and ψ can be calculated by rearranging Eq. (6), and thus, the

Similarly, three-dimensional source location is also possible to calculate in AE source location technique by increasing the number of sensors. Many other modern source location techniques are available [10, 13] and are still introducing to AE fields by AE researchers from all

The application of acoustic emission for fault detection or condition monitoring in structural health monitoring (SHM) field is versatile. Since it is a noninvasive technique, it is widely applied in different fields of nondestructive testing (NDT), nondestructive evaluation (NDE), and nondestructive monitoring (NDM) for many engineering applications. Similar application of AE in seismology is well known from its beginning of implementations. Further, recently, applications of AE in biomedical engineering field have attracted many scientists and engineers for its smart applications in condition monitoring as well. Several examples of

Out of many industrial applications of AE technique, several are mentioned as monitoring of pressure vessel, storage tank, structural materials, composites, concrete structure, steel structure, bridge, aircraft, gear, ceramics, ceramic components, and so on. In maximum cases of inspection,

$$(\Delta \mathbf{x})\_i^2 + (\Delta y)\_i^2 = |r\_i|^2 \tag{4}$$

$$(\Delta \mathbf{x})\_{\rangle}^{2} + (\Delta y)\_{\rangle}^{2} = r\_{\rangle}^{2} \tag{5}$$

where ∆*<sup>x</sup>* <sup>=</sup> *xs* –*x* and ∆*<sup>y</sup>* <sup>=</sup> *ys* –*y*, when *x* and *y* indicate the coordinates of sensor positions; however, for the source indication, the suffix *s* is used. However, *s*<sup>0</sup> indicates the reference sensor. Furthermore, suffixes *i* and *j* indicate the general number of positioning and measuring sensors, respectively, for example, in **Figure 5**, *si* indicates for sensor 1, and *sj* indicates for sensor 2. Similarly, *ri* , *rj* , and *rs* indicate the distances from the corresponding sensors to source. Applying simple solutions of above Eqs. (3)–(5), the source distance, *r*<sup>s</sup> can be calculated as follows:

$$\text{simple solutions of above Eqs. (3)-(5), the source distance, }r\_s \text{ can be calculated as follows:}$$

$$r\_s = \frac{1}{2} \left[ \frac{U\_i}{x\_i \cos \theta + y\_i \sin \theta + d\_i} \right] = \frac{1}{2} \left[ \frac{U\_i}{x\_j \cos \theta + y\_j \sin \theta + d\_j} \right] \tag{6}$$

In Eq. (6), *U*<sup>i</sup> , *U*<sup>j</sup> , *d*i , and *d*<sup>j</sup> are defined as follow:

$$\mathcal{U}\_{l} = \mathbf{x}\_{l}^{2} + y\_{l}^{2} - d\_{l}^{2} \tag{7}$$

$$\mathcal{U}\_{\rangle} = |x\_{\rangle}^2 + y\_{\rangle}^2 - d\_{\rangle}^2 \tag{8}$$

$$d\_i = r\_i - r\_s = \upsilon \cdot \Delta t\_{i\upsilon} \tag{9}$$

$$d\_{\rangle} = r\_{\rangle} - r\_s = \upsilon \cdot \Delta t\_{\neq} \tag{10}$$

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**Figure 5.** Geometrical representation of two-dimensional source location algorithm.

Similarly, the source angle (*θ*) can be calculated as follows:

*l*

30 Structural Health Monitoring from Sensing to Processing

*l*

following relations [32].

where ∆*<sup>x</sup>* <sup>=</sup> *xs*

Similarly, *ri*

In Eq. (6), *U*<sup>i</sup>

, *rj* , and *rs*

*rs* <sup>=</sup> \_\_1

, *U*<sup>j</sup> , *d*i

*xs*

(∆*x*)

(∆*x*)

–*x* and ∆*<sup>y</sup>* <sup>=</sup> *ys*

respectively, for example, in **Figure 5**, *si*

, and *d*<sup>j</sup>

*Ui* = *xi*

*Uj* = *xj*

*di* = *ri* − *rs* = *v* ∙ ∆*t*

*dj* = *rj* − *rs* = *v* ∙ ∆*t*

**3.2. Two-dimensional source location technique**

<sup>1</sup> <sup>=</sup> \_\_1 2(*t* <sup>1</sup> − *t*

<sup>2</sup> <sup>=</sup> \_\_1 <sup>2</sup> *l* − *l*

lowing relations planner or two-dimensional AE source location are done.

2).*<sup>v</sup>* <sup>=</sup> \_\_1

<sup>1</sup> <sup>=</sup> \_\_1 2

Planner or two-dimensional source location technique requires three or more AE sensors to be placed on a plane for identifying AE source. Three sensors generate three hyperbolae, which intersect each other on the monitoring plane at a common interceding point or cross-sectional point, and the point is termed as the AE source. Theoretically, three sensors are sufficient for identifying the source in two-dimensional technique; however, another extra sensor, which is called as reference sensor, improves the accuracy of the source location technique. Therefore, the placement of four sensors in a rectangular sensor array generates six sensor pairs. Calculating time of arrival from each sensor pair and correlating according to the fol-

The simple algorithm for calculating two-dimensional AE source location is based on the

Furthermore, suffixes *i* and *j* indicate the general number of positioning and measuring sensors,

] <sup>=</sup> \_\_1 2[

<sup>2</sup> + *yi* <sup>2</sup> − *di*

> <sup>2</sup> + *yj* <sup>2</sup> − *dj*

<sup>2</sup> = *rs*

<sup>2</sup> = *ri*

<sup>2</sup> = *rj*

indicates for sensor 1, and *sj*

indicate the distances from the corresponding sensors to source. Applying

–*y*, when *x* and *y* indicate the coordinates of sensor positions; how-

\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Uj xj* cos*<sup>θ</sup>* <sup>+</sup> *yj* sin*<sup>θ</sup>* <sup>+</sup> *dj*

<sup>2</sup> + *ys*

*i* <sup>2</sup> + (∆*y*)*<sup>i</sup>*

*j* <sup>2</sup> + (∆*y*)*<sup>j</sup>*

\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Ui xi* cos*<sup>θ</sup>* <sup>+</sup> *yi* sin*<sup>θ</sup>* <sup>+</sup> *di*

are defined as follow:

ever, for the source indication, the suffix *s* is used. However, *s*<sup>0</sup>

simple solutions of above Eqs. (3)–(5), the source distance, *r*<sup>s</sup>

2[

<sup>2</sup> Δ*t*.*v* (1)

<sup>2</sup> (3)

<sup>2</sup> (4)

<sup>2</sup> (5)

can be calculated as follows:

<sup>2</sup> (7)

<sup>2</sup> (8)

*io* (9)

*jo* (10)

indicates the reference sensor.

indicates for sensor 2.

] (6)

(*l* − Δ*t*.*v*) (2)

$$
\Theta = \Phi + \psi \tag{11}
$$

In Eq. (11), the parameters ϕ and ψ can be calculated by rearranging Eq. (6), and thus, the two-dimensional source location can be found.

Similarly, three-dimensional source location is also possible to calculate in AE source location technique by increasing the number of sensors. Many other modern source location techniques are available [10, 13] and are still introducing to AE fields by AE researchers from all over the world.

## **4. Smart applications of AE technique**

The application of acoustic emission for fault detection or condition monitoring in structural health monitoring (SHM) field is versatile. Since it is a noninvasive technique, it is widely applied in different fields of nondestructive testing (NDT), nondestructive evaluation (NDE), and nondestructive monitoring (NDM) for many engineering applications. Similar application of AE in seismology is well known from its beginning of implementations. Further, recently, applications of AE in biomedical engineering field have attracted many scientists and engineers for its smart applications in condition monitoring as well. Several examples of AE applications are mentioned later.

#### **4.1. Industrial applications in SHM**

Out of many industrial applications of AE technique, several are mentioned as monitoring of pressure vessel, storage tank, structural materials, composites, concrete structure, steel structure, bridge, aircraft, gear, ceramics, ceramic components, and so on. In maximum cases of inspection, standard AE features are evaluated experimentally under satisfactory experimental environments to practical application and correlated with standard values. For example, pressure vessel or other high-pressure tanks are evaluated under cyclic loading pressure [8] up to lifetime number of loading. AE sensors are attached to the tank to be tested and connected to the data acquisition components such as preamplifier and filters, and finally, the digital acquisition system saves the data to the computer where the required AE parameters are evaluated for crack or damage evaluation. Multiple sensors are placed for evaluating the damage source as well. Pipe line or drill pipe fatigue damage is also evaluated frequently by AE technique. Although fatigue loading is a complex mechanism in operation, however, it is defined by cycle number in all fatigue tests, and therefore, fatigue damage is normally evaluated based on crack propagation under certain range of applied cyclic loads. Based on application criteria, drill pipe is subjected to cyclic stress in tension, compression, torsion, and bending. Bending and rotation produce alternation between states of loading at a localized point, which is most concern to damage under fatigue loading. In drilling test rig monitoring, frequent fatigue failures are tested based on critical rotary speed, maximum tension load, notch fatigue load, etc. [33].

Most bridges are tested based on their welded joints and connections under the combinations of loading and loading environments. The general frequency of monitoring bridges is 2 years. Under visual inspection, the necessity of shutting down of its weight capacity is done when damage is found. However, in AE inspection, lane closer is not necessary as it monitors data continuously for real-time forecasting of any damage. Therefore, bridge monitoring by AE technique has increased as well [34].

and AE parametric features were calculated to represent the characteristics of crack propagation in a ferrite material under tensile loads. Applied tensile loads were simultaneously saved to the computer for evaluation as well. One experimental result showing AE parametric distribution (amplitude distribution versus tensile loads compared to AE hits) is shown in **Figure 6**. In this experiment, according to the sensor positions, oscilloscope channels (CH in figure) were defined. Furthermore, sensors 2 and 3 were placed near to the crack initiation position; sensor 1 was placed near to the loading chuck; sensor 4 was placed near to the specimen supporting chuck. Accordingly, sensor 2 (CH2) and sensor 3 (CH3) represented the maximum AE excited values in signal amplitude, whereas sensor 1 (CH1) showed the AE amplitude along with noise contamination from the loading chuck. Similarly, sensor 4 (CH4) represented the minimum value as it was the farthest from the cracking position and far from loading nose. Furthermore, amplitude excitation and distribution values of CH2 and CH3 showed that at the initiation of cracking, amplitude excitations were high due to the tensile cracking at its early stage of AE hits, and after that, as cracking took the shear loading, the amplitude values went down until it gained the maximum values at the fracture stage at their end stage of AE hits.

**Figure 6.** (a) Graphical representation of AE parametric distribution and (b) AE sensor positions in the specimen.

An experiment of two-dimensional source location technique as explained in Section 3.2 was conducted on a steel plate with generated artificial AE source based on Hsu-Nielsen [31, 37] technique. The arrival time was calculated according to the first signal recognition in AE hit as shown in **Figure 7**. Three experiments were conducted with three sensor distances, where sensorto-sensor distance was kept constant among three sensors in each experiment. Accordingly, the

was calculated. The results were compared with its actual measured data (known before for

comparison) and found good agreement as well. The results are summarized in **Table 1**.

) and source angle (*θ*), as shown in **Figure 4**,

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*4.1.2. AE source location*

source location represented by source distance (*r*<sup>s</sup>

Material testing by AE technique is also widely applicable. Structural materials, ductile materials, brittle materials, and many other materials including composite materials are tested to evaluate their cracking, breaking, and damaging characteristics for different industrial and biomedical applications. Furthermore, microstructural studies including metallurgical characteristics of many materials are also tested by different smart AE tests.

Different aerospace structures are monitored by AE technique as well. Many sensors are possible to attach to different parts of aerospace structures easily, and therefore, damage monitoring even in minute level and damage location in multidimensional features are performed by AE technique. In many smart AE techniques, real-time wireless monitoring is done by applying wireless AE sensing systems. For example, NASA installed AE sensor-based alert system on the inside of the space shuttle Discovery's wing structure for avoiding the damage of its leading edge during the reentry to the Earth atmosphere [35].

## *4.1.1. AE parametric analysis*

A material test result was conducted for showing the parametric analysis of AE technique [36]. The experiment was conducted for a cast iron specimen (ferrite) under tensile loading in an autograph tensile machine. Four AE sensors (R15α, Physical acoustics Ltd.), placed to the specimen for getting AE data due to crack damage, were connected to four preamplifiers and to a main amplifier with a gain of 40 dB. AE data were collected by a digital oscilloscope, and the collected data were analyzed for the characterization inside a personal computer. For avoiding noise, appropriate threshold values were used. All the recorded AE hits were saved, Structural Health Monitoring by Acoustic Emission Technique http://dx.doi.org/10.5772/intechopen.79483 33

**Figure 6.** (a) Graphical representation of AE parametric distribution and (b) AE sensor positions in the specimen.

and AE parametric features were calculated to represent the characteristics of crack propagation in a ferrite material under tensile loads. Applied tensile loads were simultaneously saved to the computer for evaluation as well. One experimental result showing AE parametric distribution (amplitude distribution versus tensile loads compared to AE hits) is shown in **Figure 6**. In this experiment, according to the sensor positions, oscilloscope channels (CH in figure) were defined. Furthermore, sensors 2 and 3 were placed near to the crack initiation position; sensor 1 was placed near to the loading chuck; sensor 4 was placed near to the specimen supporting chuck. Accordingly, sensor 2 (CH2) and sensor 3 (CH3) represented the maximum AE excited values in signal amplitude, whereas sensor 1 (CH1) showed the AE amplitude along with noise contamination from the loading chuck. Similarly, sensor 4 (CH4) represented the minimum value as it was the farthest from the cracking position and far from loading nose. Furthermore, amplitude excitation and distribution values of CH2 and CH3 showed that at the initiation of cracking, amplitude excitations were high due to the tensile cracking at its early stage of AE hits, and after that, as cracking took the shear loading, the amplitude values went down until it gained the maximum values at the fracture stage at their end stage of AE hits.

#### *4.1.2. AE source location*

standard AE features are evaluated experimentally under satisfactory experimental environments to practical application and correlated with standard values. For example, pressure vessel or other high-pressure tanks are evaluated under cyclic loading pressure [8] up to lifetime number of loading. AE sensors are attached to the tank to be tested and connected to the data acquisition components such as preamplifier and filters, and finally, the digital acquisition system saves the data to the computer where the required AE parameters are evaluated for crack or damage evaluation. Multiple sensors are placed for evaluating the damage source as well. Pipe line or drill pipe fatigue damage is also evaluated frequently by AE technique. Although fatigue loading is a complex mechanism in operation, however, it is defined by cycle number in all fatigue tests, and therefore, fatigue damage is normally evaluated based on crack propagation under certain range of applied cyclic loads. Based on application criteria, drill pipe is subjected to cyclic stress in tension, compression, torsion, and bending. Bending and rotation produce alternation between states of loading at a localized point, which is most concern to damage under fatigue loading. In drilling test rig monitoring, frequent fatigue failures are tested based on critical rotary

Most bridges are tested based on their welded joints and connections under the combinations of loading and loading environments. The general frequency of monitoring bridges is 2 years. Under visual inspection, the necessity of shutting down of its weight capacity is done when damage is found. However, in AE inspection, lane closer is not necessary as it monitors data continuously for real-time forecasting of any damage. Therefore, bridge monitoring by AE

Material testing by AE technique is also widely applicable. Structural materials, ductile materials, brittle materials, and many other materials including composite materials are tested to evaluate their cracking, breaking, and damaging characteristics for different industrial and biomedical applications. Furthermore, microstructural studies including metallurgical char-

Different aerospace structures are monitored by AE technique as well. Many sensors are possible to attach to different parts of aerospace structures easily, and therefore, damage monitoring even in minute level and damage location in multidimensional features are performed by AE technique. In many smart AE techniques, real-time wireless monitoring is done by applying wireless AE sensing systems. For example, NASA installed AE sensor-based alert system on the inside of the space shuttle Discovery's wing structure for avoiding the damage

A material test result was conducted for showing the parametric analysis of AE technique [36]. The experiment was conducted for a cast iron specimen (ferrite) under tensile loading in an autograph tensile machine. Four AE sensors (R15α, Physical acoustics Ltd.), placed to the specimen for getting AE data due to crack damage, were connected to four preamplifiers and to a main amplifier with a gain of 40 dB. AE data were collected by a digital oscilloscope, and the collected data were analyzed for the characterization inside a personal computer. For avoiding noise, appropriate threshold values were used. All the recorded AE hits were saved,

acteristics of many materials are also tested by different smart AE tests.

of its leading edge during the reentry to the Earth atmosphere [35].

speed, maximum tension load, notch fatigue load, etc. [33].

technique has increased as well [34].

32 Structural Health Monitoring from Sensing to Processing

*4.1.1. AE parametric analysis*

An experiment of two-dimensional source location technique as explained in Section 3.2 was conducted on a steel plate with generated artificial AE source based on Hsu-Nielsen [31, 37] technique. The arrival time was calculated according to the first signal recognition in AE hit as shown in **Figure 7**. Three experiments were conducted with three sensor distances, where sensorto-sensor distance was kept constant among three sensors in each experiment. Accordingly, the source location represented by source distance (*r*<sup>s</sup> ) and source angle (*θ*), as shown in **Figure 4**, was calculated. The results were compared with its actual measured data (known before for comparison) and found good agreement as well. The results are summarized in **Table 1**.

**Figure 7.** AE hit showing its initial recognition position of arrival signal.


healthy participants and patients of knee osteoarthritic disease joined to the experiments. A sample result of AE amplitude distribution compared with AE hit is presented in **Figure 7**. Acquisition of AE data is perfectly specified in the figure. All channels received sufficient AE data for identifying the internal conditions of knee joint. Thus, experimental results showed that monitoring of knee condition is possible by applying the AE technique successfully to

**Figure 8.** (a) Sample result of AE amplitude distribution for four sensors from the knee joint experiments and (b) schematic

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35

A feature outlook of acoustic emission (AE) technique related to the structural health monitoring has been presented in this chapter. A brief history and chronology of AE monitoring are discussed with adequate references. Basic understandings about AE technique, its experimental methodology, and applications are also summarized in this chapter. A list of frequently used AE parameters is also added here. Useful definitions of AE parameters are provided in this parametric list for understanding the theme of AE parametric analysis. Almost all of the structural health monitoring based on AE technique are conducted by the mentioned parameters. Three examples covering three important applications of AE technique are summarized at the end of the chapter. Two major wings of AE technique in structural health monitoring are AE parametric analysis and AE source location. Both of these applications are explained with appropriate examples along with experimental results in material damage and crack propagations. A smart application of AE technique in biomedical engineering field is also mentioned in this chapter as a promising scope of AE technique for the future versatile solutions. Extension of this work can be found in the future publications as well. Thus, the chapter has made easier for wider and fruitful understanding of AE technique in structural health

knee joint and to others.

of knee joint from AE sensor data were collected.

monitoring to all of its readers.

**5. Conclusions**

**Table 1.** Results of AE two-dimensional source location.

## **4.2. AE applications in biomedical health monitoring**

A successful history of AE technique in fault detection and condition monitoring encourages research to apply it to biomedical engineering field as well. Since AE technique perfectly evaluates and monitors any discontinuity and internal damage of a structure, it is successfully applied in detecting the integrity condition of human bones and joints, particularly knee joints. As detailed functional assessment of knee joint includes to identify any irregularity among its internal anatomical structures, AE sensors are installed to the knee joint and internal damages are evaluated. A common knee disease, particularly of elderly people, is osteoarthritis. It causes due to the damage of internal cartilage of knee joint. This disease causes the disability of people, and therefore, its prevalence is predicted to increase as a result of aging people in an aging society. The damage of cartilage brings the raw bone-end in contact and causes several knee diseases. In the worst case of osteoarthritis, operation is needed to replace by artificial joint with mixed satisfaction of the patient. Application of AE technique in diagnosis of cartilage damage is interestingly applied as well.

Accordingly, experiments of AE technique for identifying the integrity of knee joint were conducted [38]. Four AE sensors were placed to the knee joint, and AE data (AE features) were collected as shown in **Figure 8**. AE parameters from the knee were collected under the dynamic loading condition of knee joint by several stand-sit-stand motions of participants. Both

**Figure 8.** (a) Sample result of AE amplitude distribution for four sensors from the knee joint experiments and (b) schematic of knee joint from AE sensor data were collected.

healthy participants and patients of knee osteoarthritic disease joined to the experiments. A sample result of AE amplitude distribution compared with AE hit is presented in **Figure 7**. Acquisition of AE data is perfectly specified in the figure. All channels received sufficient AE data for identifying the internal conditions of knee joint. Thus, experimental results showed that monitoring of knee condition is possible by applying the AE technique successfully to knee joint and to others.

## **5. Conclusions**

**4.2. AE applications in biomedical health monitoring**

**Table 1.** Results of AE two-dimensional source location.

34 Structural Health Monitoring from Sensing to Processing

**Figure 7.** AE hit showing its initial recognition position of arrival signal.

**Distance Actual, θ Experimental, θ′ Actual, rs Experimental, rs Error of rs**

200 90 89.42 0.1414 0.1424 0.69 0.64 250 90 89.67 0.1768 0.1775 0.41 0.37 300 90 89.68 0.2121 0.2130 0.41 0.36

in diagnosis of cartilage damage is interestingly applied as well.

A successful history of AE technique in fault detection and condition monitoring encourages research to apply it to biomedical engineering field as well. Since AE technique perfectly evaluates and monitors any discontinuity and internal damage of a structure, it is successfully applied in detecting the integrity condition of human bones and joints, particularly knee joints. As detailed functional assessment of knee joint includes to identify any irregularity among its internal anatomical structures, AE sensors are installed to the knee joint and internal damages are evaluated. A common knee disease, particularly of elderly people, is osteoarthritis. It causes due to the damage of internal cartilage of knee joint. This disease causes the disability of people, and therefore, its prevalence is predicted to increase as a result of aging people in an aging society. The damage of cartilage brings the raw bone-end in contact and causes several knee diseases. In the worst case of osteoarthritis, operation is needed to replace by artificial joint with mixed satisfaction of the patient. Application of AE technique

 **(%) Error of θ (%)**

Accordingly, experiments of AE technique for identifying the integrity of knee joint were conducted [38]. Four AE sensors were placed to the knee joint, and AE data (AE features) were collected as shown in **Figure 8**. AE parameters from the knee were collected under the dynamic loading condition of knee joint by several stand-sit-stand motions of participants. Both A feature outlook of acoustic emission (AE) technique related to the structural health monitoring has been presented in this chapter. A brief history and chronology of AE monitoring are discussed with adequate references. Basic understandings about AE technique, its experimental methodology, and applications are also summarized in this chapter. A list of frequently used AE parameters is also added here. Useful definitions of AE parameters are provided in this parametric list for understanding the theme of AE parametric analysis. Almost all of the structural health monitoring based on AE technique are conducted by the mentioned parameters. Three examples covering three important applications of AE technique are summarized at the end of the chapter. Two major wings of AE technique in structural health monitoring are AE parametric analysis and AE source location. Both of these applications are explained with appropriate examples along with experimental results in material damage and crack propagations. A smart application of AE technique in biomedical engineering field is also mentioned in this chapter as a promising scope of AE technique for the future versatile solutions. Extension of this work can be found in the future publications as well. Thus, the chapter has made easier for wider and fruitful understanding of AE technique in structural health monitoring to all of its readers.

## **Acknowledgements**

The author expresses his sincere thanks and gratitude to all funding organizations including MEXT, Collaborating Company, Daishin Co. Ltd., and Saga University as well as to all graduate and undergraduate students of his laboratory for their continuous supports to continue all of his research topics. The author is particularly indebted to his biomedical research partner, Dr. Suya Ide (M.D.), for his enormous supports and guidance in continuing the research. The author is also obliged to all of his friends and colleagues, particularly to all participants of his research for having successful goal.

Acoustic Emission Testing & 7th International Conference on Acoustic Emission; 12-15

Structural Health Monitoring by Acoustic Emission Technique

http://dx.doi.org/10.5772/intechopen.79483

37

[9] Gorman MR, Prosser WH. AE source orientation by plate wave analysis. Journal of

[10] Christian UG, Ohtsu M, editors. Acoustic Emission Testing. Springer; 2008. DOI: 10.1007/

[11] Rindorf HJ. Acoustic Emission Source Location in Theory and in Practice. Vol. 2. Bruel

[12] Kaita I, Enoki M. Acquisition and analysis of continuous acoustic emission waveform for classification of damage sources in ceramic fiber mat. Materials Transactions.

[13] https://www.nde-ed.org/EducationResources/CommunityCollege/Other%20Methods/

[14] Forster F, Scheil E. Akustische Untersuchung der Bildung von Martensitnadeln (acoustic study of the formation of matensile needels). Zeitschrift für Metallkunde. 1936;**28**:245-247

[15] Kaiser J. A study of acoustic phenomena in tensile tests. [Dr.-Ing. dissertation]. Technical

[16] Obert L, Duvall W. The microseismic method of predicting rock failure in underground mining, Part II: Laboratory experiments. Report of Investigations 3803. Washington

[17] Obert L. The microseismic method: Discovery and early history. In: Hardy Jr, Leighton FW, editors. Proceedings 1st Conference on AE/MS. Geologic Structures and Materials.

[18] Schofield BH. Acoustic emission under applied stress. Report ARL-150. Boston: Lessels

[19] Kishinoue F. An experiment on the progression of fracture (a preliminary report). Jishin 6:24-31 (1934) translated and published by Ono K. Journal of Acoustic Emission.

[20] Yokomichi H, Ikeda I, Matsuoka K. Elastic wave propagation due to cracking of con-

[21] Ohtsu M, Ono K. A generalized theory of acoustic emission and Green's functions in a

[22] Beatttie AG. Acoustic emission, principles and instrumentation. Journal of Acoustic

[23] Nishinoiri S, Enoki M. Development of in-situ monitoring system for sintering of ceram-

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September 2012; Granada, Spain

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half space. Journal of Acoustic Emission. 1984;**3**:124-133

## **Author details**

Md. Tawhidul Islam Khan

Address all correspondence to: khan@me.saga-u.ac.jp

Department of Mechanical Engineering, Saga University, Saga, Japan

## **References**


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36 Structural Health Monitoring from Sensing to Processing

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Africa

The author expresses his sincere thanks and gratitude to all funding organizations including MEXT, Collaborating Company, Daishin Co. Ltd., and Saga University as well as to all graduate and undergraduate students of his laboratory for their continuous supports to continue all of his research topics. The author is particularly indebted to his biomedical research partner, Dr. Suya Ide (M.D.), for his enormous supports and guidance in continuing the research. The author is also obliged to all of his friends and colleagues, particularly to all participants of his

[1] Miller RK, McIntire P, editors. Acoustic Emission Testing. Nondestructive Testing Handbook. 2nd ed. Vol. 5. American Society for Nondestructive Testing. p. 603

[2] Ono K. Trends of recent acoustic emission literature. Journal of Acoustic Emission.

[3] Sachse W, Kim KY. Quantitative acoustic emission and failure mechanics of composite

[4] Meyendorf N, Frankenstein B, Schubert L. Structural health monitoring for aircraft, ground transportation vehicles, wind turbine and pipes-prognosis. In: Proceedings of 18th World Conference on Nondestructive Testing; 16-20 April 2012; Durban, South

[5] Holroyd TJ, Randall N. Use of acoustic emission for machine condition monitoring.

[6] Gorman M, Prosser WH. Application of normal mode expansion to acoustic emission

[7] Hamstad MA, Ogallagher A, Gary J. A wavelet transform applied to acoustic emission

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**Chapter 3**

Provisional chapter

**Evaluation of Diagnostic Symptoms for Object**

DOI: 10.5772/intechopen.77264

For complex objects, condition assessment is usually based on indirect symptoms related to residual processes such as vibration, noise, heat generation, etc. The number of available symptoms is often large, and it is necessary to select those which are most representative (i.e., sensitive to condition parameters). Such selection may be based on singular value decomposition (SVD). An alternative approach is proposed that employs information content measures. In order to obtain a reliable condition assessment and prognosis of its evolution (in particular, remaining useful life estimation), certain preprocessing of experimental data is necessary. This involves, among others, issues such as life cycle normalization or identification and removal of outliers. Suitable procedures are proposed and discussed. Example is presented for vibration-based symptoms of steam turbine

Keywords: diagnostic symptom, technical condition, prognosis, information content

Terms like condition assessment (which is basically equivalent to diagnosis) and prognosis are commonly used in technical sciences and have been defined in several ways. For any given class of diagnostic objects, there is a logical sequence of activities which may be summed up

• Qualitative diagnosis (or recognition-identification and localization of failures and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

• Measurement (acquisition of data that contain information on object condition)

Evaluation of Diagnostic Symptoms for Object

**Condition Diagnosis and Prognosis**

Condition Diagnosis and Prognosis

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77264

Tomasz Gałka

Tomasz Gałka

Abstract

technical condition.

including four consecutive stages [1, 2]:

1. Introduction

malfunctions)


#### **Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis** Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis

DOI: 10.5772/intechopen.77264

#### Tomasz Gałka Tomasz Gałka

[24] Ohtsu M. Acoustic emission characteristics in concrete and diagnostic applications.

[25] MISTRAS Group Inc. Express-8 AE System user's Manual, Rev 0, Part#: 7050-1000.

[26] Khan M, Islam T, Nagao T, Kondo Y, Teramoto K, Hattori N. Monitoring the fatigue damage in ductile cast iron by AE technique. International Journal of COMADEM.

[27] Shiotani T, Nakanishi Y, Iwaki K, Luo X, Haya H. Evaluation of reinforcement in damaged railway concrete piers by means of acoustic emission. Journal of Acoustic Emission.

[28] Hatano H, Watanabe T. Reciprocity calibration of acoustic emission transducers in Rayleigh wave and longitudinal wave sound field. The Journal of the Acoustical Society

[29] Hsu NN, Breckenridge FR. Characterization and calibration of acoustic emission sen-

[30] Vallen Systeme GmbH. Acoustic Emission Sensors Specification; 2015. Available from:

[31] Khan M, Islam T, Nagafuchi S, Hassan M. Structural damage localization by linear technique of acoustic emission. Open Journal of Fluid Dynamics. 2014;**4**:425-432

[32] Khan TI, Hassan M, Takata R. Effect of wave velocity in two-dimensional AE damage

[33] Gomera VP, Sokolov VL, Fedorov VP, Okotnikov AA, Saykova MS. Inspection of the pressure vessel used in petrochemical with AE examination. In: Proceedings,

[34] Shiotani T, Aggelis DG, Makishima O. Global monitoring of concrete bridge using acoustic emission. The Journal of the Acoustical Society of America. 2007;**25**:308-315 [35] Chlada M, Prevorovsky Z. Remote AE monitoring of fatigue crack growth in complex aircraft structures. In: Proceedings, 30th European Conference on Acoustic Emission Testing & 7th International Conference on Acoustic Emission; 12-15 September 2012;

[36] Rashid AA, Khan Md TI, Hidaka R. Analysis of acoustic emission and crack propagation in ductile cast iron. In: Proceedings, 21th Acoustic Emission Symposium; 9-10 November

[37] Mostofapour A, Davoodi S. A method for acoustic source location in plate-type struc-

[38] Islam KT, Harino Y. Integrity analysis of knee joint by acoustic emission technique.

ture. Mechanical Systems and Signal Processing. 2017;**93**:92-103

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locationon a steel plate. International Journal of COMADEM. 2017;**20**:1-5

Journal of Acoustic Emission. 1987;**6**:99-108

Physical Acoustic Corporation; 2014

38 Structural Health Monitoring from Sensing to Processing

of America. 1997;**101**:1450-1455

sors. Materials Evaluation. 1981;**39**:60-68

EWGAE2010; 8-10 September 2010; Vienna

2015;**18**:27-33

2006;**23**:260-271

Granada, Spain

2017; Tokushima, Japan

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77264

## Abstract

For complex objects, condition assessment is usually based on indirect symptoms related to residual processes such as vibration, noise, heat generation, etc. The number of available symptoms is often large, and it is necessary to select those which are most representative (i.e., sensitive to condition parameters). Such selection may be based on singular value decomposition (SVD). An alternative approach is proposed that employs information content measures. In order to obtain a reliable condition assessment and prognosis of its evolution (in particular, remaining useful life estimation), certain preprocessing of experimental data is necessary. This involves, among others, issues such as life cycle normalization or identification and removal of outliers. Suitable procedures are proposed and discussed. Example is presented for vibration-based symptoms of steam turbine technical condition.

Keywords: diagnostic symptom, technical condition, prognosis, information content

## 1. Introduction

Terms like condition assessment (which is basically equivalent to diagnosis) and prognosis are commonly used in technical sciences and have been defined in several ways. For any given class of diagnostic objects, there is a logical sequence of activities which may be summed up including four consecutive stages [1, 2]:



In structural health monitoring and condition-based maintenance, the third and fourth steps are of particular importance. Quantitative diagnosis is in fact an estimation of the current object condition. Once this has been accomplished, a prognosis may follow, which basically means remaining useful life (RUL) estimation on the basis of certain criteria. This is extremely important for proper and safe operation and cost-effective maintenance of complex and critical machinery.

Evolution of object condition may be described in terms of the hazard function [3, 4], which typically takes the form of the bathtub curve (Figure 1). Initially hazard function decreases with time; this may be interpreted as "running-in." During normal operation period, hazard function increase is so weak that it may be treated as constant. Finally, during the final stage of the object service life, hazard function increases with time—in theory to infinity and in practice until the highest acceptable value is attained. For a wide range of objects, reliability is well described by three-parameter Weibull distribution. In such case, hazard function in its classic form is given by [5, 6]

$$h\left(\theta; \beta, \eta, \gamma\right) = \frac{\beta}{\eta} \left(\frac{\theta - \gamma}{\eta}\right)^{\beta - 1},\tag{1}$$

For many objects it is impracticable or inconvenient to describe condition evolution in terms of the hazard function (or failure density). An alternative approach is based on the analysis of energy transformation and dissipation mechanisms, which leads to the energy processor model [1, 7]. This model implies that object condition is estimated in an indirect manner, from measurable physical quantities referred to as diagnostic symptoms. Each symptom is related to the power V(θ) of residual processes that accompany the principal process of energy transfor-

Sið Þ¼ <sup>θ</sup> <sup>Φ</sup> <sup>V</sup><sup>0</sup>

Sið Þ¼ <sup>θ</sup> Si<sup>0</sup> ln <sup>1</sup>

for the latter; in both cases, Si<sup>0</sup> = Si(θ = 0) and γ is the shape factor. For a given object, if sufficient database is available, it is possible to estimate θ<sup>b</sup> by relatively simple fitting procedure. This, in turn, allows to estimate RUL. It has to be kept in mind that θ<sup>b</sup> is obviously not equivalent to

Large and complex objects usually generate many diagnostic symptoms, and their number in fact has no upper limit. It has to be kept in mind that values of these symptoms depend not only on condition parameters. If all symptoms Si are expressed in the form of a vector S(θ),

where X, R, and Z denote vectors of condition parameters, control parameters, and interference, respectively. Obviously individual symptoms differ in their sensitivity to the components of all these vectors; it is thus necessary to select those which can be regarded "the best." The problem of selection was addressed at early stages of technical diagnostic development (see, e.g., [9]). Initially, at the stage of qualitative diagnosis, the principal criterion was symptom sensitivity to condition parameters. Quantitative diagnosis and prognosis imply a need to follow object condition evolution with time; thus, the symptom which best represents this process should be

RUL, unless the most primitive "run-to-breakdown" operational policy is employed.

where V<sup>0</sup> = V(θ = 0) and Φ is the symptom operator and θ<sup>b</sup> denotes time to breakdown. Detailed description can be found in literature; several modifications have been proposed [1, 8], but basic principles have remained unchanged. The Si(θ) given by Eq. (2) and referred to as symptom life curve is a monotonically increasing function with a vertical asymptote at θ = θb. As for the symptom operator, Weibull and Fréchet functions have been shown to give consistent

1 � θ=θ<sup>b</sup>

1 � θ=θ<sup>b</sup> <sup>1</sup>=<sup>γ</sup>

Sið Þ¼ <sup>θ</sup> Si0ð Þ �lnθ=θ<sup>b</sup> �1=<sup>γ</sup> (4)

Sð Þ¼ θ F½ � Xð Þ θ ; Rð Þ θ ;Zð Þ θ , (5)

(2)

http://dx.doi.org/10.5772/intechopen.77264

Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis

(3)

41

mation. In the simplest case, the ith symptom Si(θ) is given by

results; they yield Si(θ) in the forms of

then the following general relation holds [1, 9]:

considered the most suitable one.

for the former and

where θ denotes time and β, η, and γ are parameters; γ is the location parameter (set to zero if θ = 0 corresponds to the beginning of object life—in such case, two-parameter distribution is obtained); η denotes characteristic life; and β is the shape factor. Cases β < 1, β = 1, and β > 1 correspond to three consecutive periods shown in Figure 1.

Figure 1. Typical shape of the hazard function (bathtub curve).

For many objects it is impracticable or inconvenient to describe condition evolution in terms of the hazard function (or failure density). An alternative approach is based on the analysis of energy transformation and dissipation mechanisms, which leads to the energy processor model [1, 7]. This model implies that object condition is estimated in an indirect manner, from measurable physical quantities referred to as diagnostic symptoms. Each symptom is related to the power V(θ) of residual processes that accompany the principal process of energy transformation. In the simplest case, the ith symptom Si(θ) is given by

$$S\_i(\theta) = \Phi\left(\frac{V\_0}{1 - \theta/\theta\_b}\right) \tag{2}$$

where V<sup>0</sup> = V(θ = 0) and Φ is the symptom operator and θ<sup>b</sup> denotes time to breakdown. Detailed description can be found in literature; several modifications have been proposed [1, 8], but basic principles have remained unchanged. The Si(θ) given by Eq. (2) and referred to as symptom life curve is a monotonically increasing function with a vertical asymptote at θ = θb. As for the symptom operator, Weibull and Fréchet functions have been shown to give consistent results; they yield Si(θ) in the forms of

$$S\_i(\theta) = S\_{i0} \left( \ln \frac{1}{1 - \theta/\theta\_b} \right)^{1/\gamma} \tag{3}$$

for the former and

• Quantitative diagnosis (estimation of damage advancement)

In structural health monitoring and condition-based maintenance, the third and fourth steps are of particular importance. Quantitative diagnosis is in fact an estimation of the current object condition. Once this has been accomplished, a prognosis may follow, which basically means remaining useful life (RUL) estimation on the basis of certain criteria. This is extremely important for proper and safe operation and cost-effective maintenance of complex and critical

Evolution of object condition may be described in terms of the hazard function [3, 4], which typically takes the form of the bathtub curve (Figure 1). Initially hazard function decreases with time; this may be interpreted as "running-in." During normal operation period, hazard function increase is so weak that it may be treated as constant. Finally, during the final stage of the object service life, hazard function increases with time—in theory to infinity and in practice until the highest acceptable value is attained. For a wide range of objects, reliability is well described by three-parameter Weibull distribution. In such case, hazard function in its classic

η

where θ denotes time and β, η, and γ are parameters; γ is the location parameter (set to zero if θ = 0 corresponds to the beginning of object life—in such case, two-parameter distribution is obtained); η denotes characteristic life; and β is the shape factor. Cases β < 1, β = 1, and β > 1

θ � γ η <sup>β</sup>�<sup>1</sup>

, (1)

<sup>h</sup> <sup>θ</sup>; <sup>β</sup>; <sup>η</sup>; <sup>γ</sup> <sup>¼</sup> <sup>β</sup>

correspond to three consecutive periods shown in Figure 1.

Figure 1. Typical shape of the hazard function (bathtub curve).

• Prognosis (forecast for object operation in future)

40 Structural Health Monitoring from Sensing to Processing

machinery.

form is given by [5, 6]

$$\mathcal{S}\_i(\theta) = \mathcal{S}\_{i0} \left( -\ln \theta / \theta\_b \right)^{-1/\gamma} \tag{4}$$

for the latter; in both cases, Si<sup>0</sup> = Si(θ = 0) and γ is the shape factor. For a given object, if sufficient database is available, it is possible to estimate θ<sup>b</sup> by relatively simple fitting procedure. This, in turn, allows to estimate RUL. It has to be kept in mind that θ<sup>b</sup> is obviously not equivalent to RUL, unless the most primitive "run-to-breakdown" operational policy is employed.

Large and complex objects usually generate many diagnostic symptoms, and their number in fact has no upper limit. It has to be kept in mind that values of these symptoms depend not only on condition parameters. If all symptoms Si are expressed in the form of a vector S(θ), then the following general relation holds [1, 9]:

$$\mathbf{S}(\theta) = F[\mathbf{X}(\theta), \mathbf{R}(\theta), \mathbf{Z}(\theta)], \tag{5}$$

where X, R, and Z denote vectors of condition parameters, control parameters, and interference, respectively. Obviously individual symptoms differ in their sensitivity to the components of all these vectors; it is thus necessary to select those which can be regarded "the best." The problem of selection was addressed at early stages of technical diagnostic development (see, e.g., [9]). Initially, at the stage of qualitative diagnosis, the principal criterion was symptom sensitivity to condition parameters. Quantitative diagnosis and prognosis imply a need to follow object condition evolution with time; thus, the symptom which best represents this process should be considered the most suitable one.

This chapter is devoted mainly to symptom evaluation and selection methods based on the analysis of information content measures. Some attention shall, however, also be paid to the method employing the singular value decomposition, the first that has been used for this purpose.

Suitability of symptom evaluation methods has been verified for a number of vibration-based symptoms generated by steam turbines operated at utility power plants. Details on symptom generation mechanisms may be found, e.g., in [1, 10, 11]. Absolute vibration velocity was recorded in the form of 23% constant percentage bandwidth (CPB) spectra, at points located at bearings and low-pressure turbine casings. Piezoelectric accelerometers were used with magnetic mountings, which allows for a frequency range well above 10 kHz. This implies that both "harmonic" (i.e., resulting directly from rotational motion) and "blade" (i.e., generated by the fluid flow system) components are recorded. Vibration amplitudes in frequency bands determined from turbine vibrodiagnostic models [1, 11] are the diagnostic symptoms to be evaluated. It has to be stressed here that presented methods are valid for a broad class of various diagnostic symptoms, irrespective of their physical origin.

## 2. Singular value decomposition

Singular value decomposition (SVD) is well known from linear algebra; concise description can be found, e.g., in [12]. To the author's best knowledge, the idea to employ this method in technical diagnostics goes back to the late 1990s [13]. Application for vibration-based symptoms has shown this method to give consistent results [14].

The first step is to represent symptom value database in the form of an m � n matrix O, where m denotes the number of symptoms and n is the number of symptom value readings. In principle, symptoms of different physical origins are compared, so all are normalized with respect to their values at θ = 0; moreover, 1 is subtracted from all normalized values, so they start from zero and are dimensionless. In accordance with general SVD rules, matrix O can be expressed as the following product:

$$\mathbf{O} = \mathbf{U} \ast \boldsymbol{\Sigma} \ast \mathbf{V}^T \tag{6}$$

<sup>O</sup> <sup>¼</sup> <sup>X</sup> p

AL<sup>t</sup> <sup>¼</sup> <sup>u</sup><sup>T</sup>

discriminants, namely

tion parameters are typically nonmeasurable.

t¼1

According to [15] and following notation used herein, the tth fault can be described by two

This means that this fault can be expressed in terms of left-singular or right-singular vectors, which are generally interpreted as "input" and "output" [13, 15]. In the case of system condition evolution, "input" represents condition parameters and "output" represents symptoms. Obviously, the second discriminant, given by Eq. (10), is of practical use here, as condi-

SVD analysis may be performed using one of available software packages. In practical applications the first step is to analyze individual singular values. For a comparatively new object, the descent of consecutive singular values is rather slow; this means that dominant failure mode has not yet appeared. On the other hand, with considerable lifetime consumption degree, the first singular value dominates. Examples are shown in Figure 2. They refer to vibration-based symptoms generated by steam turbine fluid flow systems. In both cases illustrated in Figure 2, there are six such symptoms. For a turbine with a few dozen thousand hours logged (Figure 2a), contributions of the first three singular values into generalized damage are 36, 29, and 17%, respectively. For the second turbine (Figure 2b), which has logged well over 200,000 hours, corresponding values are 48, 24.5, and 10%—the difference is clearly seen. The second step is to calculate contributions of individual symptoms into several (e.g., three) first singular values. Corresponding graphs are shown in Figure 3. For the first turbine,

Figure 2. Contributions of singular values into generalized damage; (a) 260 MW unit, low-pressure turbine casing, rear

part left; (b) 200 MW unit, low-pressure turbine casing, front part right (see main text for details).

σi∙ ut∗v<sup>t</sup>

<sup>t</sup> <sup>∗</sup><sup>O</sup> <sup>¼</sup> <sup>σ</sup>t∙v<sup>T</sup>

<sup>T</sup> � � (8)

http://dx.doi.org/10.5772/intechopen.77264

43

<sup>t</sup> (10)

SD<sup>t</sup> ¼ O∗v<sup>t</sup> ¼ σt∙u<sup>t</sup> (9)

Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis

where U and V are orthogonal matrices (n � n and m � m, respectively) and Σ is a diagonal m � n matrix, Σ = diag(σi). If σ<sup>i</sup> components are arranged in the descending order, which is conventionally accepted, the representation given by Eq. (6) is unique. Components σ<sup>i</sup> correspond to generalized faults, so that the sum given by

$$F(\theta) = \sum\_{i=1}^{p} \sigma\_i(\theta)\_i \tag{7}$$

where p = min(m, n) represents the total damage advancement or lifetime consumption degree. Columns of U and V matrices are left-singular and right-singular vectors, denoted by u<sup>t</sup> and vt, respectively, with 1 ≤ t ≤ n. Eq. (6) can thus be rewritten as

Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis http://dx.doi.org/10.5772/intechopen.77264 43

$$\mathbf{O} = \sum\_{t=1}^{p} \sigma\_i \cdot \left(\mathbf{u}\_t \ast \mathbf{v}\_t^T\right) \tag{8}$$

According to [15] and following notation used herein, the tth fault can be described by two discriminants, namely

This chapter is devoted mainly to symptom evaluation and selection methods based on the analysis of information content measures. Some attention shall, however, also be paid to the method employing the singular value decomposition, the first that has been used for this

Suitability of symptom evaluation methods has been verified for a number of vibration-based symptoms generated by steam turbines operated at utility power plants. Details on symptom generation mechanisms may be found, e.g., in [1, 10, 11]. Absolute vibration velocity was recorded in the form of 23% constant percentage bandwidth (CPB) spectra, at points located at bearings and low-pressure turbine casings. Piezoelectric accelerometers were used with magnetic mountings, which allows for a frequency range well above 10 kHz. This implies that both "harmonic" (i.e., resulting directly from rotational motion) and "blade" (i.e., generated by the fluid flow system) components are recorded. Vibration amplitudes in frequency bands determined from turbine vibrodiagnostic models [1, 11] are the diagnostic symptoms to be evaluated. It has to be stressed here that presented methods are valid for a broad class of

Singular value decomposition (SVD) is well known from linear algebra; concise description can be found, e.g., in [12]. To the author's best knowledge, the idea to employ this method in technical diagnostics goes back to the late 1990s [13]. Application for vibration-based symp-

The first step is to represent symptom value database in the form of an m � n matrix O, where m denotes the number of symptoms and n is the number of symptom value readings. In principle, symptoms of different physical origins are compared, so all are normalized with respect to their values at θ = 0; moreover, 1 is subtracted from all normalized values, so they start from zero and are dimensionless. In accordance with general SVD rules, matrix O can be

where U and V are orthogonal matrices (n � n and m � m, respectively) and Σ is a diagonal m � n matrix, Σ = diag(σi). If σ<sup>i</sup> components are arranged in the descending order, which is conventionally accepted, the representation given by Eq. (6) is unique. Components σ<sup>i</sup> corre-

> <sup>F</sup>ð Þ¼ <sup>θ</sup> <sup>X</sup> p

> > i¼1

where p = min(m, n) represents the total damage advancement or lifetime consumption degree. Columns of U and V matrices are left-singular and right-singular vectors, denoted by u<sup>t</sup> and vt,

<sup>O</sup> <sup>¼</sup> <sup>U</sup>∗Σ∗V<sup>T</sup> (6)

σið Þ θ , (7)

various diagnostic symptoms, irrespective of their physical origin.

toms has shown this method to give consistent results [14].

spond to generalized faults, so that the sum given by

respectively, with 1 ≤ t ≤ n. Eq. (6) can thus be rewritten as

2. Singular value decomposition

42 Structural Health Monitoring from Sensing to Processing

expressed as the following product:

purpose.

$$\mathbf{^0 \mathbf{D}\_t = \mathbf{O} \ast \mathbf{v}\_t = \sigma\_t \cdot \mathbf{u}\_t} \tag{9}$$

$$\mathbf{AL}\_t = \mathbf{u}\_t^T \ast \mathbf{O} = \sigma\_t \cdot \mathbf{v}\_t^T \tag{10}$$

This means that this fault can be expressed in terms of left-singular or right-singular vectors, which are generally interpreted as "input" and "output" [13, 15]. In the case of system condition evolution, "input" represents condition parameters and "output" represents symptoms. Obviously, the second discriminant, given by Eq. (10), is of practical use here, as condition parameters are typically nonmeasurable.

SVD analysis may be performed using one of available software packages. In practical applications the first step is to analyze individual singular values. For a comparatively new object, the descent of consecutive singular values is rather slow; this means that dominant failure mode has not yet appeared. On the other hand, with considerable lifetime consumption degree, the first singular value dominates. Examples are shown in Figure 2. They refer to vibration-based symptoms generated by steam turbine fluid flow systems. In both cases illustrated in Figure 2, there are six such symptoms. For a turbine with a few dozen thousand hours logged (Figure 2a), contributions of the first three singular values into generalized damage are 36, 29, and 17%, respectively. For the second turbine (Figure 2b), which has logged well over 200,000 hours, corresponding values are 48, 24.5, and 10%—the difference is clearly seen. The second step is to calculate contributions of individual symptoms into several (e.g., three) first singular values. Corresponding graphs are shown in Figure 3. For the first turbine,

Figure 2. Contributions of singular values into generalized damage; (a) 260 MW unit, low-pressure turbine casing, rear part left; (b) 200 MW unit, low-pressure turbine casing, front part right (see main text for details).

H ¼ �K

^ i

> Xn i¼1

h ¼ �K

ð ∞

�∞

Shannon entropy was originally introduced for verbal communication; hence, a discrete random variable is involved. A diagnostic symptom in the sense of the energy processor model is in general continuous, so a derivative of H known as continuous or differential entropy should be

where p(Si) is the probability density function. Despite formal similarity, Eq. (14) is not just a limiting case of Eq. (11) for n ! ∞. Contrary to H, continuous entropy is not invariant under change of variables [19]. Moreover, h can be negative, although a satisfactory physical explanation of the negative information content is still lacking. From the practical point of view, continuous entropy is very convenient, as for widely employed statistical distributions it is

It may be added here that several other entropy types have been proposed, e.g., by Hartley [20], Rényi [16], or Tsallis [21]. Their use, however, has been limited. Hartley entropy is a specific case of the Shannon entropy, while Rényi entropy may be viewed by its generalization. Both Rényi and Tsallis entropies involve certain adjustable parameters of rather unclear phys-

For the purpose of condition symptom evaluation, the time window procedure may be employed. A window containing sufficient number of Si(θ) readings is moved along the time axis; for each position, statistical distribution parameters within it are determined, and in this way the h(θ) curve is obtained. This in turn allows for estimation of the information content measure (ICM) decrease rate. In practice this involves certain problems which shall be

Obviously, in order to employ the abovementioned procedure, symptom distribution type has to be determined. In general, distributions of diagnostic symptom values are of the right-hand

dits, respectively. Obviously

used. It is given by (see, e.g., [18])

discussed in the following section.

3.2. Shortcomings

3.2.1. Distribution type

given by relatively simple analytical expressions.

ical meanings, which are generally difficult to estimate.

Xn i¼1 pi logbpi

where K is a constant depending on units used (irrelevant if only decrease rate is of interest). Logarithm base b is typically set at 2, Euler constant, or 10, H being expressed in bits, nats, and

, (11)

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45

0 ≤ pi ≤ 1, (12)

Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis

pi ¼ 1: (13)

p Sð Þ<sup>i</sup> logbp Sð Þ<sup>i</sup> dSi, (14)

Figure 3. Contributions of individual symptoms into the first three singular values: (a) as in Figure 2a and (b) as in Figure 2b.

dominant symptoms cannot be identified, although we may infer that symptom numbers 1 and 5 can be skipped. For the second turbine, however, dominance of symptom numbers 5 and 6 is clearly seen, and they may be judged most sensitive to the fluid flow system lifetime consumption.

## 3. Information content measures

## 3.1. The idea

The abovementioned energy processor model is, by its very nature, deterministic. From Eq. (5), however, it is clearly seen that symptom values depend not only on deterministic condition parameters Xi(θ) but also on control parameters Ri(θ) and interferences Zi(θ), which are random variables. Therefore, any symptom Si(θ) should in principle be treated as a random variable with time-dependent parameters.

For a given object operated at a given location, it is reasonable to assume that Ri(θ) and Zi(θ) are characterized by statistical distributions with time constant parameters. At the same time, from Eq. (2) it is clearly seen that the influence of lifetime consumption θ/θ<sup>b</sup> (or, more generally, of deterministic condition parameters) will increase as θ ! θb. This means that Si(θ) will become more deterministic or, to put it in a different way, more predictable. As pointed out in [16], this corresponds to information content decrease, in the sense of Shannon entropy [17]. Therefore, a symptom with the highest rate of an information content measure which decreases with time is the one that is most sensitive to lifetime consumption mechanisms.

Investigations of information content and its measures were pioneered by Claude E. Shannon. In his fundamental work [17], he introduced an information content measure H(p1, p2, …, pn), later termed Shannon entropy, where pi is the probability of the ith event, and showed it to have the following form:

Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis http://dx.doi.org/10.5772/intechopen.77264 45

$$H = -K\sum\_{i=1}^{n} p\_i \log\_b p\_{i'} \tag{11}$$

where K is a constant depending on units used (irrelevant if only decrease rate is of interest). Logarithm base b is typically set at 2, Euler constant, or 10, H being expressed in bits, nats, and dits, respectively. Obviously

$$\bigwedge\_{i} 0 \le p\_i \le 1,\tag{12}$$

$$\sum\_{i=1}^{n} p\_i = 1.\tag{13}$$

Shannon entropy was originally introduced for verbal communication; hence, a discrete random variable is involved. A diagnostic symptom in the sense of the energy processor model is in general continuous, so a derivative of H known as continuous or differential entropy should be used. It is given by (see, e.g., [18])

$$h = -K \int\_{-\infty}^{\infty} p(\mathcal{S}\_i) \log\_b p(\mathcal{S}\_i) dS\_{i\nu} \tag{14}$$

where p(Si) is the probability density function. Despite formal similarity, Eq. (14) is not just a limiting case of Eq. (11) for n ! ∞. Contrary to H, continuous entropy is not invariant under change of variables [19]. Moreover, h can be negative, although a satisfactory physical explanation of the negative information content is still lacking. From the practical point of view, continuous entropy is very convenient, as for widely employed statistical distributions it is given by relatively simple analytical expressions.

It may be added here that several other entropy types have been proposed, e.g., by Hartley [20], Rényi [16], or Tsallis [21]. Their use, however, has been limited. Hartley entropy is a specific case of the Shannon entropy, while Rényi entropy may be viewed by its generalization. Both Rényi and Tsallis entropies involve certain adjustable parameters of rather unclear physical meanings, which are generally difficult to estimate.

For the purpose of condition symptom evaluation, the time window procedure may be employed. A window containing sufficient number of Si(θ) readings is moved along the time axis; for each position, statistical distribution parameters within it are determined, and in this way the h(θ) curve is obtained. This in turn allows for estimation of the information content measure (ICM) decrease rate. In practice this involves certain problems which shall be discussed in the following section.

#### 3.2. Shortcomings

dominant symptoms cannot be identified, although we may infer that symptom numbers 1 and 5 can be skipped. For the second turbine, however, dominance of symptom numbers 5 and 6 is clearly seen, and they may be judged most sensitive to the fluid flow system lifetime

Figure 3. Contributions of individual symptoms into the first three singular values: (a) as in Figure 2a and (b) as in

The abovementioned energy processor model is, by its very nature, deterministic. From Eq. (5), however, it is clearly seen that symptom values depend not only on deterministic condition parameters Xi(θ) but also on control parameters Ri(θ) and interferences Zi(θ), which are random variables. Therefore, any symptom Si(θ) should in principle be treated as a random

For a given object operated at a given location, it is reasonable to assume that Ri(θ) and Zi(θ) are characterized by statistical distributions with time constant parameters. At the same time, from Eq. (2) it is clearly seen that the influence of lifetime consumption θ/θ<sup>b</sup> (or, more generally, of deterministic condition parameters) will increase as θ ! θb. This means that Si(θ) will become more deterministic or, to put it in a different way, more predictable. As pointed out in [16], this corresponds to information content decrease, in the sense of Shannon entropy [17]. Therefore, a symptom with the highest rate of an information content measure which decreases with time is the one that is most sensitive to lifetime consumption mechanisms.

Investigations of information content and its measures were pioneered by Claude E. Shannon. In his fundamental work [17], he introduced an information content measure H(p1, p2, …, pn), later termed Shannon entropy, where pi is the probability of the ith event, and showed it to have

consumption.

Figure 2b.

3.1. The idea

the following form:

3. Information content measures

44 Structural Health Monitoring from Sensing to Processing

variable with time-dependent parameters.

#### 3.2.1. Distribution type

Obviously, in order to employ the abovementioned procedure, symptom distribution type has to be determined. In general, distributions of diagnostic symptom values are of the right-hand tailed type [1]. Weibull and gamma distributions are commonly used, with the probability density functions given by

$$f\_{\mathcal{W}}(\mathbf{x}) = \frac{k}{\lambda^k} \mathbf{x}^{k-1} \exp\left(-\frac{\mathbf{x}^k}{\lambda^k}\right) \tag{15}$$

and

$$f\_G(\mathbf{x}) = \frac{\mathbf{x}^{k-1} \mathbf{exp}\left(-\frac{\mathbf{x}}{\Lambda}\right)}{\lambda^k \Gamma(k)},\tag{16}$$

respectively, where k is the shape factor, λ denotes the scale factor, and Γ is the gamma function. It has been shown for a number of cases [1, 22, 23] that results obtained with these two distributions are quantitatively similar. Moreover, although this might seem strange, normal distribution given by

$$f\_N(\mathbf{x}) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{\left(\mathbf{x} - \boldsymbol{\mu}\right)^2}{2\sigma^2}\right) \tag{17}$$

(μ and σ denote mean value and standard deviation, respectively) yields very similar results; this greatly simplifies calculations. Continuous entropy for these three distributions is given by the following relations [24]:

$$h\_W(\mathbf{x}) = \frac{(k-1)\gamma\_E}{k} + \ln\frac{\lambda}{k} + 1,\tag{18}$$

Sið Þ θ<sup>k</sup> Sið Þ θ<sup>k</sup>�<sup>1</sup>

Sið Þ θ<sup>k</sup> Sið Þ θ<sup>k</sup>�<sup>1</sup>

trimming is illustrated in Figure 5.

pressure fluid flow system—after [23], © JVE Journals).

3.2.3. Stationarity

<sup>&</sup>gt; ch and Sið Þ <sup>θ</sup><sup>k</sup>

Figure 4. Comparison of distribution fitting results (260 MW steam turbine, vibration component generated by high-

<sup>&</sup>lt; cl and Sið Þ <sup>θ</sup><sup>k</sup>

then Si(θk) is considered as an outlier and replaced by the average of two adjacent readings. Upper and lower thresholds, ch and cl, are adjusted experimentally and depend on the object. In practice, situation described by Eq. (21) is much more frequent, mainly as a result of the influence of control parameters and/or interference (cf. Eq. (5)). Very low symptom value readings, as in Eq. (22), are usually caused by plain measurement errors. Effect of peak

Fitting continuous distributions to experimental symptom value histograms within the time window limits require at least weak stationarity. This implies that for every symptom Si mean value and autocovariance must not change with time. In view of the fact that Si(θ) has a vertical asymptote at θb, this may be considered valid only for θ < < θb. As already mentioned, it may be assumed that control and interference (Eq. (5)) are represented by stationary stochastic processes. Therefore, Si(θ) may be viewed a trend stationary process, and, if the deterministic trend is removed, what is left is a stationary process [28]. In fact over a hundred years ago, it was pointed out that, in time series analysis, a measure of deviation from trend and not from

Sið Þ θ<sup>k</sup>þ<sup>1</sup>

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47

Sið Þ θ<sup>k</sup>þ<sup>1</sup>

> ch, (21)

< cl, (22)

$$h\_G(\mathbf{x}) = \ln(\lambda \Gamma(k) + (1 - k)\psi(k) + k) \tag{19}$$

$$h\_N(\mathbf{x}) = \ln \left( \sigma \sqrt{2\pi e} \right),\tag{20}$$

where γ<sup>E</sup> is the Euler-Mascheroni constant and ψ(x) is the digamma function. An example of comparison of results obtained with gamma, and Weibull and normal distributions is shown in Figure 4.

#### 3.2.2. Outliers

Diagnostic symptom time histories often exhibit a considerable number of outliers. According to [25], "an outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs"; there is no generally accepted precise definition. From the point of view of information theory, outliers are equivalent to noise. As with the definition, there is no universal method for removing outliers. The "three-sigma rule," which is often used for this purpose, is not applicable to distributions with long right-hand tails [26]. Three-point averaging [27] merely flattens outliers instead of removing them. The author has suggested a procedure referred to as "peak trimming" [1], based on comparison of a data point with two adjacent points. If for the Si(θk) symptom value reading one of the following criteria is met:

Figure 4. Comparison of distribution fitting results (260 MW steam turbine, vibration component generated by highpressure fluid flow system—after [23], © JVE Journals).

$$\frac{S\_i(\theta\_k)}{S\_i(\theta\_{k-1})} > c\_\hbar \text{ and } \frac{S\_i(\theta\_k)}{S\_i(\theta\_{k+1})} > c\_{\hbar\nu} \tag{21}$$

$$\frac{S\_i(\theta\_k)}{S\_i(\theta\_{k-1})} < c\_l \text{ and } \frac{S\_i(\theta\_k)}{S\_i(\theta\_{k+1})} < c\_{l'} \tag{22}$$

then Si(θk) is considered as an outlier and replaced by the average of two adjacent readings. Upper and lower thresholds, ch and cl, are adjusted experimentally and depend on the object. In practice, situation described by Eq. (21) is much more frequent, mainly as a result of the influence of control parameters and/or interference (cf. Eq. (5)). Very low symptom value readings, as in Eq. (22), are usually caused by plain measurement errors. Effect of peak trimming is illustrated in Figure 5.

#### 3.2.3. Stationarity

tailed type [1]. Weibull and gamma distributions are commonly used, with the probability

exp � xk λk � �

> λ � �

2σ<sup>2</sup> !

hGð Þ¼ x lnðλΓð Þþ k ð Þ 1 � k ψð Þþ k k, (19)

<sup>Γ</sup>ð Þ<sup>k</sup> , (16)

<sup>k</sup> <sup>þ</sup> <sup>1</sup>, (18)

� � <sup>p</sup> , (20)

xk�1exp � <sup>x</sup>

<sup>2</sup>πσ<sup>2</sup> <sup>p</sup> exp � <sup>x</sup> � <sup>μ</sup> � �<sup>2</sup>

<sup>k</sup> <sup>þ</sup> ln <sup>λ</sup>

2πe

(μ and σ denote mean value and standard deviation, respectively) yields very similar results; this greatly simplifies calculations. Continuous entropy for these three distributions is given by

ð Þ k � 1 γ<sup>E</sup>

hNð Þ¼ <sup>x</sup> ln <sup>σ</sup> ffiffiffiffiffiffiffiffi

where γ<sup>E</sup> is the Euler-Mascheroni constant and ψ(x) is the digamma function. An example of comparison of results obtained with gamma, and Weibull and normal distributions is shown

Diagnostic symptom time histories often exhibit a considerable number of outliers. According to [25], "an outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs"; there is no generally accepted precise definition. From the point of view of information theory, outliers are equivalent to noise. As with the definition, there is no universal method for removing outliers. The "three-sigma rule," which is often used for this purpose, is not applicable to distributions with long right-hand tails [26]. Three-point averaging [27] merely flattens outliers instead of removing them. The author has suggested a procedure referred to as "peak trimming" [1], based on comparison of a data point with two adjacent points. If for the Si(θk) symptom value reading one of the following criteria is met:

λk

respectively, where k is the shape factor, λ denotes the scale factor, and Γ is the gamma function. It has been shown for a number of cases [1, 22, 23] that results obtained with these two distributions are quantitatively similar. Moreover, although this might seem strange,

(15)

(17)

k <sup>λ</sup><sup>k</sup> xk�<sup>1</sup>

f <sup>W</sup>ð Þ¼ x

f <sup>G</sup>ð Þ¼ x

1 ffiffiffiffiffiffiffiffiffiffi

f <sup>N</sup>ð Þ¼ x

hW ð Þ¼ x

density functions given by

46 Structural Health Monitoring from Sensing to Processing

normal distribution given by

the following relations [24]:

in Figure 4.

3.2.2. Outliers

and

Fitting continuous distributions to experimental symptom value histograms within the time window limits require at least weak stationarity. This implies that for every symptom Si mean value and autocovariance must not change with time. In view of the fact that Si(θ) has a vertical asymptote at θb, this may be considered valid only for θ < < θb. As already mentioned, it may be assumed that control and interference (Eq. (5)) are represented by stationary stochastic processes. Therefore, Si(θ) may be viewed a trend stationary process, and, if the deterministic trend is removed, what is left is a stationary process [28]. In fact over a hundred years ago, it was pointed out that, in time series analysis, a measure of deviation from trend and not from

Figure 5. Effect of peak trimming: raw (a) and peak-trimmed (b) symptom time histories. Data refer to the intermediatepressure turbine of a 260 MW unit.

some "mean" or "average" should be taken into account [29]. In other words, trend normalization should be performed prior to ICM analysis.

Trend may be determined by fitting a suitable function to experimental symptom time history. Weibull and Fréchet functions may be used for this purpose; for low values of θ, exponential function may be a good approximation. An obvious prerequisite is lack of abrupt (stepwise) changes; this issue shall be discussed in detail in the following section. Once this is performed, a procedure may be employed wherein each symptom value reading Si(θ) is replaced by trendnormalized value given by [23]

$$S\_i'(\theta) = S\_i(\theta) \frac{\mathbb{S}\_{it}(0)}{\mathbb{S}\_{it}(\theta)},\tag{23}$$

3.2.4. Abrupt changes

schematically in Figure 7.

Complex and costly machines like, for example, power-generating units are usually designed for long service life. During the period between commissioning and final withdrawal from use, they are usually subject to various processes of maintenance, repair, and overhaul. Each of them introduces changes of object properties, which influence both diagnostic symptom generation mechanisms and their propagation from origin to measurement points. So far, it has been assumed (tacitly) that each Si(θ) function, or symptom life curve, is a superposition of a monotonic and continuous trend Sit(θ) and random fluctuations. In general this is not the case. Deterministic trend is in fact a sequence of symptom life curves, each being characterized by some specific values of Si(0) and θb. Of course repair or overhaul is performed before the breakdown, so of each curve is represented by a section of the length of θ<sup>0</sup> < θb. This is shown

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Figure 7 clearly shows that, if fitting continuous function to experimental data is expected to yield consistent results, abrupt changes should be eliminated. In principle this is relatively simple. Each life cycle and hence each symptom life curve are characterized by the so-called logistic vector [7], which describes its "quality." This vector may be replaced by its scalar measure L, which influences both Si(0) and θb. For a sequence such as shown in Figure 7, one cycle is chosen as a reference; it may be convenient to use the one with the lowest initial value for this purpose, but this is not mandatory. Its value for θ = 0 is taken as a reference Sr(0). Then, for each other cycle, a normalizing factor Fi = Si(0)/Sr(0) is determined, and normalization is

This idea may seem simple, but precise determination of the moment of transition from a life cycle to the next one may be problematic. Sufficient operational documentation is not always available, and transitions are often masked by random fluctuations. A method for their

obtained by simple multiplication of all symptom readings in this cycle by 1/Fi.

Figure 7. Schematic representation of the symptom life curve sequence.

where subscript t denotes value determined from the estimated trend. An example of trend normalization (Weibull function fitting) is shown in Figure 6.

Figure 6. An example of standard peak-trimmed (a) and trend-normalized (b) time histories; data refer to the highpressure turbine of a 230 MW unit.

## 3.2.4. Abrupt changes

some "mean" or "average" should be taken into account [29]. In other words, trend normali-

Figure 5. Effect of peak trimming: raw (a) and peak-trimmed (b) symptom time histories. Data refer to the intermediate-

Trend may be determined by fitting a suitable function to experimental symptom time history. Weibull and Fréchet functions may be used for this purpose; for low values of θ, exponential function may be a good approximation. An obvious prerequisite is lack of abrupt (stepwise) changes; this issue shall be discussed in detail in the following section. Once this is performed, a procedure may be employed wherein each symptom value reading Si(θ) is replaced by trend-

ð Þ¼ <sup>θ</sup> Sið Þ <sup>θ</sup> Sitð Þ<sup>0</sup>

where subscript t denotes value determined from the estimated trend. An example of trend

Figure 6. An example of standard peak-trimmed (a) and trend-normalized (b) time histories; data refer to the high-

Sitð Þ <sup>θ</sup> , (23)

S0 i

normalization (Weibull function fitting) is shown in Figure 6.

zation should be performed prior to ICM analysis.

48 Structural Health Monitoring from Sensing to Processing

normalized value given by [23]

pressure turbine of a 230 MW unit.

pressure turbine of a 260 MW unit.

Complex and costly machines like, for example, power-generating units are usually designed for long service life. During the period between commissioning and final withdrawal from use, they are usually subject to various processes of maintenance, repair, and overhaul. Each of them introduces changes of object properties, which influence both diagnostic symptom generation mechanisms and their propagation from origin to measurement points. So far, it has been assumed (tacitly) that each Si(θ) function, or symptom life curve, is a superposition of a monotonic and continuous trend Sit(θ) and random fluctuations. In general this is not the case. Deterministic trend is in fact a sequence of symptom life curves, each being characterized by some specific values of Si(0) and θb. Of course repair or overhaul is performed before the breakdown, so of each curve is represented by a section of the length of θ<sup>0</sup> < θb. This is shown schematically in Figure 7.

Figure 7 clearly shows that, if fitting continuous function to experimental data is expected to yield consistent results, abrupt changes should be eliminated. In principle this is relatively simple. Each life cycle and hence each symptom life curve are characterized by the so-called logistic vector [7], which describes its "quality." This vector may be replaced by its scalar measure L, which influences both Si(0) and θb. For a sequence such as shown in Figure 7, one cycle is chosen as a reference; it may be convenient to use the one with the lowest initial value for this purpose, but this is not mandatory. Its value for θ = 0 is taken as a reference Sr(0). Then, for each other cycle, a normalizing factor Fi = Si(0)/Sr(0) is determined, and normalization is obtained by simple multiplication of all symptom readings in this cycle by 1/Fi.

This idea may seem simple, but precise determination of the moment of transition from a life cycle to the next one may be problematic. Sufficient operational documentation is not always available, and transitions are often masked by random fluctuations. A method for their

Figure 7. Schematic representation of the symptom life curve sequence.

detection is thus necessary. Such method may be based on techniques originally developed for statistical process control.

In the 1920s Walter A. Shewhart developed a tool for determining whether a process (e.g., manufacturing) is under control, known as the process control chart. If that was the case, no modifications of process or control were needed; otherwise, an intervention was necessary, in order to restore stable and controlled operation [30]. In 1954 E.S. Page proposed a more sensitive process control chart, employing cumulative sum and consequently named CUSUM [31]. His approach consisted in introducing a quantity originally referred to as a "quality number," developing an algorithm to estimate its changes and establishing a quantitative criterion. In general this quality number is a statistical parameter. If this procedure is employed for mean value, it can be used for detecting abrupt changes [32].

Let us assume that a variable x characterizes the process under consideration; its consecutive readings are x1, x2, …, xN. Each sample 〈x1, …, xi〉 has a probability density function given by pi(xi, φ); φ is a parameter which changes from φ<sup>0</sup> to φ<sup>1</sup> when an abrupt change occurs. The loglikelihood ratio ci given by

$$\mathbf{c}\_{i} = \ln \frac{p(\mathbf{x}\_{i}, \ \boldsymbol{\varphi}\_{1})}{p(\mathbf{x}\_{i}, \boldsymbol{\varphi}\_{0})} \tag{24}$$

Figure 8. Example of CUSUM method application: normalized symptom (1) and cumulative sum (2) plotted against time.

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Figure 9. Cumulative sum time history obtained without (solid line) and with (dotted line) outlier removing (after [33], ©

British Institute of Non-Destructive Testing).

Data refer to vibration generated by high-pressure fluid flow system of a 200 MW steam turbine.

defines the figure of merit. Cumulative sum Cm is then defined by

$$\mathbf{C}\_{\text{m}} = \sum\_{i=1}^{m} c\_i \tag{25}$$

If φ is sample mean, then Cm time history can be used for abrupt change detection. If there is no continuous trend, i.e., the process is stationary, Cm will fluctuate around zero and exhibit an upward or downward drift when an abrupt increase or decrease, respectively, has occurred. As already mentioned, in the case of a diagnostic symptom, there will always be such trend which can be neglected only for θ < < θb. Thus, Cm does not fluctuate around zero, but exhibits a continuous trend. An abrupt change, if sufficiently large, will then be indicated by a reversal of the Cm(θ) trend. This method can be employed for detecting transitions between consecutive life cycles. For normal distribution which, as noted earlier, is often a good approximation, Cm is given by a simple expression:

$$\mathcal{C}\_{m} = \sum\_{i=1}^{m} \left(\mathbf{x}\_{i} - \boldsymbol{\mu}\_{0}\right),\tag{26}$$

where μ<sup>0</sup> denotes sample mean. It is easily understood by intuition that, in order to obtain a reliable result, removal of outliers is mandatory [33]. Examples are shown in Figures 8 and 9.

#### 3.2.5. Representativeness factor

It may be said, in a descriptive manner, that ICM is a measure of the degree of process organization around a monotonically increasing trend. However, the rate of this increase should also be Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis http://dx.doi.org/10.5772/intechopen.77264 51

detection is thus necessary. Such method may be based on techniques originally developed for

In the 1920s Walter A. Shewhart developed a tool for determining whether a process (e.g., manufacturing) is under control, known as the process control chart. If that was the case, no modifications of process or control were needed; otherwise, an intervention was necessary, in order to restore stable and controlled operation [30]. In 1954 E.S. Page proposed a more sensitive process control chart, employing cumulative sum and consequently named CUSUM [31]. His approach consisted in introducing a quantity originally referred to as a "quality number," developing an algorithm to estimate its changes and establishing a quantitative criterion. In general this quality number is a statistical parameter. If this procedure is employed

Let us assume that a variable x characterizes the process under consideration; its consecutive readings are x1, x2, …, xN. Each sample 〈x1, …, xi〉 has a probability density function given by pi(xi, φ); φ is a parameter which changes from φ<sup>0</sup> to φ<sup>1</sup> when an abrupt change occurs. The log-

ci <sup>¼</sup> ln p xi; <sup>φ</sup><sup>1</sup>

Cm <sup>¼</sup> <sup>X</sup><sup>m</sup> i¼1

If φ is sample mean, then Cm time history can be used for abrupt change detection. If there is no continuous trend, i.e., the process is stationary, Cm will fluctuate around zero and exhibit an upward or downward drift when an abrupt increase or decrease, respectively, has occurred. As already mentioned, in the case of a diagnostic symptom, there will always be such trend which can be neglected only for θ < < θb. Thus, Cm does not fluctuate around zero, but exhibits a continuous trend. An abrupt change, if sufficiently large, will then be indicated by a reversal of the Cm(θ) trend. This method can be employed for detecting transitions between consecutive life cycles. For normal distribution which, as noted earlier, is often a good approximation, Cm is

> Cm <sup>¼</sup> <sup>X</sup><sup>m</sup> i¼1

xi � μ<sup>0</sup>

where μ<sup>0</sup> denotes sample mean. It is easily understood by intuition that, in order to obtain a reliable result, removal of outliers is mandatory [33]. Examples are shown in Figures 8 and 9.

It may be said, in a descriptive manner, that ICM is a measure of the degree of process organization around a monotonically increasing trend. However, the rate of this increase should also be

� � p xi; φ<sup>0</sup>

� � (24)

ci (25)

� �, (26)

for mean value, it can be used for detecting abrupt changes [32].

defines the figure of merit. Cumulative sum Cm is then defined by

statistical process control.

50 Structural Health Monitoring from Sensing to Processing

likelihood ratio ci given by

given by a simple expression:

3.2.5. Representativeness factor

Figure 8. Example of CUSUM method application: normalized symptom (1) and cumulative sum (2) plotted against time. Data refer to vibration generated by high-pressure fluid flow system of a 200 MW steam turbine.

Figure 9. Cumulative sum time history obtained without (solid line) and with (dotted line) outlier removing (after [33], © British Institute of Non-Destructive Testing).

taken into account in symptom evaluation. Organization may take place around a weakly increasing curve; such symptom is only weakly sensitive to object condition evolution and as such is of little use, despite marked ICM decrease. A measure is thus required that would combine both sensitivity to condition parameters and a degree of process organization [23, 33]. Such measure, termed representativeness factor R, is proposed in the following manner. Linear approximation is used for continuous entropy:and Weibull approximation for normalized symptom:

$$h(\theta) \approx h(\theta = 0) - A \cdot \theta \quad (A > 0) \tag{27}$$

$$s\_i(\theta) \approx \left[ \ln \frac{1}{1 - \theta/\theta\_b} \right]^{1/\gamma};\tag{28}$$

representativeness factor is then defined as

$$R = \frac{A}{\mathcal{V}}.\tag{29}$$

Figure 10. Cumulative sum time history: 260 MW unit, front intermediate-pressure turbine bearing, axial direction, 4 kHz

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Figure 11. Examples of continuous entropy time histories: for symptoms 1 and 16, entropy is decreasing, while for

symptom 9, there is an increasing trend accompanied by large irregularities.

band.

Obviously, R should be positive: the larger the R, the more representative is the symptom under consideration. Alternative approach may be adopted for Fréchet approximation; the choice of either of these approximations does not influence qualitative results of symptom assessment.

## 4. Examples

Measurement data for the first example were obtained with the intermediate-pressure turbine of a 260 MW power-generating unit; the first measurement was performed shortly after commissioning, and available data cover the period of almost 10 years. Vibration velocity was recorded at the front and rear bearings, in three mutually perpendicular directions. Components generated by turbine fluid flow system are contained in four 23% CPB bands, which give 24 available symptoms. Of these, as many as 13 symptoms have revealed no increasing trend; this may be attributed to comparatively short period of operation, as evolution of the fluid flow system condition is usually rather slow. For the remaining 11 symptoms, measured values were normalized, and peak trimming was performed (Eqs. (21) and (22), with ch = 1.5 and cl = 0.7). It was followed by CUSUM analysis, which revealed an abrupt change at about 2200 days (see Figure 10). Normalization was thus performed according to the procedure outlined in Section 3.2.4. Trend normalization was based on the Weibull function assumption. Data processed in this manner were used for ICM analysis, with time window length of 25 points and normal distribution assumption (cf. Section 3.2.1).

Continuous entropy time histories are in some cases rather irregular, but nonetheless six of them exhibit a decreasing trend; an example is shown in Figure 11. For these six cases, representativeness factor was calculated in accordance with Eq. (29). Results are shown in Table 1. It is easily seen that the values of R vary within broad limits. Without doubt symptoms numbered 1 and 2 Evaluation of Diagnostic Symptoms for Object Condition Diagnosis and Prognosis http://dx.doi.org/10.5772/intechopen.77264 53

taken into account in symptom evaluation. Organization may take place around a weakly increasing curve; such symptom is only weakly sensitive to object condition evolution and as such is of little use, despite marked ICM decrease. A measure is thus required that would combine both sensitivity to condition parameters and a degree of process organization [23, 33]. Such measure, termed representativeness factor R, is proposed in the following manner. Linear approximation is used for continuous entropy:and Weibull approximation for normalized

sið Þ <sup>θ</sup> <sup>≈</sup> ln <sup>1</sup>

1 � θ=θ<sup>b</sup> <sup>1</sup>=<sup>γ</sup>

<sup>R</sup> <sup>¼</sup> <sup>A</sup>

Obviously, R should be positive: the larger the R, the more representative is the symptom under consideration. Alternative approach may be adopted for Fréchet approximation; the choice of either of these approximations does not influence qualitative results of symptom

Measurement data for the first example were obtained with the intermediate-pressure turbine of a 260 MW power-generating unit; the first measurement was performed shortly after commissioning, and available data cover the period of almost 10 years. Vibration velocity was recorded at the front and rear bearings, in three mutually perpendicular directions. Components generated by turbine fluid flow system are contained in four 23% CPB bands, which give 24 available symptoms. Of these, as many as 13 symptoms have revealed no increasing trend; this may be attributed to comparatively short period of operation, as evolution of the fluid flow system condition is usually rather slow. For the remaining 11 symptoms, measured values were normalized, and peak trimming was performed (Eqs. (21) and (22), with ch = 1.5 and cl = 0.7). It was followed by CUSUM analysis, which revealed an abrupt change at about 2200 days (see Figure 10). Normalization was thus performed according to the procedure outlined in Section 3.2.4. Trend normalization was based on the Weibull function assumption. Data processed in this manner were used for ICM analysis, with time window length of 25

Continuous entropy time histories are in some cases rather irregular, but nonetheless six of them exhibit a decreasing trend; an example is shown in Figure 11. For these six cases, representativeness factor was calculated in accordance with Eq. (29). Results are shown in Table 1. It is easily seen that the values of R vary within broad limits. Without doubt symptoms numbered 1 and 2

points and normal distribution assumption (cf. Section 3.2.1).

hð Þ θ ≈ hð Þ� θ ¼ 0 A∙θ ð Þ A > 0 (27)

; (28)

<sup>γ</sup> : (29)

symptom:

assessment.

4. Examples

representativeness factor is then defined as

52 Structural Health Monitoring from Sensing to Processing

Figure 10. Cumulative sum time history: 260 MW unit, front intermediate-pressure turbine bearing, axial direction, 4 kHz band.

Figure 11. Examples of continuous entropy time histories: for symptoms 1 and 16, entropy is decreasing, while for symptom 9, there is an increasing trend accompanied by large irregularities.


• Comparatively high contributions of symptom number 5, which has a low representative-

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• Comparatively high contributions of symptom number 9, which is absent in Table 1 (lack

Before commenting on these findings, a second example will follow, this time for a comparatively old 200 MW unit with over 200,000 hours logged; available database covers over 16 years. Fluid flow system of the high-pressure turbine generates vibration components that are contained in ten 23% CPB frequency bands. Given two bearings and three directions, this means that as many as 60 symptoms have to be analyzed. In order to simplify the picture, a two-stage procedure was employed [33]. First, for every measurement point and direction, two dominant symptoms were selected using the SVD approach. Twelve symptoms selected in this manner were then analyzed with both SVD and ICM methods. Results are shown in Figure 13

In Table 2, cases with R < 0 have been deliberately included, in order to demonstrate that symptoms with comparatively good rating based on the SVD analysis—in this case, symptom No. 2—sometimes have to be rejected. On the other hand, symptoms with rather high values of R—e.g., numbers 5, 10, and 12—are poorly rated by the SVD method. In fact, only symptom

Figure 13. Contributions of individual symptoms into the first three singular values (200 MW unit, high-pressure turbine

ness factor

and Table 2.

(after [33], © JVE journals)).

• Better result for symptom number 18

numbers 3 and 4 are chosen on the basis of both methods.

of entropy decreasing trend)

FB and RB denote the front and rear bearings, respectively; V, H, and A correspond to measurement directions (vertical, horizontal, and radial) (260 MW unit, intermediate-pressure turbine).

Table 1. Results of calculations for six symptoms; γ is dimensionless, and entropy decrease rate and representativeness factor are given in arbitrary units.

are the most representative ones. Symptoms 16, 18, and 24 are certainly inferior, while representativeness of symptom 5 is weak. In this manner, symptoms may be identified that are most suitable for fluid flow system condition assessment.

Figure 12 shows contributions of all 11 symptoms that exhibit an increasing trend into the first three singular values. It may be noted that results are basically consistent with those shown in Table 1. The main differences are:

Figure 12. Contributions of individual symptoms into the first three singular values (260 MW unit, intermediate-pressure turbine (only symptoms that reveal an increasing trend have been included)).


are the most representative ones. Symptoms 16, 18, and 24 are certainly inferior, while representativeness of symptom 5 is weak. In this manner, symptoms may be identified that are most

FB and RB denote the front and rear bearings, respectively; V, H, and A correspond to measurement directions (vertical,

Table 1. Results of calculations for six symptoms; γ is dimensionless, and entropy decrease rate and representativeness

Symptom number Symptom description (kHz) Value of γ Entropy decrease rate Representativeness factor

 FB-V 3.15 11.24 0.960 85.44 <sup>10</sup><sup>3</sup> FB-V 4 10.64 0.905 85.07 <sup>10</sup><sup>3</sup> FB-H 3.15 500.0 0.010 0.02 <sup>10</sup><sup>3</sup> RB-V 6.3 52.63 0.775 14.73 <sup>10</sup><sup>3</sup> RB-H 4 52.63 0.497 9.44 <sup>10</sup><sup>3</sup> RB-A 6.3 55.56 0.637 11.47 <sup>10</sup><sup>3</sup>

Figure 12 shows contributions of all 11 symptoms that exhibit an increasing trend into the first three singular values. It may be noted that results are basically consistent with those shown in

Figure 12. Contributions of individual symptoms into the first three singular values (260 MW unit, intermediate-pressure

turbine (only symptoms that reveal an increasing trend have been included)).

suitable for fluid flow system condition assessment.

horizontal, and radial) (260 MW unit, intermediate-pressure turbine).

54 Structural Health Monitoring from Sensing to Processing

Table 1. The main differences are:

factor are given in arbitrary units.

• Comparatively high contributions of symptom number 9, which is absent in Table 1 (lack of entropy decreasing trend)

Before commenting on these findings, a second example will follow, this time for a comparatively old 200 MW unit with over 200,000 hours logged; available database covers over 16 years. Fluid flow system of the high-pressure turbine generates vibration components that are contained in ten 23% CPB frequency bands. Given two bearings and three directions, this means that as many as 60 symptoms have to be analyzed. In order to simplify the picture, a two-stage procedure was employed [33]. First, for every measurement point and direction, two dominant symptoms were selected using the SVD approach. Twelve symptoms selected in this manner were then analyzed with both SVD and ICM methods. Results are shown in Figure 13 and Table 2.

In Table 2, cases with R < 0 have been deliberately included, in order to demonstrate that symptoms with comparatively good rating based on the SVD analysis—in this case, symptom No. 2—sometimes have to be rejected. On the other hand, symptoms with rather high values of R—e.g., numbers 5, 10, and 12—are poorly rated by the SVD method. In fact, only symptom numbers 3 and 4 are chosen on the basis of both methods.

Figure 13. Contributions of individual symptoms into the first three singular values (200 MW unit, high-pressure turbine (after [33], © JVE journals)).


and tested. This approach has been applied for vibration-based symptoms of steam turbines operated by power plants and shown to give consistent results. In general it can be applied to any symptom, irrespective of its physical origin, as well as for other machines or structures. In the author's view, possible further development should be concentrated on the preprocessing of measurement data and improvement of the representativeness factor. Other information content measures might also be worth considering; however, the best results have so far been obtained

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[1] Gałka T. Evolution of Symptoms in Vibration-Based Turbomachinery Diagnostics. Radom: Publishing House of the Institute for Sustainable Technologies; 2013. 186 p

[2] Randall RB. State of the art in monitoring rotating machinery. Sound and Vibration. 2004,

[4] Vachtsevanos G, Lewis FL, Roemer M, Hess A, Wu B. Intelligent Fault Diagnosis and

[5] Weibull W. A statistical distribution function of wide applicability. Journal of Applied

[6] Zhai LY, Lu WF, Liu Y, Li X, Vachtsevanos G. Analysis of time-to-failure data with Weibull model in product life cycle management. In: Nee AYC, Song B, Ong SK, editors. Re-engineering Manufacturing for Sustainability. Singapore: Springer; 2013. pp. 699-704

[7] Cempel C, Natke HG. The modeling of energy transforming and energy recycling sys-

[3] Chestnut H. Systems Engineering Tools. New York: Wiley; 1965. 646 p

Prognosis for Engineering Systems. New York: Wiley; 2006. 434 p

tems. Journal of System Engineering. 1996;6:79-88

with continuous entropy.

Conflict of interest

Author details

Tomasz Gałka

References

The author of this text has no conflict of interest to declare.

Address all correspondence to: tomasz.galka@ien.com.pl

Institute of Power Engineering, Warsaw, Poland

2004;3, 5:14, 10-20 (part 1), 16 (part 2)

Mechanics. 1951;18:293-297

Table 2. Representativeness factor values calculated for 12 symptoms from Figure 13 (after [33], © JVE Journals).

In order to comment on these two examples, it has first to be noted that neither SVD nor ICM approach can be considered a reference one. It seems that discrepancies between the results obtained with both may be attributed to at least two possible causes. First, preprocessing of measurement data is based on relatively simple procedures, and their inherent deficiencies such as inadequate robustness—may influence the final result. Second, the SVD method does not disqualify cases with entropy increase, which are rejected within the ICM approach. This question requires further study. As pointed out in [33], it seems justified to state that symptoms selected on the basis of both methods can be safely labeled as the most suitable ones for object condition assessment and prognosis.

## 5. Conclusions

In this chapter, a relatively straightforward and simple method is presented for evaluation of diagnostic symptoms from the point of view of their suitability for assessment and prognosis of technical condition evolution. For this purpose, the proper choice of symptoms is of prime importance. This is particularly important for complex objects that generate a large numbers of various symptoms. In most cases it is very difficult, or even impossible, to make such choice in a direct manner, even with extensive knowledge on object layout and operation. The proposed method is based on an analysis of an information content measure as a function of time, and the basic assumption is that the greater is general damage advancement, the more deterministic, and hence predictable the symptom becomes. It turns out, however, that in order to obtain reliable results certain preprocessing of measurement data is mandatory. Results of this method have been compared with those obtained from singular value analysis, which had been earlier proposed

and tested. This approach has been applied for vibration-based symptoms of steam turbines operated by power plants and shown to give consistent results. In general it can be applied to any symptom, irrespective of its physical origin, as well as for other machines or structures. In the author's view, possible further development should be concentrated on the preprocessing of measurement data and improvement of the representativeness factor. Other information content measures might also be worth considering; however, the best results have so far been obtained with continuous entropy.

## Conflict of interest

The author of this text has no conflict of interest to declare.

## Author details

Tomasz Gałka

In order to comment on these two examples, it has first to be noted that neither SVD nor ICM approach can be considered a reference one. It seems that discrepancies between the results obtained with both may be attributed to at least two possible causes. First, preprocessing of measurement data is based on relatively simple procedures, and their inherent deficiencies such as inadequate robustness—may influence the final result. Second, the SVD method does not disqualify cases with entropy increase, which are rejected within the ICM approach. This question requires further study. As pointed out in [33], it seems justified to state that symptoms selected on the basis of both methods can be safely labeled as the most suitable ones for object

Table 2. Representativeness factor values calculated for 12 symptoms from Figure 13 (after [33], © JVE Journals).

Symptom number Symptom description (KHz) Representativeness factor

 FB-V 6.3 0.63 <sup>10</sup><sup>3</sup> FB-V 8 15.30 <sup>10</sup><sup>3</sup> FB-H 5 6.97 <sup>10</sup><sup>3</sup> FB-H 6.3 5.57 <sup>10</sup><sup>3</sup> FB-A 6.3 8.84 <sup>10</sup><sup>3</sup> FB-A 8 3.77 <sup>10</sup><sup>3</sup> RB-V 5 1.93 <sup>10</sup><sup>3</sup> RB-V 8 1.17 <sup>10</sup><sup>3</sup> RB-H 6.3 0.20 <sup>10</sup><sup>3</sup> RB-H 8 4.14 <sup>10</sup><sup>3</sup> RB-A 2 2.52 <sup>10</sup><sup>3</sup> RB-A 8 5.69 <sup>10</sup><sup>3</sup>

56 Structural Health Monitoring from Sensing to Processing

In this chapter, a relatively straightforward and simple method is presented for evaluation of diagnostic symptoms from the point of view of their suitability for assessment and prognosis of technical condition evolution. For this purpose, the proper choice of symptoms is of prime importance. This is particularly important for complex objects that generate a large numbers of various symptoms. In most cases it is very difficult, or even impossible, to make such choice in a direct manner, even with extensive knowledge on object layout and operation. The proposed method is based on an analysis of an information content measure as a function of time, and the basic assumption is that the greater is general damage advancement, the more deterministic, and hence predictable the symptom becomes. It turns out, however, that in order to obtain reliable results certain preprocessing of measurement data is mandatory. Results of this method have been compared with those obtained from singular value analysis, which had been earlier proposed

condition assessment and prognosis.

5. Conclusions

Address all correspondence to: tomasz.galka@ien.com.pl

Institute of Power Engineering, Warsaw, Poland

## References


[8] Gałka T, Tabaszewski M. An application of statistical symptoms in machine condition diagnostics. Mechanical Systems and Signal Processing. 2011;25:253-265

[25] Hodge VI, Austin J. A survey of outlier detection methodologies. Artificial Intelligence

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[26] Maronna RA, Martin RD, Yohai VJ. Robust Statistics. Theory and Methods. Chichester:

[27] Cempel C, Tabaszewski M. Multidimensional condition monitoring of the machines in non-stationary operation. Mechanical Systems and Signal Processing. 2007;21:1233-1247

[28] Nielsen HB. Non-stationary time series and unit root tests [Internet] 2005. Available from: http://www.econ.ku.dk/metrics/econometrics2\_05\_ii/slides/08\_unitroottests\_2pp.pdf

[29] Yule GU. The applications of the method of correlation to social and economic statistics.

[30] Wheeler DJ. Understanding Variation: The Key to Managing Chaos. Knoxville: SPC Press;

[32] Basseville M, Nikiforov IV. Detection of Abrupt Changes: Theory and Application. Upper

[33] Gałka T. On the problem of abrupt changes detection in diagnostic symptom time histories. In: Proceedings of the 1st World Congress on Condition Monitoring, London, UK;

Journal of the Royal Statistical Society. 1909;72:721-730

Saddle River: Prentice-Hall; 1993. 528 p

[31] Page ES. Continuous inspection scheme. Biometrika. 1954;41:100-115

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[Accessed: 2018-02-28]

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[8] Gałka T, Tabaszewski M. An application of statistical symptoms in machine condition

[9] Cempel C, Haddad SD. Vibroacoustic Condition Monitoring. New York: Ellis Horwood;

[10] Orłowski Z, Gałka T. Vibrodiagnostics of steam turbines in the blade frequency range. In: Proceedings of the COMADEM'98 International Conference. Australia: Monash Univer-

[11] Gałka T. Vibration-based diagnostics of steam turbines. In: Gökçek M, editor. Mechanical

[12] Golub GH, Reinsch C. Singular value decomposition and least square solutions.

[13] Natke HG, Cempel C. The symptom observation matrix for monitoring and diagnostics.

[14] Gałka T. Application of the singular value decomposition method in steam turbine diagnostics. In: Proceedings of the CM2010/MFPT Conference, Stratford-upon-Avon, UK.

[15] Cempel C. Multidimensional condition monitoring of mechanical systems in operation.

[16] Rényi A. On some measures of entropy and information. In: Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability; 1961. p. 547-561

[17] Shannon CE. A mathematical theory of communication. The Bell System Technical Jour-

[18] Ihara S. Information Theory for Continuous Systems. Singapore: World Scientific; 1993.

[19] Jaynes ET. Prior probabilities. IEEE Transactions on Systems Science and Cybernetics.

[20] RVL H. Transmission of information. The Bell System Technical Journal. 1928;7:535-563

[21] Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Phys-

[22] Schömig AK, Rose O. On the suitability of the Weibull distribution for the approximation of machine failures. In: Proceedings of Industrial Engineering Research Conference,

[23] Gałka T. A comparison of two symptom selection methods in vibration-based turboma-

[24] Lazo A, Rathie P. On the entropy of continuous probability distributions. IEEE Trans-

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Portland, USA; 2003


**Chapter 4**

Provisional chapter

**Application and Challenges of Signal Processing**

Application and Challenges of Signal Processing

**Techniques for Lamb Waves Structural Integrity**

Techniques for Lamb Waves Structural Integrity

**Optimization Techniques**

Optimization Techniques

Zenghua Liu and Honglei Chen

Zenghua Liu and Honglei Chen

http://dx.doi.org/10.5772/intechopen.78381

Abstract

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

compensation techniques are summarized.

integrity evaluation

1. Introduction

**Evaluation: Part A-Lamb Waves Signals Emitting and**

DOI: 10.5772/intechopen.78381

Lamb waves have been widely studied in structural integrity evaluation during the past decades with their low-attenuation and multi-defects sensitive nature. The performance of the evaluation has close relationship with the vibration property and the frequency of Lamb waves signals. Influenced by the nature of Lamb waves and the environment, the received signals may be difficult to interpret that limits the performance of the detection. So pure Lamb waves mode emitting and high-resolution signals acquisition play important roles in Lamb waves structural integrity evaluation. In this chapter, the basic theory of Lamb waves nature and some environment factors that should be considered in structural integrity evaluation are introduced. Three kinds of typical transduces used for specific Lamb waves mode emitting and sensing are briefly introduced. Then the development of techniques to improve the interpretability of signals are discussed, including the waveform modulation techniques, multi-scale analysis techniques and the temperature effect

Keywords: Lamb waves, plate, transducers, signal optimization techniques, structural

Plate-like structures made with metallic and composite materials have been widely used in various of engineering fields including aerospace and civil engineering. During the manufacturing, processing and usage, various type of damage may be induced in these structures. For

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Evaluation: Part A-Lamb Waves Signals Emitting and

#### **Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part A-Lamb Waves Signals Emitting and Optimization Techniques** Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part A-Lamb Waves Signals Emitting and Optimization Techniques

DOI: 10.5772/intechopen.78381

Zenghua Liu and Honglei Chen Zenghua Liu and Honglei Chen

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78381

#### Abstract

Lamb waves have been widely studied in structural integrity evaluation during the past decades with their low-attenuation and multi-defects sensitive nature. The performance of the evaluation has close relationship with the vibration property and the frequency of Lamb waves signals. Influenced by the nature of Lamb waves and the environment, the received signals may be difficult to interpret that limits the performance of the detection. So pure Lamb waves mode emitting and high-resolution signals acquisition play important roles in Lamb waves structural integrity evaluation. In this chapter, the basic theory of Lamb waves nature and some environment factors that should be considered in structural integrity evaluation are introduced. Three kinds of typical transduces used for specific Lamb waves mode emitting and sensing are briefly introduced. Then the development of techniques to improve the interpretability of signals are discussed, including the waveform modulation techniques, multi-scale analysis techniques and the temperature effect compensation techniques are summarized.

Keywords: Lamb waves, plate, transducers, signal optimization techniques, structural integrity evaluation

## 1. Introduction

Plate-like structures made with metallic and composite materials have been widely used in various of engineering fields including aerospace and civil engineering. During the manufacturing, processing and usage, various type of damage may be induced in these structures. For

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

example, corrosion and fatigue cracks are common defects in metal plates, while the main defects in composite plates are delamination, debonding, etc. Thus, it is important to develop defects detection and monitoring techniques to ensure the integrity of plate structures. Lamb waves have multi-modes, full cross-section distribution and low-attenuation nature in plates and can be used for multi-type defects detection in large scale. Combined with modern signal detection instruments and signal processing techniques, there are a lot of research and application of Lamb waves for off-line and on-line structure integrity evaluation [1–3].

Lamb waves are a type of elastic waves that remain the constraint between two parallel free surfaces, such as the upper and lower surfaces of a plate or shell, which contribute both longitudinal and shear partial wave components, as shown in Figure 1(a). According to the particle vibration mode, mainly two kinds of Lamb waves modes are formed as the interaction of longitudinal and shear partial waves, symmetric (S) modes and anti-symmetric (A) modes shown in Figure 1(b). Lamb waves theory, which is fully documented in literatures [4–6], assumes the derivation formula in a cylindrical coordinate of the three-dimensional (3D) waves as

$$\begin{cases} \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + \frac{\alpha^2}{c\_l^2} \phi = 0\\ \frac{\partial^2 \psi}{\partial x^2} + \frac{\partial^2 \psi}{\partial y^2} + \frac{\alpha^2}{c\_s^2} \psi = 0 \end{cases} \tag{1}$$

Young's module is 70.753 GPa and Poisson's ratio is 0.33. It is easy to find that the particle vibration show out anti-symmetric and symmetric forms for A modes and S modes, respectively. As shown in Figure 1(c) and (d), there are at least four modes under the frequencythickness 8.0 MHz-mm including the fundamental modes (A0 and S0). The group velocities and the wavenumbers change with frequency for these Lamb waves modes, termed the

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63

Defects in structures induce the scattering profiles and cause the change of the velocity and attenuation in the magnitude of Lamb waves signals. Besides the defects, there are still many other factors may induce the vibration, interpretability of the received Lamb waves signals in structural integrity evaluation. These factors are the Lamb waves nature, the property of transducers and plate structures, the environmental and operational conditions. Some of the

1. Dispersion of Lamb waves complexes the received signals that induce the signals extension in both spatial and temporal domain; multi-modes of Lamb waves and echoes from

2. Property of the transducers influences the performance of Lamb waves signals and the wavefield, such as the disk-wrapped electrode induces the non-axisymmetric wavefield [7], signal amplitude variation with a different type of adhesive and PZT thickness effects

Figure 1. Characteristic of Lamb waves in an aluminum plate drawn with DISPERSE. (a) Oblique incidence method for Lamb waves generation; (b) vibration property of Lamb waves; (c) group velocity dispersion curves; (d) wavenumber

the multi-defects cause the waveform overlapping in received signals.

dispersion nature of Lamb waves.

dispersion curves.

influence by these factors is expressed below.

where ϕ and ψ are potential functions, c<sup>2</sup> <sup>l</sup> <sup>¼</sup> <sup>λ</sup> <sup>þ</sup> <sup>2</sup><sup>μ</sup> � �=<sup>r</sup> and <sup>c</sup><sup>2</sup> <sup>s</sup> ¼ μ=r are the longitudinal and shear wave velocities, respectively, λ and μ are the Lamé constants and r is the mass density.

Under the stress-free boundary conditions at the upper and lower surfaces, Lamb waves equation can be obtained with the separation variable solution method

$$\frac{\tan \beta d}{\tan \alpha d} = -\left[\frac{4k^2 \alpha \beta}{\left(k^2 - \beta^2\right)^2}\right]^{\pm 1},\tag{2}$$

where <sup>d</sup> is the half thickness of plates, <sup>k</sup> is the wavenumber, <sup>k</sup><sup>2</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>=c<sup>2</sup> <sup>p</sup>, cp is the phase velocity, <sup>α</sup><sup>2</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>=c<sup>2</sup> <sup>l</sup> � k 2 , <sup>β</sup><sup>2</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>=c<sup>2</sup> <sup>s</sup> � k 2 . The plus sign corresponds to symmetric vibration and the minus to anti-symmetric vibration. A series of eigenvalues k S <sup>i</sup> and k A <sup>i</sup> corresponding various Lamb waves mode shapes are obtained by solving Eq. (2). The S modes and A modes are denoted with Si and Ai, respectively, where the subscript i indicates the order of the modes and equals 0,1,2…. The relationship cp = ω/k yields the dispersive wave velocity which is a function of the product between the frequency and the plate thickness. The wavelength is defined as λ = cp/f. The group velocity, cg, can be derived from the phase velocity with

$$c\_{\mathcal{S}} = c\_p^2 \left( c\_p - f d \frac{\partial c\_p}{\partial (f d)} \right)^{-1}. \tag{3}$$

Figure 1(c) and (d) shows dispersion curves of Lamb waves in an aluminum plate drawn with DISPERSE. The mechanical property of the plate is defined as: the density is 2.7 g/cm<sup>3</sup> ,

Young's module is 70.753 GPa and Poisson's ratio is 0.33. It is easy to find that the particle vibration show out anti-symmetric and symmetric forms for A modes and S modes, respectively. As shown in Figure 1(c) and (d), there are at least four modes under the frequencythickness 8.0 MHz-mm including the fundamental modes (A0 and S0). The group velocities and the wavenumbers change with frequency for these Lamb waves modes, termed the dispersion nature of Lamb waves.

example, corrosion and fatigue cracks are common defects in metal plates, while the main defects in composite plates are delamination, debonding, etc. Thus, it is important to develop defects detection and monitoring techniques to ensure the integrity of plate structures. Lamb waves have multi-modes, full cross-section distribution and low-attenuation nature in plates and can be used for multi-type defects detection in large scale. Combined with modern signal detection instruments and signal processing techniques, there are a lot of research and application of Lamb waves

Lamb waves are a type of elastic waves that remain the constraint between two parallel free surfaces, such as the upper and lower surfaces of a plate or shell, which contribute both longitudinal and shear partial wave components, as shown in Figure 1(a). According to the particle vibration mode, mainly two kinds of Lamb waves modes are formed as the interaction of longitudinal and shear partial waves, symmetric (S) modes and anti-symmetric (A) modes shown in Figure 1(b). Lamb waves theory, which is fully documented in literatures [4–6], assumes the

derivation formula in a cylindrical coordinate of the three-dimensional (3D) waves as

∂2 ϕ ∂y<sup>2</sup> þ

∂2 ψ ∂y<sup>2</sup> þ

shear wave velocities, respectively, λ and μ are the Lamé constants and r is the mass density. Under the stress-free boundary conditions at the upper and lower surfaces, Lamb waves

ω2 c2 l ϕ ¼ 0

ω2 c2 s ψ ¼ 0

<sup>l</sup> <sup>¼</sup> <sup>λ</sup> <sup>þ</sup> <sup>2</sup><sup>μ</sup> � �=<sup>r</sup> and <sup>c</sup><sup>2</sup>

2 αβ

" #�<sup>1</sup>

∂cp ∂ð Þ fd � ��<sup>1</sup>

k <sup>2</sup> � <sup>β</sup><sup>2</sup> � �<sup>2</sup>

Lamb waves mode shapes are obtained by solving Eq. (2). The S modes and A modes are denoted with Si and Ai, respectively, where the subscript i indicates the order of the modes and equals 0,1,2…. The relationship cp = ω/k yields the dispersive wave velocity which is a function of the product between the frequency and the plate thickness. The wavelength is defined as

Figure 1(c) and (d) shows dispersion curves of Lamb waves in an aluminum plate drawn with DISPERSE. The mechanical property of the plate is defined as: the density is 2.7 g/cm<sup>3</sup>

,

. The plus sign corresponds to symmetric vibration and the

S <sup>i</sup> and k A (1)

,

<sup>s</sup> ¼ μ=r are the longitudinal and

, (2)

: (3)

<sup>p</sup>, cp is the phase velocity,

<sup>i</sup> corresponding various

∂2 ϕ ∂x<sup>2</sup> þ

8 >>><

>>>:

equation can be obtained with the separation variable solution method

where <sup>d</sup> is the half thickness of plates, <sup>k</sup> is the wavenumber, <sup>k</sup><sup>2</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>=c<sup>2</sup>

λ = cp/f. The group velocity, cg, can be derived from the phase velocity with

cg ¼ c 2 <sup>p</sup> cp � fd

<sup>s</sup> � k 2

minus to anti-symmetric vibration. A series of eigenvalues k

tan βd

tan <sup>α</sup><sup>d</sup> ¼ � <sup>4</sup><sup>k</sup>

where ϕ and ψ are potential functions, c<sup>2</sup>

, <sup>β</sup><sup>2</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>=c<sup>2</sup>

<sup>α</sup><sup>2</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>=c<sup>2</sup>

<sup>l</sup> � k 2 ∂2 ψ ∂x<sup>2</sup> þ

for off-line and on-line structure integrity evaluation [1–3].

62 Structural Health Monitoring from Sensing to Processing

Defects in structures induce the scattering profiles and cause the change of the velocity and attenuation in the magnitude of Lamb waves signals. Besides the defects, there are still many other factors may induce the vibration, interpretability of the received Lamb waves signals in structural integrity evaluation. These factors are the Lamb waves nature, the property of transducers and plate structures, the environmental and operational conditions. Some of the influence by these factors is expressed below.


Figure 1. Characteristic of Lamb waves in an aluminum plate drawn with DISPERSE. (a) Oblique incidence method for Lamb waves generation; (b) vibration property of Lamb waves; (c) group velocity dispersion curves; (d) wavenumber dispersion curves.

[8], Lamb waves signals emitted with the laser beam and PZT show non-stationary and stationary property, respectively.

typical transducers and their application for specific mode of Lamb waves emitting and

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Piezoelectric materials have piezoelectric effect that can be used to achieve energy conversion between mechanical energy and electrical energy. As shown in Figure 2(a), when the piezoelectric material is loaded with an alternating voltage, it may produce an oscillatory mechanical vibration, and form pressure at its surface or sound waves in the around air. Vice versa, an oscillatory expansion and contraction of the material produce an alternating voltage at the terminal. This phenomenon is named as the piezoelectric effect. The geometry size, polarization direction and the voltage frequency have influence on the vibration mode of the piezoelectric materials. Many kinds of piezoelectric transducers have been designed in laboratories

Piezoelectric wafer active transducers (PWATs) have relative simple round or rectangle geometrical shapes. Typically, these transducers have electrodes on the top and bottom surfaces as plotted in Figure 2(b). With the piezoelectric effect, PWATs actuate and sense Lamb waves signals in the structure directly through in-plane strain coupling. More differences between the PWATs and conventional ultrasonic transducers are listed in Ref. [19]. Interdigital transducers (IDTs) have electrodes shaped in a comb pattern that are designed with traditional piezoelectric ceramics or the novel piezoelectric materials, such as macro-fiber composite (MFC) [20] and poly vinylidene fluoride (PVDF) piezoelectric polymer film [21–23]. Figure 2(c) plots an interdigital transducer. Through adjusting the space between adjacent interdigital electrodes, IDTs are able to generate Lamb waves with a specific wavelength. Comparing with the piezoelectric ceramics, the novel piezoelectric materials feature better flexibility, higher dimensional stability and more stable piezoelectric coefficients over time. They can be of various shape to cope with curved surfaces for signal sensing in low frequency range due to their weak driving. The tunable IDTs have a series of density distributed discrete electrode stripes that are connected in various configurations [24]. In the application, Lamb waves with different wavelengths can be emitted through adjusting the configuration of the interdigital electrodes. As shown in Figure 2(d), air-coupled ultrasonic transducers [25] are often used for non-contact

Figure 2. Typical piezoelectric effect-based transducers. (a) Piezoelectric effect; (b) PWAT; (c) Interdigital transducer; (d)

sensing.

2.1. Piezoelectric transducers

and corporations.

air-coupled transducers.


As illustrated in the above content, the factors influencing signals features, the environmental and operation condition, Lamb waves, transducers, plate-like structures and the defects are combined and form a close detection/monitoring ecosystem in which the transducers realize the energy conversion between the systems and the structures. Meanwhile the properties of transducers have influence on the detection/monitoring systems setting strategies and the emitting and sensing of Lamb waves. All these have decided that transducers play a very important role in structure integrity evaluation. Signal processing technologies are adopted to optimize and analysis the acquired data and finally realize structure state evaluation. When the received data have relatively high resolution and interpretability, defects imaging techniques and the intelligent recognition techniques are directly applied for structure integrity evaluation; otherwise, the signals should be pre-processed with signal optimization techniques to improve their resolution and interpretability through modulating waveforms, multi-scale analysis and temperature effect compensation. Considering the importance roles of transducers and the signal processing strategies used in Lamb waves based structure integrity evaluation, the structure of this chapter is setting as: Section 2 introduces several kinds of transducers used for Lamb waves emitting and sensing. Then some signal processing technologies for dispersion compensation, time-frequency analysis and overlapping waveform decomposition, and illuminating the influence temperature effects are briefly reviewed in Section 3. Finally, a short summary and conclusions are provided.

## 2. Transducers and specific Lamb wave mode emitting

There are mainly three kinds of transduction mechanism used for the design of the transducers in structure integrity evaluation, including piezoelectric effect, electromagnetic ultrasonic coupling mechanisms and laser thermodynamics. In this section, we will briefly review some typical transducers and their application for specific mode of Lamb waves emitting and sensing.

## 2.1. Piezoelectric transducers

[8], Lamb waves signals emitted with the laser beam and PZT show non-stationary and

3. Material and structure of plates yield the wavefield, such as anisotropic property of composite plates leading the inhomogeneity distribution of wavefield in spatial and temporal dimensions [9, 10], echoes from the edges, stiffeners, bolts and rivets in the complex

4. Environmental and operational condition change the material properties and further influence the emitting, propagation and the sensing of Lamb waves [12, 13], typically the temperature and the local concentrated stress. The temperature changes (a) the plate material stiffness affects the waves phase/group velocity [14, 15]; (b) the dielectric permittivity and piezoelectric coefficient of piezoelectric transducers [16] and (c) the adhesive stiffness and then modifies the transducer-plate bonding shear stress transmission and minor thermal expansion/contraction occurring within the adhesive layer can yield to a slight shift in the peak frequency response [17]. The variation of the loads during usage changes resulting a slight anisotropy of the structure and further induces the velocity directionality [18]. Meanwhile, it also induces the time shifts effect under loads conditions

As illustrated in the above content, the factors influencing signals features, the environmental and operation condition, Lamb waves, transducers, plate-like structures and the defects are combined and form a close detection/monitoring ecosystem in which the transducers realize the energy conversion between the systems and the structures. Meanwhile the properties of transducers have influence on the detection/monitoring systems setting strategies and the emitting and sensing of Lamb waves. All these have decided that transducers play a very important role in structure integrity evaluation. Signal processing technologies are adopted to optimize and analysis the acquired data and finally realize structure state evaluation. When the received data have relatively high resolution and interpretability, defects imaging techniques and the intelligent recognition techniques are directly applied for structure integrity evaluation; otherwise, the signals should be pre-processed with signal optimization techniques to improve their resolution and interpretability through modulating waveforms, multi-scale analysis and temperature effect compensation. Considering the importance roles of transducers and the signal processing strategies used in Lamb waves based structure integrity evaluation, the structure of this chapter is setting as: Section 2 introduces several kinds of transducers used for Lamb waves emitting and sensing. Then some signal processing technologies for dispersion compensation, time-frequency analysis and overlapping waveform decomposition, and illuminating the influence temperature effects are briefly reviewed in

structure reduce the interpretability of the received Lamb waves signals [11].

that are of the same order as those caused by temperature change.

Section 3. Finally, a short summary and conclusions are provided.

2. Transducers and specific Lamb wave mode emitting

There are mainly three kinds of transduction mechanism used for the design of the transducers in structure integrity evaluation, including piezoelectric effect, electromagnetic ultrasonic coupling mechanisms and laser thermodynamics. In this section, we will briefly review some

stationary property, respectively.

64 Structural Health Monitoring from Sensing to Processing

Piezoelectric materials have piezoelectric effect that can be used to achieve energy conversion between mechanical energy and electrical energy. As shown in Figure 2(a), when the piezoelectric material is loaded with an alternating voltage, it may produce an oscillatory mechanical vibration, and form pressure at its surface or sound waves in the around air. Vice versa, an oscillatory expansion and contraction of the material produce an alternating voltage at the terminal. This phenomenon is named as the piezoelectric effect. The geometry size, polarization direction and the voltage frequency have influence on the vibration mode of the piezoelectric materials. Many kinds of piezoelectric transducers have been designed in laboratories and corporations.

Piezoelectric wafer active transducers (PWATs) have relative simple round or rectangle geometrical shapes. Typically, these transducers have electrodes on the top and bottom surfaces as plotted in Figure 2(b). With the piezoelectric effect, PWATs actuate and sense Lamb waves signals in the structure directly through in-plane strain coupling. More differences between the PWATs and conventional ultrasonic transducers are listed in Ref. [19]. Interdigital transducers (IDTs) have electrodes shaped in a comb pattern that are designed with traditional piezoelectric ceramics or the novel piezoelectric materials, such as macro-fiber composite (MFC) [20] and poly vinylidene fluoride (PVDF) piezoelectric polymer film [21–23]. Figure 2(c) plots an interdigital transducer. Through adjusting the space between adjacent interdigital electrodes, IDTs are able to generate Lamb waves with a specific wavelength. Comparing with the piezoelectric ceramics, the novel piezoelectric materials feature better flexibility, higher dimensional stability and more stable piezoelectric coefficients over time. They can be of various shape to cope with curved surfaces for signal sensing in low frequency range due to their weak driving. The tunable IDTs have a series of density distributed discrete electrode stripes that are connected in various configurations [24]. In the application, Lamb waves with different wavelengths can be emitted through adjusting the configuration of the interdigital electrodes. As shown in Figure 2(d), air-coupled ultrasonic transducers [25] are often used for non-contact

Figure 2. Typical piezoelectric effect-based transducers. (a) Piezoelectric effect; (b) PWAT; (c) Interdigital transducer; (d) air-coupled transducers.

and non-contaminating ultrasonic scanning detection. The proportion of the ultrasonic energy transmitted through an interface depends on the acoustic impedance match ratio of the two materials. The higher match ratio, the more energy is transmitted into the plates. Thus, it is important to minimize these losses to obtain an acceptable signal to noise ratio. With the development of micro-electro-mechanical technology, micro-machined ultrasonic transducers are researched [26] that have many advantages over conventional ultrasonic transducers, including miniature size, low power consumption and the ability to create one-dimensional (1D) and two-dimensional (2D) array structures.

force, magnetostriction mechanism and magnetizing force. In addition, Lorentz force mechanism exists in all conductive materials, whereas the magnetostriction mechanism only exists in ferromagnetic materials. Compared with the other two mechanisms, the magnetizing force is very weak and is often neglected in studies. Various types of EMAT can be designed by changing the configuration of the permanent magnet and coil to realize easily the attenuation of pure Lamb waves mode. Figure 3(b) shows the EMAT with solenoid sensing coils and a cylindrical magnet;

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By adjusting the spacing of meandered line coils equal to the half wavelength of Lamb waves, EMAT can easily realize Lamb waves emitting and sensing at specific frequency. Meanwhile, researchers have developed many kinds of EMATs through specific design of the geometry and the position of the magnets and coils [38], including omnidirectional S0 mode EMAT [39], omnidirectional A0 mode EMAT [40] and directional magnetostrictive patch transducer [41]. While the EMAT is difficult to generate a pure Lamb wave mode when dispersion curves of several modes are close together; however, by narrowing the frequency bandwidth via a large number of cycles in the excitation signal, pure mode generation via an EMAT is shown to be possible even in areas of closely spaced modes [42]. Experimentally, the EMAT can scan along the surface, while the loading voltage is often very high compared with that of piezoelectric transducers. EMATs are also used for high-order Lamb waves emitting and sensing in a 6mm-

Laser ultrasonic systems (LUS) have three basic functional components: a generation laser, a detection laser and a detector. The generation laser emits a laser beam that irritates on the surface of plates to generate ultrasonic waves based on thermoelastic regime or ablation regime. In the thermoplastic regime, the ultrasonic waves are generated from the thermoelastic

Figure 3. Electromagnetic ultrasonic coupling mechanisms transducers. (a) Principle of the electromagnetic ultrasonic coupling mechanism; EMAT with four solenoid sensing coils and a cylindrical magnet [43]; Panametrics E110-SB EMAT.

Figure 3(c) shows the Panametrics E110-SB EMAT developed by OLYMPUS.

thick steel plate [43].

2.3. Laser ultrasonic systems

The techniques for pure mode emitting and sensing have been studied with the piezoelectic transducers. Theoretical models researches of PWATs [27] show that the displacements at the plate surface is a function of an interelement distance for a specific Lamb waves mode. With the theory, dual-element transducers are placed at a specific distance on the same surface of a plate for pure A0 mode emitting, or two dual PZTs (concentric disc and ring) structure is adopted to tune the excitated signal properly for specific mode emitting, or to decompose both mode contributions in the received signals [28]. The IDTs can realize pure mode emitting by adjusting the interspace between individual electronic elements of the piezoelectric array or adding backing materials to the elements [29]. While the interaction between individual elements may have a significant influence on the performance of the IDTs, these effects cannot be neglected even in the case of low frequency excitation. Researchers deposited symmetrical transducers on both sides of the plate to generate pure Lamb waves mode [30], in which for electric symmetrical connection to the two transducers, S0 mode is generated, vice versa, for the anti-symmetrical electric connection, A0 mode is strong and S0 mode is suppressed. Degertekin et al. [31] added hertzian contacts between the plates and the end of specially designed quartz rods, which guide anti-symmetric modes generated by PZT-5H transducers bonded at their other end. For an angle beam transducer, a low-attenuation Lamb waves mode was generated by setting the incidence angle [32]. Other literatures studied theoretical model of the PWAS-related Lamb waves to identify the single mode emitting frequency, then adopted the post-process technique, such as time reversal, to enhance the mode purity [33, 34]. As the symmetric modes have more energy components in the out-of-plane direction, air-coupled ultrasonic transducer can be very suitable for pure A0 mode emitting and sensing [35]. The high-order or high frequency-thickness Lamb waves have more complex wave structure and shorter wavelength, while more sensitive to the characteristic change of plates. Higher Order Mode Cluster (HOMC) is proposed by Jayaraman et al. [36], it used the nature that multiple modes concentrate together to form a cluster. Khalili et al. [37] realized single Lamb waves mode emitting at 20 MHz-mm with the HOMC method.

#### 2.2. Electromagnetic acoustic transducer

Electromagnetic acoustic transducer (EMAT) consists of permanent magnets, coils and a metal material in which the magnets introduce the static magnetic field. The principle of the electromagnetic ultrasonic coupling mechanisms is shown in Figure 3(a). When the current is loaded on the coils, eddy currents will be generated in the conductive structure and form three kinds of electromagnetic coupling mechanisms for ultrasonic waves emitting and sensing: Lorentz force, magnetostriction mechanism and magnetizing force. In addition, Lorentz force mechanism exists in all conductive materials, whereas the magnetostriction mechanism only exists in ferromagnetic materials. Compared with the other two mechanisms, the magnetizing force is very weak and is often neglected in studies. Various types of EMAT can be designed by changing the configuration of the permanent magnet and coil to realize easily the attenuation of pure Lamb waves mode. Figure 3(b) shows the EMAT with solenoid sensing coils and a cylindrical magnet; Figure 3(c) shows the Panametrics E110-SB EMAT developed by OLYMPUS.

By adjusting the spacing of meandered line coils equal to the half wavelength of Lamb waves, EMAT can easily realize Lamb waves emitting and sensing at specific frequency. Meanwhile, researchers have developed many kinds of EMATs through specific design of the geometry and the position of the magnets and coils [38], including omnidirectional S0 mode EMAT [39], omnidirectional A0 mode EMAT [40] and directional magnetostrictive patch transducer [41]. While the EMAT is difficult to generate a pure Lamb wave mode when dispersion curves of several modes are close together; however, by narrowing the frequency bandwidth via a large number of cycles in the excitation signal, pure mode generation via an EMAT is shown to be possible even in areas of closely spaced modes [42]. Experimentally, the EMAT can scan along the surface, while the loading voltage is often very high compared with that of piezoelectric transducers. EMATs are also used for high-order Lamb waves emitting and sensing in a 6mmthick steel plate [43].

## 2.3. Laser ultrasonic systems

and non-contaminating ultrasonic scanning detection. The proportion of the ultrasonic energy transmitted through an interface depends on the acoustic impedance match ratio of the two materials. The higher match ratio, the more energy is transmitted into the plates. Thus, it is important to minimize these losses to obtain an acceptable signal to noise ratio. With the development of micro-electro-mechanical technology, micro-machined ultrasonic transducers are researched [26] that have many advantages over conventional ultrasonic transducers, including miniature size, low power consumption and the ability to create one-dimensional

The techniques for pure mode emitting and sensing have been studied with the piezoelectic transducers. Theoretical models researches of PWATs [27] show that the displacements at the plate surface is a function of an interelement distance for a specific Lamb waves mode. With the theory, dual-element transducers are placed at a specific distance on the same surface of a plate for pure A0 mode emitting, or two dual PZTs (concentric disc and ring) structure is adopted to tune the excitated signal properly for specific mode emitting, or to decompose both mode contributions in the received signals [28]. The IDTs can realize pure mode emitting by adjusting the interspace between individual electronic elements of the piezoelectric array or adding backing materials to the elements [29]. While the interaction between individual elements may have a significant influence on the performance of the IDTs, these effects cannot be neglected even in the case of low frequency excitation. Researchers deposited symmetrical transducers on both sides of the plate to generate pure Lamb waves mode [30], in which for electric symmetrical connection to the two transducers, S0 mode is generated, vice versa, for the anti-symmetrical electric connection, A0 mode is strong and S0 mode is suppressed. Degertekin et al. [31] added hertzian contacts between the plates and the end of specially designed quartz rods, which guide anti-symmetric modes generated by PZT-5H transducers bonded at their other end. For an angle beam transducer, a low-attenuation Lamb waves mode was generated by setting the incidence angle [32]. Other literatures studied theoretical model of the PWAS-related Lamb waves to identify the single mode emitting frequency, then adopted the post-process technique, such as time reversal, to enhance the mode purity [33, 34]. As the symmetric modes have more energy components in the out-of-plane direction, air-coupled ultrasonic transducer can be very suitable for pure A0 mode emitting and sensing [35]. The high-order or high frequency-thickness Lamb waves have more complex wave structure and shorter wavelength, while more sensitive to the characteristic change of plates. Higher Order Mode Cluster (HOMC) is proposed by Jayaraman et al. [36], it used the nature that multiple modes concentrate together to form a cluster. Khalili et al. [37] realized single Lamb waves

Electromagnetic acoustic transducer (EMAT) consists of permanent magnets, coils and a metal material in which the magnets introduce the static magnetic field. The principle of the electromagnetic ultrasonic coupling mechanisms is shown in Figure 3(a). When the current is loaded on the coils, eddy currents will be generated in the conductive structure and form three kinds of electromagnetic coupling mechanisms for ultrasonic waves emitting and sensing: Lorentz

(1D) and two-dimensional (2D) array structures.

66 Structural Health Monitoring from Sensing to Processing

mode emitting at 20 MHz-mm with the HOMC method.

2.2. Electromagnetic acoustic transducer

Laser ultrasonic systems (LUS) have three basic functional components: a generation laser, a detection laser and a detector. The generation laser emits a laser beam that irritates on the surface of plates to generate ultrasonic waves based on thermoelastic regime or ablation regime. In the thermoplastic regime, the ultrasonic waves are generated from the thermoelastic

Figure 3. Electromagnetic ultrasonic coupling mechanisms transducers. (a) Principle of the electromagnetic ultrasonic coupling mechanism; EMAT with four solenoid sensing coils and a cylindrical magnet [43]; Panametrics E110-SB EMAT.

expansions of materials. While, in the ablation regime, the ultrasonic waves are generated from the material removal that will induce damage to the surface of plates. The laser ultrasonic systems are carefully set to work in the thermoelastic regime in Lamb waves integrity evaluation. Additionally, the laser-generated Lamb waves signal is a broad bandwidth signal in which several Lamb wave modes can be acquired in a single measurement, providing more opportunities to selectively generate the desired modes. Figure 4(a) plots the elastic waves generated by laser beam under thermoelastic regime.

varying the interface fringe spacing, the acoustic frequency is easily and continuously tunable

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

Other transducers used in structural integrity evaluation but not just piezoelectric ceramic fibers, fiber optic transducers [50] and microelectronic transducers. Piezoelectric fibers having a metal core can activate Lamb waves in composite plates transverse to the fibers with radial displacement components originating from the d<sup>33</sup> coupling coefficient. They can also generate Lamb waves in the direction of the piezoelectric fibers using the d<sup>31</sup> coupling coefficient. The fiber optic transducers are used for Lamb wave sensing, through connecting a fiber Bragg gratings (FBG) filter with a photodetector, the light intensity induced by the Lamb waves, rather than strain itself, can be sensed at a high sampling rate. The FBG has strong directivity

The signal processing techniques for improving the resolution and the interpretability of Lamb wave signals are termed as the signal optimization techniques in this section. There are waveform modulation techniques such as multi-scale analysis techniques and temperature effect compensation techniques. These techniques are adopted for Lamb waves dispersion compensation, high-resolution signal emitting and sensing, overlapping waveforms decom-

When an excitation signal, f(t), is emitted into a plate at original position, the received signal, u

where F(ω) is the Fourier transform of the excitation signal and k is the angular wavenumber. In Eq. (4), there are several parameters that decide the signal resolution and interpretability, including the amplitude, phase and frequency variation with the duration. The signal processing techniques process through modulating these fundamental signal parameters for adjusting the signal waveforms are termed waveform modulation techniques that are used for Lamb waves dispersion compensation, high-resolution Lamb waves detection and defects information extrac-

Signal processing techniques for dispersion compensation are realized through modulating the frequency or the wavenumbers of the received Lamb waves signals, because the dispersion nature of Lamb waves is shown as the nonlinear characteristic of signal phase in mathematical form. Time recompression technique [51] compensates the dispersion using spatial phase shift arising at each signal frequency component from the propagation of the waves over a large distance. The back-propagation function in the technique can only provide the first-order phase shift. Time-distance mapping technique [52] compresses dispersive signals by converting the

Fð Þ ω e

<sup>j</sup>ð Þ <sup>ω</sup>t�kx dω, (4)

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69

pensation, time-frequency analysis and temperature effect compensation.

u xð Þ¼ ; t

1 2π ð∞ �∞

from 2.5 to 23 MHz.

in sensing Lamb wave signals.

3. Signal optimization techniques

3.1. Waveform modulation techniques

(x,t), at x position can be expressed as

tion in structural integrity evaluation.

The detection laser and detector are used for ultrasonic waves detection based on various principle including Doppler frequency shift, speckle interferogram and Fabry-Pérot detection schemes. A laser vibrometer principle of operation allows for measuring velocity of a point along the axis of laser beam incidence onto the surface based on the Doppler frequency shift principle. In 1997, researchers started sensing the out-of-plane displacements of Lamb waves with an optical fiber Michelson interferometer. The progress in the development of equipment related to scanning laser Doppler vibrometry (SLDV) resulted in the availability of the full wavefield measurements of Lamb waves propagating in metallic specimens. Shearography is an interferometric technique for surface vibration measurement. In a digital shearography system, the inspected object is illuminated by an expanded laser beam, forming a speckle pattern. The speckle patterns are optically processed by a shearing device, and the resultant interferogram is recorded by a charge-coupled device camera. Speckle interferogram, recorded before and after object deformation, are correlated to yield correlation fringes. The phase of these fringes can represent the displacement gradient of the specimen. More detail information about the system is introduced in Ref. [44]. The elastic waves generate a change in the index of refraction of the surface, incident laser beams will deflect slightly and thus change course. This detected change is converted into an electrical signal. Figure 4(b) plots the laser ultrasonic principle.

As the laser beam is irritated on the normal direction of the out-of-plane that is the main displacement components of anti-symmetric modes. In the detection process, people can adjust the shape and the spatial distribution of the laser beams to reduce the energy loss and further form a specific modes wave. Many types optical path adjusting elements are adopted for specific Lamb waves mode emitting, including Fresnel lens, rectangular cylinder lens [45, 46], marks for creating predetermined spatial laser light distributions [47] and periodic spatial array of laser sources [48]. The interference pattern of two high power laser beams on a sample surface produces periodic heating and then generating anti-symmetric Lamb waves [49]. By

Figure 4. Principle and systems for laser ultrasonic inspection. (a) Elastic waves generated by laser beam under thermoelastic regime; (b) laser ultrasonic principle.

varying the interface fringe spacing, the acoustic frequency is easily and continuously tunable from 2.5 to 23 MHz.

Other transducers used in structural integrity evaluation but not just piezoelectric ceramic fibers, fiber optic transducers [50] and microelectronic transducers. Piezoelectric fibers having a metal core can activate Lamb waves in composite plates transverse to the fibers with radial displacement components originating from the d<sup>33</sup> coupling coefficient. They can also generate Lamb waves in the direction of the piezoelectric fibers using the d<sup>31</sup> coupling coefficient. The fiber optic transducers are used for Lamb wave sensing, through connecting a fiber Bragg gratings (FBG) filter with a photodetector, the light intensity induced by the Lamb waves, rather than strain itself, can be sensed at a high sampling rate. The FBG has strong directivity in sensing Lamb wave signals.

## 3. Signal optimization techniques

expansions of materials. While, in the ablation regime, the ultrasonic waves are generated from the material removal that will induce damage to the surface of plates. The laser ultrasonic systems are carefully set to work in the thermoelastic regime in Lamb waves integrity evaluation. Additionally, the laser-generated Lamb waves signal is a broad bandwidth signal in which several Lamb wave modes can be acquired in a single measurement, providing more opportunities to selectively generate the desired modes. Figure 4(a) plots the elastic waves

The detection laser and detector are used for ultrasonic waves detection based on various principle including Doppler frequency shift, speckle interferogram and Fabry-Pérot detection schemes. A laser vibrometer principle of operation allows for measuring velocity of a point along the axis of laser beam incidence onto the surface based on the Doppler frequency shift principle. In 1997, researchers started sensing the out-of-plane displacements of Lamb waves with an optical fiber Michelson interferometer. The progress in the development of equipment related to scanning laser Doppler vibrometry (SLDV) resulted in the availability of the full wavefield measurements of Lamb waves propagating in metallic specimens. Shearography is an interferometric technique for surface vibration measurement. In a digital shearography system, the inspected object is illuminated by an expanded laser beam, forming a speckle pattern. The speckle patterns are optically processed by a shearing device, and the resultant interferogram is recorded by a charge-coupled device camera. Speckle interferogram, recorded before and after object deformation, are correlated to yield correlation fringes. The phase of these fringes can represent the displacement gradient of the specimen. More detail information about the system is introduced in Ref. [44]. The elastic waves generate a change in the index of refraction of the surface, incident laser beams will deflect slightly and thus change course. This detected change is

converted into an electrical signal. Figure 4(b) plots the laser ultrasonic principle.

As the laser beam is irritated on the normal direction of the out-of-plane that is the main displacement components of anti-symmetric modes. In the detection process, people can adjust the shape and the spatial distribution of the laser beams to reduce the energy loss and further form a specific modes wave. Many types optical path adjusting elements are adopted for specific Lamb waves mode emitting, including Fresnel lens, rectangular cylinder lens [45, 46], marks for creating predetermined spatial laser light distributions [47] and periodic spatial array of laser sources [48]. The interference pattern of two high power laser beams on a sample surface produces periodic heating and then generating anti-symmetric Lamb waves [49]. By

Figure 4. Principle and systems for laser ultrasonic inspection. (a) Elastic waves generated by laser beam under

thermoelastic regime; (b) laser ultrasonic principle.

generated by laser beam under thermoelastic regime.

68 Structural Health Monitoring from Sensing to Processing

The signal processing techniques for improving the resolution and the interpretability of Lamb wave signals are termed as the signal optimization techniques in this section. There are waveform modulation techniques such as multi-scale analysis techniques and temperature effect compensation techniques. These techniques are adopted for Lamb waves dispersion compensation, high-resolution signal emitting and sensing, overlapping waveforms decompensation, time-frequency analysis and temperature effect compensation.

## 3.1. Waveform modulation techniques

When an excitation signal, f(t), is emitted into a plate at original position, the received signal, u (x,t), at x position can be expressed as

$$u(\mathbf{x},t) = \frac{1}{2\pi} \int\_{-\infty}^{\infty} F(\omega)e^{j(\omega t - k\mathbf{x})} d\omega,\tag{4}$$

where F(ω) is the Fourier transform of the excitation signal and k is the angular wavenumber. In Eq. (4), there are several parameters that decide the signal resolution and interpretability, including the amplitude, phase and frequency variation with the duration. The signal processing techniques process through modulating these fundamental signal parameters for adjusting the signal waveforms are termed waveform modulation techniques that are used for Lamb waves dispersion compensation, high-resolution Lamb waves detection and defects information extraction in structural integrity evaluation.

Signal processing techniques for dispersion compensation are realized through modulating the frequency or the wavenumbers of the received Lamb waves signals, because the dispersion nature of Lamb waves is shown as the nonlinear characteristic of signal phase in mathematical form. Time recompression technique [51] compensates the dispersion using spatial phase shift arising at each signal frequency component from the propagation of the waves over a large distance. The back-propagation function in the technique can only provide the first-order phase shift. Time-distance mapping technique [52] compresses dispersive signals by converting the signals in frequency domain to a specific propagation distance by back-propagating signals to t = 0 using the known dispersion relation. Considering the relationship between the angle frequency ω and the wavenumber, backward Lamb waves of Eq. (4) at x can be expressed as

$$
\mu\_b(-\infty) = \frac{1}{2\pi} \int\_{-\infty}^{\infty} \mathcal{U}(\omega) e^{j\mathbf{k}\cdot\mathbf{r}} d\omega = \frac{1}{2\pi} \int\_{-\infty}^{\infty} \mathcal{U}(\omega) \mathbf{c}\_8(\omega) e^{j\mathbf{k}\cdot\mathbf{r}} d\mathbf{k},\tag{5}
$$

k<sup>0</sup> = ωc/cp(ωc), k<sup>1</sup> ¼ dk0=dωj

distance of the interested wave packet.

the virtual time reversal technique, and can be expressed as

<sup>ω</sup>¼ω<sup>c</sup> <sup>¼</sup> <sup>1</sup>=cgð Þ <sup>ω</sup><sup>c</sup> , <sup>H</sup>(�ω) = <sup>e</sup>

and more detail process of them are introduced in Refs [51–53, 57–60].

dispersion function and K0(ω) is the wavenumber that determines the dispersion relation of Lamb waves mode. The above-mentioned techniques are performed with the received Lamb waves signals that can be named as the post-processing dispersion compensation techniques

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

The other signal processing strategy for high-resolution detection is realized through modulating the waveform of excitation signals, termed the excitation modulation techniques, in which the excitations are built based on the dispersion characteristics of Lamb waves, the propagation distance and the travel time [61] or utilize the chirp technique to established effects on the original excitation signal for a given compensation distance, and thus the response extraction and the dispersion compensation can be made simultaneously [62]. For pulse compression (PuC) techniques, a δ-like wave packet can be generated with a broader auto-correlation of a specific waveform including linear chirp signal, nonlinear chirp signal, Barker code and Golay complementary code. The linear chirp has the smallest main lobe width, corresponding to the best inspection resolution; the nonlinear chirp and Golay complementary code are with smaller sidelobe level, corresponding to the better performance in terms of side lobe cancelation [63], and the waveform comparisons are still effective with small errors in dispersion compensation. Malo et al. [64] presented a 2D compressed analysis, which combines pulse compression and dispersion compensation techniques in order to improve the SNR, temporal-spatial resolution and extract accurate time of arrival of responses. Yücel et al. [65] utilizes maximal length sequence (MLS) signals to produce a brute-force search-based dispersion compensation and cross-correlation for defects location. Compared with a linear broadband chirp, the technique using MLS combined with cross-correlation can improve SNR and facilitate the accurate extraction of time-of-flight (ToF), even in complex multimode situation. Marchi et al. [66] proposed a code division strategy based on the warped frequency transform. In the first, the proposed procedure encodes actuation pulses using Gold sequences. Then for each considered actuator, the acquired signals are compensated from dispersion by cross-correlating the warped version of the actuated and received signals. Compensated signals from the base for a final wavenumber imaging meant at emphasizing defects and/or anomalies by removing incident wavefield and edge reflections. Hua et al. [67] proposed pulse energy evolution method for high-resolution Lamb wave inspection. Some conclusions were obtained as follows. Linear chirp signal combined with pulse compression provides a δ-like excitation with a high signal-to-noise ratio. By the application of dispersion compensation with systemically varied compensation distances, an evolution of compensation degree curve can be obtained to estimate the actual propagation

Time reversal (TR) technique can focus the elastic waves to its original shape by time-domain reversal of the received signal with the reciprocity principle. Figure 5 shows the principle diagram of time reversal technique that consists of the forward propagation and backward propagation. In the forward propagation, a signal, f(t), is emitted into the plate by the transducer A, and received by transducer B. Then received signal is reversed in time domain and reemitted by the transducer A in the backward propagation process. The final TR processed result is received signal at transducer B. To avoid the inconvenience in the process of classical time reversal, a pure numerical signal process technique for TR technique is developed, termed

�ik(�ω)<sup>x</sup> is the phase spectrum of the

http://dx.doi.org/10.5772/intechopen.78381

71

where ω<sup>0</sup> is the specific frequency and U(ω) is the Fourier transform of the original received signal, u(x,t).

Beside interpolating G(ω) and cg(ω), the variables in spatial-wavenumber domains in timefrequency domains are needed to ensure the calculation accuracy. Spectral warping technique [53–55] was applied for the removal of dispersion from a signal in time-space domain using frequency transformation. The rescaling is defined mathematically by a composition of the signal spectrum with a function closely related to the dispersion relation that is independent of propagation distances and can be applied to signals consisting of multiple arrivals with the same dispersion characteristics. The wideband dispersion reversal technique [56], as expressed in Eq. (6), makes use of a priori knowledge of the dispersion characteristics to synthesize the corresponding dispersion reversal excitations, which is able to selectively excite the selfcompensation pure mode waveforms.

$$\begin{split} \text{WDR}[\boldsymbol{\mu}(\tau\_{0}-t)] &= \frac{1}{2\pi} \int\_{-\infty}^{+\infty} \boldsymbol{U}(-\omega) \boldsymbol{e}^{-j\omega \tau\_{0}} \cdot \boldsymbol{H}'(\omega) \boldsymbol{e}^{j\omega t} d\omega \\ &= \frac{1}{2\pi} \int\_{-\infty}^{+\infty} \boldsymbol{F}(-\omega) \cdot \boldsymbol{H}'(-\omega) \cdot \boldsymbol{H}'(\omega) \boldsymbol{e}^{j\omega (t-\tau\_{0})} d\omega \\ &= \frac{1}{2\pi} \int\_{-\infty}^{+\infty} \boldsymbol{F}(-\omega) \boldsymbol{e}^{j\omega (t-\tau\_{0})} d\omega \\ &= \boldsymbol{f}(\tau\_{0}-t), \end{split} \tag{6}$$

The above-mentioned algorithms are limited in practical application as the propagation distance may be unknown. Wavenumber curves linearization technique [57, 58] uses the first- or secondorder Taylor expansion to linearize the nonlinear wavenumber. It is independent on the propagation distance and can be applied to the signals constructed with multiple arrivals with the same wave mode or dispersion characteristics. It has less computation efforts than the timedistance mapping technique. With the idea of nonlinear wavenumber linearization, Cai et al. [59] extended the wavenumber linearization technique and developed the linearly dispersive signal construction and non-dispersive signal construction method these are expressed as

$$\begin{split} \mu\_{\text{lin}}(t) &= \frac{1}{2\pi} \int\_{-\infty}^{\infty} M(\omega - \omega\_c) e^{-i[k\_0 + k\_1(\omega - \omega\_c)]\mathbf{x} + i\omega t} \\ &= \frac{e^{i\omega\_c t - ik\_0 \mathbf{x}}}{2\pi} \int\_{-\infty}^{+\infty} M(\omega) e^{-i\omega k\_1 \mathbf{x} + i\omega t} d\omega \\ &= m(t - k\_1 \mathbf{x}) e^{i\omega\_c t - ik\_0 \mathbf{x}} \\ &= f(t - k\_1 \mathbf{x}) e^{i(k\_1 \omega\_c - k\_0)\mathbf{x}} \end{split} \tag{7}$$

where τ<sup>0</sup> is a time delay constant, M(ω-ωc) = u(ω) is the Fourier transform result of the amplitude modulation function with shift ωc, ω<sup>c</sup> is the center frequency of the excitation, k<sup>0</sup> = ωc/cp(ωc), k<sup>1</sup> ¼ dk0=dωj <sup>ω</sup>¼ω<sup>c</sup> <sup>¼</sup> <sup>1</sup>=cgð Þ <sup>ω</sup><sup>c</sup> , <sup>H</sup>(�ω) = <sup>e</sup> �ik(�ω)<sup>x</sup> is the phase spectrum of the dispersion function and K0(ω) is the wavenumber that determines the dispersion relation of Lamb waves mode. The above-mentioned techniques are performed with the received Lamb waves signals that can be named as the post-processing dispersion compensation techniques and more detail process of them are introduced in Refs [51–53, 57–60].

signals in frequency domain to a specific propagation distance by back-propagating signals to t = 0 using the known dispersion relation. Considering the relationship between the angle frequency ω and the wavenumber, backward Lamb waves of Eq. (4) at x can be expressed as

> jkxd<sup>ω</sup> <sup>¼</sup> <sup>1</sup> 2π ð∞ �∞

where ω<sup>0</sup> is the specific frequency and U(ω) is the Fourier transform of the original received

Beside interpolating G(ω) and cg(ω), the variables in spatial-wavenumber domains in timefrequency domains are needed to ensure the calculation accuracy. Spectral warping technique [53–55] was applied for the removal of dispersion from a signal in time-space domain using frequency transformation. The rescaling is defined mathematically by a composition of the signal spectrum with a function closely related to the dispersion relation that is independent of propagation distances and can be applied to signals consisting of multiple arrivals with the same dispersion characteristics. The wideband dispersion reversal technique [56], as expressed in Eq. (6), makes use of a priori knowledge of the dispersion characteristics to synthesize the corresponding dispersion reversal excitations, which is able to selectively excite the self-

Uð Þ ω cgð Þ ω e

jkxdk, (5)

(6)

(7)

ubð Þ¼ �x

70 Structural Health Monitoring from Sensing to Processing

compensation pure mode waveforms.

signal, u(x,t).

1 2π ð∞ �∞

WDR½ �¼ uð Þ τ<sup>0</sup> � t

ðþ<sup>∞</sup> �∞

> ¼ 1 2π

¼ 1 2π

ulinðÞ¼ t

Uð Þ ω e

1 2π

Fð Þ� �ω H<sup>0</sup>

construction and non-dispersive signal construction method these are expressed as

1 2π ð∞ �∞

<sup>¼</sup> <sup>e</sup><sup>i</sup>ω<sup>c</sup> <sup>t</sup>�ik0<sup>x</sup> 2π

ðþ<sup>∞</sup> �∞

ðþ<sup>∞</sup> �∞

Uð Þ �ω e

ð Þ� �ω H<sup>0</sup>

Fð Þ �ω e

¼ fð Þ τ<sup>0</sup> � t ,

The above-mentioned algorithms are limited in practical application as the propagation distance may be unknown. Wavenumber curves linearization technique [57, 58] uses the first- or secondorder Taylor expansion to linearize the nonlinear wavenumber. It is independent on the propagation distance and can be applied to the signals constructed with multiple arrivals with the same wave mode or dispersion characteristics. It has less computation efforts than the timedistance mapping technique. With the idea of nonlinear wavenumber linearization, Cai et al. [59] extended the wavenumber linearization technique and developed the linearly dispersive signal

Mð Þ ω � ω<sup>c</sup> e

<sup>¼</sup> m tð Þ � <sup>k</sup>1<sup>x</sup> ei<sup>ω</sup><sup>c</sup> <sup>t</sup>�ik0<sup>x</sup> <sup>¼</sup> f tð Þ � <sup>k</sup>1<sup>x</sup> <sup>e</sup>i kð Þ <sup>1</sup>ωc�k<sup>0</sup> x,

where τ<sup>0</sup> is a time delay constant, M(ω-ωc) = u(ω) is the Fourier transform result of the amplitude modulation function with shift ωc, ω<sup>c</sup> is the center frequency of the excitation,

Mð Þ ω e

ðþ<sup>∞</sup> �∞

�jωτ<sup>0</sup> � <sup>H</sup><sup>0</sup>

�i k0þk1ð Þ ω�ω<sup>c</sup> ½ �xþiωt

dω

�iωk1xþiωt

ð Þ ω e

<sup>j</sup>ωð Þ <sup>t</sup>�τ<sup>0</sup> dω

ð Þ ω e jωt dω

<sup>j</sup>ωð Þ <sup>t</sup>�τ<sup>0</sup> dω

The other signal processing strategy for high-resolution detection is realized through modulating the waveform of excitation signals, termed the excitation modulation techniques, in which the excitations are built based on the dispersion characteristics of Lamb waves, the propagation distance and the travel time [61] or utilize the chirp technique to established effects on the original excitation signal for a given compensation distance, and thus the response extraction and the dispersion compensation can be made simultaneously [62]. For pulse compression (PuC) techniques, a δ-like wave packet can be generated with a broader auto-correlation of a specific waveform including linear chirp signal, nonlinear chirp signal, Barker code and Golay complementary code. The linear chirp has the smallest main lobe width, corresponding to the best inspection resolution; the nonlinear chirp and Golay complementary code are with smaller sidelobe level, corresponding to the better performance in terms of side lobe cancelation [63], and the waveform comparisons are still effective with small errors in dispersion compensation. Malo et al. [64] presented a 2D compressed analysis, which combines pulse compression and dispersion compensation techniques in order to improve the SNR, temporal-spatial resolution and extract accurate time of arrival of responses. Yücel et al. [65] utilizes maximal length sequence (MLS) signals to produce a brute-force search-based dispersion compensation and cross-correlation for defects location. Compared with a linear broadband chirp, the technique using MLS combined with cross-correlation can improve SNR and facilitate the accurate extraction of time-of-flight (ToF), even in complex multimode situation. Marchi et al. [66] proposed a code division strategy based on the warped frequency transform. In the first, the proposed procedure encodes actuation pulses using Gold sequences. Then for each considered actuator, the acquired signals are compensated from dispersion by cross-correlating the warped version of the actuated and received signals. Compensated signals from the base for a final wavenumber imaging meant at emphasizing defects and/or anomalies by removing incident wavefield and edge reflections. Hua et al. [67] proposed pulse energy evolution method for high-resolution Lamb wave inspection. Some conclusions were obtained as follows. Linear chirp signal combined with pulse compression provides a δ-like excitation with a high signal-to-noise ratio. By the application of dispersion compensation with systemically varied compensation distances, an evolution of compensation degree curve can be obtained to estimate the actual propagation distance of the interested wave packet.

Time reversal (TR) technique can focus the elastic waves to its original shape by time-domain reversal of the received signal with the reciprocity principle. Figure 5 shows the principle diagram of time reversal technique that consists of the forward propagation and backward propagation. In the forward propagation, a signal, f(t), is emitted into the plate by the transducer A, and received by transducer B. Then received signal is reversed in time domain and reemitted by the transducer A in the backward propagation process. The final TR processed result is received signal at transducer B. To avoid the inconvenience in the process of classical time reversal, a pure numerical signal process technique for TR technique is developed, termed the virtual time reversal technique, and can be expressed as

$$f\_{\rm TR}(t) = \text{ifft} \left\{ \text{fft}[\mu(-t)] \frac{\text{fft}[\mu(t)]}{\text{fft}[f(t)]} \right\},\tag{8}$$

STFT divides a signal into blocks with fixed window width that controls the trade-off of bias and variance. Shorter window leads to poor frequency resolution, while longer window improves the frequency resolution but compromises the stationary assumption within the window. Thus researchers adopted variable window width instead of constant-width [77, 78] into the STFT to deal with the local resolution requirement. CWT projects a signal into a class of kernel function, termed mother wavelet, that usage of scale factor that is inversely proportional to the frequency of the given signal. Limited by the Heisenberg uncertainty principle that can be briefly described as the time-frequency windows have constant area, its results have higher frequency resolution and lower time resolution for lower frequency components, while have lower frequency resolution and higher time resolution for higher frequency components. Meanwhile the frequency resolution at the same scale level cannot be adaptively adjusted. The time-frequency representation concentration cannot be significantly improved for non-stationary signal with rapidly time-varying frequency component with the STFT and CWT. Reassignment method is a post-processing technique putting forwards to improve the readability of time-frequency representation. Through assigning the average of energy in a domain to the gravity center of these energy contributions, the reassignment technology reduces energy spread of time-frequency representation at the cost of greater computational complexity. However, it is sensitive to the noise, and inevitably introduces interference terms since the computed gravity center unnecessarily represents the real energy distribution of the interested signal. Wigner-Ville distribution (WVD) is a representative of bilinear time-frequency analysis in which the process is based on the Fourier transform of instantaneous auto-correlation function of the signal. WVD could generate time-frequency representation with the high concentration, while it also introduces plenty of cross-terms. Hilbert-Huang transform uses empirical mode decomposition (EMD) to decompose a signal into several intrinsic mode functions (IMF) along with a trend and obtain instantaneous frequency [79]. EMD is a data-driven signal decomposition technique that sequentially extracts zero-mean regular/distorted harmonics from a signal, starting from high- to low- frequency components, and it is a dyadic filter equivalent to an adaptive wavelet. While the end effects influence the performance of the signal decomposition and distort the results. For this case, researchers proposed various signal extension technique to solve the problem of end effects, including feature-based extension, mirror images, predic-

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

http://dx.doi.org/10.5772/intechopen.78381

73

The general formula of Gabor transform, Chirplet transform and asymmetric Gaussian Chirplet transform can be expressed as Eqs. (11) and (12). Their results are the inner product

> ðþ<sup>∞</sup> �∞

cos <sup>ω</sup>ð Þþ <sup>t</sup> � <sup>τ</sup> <sup>ϕ</sup> � �, Gabor

cos ωð Þþ t � τ ζð Þ t � τ

cos ωð Þþ t � τ ζð Þ t � τ

u tð Þg<sup>∗</sup>

<sup>2</sup> <sup>þ</sup> <sup>ϕ</sup> h i, Gaussian Chirplet

h i, asymmetric Gaussian Chirplet,

<sup>2</sup> <sup>þ</sup> <sup>ϕ</sup>

<sup>τ</sup>,ω,Θð Þt dt, (11)

(12)

between the signal u(t) and the complex conjugate of kernel function gτ,ω,Θ.

yð Þ¼ τ; ω; Θ

tion methods and pattern comparison [80].

e �<sup>π</sup> <sup>t</sup>�<sup>τ</sup> ð Þ<sup>s</sup> 2

ffiffiffiffiffiffi <sup>2</sup><sup>π</sup> <sup>p</sup> <sup>s</sup> � ��1=<sup>2</sup>

ae�αð Þ <sup>1</sup>�rtanhð Þ <sup>κ</sup>ð Þ <sup>t</sup>�<sup>τ</sup> ð Þ <sup>t</sup>�<sup>τ</sup> <sup>2</sup>

e �<sup>π</sup> <sup>t</sup>�<sup>τ</sup> ð Þ<sup>s</sup> 2

g tðÞ¼

8 >>>><

>>>>:

where f(t) is the excitation signal, u(t) is the original received Lamb waves signal, u(-t) is the time reversal result of signal of u(t), fTR(t) is the time reversal result, fft and ifft are the fast Fourier transform and its inverse transform.

It has been studied for dispersed compression [60, 68] and defects information extraction [69, 70]. Zeng et al. [70] carefully designed the amplitude of the input signal before the time reversal process. Huang et al. [71] used a weight vector to modulated the signal in both the forward and backward processes, the vector is obtained as the product of the reciprocal of amplitude dispersion and a window function that varies with the excitation signal adaptively, and its shape is also determined by a threshold. The advantages of single mode tuning in the application of time reversal damage detection are highlighted in Refs. [33,71]. The adhesive, host plate, transducer and excitation parameters are also influenced on the performance of time reversibility of Lamb waves.

#### 3.2. Multi-scale analysis techniques

Multi-scale analysis techniques map a 1D signal into a high dimensional space with transform based on a kernel function, including short-time Fourier transform (STFT), Wavelet transform (the continue wavelet transform (CWT), the discrete wavelet transform (DWT) and wave packet transform), Gabor transform [72], Chirplet transform [73] and asymmetric Gaussian Chirplet transform [74, 75]. When the mapping data space express the changing frequency of the signal parameters, the algorithm can be used for time-frequency analysis [76]. In other case, the mapping data space indicates the inner product between the signal and a kernel function, the algorithm can be used for Lamb waves mode identification and overlapping waveforms decomposition. The formula of STFT and CWT can be expressed as Eq. (9) and Eq. (10), respectively.

$$y(\omega, \tau) = \int\_{-\infty}^{+\infty} u(t)w(t-\tau)e^{-j\omega t}dt,\tag{9}$$

$$y(s,\tau) = \frac{1}{\sqrt{s}} \int\_{-\infty}^{+\infty} u(t) \psi^\* \left(\frac{t-\tau}{s}\right) dt,\tag{10}$$

where w(t) is the window function, commonly a rectangle window, Hanning window or Gaussian window; u(t) is the sensing Lamb waves signal, ψ is the mother wavelet, τ is the shift step in time-axis, s is the scale and \* indicates the complex conjugate operation.

Figure 5. Principle diagram of time reversal technique.

f TRðÞ¼ t ifft fft½ � uð Þ �t

Fourier transform and its inverse transform.

72 Structural Health Monitoring from Sensing to Processing

time reversibility of Lamb waves.

3.2. Multi-scale analysis techniques

Figure 5. Principle diagram of time reversal technique.

where f(t) is the excitation signal, u(t) is the original received Lamb waves signal, u(-t) is the time reversal result of signal of u(t), fTR(t) is the time reversal result, fft and ifft are the fast

It has been studied for dispersed compression [60, 68] and defects information extraction [69, 70]. Zeng et al. [70] carefully designed the amplitude of the input signal before the time reversal process. Huang et al. [71] used a weight vector to modulated the signal in both the forward and backward processes, the vector is obtained as the product of the reciprocal of amplitude dispersion and a window function that varies with the excitation signal adaptively, and its shape is also determined by a threshold. The advantages of single mode tuning in the application of time reversal damage detection are highlighted in Refs. [33,71]. The adhesive, host plate, transducer and excitation parameters are also influenced on the performance of

Multi-scale analysis techniques map a 1D signal into a high dimensional space with transform based on a kernel function, including short-time Fourier transform (STFT), Wavelet transform (the continue wavelet transform (CWT), the discrete wavelet transform (DWT) and wave packet transform), Gabor transform [72], Chirplet transform [73] and asymmetric Gaussian Chirplet transform [74, 75]. When the mapping data space express the changing frequency of the signal parameters, the algorithm can be used for time-frequency analysis [76]. In other case, the mapping data space indicates the inner product between the signal and a kernel function, the algorithm can be used for Lamb waves mode identification and overlapping waveforms decomposition. The formula of STFT and CWT can be expressed as Eq. (9) and Eq. (10), respectively.

yð Þ¼ ω; τ

y sð Þ¼ ; τ

ðþ<sup>∞</sup> �∞

1 ffiffi s p ðþ<sup>∞</sup> �∞

step in time-axis, s is the scale and \* indicates the complex conjugate operation.

u tð Þw tð Þ � τ e

where w(t) is the window function, commonly a rectangle window, Hanning window or Gaussian window; u(t) is the sensing Lamb waves signal, ψ is the mother wavelet, τ is the shift

u tð Þψ<sup>∗</sup> <sup>t</sup> � <sup>τ</sup> s � �

�jωt

fft½ � u tð Þ fft½ � f tð Þ

, (8)

dt, (9)

dt, (10)

� �

STFT divides a signal into blocks with fixed window width that controls the trade-off of bias and variance. Shorter window leads to poor frequency resolution, while longer window improves the frequency resolution but compromises the stationary assumption within the window. Thus researchers adopted variable window width instead of constant-width [77, 78] into the STFT to deal with the local resolution requirement. CWT projects a signal into a class of kernel function, termed mother wavelet, that usage of scale factor that is inversely proportional to the frequency of the given signal. Limited by the Heisenberg uncertainty principle that can be briefly described as the time-frequency windows have constant area, its results have higher frequency resolution and lower time resolution for lower frequency components, while have lower frequency resolution and higher time resolution for higher frequency components. Meanwhile the frequency resolution at the same scale level cannot be adaptively adjusted. The time-frequency representation concentration cannot be significantly improved for non-stationary signal with rapidly time-varying frequency component with the STFT and CWT. Reassignment method is a post-processing technique putting forwards to improve the readability of time-frequency representation. Through assigning the average of energy in a domain to the gravity center of these energy contributions, the reassignment technology reduces energy spread of time-frequency representation at the cost of greater computational complexity. However, it is sensitive to the noise, and inevitably introduces interference terms since the computed gravity center unnecessarily represents the real energy distribution of the interested signal. Wigner-Ville distribution (WVD) is a representative of bilinear time-frequency analysis in which the process is based on the Fourier transform of instantaneous auto-correlation function of the signal. WVD could generate time-frequency representation with the high concentration, while it also introduces plenty of cross-terms. Hilbert-Huang transform uses empirical mode decomposition (EMD) to decompose a signal into several intrinsic mode functions (IMF) along with a trend and obtain instantaneous frequency [79]. EMD is a data-driven signal decomposition technique that sequentially extracts zero-mean regular/distorted harmonics from a signal, starting from high- to low- frequency components, and it is a dyadic filter equivalent to an adaptive wavelet. While the end effects influence the performance of the signal decomposition and distort the results. For this case, researchers proposed various signal extension technique to solve the problem of end effects, including feature-based extension, mirror images, prediction methods and pattern comparison [80].

The general formula of Gabor transform, Chirplet transform and asymmetric Gaussian Chirplet transform can be expressed as Eqs. (11) and (12). Their results are the inner product between the signal u(t) and the complex conjugate of kernel function gτ,ω,Θ.

$$y(\tau, \omega; \Theta) = \int\_{-\infty}^{+\infty} u(t) g^\*\_{\tau, \omega, \Theta}(t) dt,\tag{11}$$

$$\log(t) = \begin{cases} e^{-\pi \left(\frac{t-\tau}{s}\right)^2} \cos\left[\omega (t-\tau) + \phi\right], & \text{Gabor} \\ \left(\sqrt{2\pi} \text{s}\right)^{-1/2} e^{-\pi \left(\frac{t-\tau}{s}\right)^2} \cos\left[\omega (t-\tau) + \zeta (t-\tau)^2 + \phi\right], & \text{Gaussian Chirplet} \\ a e^{-\pi (1-\tau \tanh(\kappa(t-\tau))) (t-\tau)^2} \cos\left[\omega (t-\tau) + \zeta (t-\tau)^2 + \phi\right], & \text{symmetrie Gaussian Chirplet}, \end{cases} \tag{12}$$

where ζ is the linear chirp rate, ϕ is the phase, a is the amplitude, α is the decay rate controlling the signal bandwidth, r is the asymmetry factor controlling the skewness of the window and tanh(κt) is hyperbolic tangent function of order κ, a positive constant integer. The detail description of Eq. (11) is given in Refs [81, 82]. Gabor transform and the Chirplet transform projects a signal energy distribution in a time-frequency plane, which does not induce interference terms [83]. An important advantage of such analysis is to provide highly concentrated time-frequency representation with signal-dependent resolution. Especially for the latter one, there are many parameters adaptively adjusted for an accuracy mapping the signal features, including the center frequency, arrival time, duration and frequency-varying characteristics. These two algorithms can also be used for decomposition of the overlapping waveforms.

The signal decomposition is based on a reasonable assumption that a signal can be expressed as a sum of several wave packets, as shown in Eq. (14).

$$u(t) = \sum\_{n=0}^{N-1} \left< R^n u, \mathbf{g}\_{\gamma n} \right> \mathbf{g}\_{\gamma n} + \mathbf{R}^N u,\tag{13}$$

best atom is first selected, and then, its scale and the chirp rate are locally optimized so as to get a 'good' chirp atom. While the successive parameter estimation is a suboptimal method. The error in one parameter estimate due to noise will induce errors in estimation of other parameters. Zeng et al. [89] combined the adaptive Chirplet transform and the time-varying bandpass filtering provides a methodology for extracting interest waveforms from the overall Lamb

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

The signals received under a vibration of temperature condition can be expressed as [90, 91].

N

ajsj <sup>t</sup> � tjβ δð Þ <sup>T</sup> � �, (15)

http://dx.doi.org/10.5772/intechopen.78381

h i, ð Þ OBS (16)

th wave packet

75

<sup>p</sup>, kp is the change in phase

j¼1

respectively, β(δT) is the shift in arrival times of wave packets in each time-trace with respect to

The optimal baseline selection (OBS) and the baseline signal stretch (BSS) are widely studied [92] for elimination the temperature effect in Lamb waves based structure integrity evaluation. In OBS technique, a pre-built database under different temperatures is built. The process for OBS includes (1) recording a set of baseline waveforms from the intact specimen at temperatures spanning the expected operating range; (2) selecting a waveform from the baseline set, which the temperature is the closest to the measured signal; (3) adjusting the baseline waveform to best match the signal, then calculating an error parameter between the signal and the adjusting waveform and (4) comparing these parameters with a threshold to determine the structural status. A large number of baselines data are needed even for small temperature steps to ensure the accuracy of the extracted defects waveforms that increase computational and memory costs. Meanwhile the damage manifests itself and the noise will rise the OBS error [93]. Wang et al. [94] combined the OBS and the adaptive filter to compensate the temperature variations. The simplistic representation of the signal and the choice of activation function are the main limitations of this technology. BSS modified a single baseline time-trace to match the field time-trace to compensate the temperature effect. In BSS, the time-axis of the baseline time-trace is stretched by a stretch factor to yield a new time-trace, while the BBS is strongly dependent on the mode purity and structural complexity. The OBS and the BBS can be combined to form a robust temperature compensation strategy [90, 95]. The reduction in the number of baselines in the database is limited by the maximum temperature gap between baselines, which can be compensated for by the optimal stretch without loss of sensitivity; this is a function of mode purity, signal complexity and the maximum propagation distance to

u tð Þ¼ ; <sup>T</sup><sup>0</sup> <sup>þ</sup> <sup>δ</sup><sup>T</sup> <sup>X</sup>

where aj, sj and tj are the amplitude, the waveform and the arrival time of the j

cover the whole structure expressed in wavelengths [96]. Their formula are

X N

j¼1 am j s m <sup>j</sup> t � t m <sup>j</sup> β δð Þ Tm

umð Þ¼ t; Tm

their values at an arbitrary fixed temperature, <sup>β</sup> <sup>¼</sup> <sup>1</sup> � <sup>δ</sup><sup>T</sup> � cgkp=c<sup>2</sup>

wave signals.

velocity with temperature.

3.3. Temperature effect compensation techniques

where u(x,t) is the signal received at x that contains the first arrival waves, the echoes from the edges of plates and the defects; RNu is the residual term; N is the number of iterations; gγ<sup>n</sup> is the matching atoms that fit to the residual term Rn u, which is the residual left after subtracting results of previous iterations; gγ<sup>i</sup> is the atoms in a pre-built over-complete dictionary or a sub-type of a kernel function. The derivation processes of parameters Rn u and gγ<sup>n</sup> can be expressed as

$$\begin{cases} \mathcal{R}^0 u = u(t) \\ \mathcal{R}^{n+1} u = \mathcal{R}^n u - \left< \mathcal{R}^n u, \mathcal{g}\_{\gamma n} \right> \mathcal{g}\_{\gamma n} \,. \end{cases} \tag{14}$$
 
$$\mathcal{g}\_{\gamma n} = \arg \max\_{\mathcal{g}\_{\gamma i} \in D} \left| \left< \mathcal{R}^n u, \mathcal{g}\_{\gamma i} \right> \right| $$

In the process of the wave packets decomposition, the atoms can be selected from a pre-built dictionary or sub-type of a kernel function. The dictionary can be built based on the pre-analysis of the excitation [84], the interaction between Lamb waves and defects [85], etc. Mallat et al. [86] introduced the matching pursuit with time-frequency dictionaries. The decomposition based the Gabor transform and the Gaussian Chirplet transform are suitable for the signals with symmetric envelops, while the sensing signals often have asymmetric envelops induced by the dispersion nature of Lamb waves. Thus, the asymmetric Gaussian Chirplet is designed for decomposition the dispersive Lamb waves signal benefiting from its specific designed windows.

Matching pursuit algorithm is a highly adaptive signal decomposition and approximation method for de-noising, wave parameter estimation and feature extraction [86, 87], while it does not provide the best approximation to signal by a linear combination of atoms from a dictionary or a sub-type of kernel function. Actually, many parameters need to be estimated in each iteration step to get a best approximant, it is an NP-hard problem. Therefore, a suitable parameter evaluation algorithm is very important for signal decomposition algorithms. The successive parameters estimation algorithm [88] and the fast ridge pursuit algorithm [82] are most used algorithms for estimation of the atom parameter. In each iteration of the pursuit, the best atom is first selected, and then, its scale and the chirp rate are locally optimized so as to get a 'good' chirp atom. While the successive parameter estimation is a suboptimal method. The error in one parameter estimate due to noise will induce errors in estimation of other parameters. Zeng et al. [89] combined the adaptive Chirplet transform and the time-varying bandpass filtering provides a methodology for extracting interest waveforms from the overall Lamb wave signals.

#### 3.3. Temperature effect compensation techniques

where ζ is the linear chirp rate, ϕ is the phase, a is the amplitude, α is the decay rate controlling the signal bandwidth, r is the asymmetry factor controlling the skewness of the window and tanh(κt) is hyperbolic tangent function of order κ, a positive constant integer. The detail description of Eq. (11) is given in Refs [81, 82]. Gabor transform and the Chirplet transform projects a signal energy distribution in a time-frequency plane, which does not induce interference terms [83]. An important advantage of such analysis is to provide highly concentrated time-frequency representation with signal-dependent resolution. Especially for the latter one, there are many parameters adaptively adjusted for an accuracy mapping the signal features, including the center frequency, arrival time, duration and frequency-varying characteristics. These two algorithms can also be used for decomposition of the overlapping waveforms.

The signal decomposition is based on a reasonable assumption that a signal can be expressed

<sup>R</sup>nu; <sup>g</sup>γ<sup>n</sup> D E

where u(x,t) is the signal received at x that contains the first arrival waves, the echoes from the edges of plates and the defects; RNu is the residual term; N is the number of iterations; gγ<sup>n</sup> is the

of previous iterations; gγ<sup>i</sup> is the atoms in a pre-built over-complete dictionary or a sub-type of a

<sup>u</sup> <sup>¼</sup> RNu � Rnu; <sup>g</sup>γ<sup>n</sup>

� �

gγ<sup>i</sup> ∈ D

In the process of the wave packets decomposition, the atoms can be selected from a pre-built dictionary or sub-type of a kernel function. The dictionary can be built based on the pre-analysis of the excitation [84], the interaction between Lamb waves and defects [85], etc. Mallat et al. [86] introduced the matching pursuit with time-frequency dictionaries. The decomposition based the Gabor transform and the Gaussian Chirplet transform are suitable for the signals with symmetric envelops, while the sensing signals often have asymmetric envelops induced by the dispersion nature of Lamb waves. Thus, the asymmetric Gaussian Chirplet is designed for decomposition

Matching pursuit algorithm is a highly adaptive signal decomposition and approximation method for de-noising, wave parameter estimation and feature extraction [86, 87], while it does not provide the best approximation to signal by a linear combination of atoms from a dictionary or a sub-type of kernel function. Actually, many parameters need to be estimated in each iteration step to get a best approximant, it is an NP-hard problem. Therefore, a suitable parameter evaluation algorithm is very important for signal decomposition algorithms. The successive parameters estimation algorithm [88] and the fast ridge pursuit algorithm [82] are most used algorithms for estimation of the atom parameter. In each iteration of the pursuit, the

D E

Rnu; <sup>g</sup>γ<sup>i</sup> �D E

gγ<sup>n</sup>

:

� � �

u ¼ u tð Þ

gγ<sup>n</sup> ¼ arg max

the dispersive Lamb waves signal benefiting from its specific designed windows.

<sup>g</sup>γ<sup>n</sup> <sup>þ</sup> RNu, (13)

u, which is the residual left after subtracting results

u and gγ<sup>n</sup> can be expressed as

(14)

as a sum of several wave packets, as shown in Eq. (14).

kernel function. The derivation processes of parameters Rn

8 >>>><

>>>>:

matching atoms that fit to the residual term Rn

74 Structural Health Monitoring from Sensing to Processing

u tðÞ¼

N X�1 n¼0

R0

Rnþ<sup>1</sup>

The signals received under a vibration of temperature condition can be expressed as [90, 91].

$$u(t; T\_0 + \delta T) = \sum\_{j=1}^{N} a\_j \mathbf{s}\_j \left[ t - t\_j \beta(\delta T) \right],\tag{15}$$

where aj, sj and tj are the amplitude, the waveform and the arrival time of the j th wave packet respectively, β(δT) is the shift in arrival times of wave packets in each time-trace with respect to their values at an arbitrary fixed temperature, <sup>β</sup> <sup>¼</sup> <sup>1</sup> � <sup>δ</sup><sup>T</sup> � cgkp=c<sup>2</sup> <sup>p</sup>, kp is the change in phase velocity with temperature.

The optimal baseline selection (OBS) and the baseline signal stretch (BSS) are widely studied [92] for elimination the temperature effect in Lamb waves based structure integrity evaluation. In OBS technique, a pre-built database under different temperatures is built. The process for OBS includes (1) recording a set of baseline waveforms from the intact specimen at temperatures spanning the expected operating range; (2) selecting a waveform from the baseline set, which the temperature is the closest to the measured signal; (3) adjusting the baseline waveform to best match the signal, then calculating an error parameter between the signal and the adjusting waveform and (4) comparing these parameters with a threshold to determine the structural status. A large number of baselines data are needed even for small temperature steps to ensure the accuracy of the extracted defects waveforms that increase computational and memory costs. Meanwhile the damage manifests itself and the noise will rise the OBS error [93]. Wang et al. [94] combined the OBS and the adaptive filter to compensate the temperature variations. The simplistic representation of the signal and the choice of activation function are the main limitations of this technology. BSS modified a single baseline time-trace to match the field time-trace to compensate the temperature effect. In BSS, the time-axis of the baseline time-trace is stretched by a stretch factor to yield a new time-trace, while the BBS is strongly dependent on the mode purity and structural complexity. The OBS and the BBS can be combined to form a robust temperature compensation strategy [90, 95]. The reduction in the number of baselines in the database is limited by the maximum temperature gap between baselines, which can be compensated for by the optimal stretch without loss of sensitivity; this is a function of mode purity, signal complexity and the maximum propagation distance to cover the whole structure expressed in wavelengths [96]. Their formula are

$$\mu\_m(t; T\_m) = \sum\_{j=1}^{N} a\_j^m s\_j^m \left[ t - t\_j^m \beta(\delta T\_m) \right], \quad \text{(OBS)}\tag{16}$$

$$\left(\widehat{\mu}\left(t; T\_0, \widehat{\boldsymbol{\beta}}\right)\right) = \mu\left(t/\widehat{\boldsymbol{\beta}}; T\_0\right) = \sum\_{j=1}^{N} a\_j \mathbf{s}\_j \left(t/\widehat{\boldsymbol{\beta}} - \boldsymbol{t}\_j\right), \quad \text{(BSS)}\tag{17}$$

including Lorentz force, magnetostriction mechanism and magnetizing force. Through adjusting the configuration of the permanent magnets, coils, EMATs can used for relatively pure Lamb waves modes emitting and sensing at specific frequency, including the A modes, S modes. Laser ultrasonic systems commonly consist of a laser transmitter, a laser receiver and a laser demodulator and are very complex systems that designed with the shearography and the laser vibrometer techniques. In the structure integrity evaluation, the system works under the thermoelastic regime, not the ablation regime, for emitting Lamb waves without the hurt of structure. Through scanning the surface of the plates, the

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

http://dx.doi.org/10.5772/intechopen.78381

77

full wavefield Lamb waves can be acquired with the laser ultrasonic system.

in Lamb waves defects detection.

2. The waveform modulation techniques, multi-scale analysis techniques and temperature effect compensation techniques are developed to optimize the resolution and interpretability of received Lamb waves signals. Among them, the waveform modulation techniques are used to acquire signals that have more regular waveforms through modulating the phase parameters or the excitation waveforms based on the Lamb waves dispersion principle and the δ-like waveform response of specific waves. After the process, the ToF and the scatterers echoes can be analyzed easily. During the process of the time recompression technique, the time-distance mapping technique, the spectral warping technique and the wideband dispersion reversal technique, the propagation should be known that limits their application potentials. The nonlinear wavenumber linearization technique can realize dispersion compensation without the propagation distance parameter. Pulse compression technique also attracts many attentions for generating that high improve the resolution of the received signals, but it still exists many challenges for field application. TR technique is built with the acoustic reciprocity principle for dispersion compensation and damage feature extraction and is easily realized in applications, while it often cannot get ideal dispersion compensation results. It is more suitable for defects feature extraction

3. Multi-scale analysis techniques are performed through mapping a signal into a multiparameters data space with a function transform or matching pursuit operation. The transforms based on a kernel function include STFT, CWT, DWT, Gabor transform, Chirplet transform and asymmetric Gaussian Chirplet transform that have been used for time-frequency analysis and overlapping wave packets decomposition. Among them, the wavelet transforms and the Chirplet-based transforms are more attractive as their flexible and more parameter adjusting probability in signal processing. Particularly for the asymmetric Gaussian Chirplet transform has the ability for accuracy decompose the signals with the dispersion characteristics. The dictionary based on overlapping waveforms decomposition techniques is also very attractive. The OBS, the BBS and physics-based approaches are proposed for compensating the temperature effect. OBS is performed with a pre-built database under different temperatures where large number of baseline data are acquired under various temperature conditions. In BSS, the time-axis of the baseline timetrace is stretched by a stretch factor to yield a new time-trace, but it is sensitive to the resolution and the interpretability of Lamb wave signals. The combination of the OBS and BSS can effectively eliminate the shortage in both of the algorithms and have a robust performance in temperature effect compensation. Physics-based approach realizes the

where um is the mth time-trace from the baseline dataset, Tm= T0+δTm refers to as the baseline dataset and β(δTm) is the fractional shift in arrival times of wave packets in each time-trace with respect to their values at an arbitrary fixed temperature. bβ is a stretch factor to yield a new time-trace <sup>b</sup>u t; <sup>T</sup>0; <sup>b</sup><sup>β</sup> � �.

Other techniques have been proposed for compensation the temperature effect. Physics-based approach builds the compensation data through analyzing the temperature effect on the structures and transducers [97]. This approach needs to train with prior data, which are always unavailable. Fendzi et al. [98] presented a data-driven temperature compensation approach, which considers a representation of the piezo-sensor signal through its Hilbert transform that allows one to extract the amplitude factor and the phase shift in signals, while its compensation accuracy depends on the length of the time window that should be considered in the temperature compensation parameters estimation. Liu et al. [99] proposed a baseline signal reconstruction technique in which the Hilbert transform is used to compensate the phase of baseline signals and the orthogonal matching pursuit is used to compensate the amplitude of baseline signal. Dao et al. [100] combined the cointegration technique and fractal signal processing to effective removal of undesired multiple temperature trends in Lamb waves signals. The former technique relies on the analysis of non-stationary behavior, whereas the latter brings the concept of multi-resolution wavelet decomposition of time series. While the self-similar pattern of cointegration residuals will be broken when damage is present.

## 4. Summary and conclusions

Lamb waves are a type of elastic waves propagating in plate-like structures that have been widely studied for defects location, sizing and recognition during the past decades. The detection or monitoring system settings, the transducers, the nature of Lamb waves, the environment and operational condition are three key factors influence Lamb waves emitting and sensing, and further decide the design and the performance of signal processing techniques. Considering the important roles of transducers and the signal processing techniques in Lamb waves based structure integrity evaluation, various transducers and signal processing technologies are proposed and developed, and that are briefly reviewed in this chapter.

1. The transducers for Lamb waves emitting and sensing in structure integrity evaluation are mainly based on three types of transduce mechanisms, including piezoelectric effect, electromagnetic acoustic transducer mechanism and laser ultrasonic technique. Piezoelectric transducers, EMAT and laser ultrasonic systems are mostly used for Lamb waves emitting and sensing in structure integrity evaluation. The PWAT, IDTs, the air-coupled transducers are designed with the piezoelectric materials that has high energy conversion efficiency. EMATs are working under electromagnetic acoustic transducer mechanism, including Lorentz force, magnetostriction mechanism and magnetizing force. Through adjusting the configuration of the permanent magnets, coils, EMATs can used for relatively pure Lamb waves modes emitting and sensing at specific frequency, including the A modes, S modes. Laser ultrasonic systems commonly consist of a laser transmitter, a laser receiver and a laser demodulator and are very complex systems that designed with the shearography and the laser vibrometer techniques. In the structure integrity evaluation, the system works under the thermoelastic regime, not the ablation regime, for emitting Lamb waves without the hurt of structure. Through scanning the surface of the plates, the full wavefield Lamb waves can be acquired with the laser ultrasonic system.

<sup>b</sup>u t; <sup>T</sup>0; <sup>b</sup><sup>β</sup> � �

76 Structural Health Monitoring from Sensing to Processing

time-trace <sup>b</sup>u t; <sup>T</sup>0; <sup>b</sup><sup>β</sup>

� �

4. Summary and conclusions

.

¼ u t=bβ; T<sup>0</sup> � � <sup>¼</sup> <sup>X</sup> N

where um is the mth time-trace from the baseline dataset, Tm= T0+δTm refers to as the baseline dataset and β(δTm) is the fractional shift in arrival times of wave packets in each time-trace with respect to their values at an arbitrary fixed temperature. bβ is a stretch factor to yield a new

Other techniques have been proposed for compensation the temperature effect. Physics-based approach builds the compensation data through analyzing the temperature effect on the structures and transducers [97]. This approach needs to train with prior data, which are always unavailable. Fendzi et al. [98] presented a data-driven temperature compensation approach, which considers a representation of the piezo-sensor signal through its Hilbert transform that allows one to extract the amplitude factor and the phase shift in signals, while its compensation accuracy depends on the length of the time window that should be considered in the temperature compensation parameters estimation. Liu et al. [99] proposed a baseline signal reconstruction technique in which the Hilbert transform is used to compensate the phase of baseline signals and the orthogonal matching pursuit is used to compensate the amplitude of baseline signal. Dao et al. [100] combined the cointegration technique and fractal signal processing to effective removal of undesired multiple temperature trends in Lamb waves signals. The former technique relies on the analysis of non-stationary behavior, whereas the latter brings the concept of multi-resolution wavelet decomposition of time series. While the

self-similar pattern of cointegration residuals will be broken when damage is present.

Lamb waves are a type of elastic waves propagating in plate-like structures that have been widely studied for defects location, sizing and recognition during the past decades. The detection or monitoring system settings, the transducers, the nature of Lamb waves, the environment and operational condition are three key factors influence Lamb waves emitting and sensing, and further decide the design and the performance of signal processing techniques. Considering the important roles of transducers and the signal processing techniques in Lamb waves based structure integrity evaluation, various transducers and signal processing technologies are proposed and developed, and that are briefly reviewed in this chapter.

1. The transducers for Lamb waves emitting and sensing in structure integrity evaluation are mainly based on three types of transduce mechanisms, including piezoelectric effect, electromagnetic acoustic transducer mechanism and laser ultrasonic technique. Piezoelectric transducers, EMAT and laser ultrasonic systems are mostly used for Lamb waves emitting and sensing in structure integrity evaluation. The PWAT, IDTs, the air-coupled transducers are designed with the piezoelectric materials that has high energy conversion efficiency. EMATs are working under electromagnetic acoustic transducer mechanism,

j¼1

ajsj t=bβ � tj � �

, ð Þ BSS (17)


compensation through analysis the temperature effect on the structures and the transducers that is time consuming for field application.

[6] Worden K. Rayleigh and Lamb waves-basic principles. Strain. 2001;37:167-172. DOI:

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

http://dx.doi.org/10.5772/intechopen.78381

79

[7] Moll J, Golub MV, Glushkov E, Glushkova N, Fritzen CP. Non-axisymmetric Lamb wave excitation by piezoelectric wafer active sensors. Sensors and Actuators, A: Physical. 2012;

[8] Ha S, Lonkar K, Mittal A, Chang FK. Adhesive layer effects on PZT-induced Lamb waves at elevated temperatures. Structural Health Monitoring. 2010;9:247-256. DOI: 10.1177/

[9] Bratton RL, Datta SK, Shah AH. Anisotropy effects on Lamb waves in composite plates. In: Proceedings of the Review of Progress in Quantitative Nondestructive Evaluation.

[10] He CF, Liu HY, Liu ZH, Wu B. The propagation of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates. Journal of Sound and Vibration. 2013;332:

[11] Wang L, Yuan FG. Group velocity and characteristic wave curves of Lamb waves in composites: Modeling and experiments. Composites Science and Technology. 2007;67:

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[13] Pei N, Bond LJ. Comparison of acoustoelastic Lamb wave propagation in stressed plates for different measurement orientations. The Journal of the Acoustical Society of America.

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[15] di Scalea FL, Matt H, Bartoli I. The response of rectangular piezoelectric sensors to Rayleigh and lamb ultrasonic waves. The Journal of the Acoustical Society of America.

[16] Marzani A, Salamone S. Numerical prediction and experimental verification of temperature effect on plate waves generated and received by piezoceramic sensors. Mechanical Systems and Signal Processing. 2012;30:204-217. DOI: 10.1016/j.ymssp.2011.11.003

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[18] Lee SJ, Gandhi N, Michaels JE, Michaels TE. Comparison of the effects of applied loads and temperature variations on guided wave propagation. In: Proceedings of the 37th

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Berlin: Springer; 1989. pp. 197-204

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2017;142:327-331. DOI: 10.1121/1.5004388

2007;121:175-187. DOI: 10.1121/1.2400668

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## Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51475012, 11772014, 11527801, and 11272021).

## Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

## Author details

Zenghua Liu\* and Honglei Chen

\*Address all correspondence to: liuzenghua@bjut.edu.cn

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China

## References


[6] Worden K. Rayleigh and Lamb waves-basic principles. Strain. 2001;37:167-172. DOI: 10.1111/j.1475-1305.2001.tb01254.x

compensation through analysis the temperature effect on the structures and the trans-

This work was supported by the National Natural Science Foundation of China (Grant Nos.

We declare that we do not have any commercial or associative interest that represents a conflict

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of

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78 Structural Health Monitoring from Sensing to Processing

of interest in connection with the work submitted.

\*Address all correspondence to: liuzenghua@bjut.edu.cn

Acknowledgements

Conflict of interest

Author details

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**Chapter 5**

Provisional chapter

**Application and Challenges of Signal Processing**

Application and Challenges of Signal Processing

**Techniques for Lamb Waves Structural Integrity**

Techniques for Lamb Waves Structural Integrity

**Techniques**

Abstract

networks.

1. Introduction

structural integrity evaluation

Techniques

Zenghua Liu and Honglei Chen

Zenghua Liu and Honglei Chen

http://dx.doi.org/10.5772/intechopen.79475

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Evaluation: Part B-Defects Imaging and Recognition**

DOI: 10.5772/intechopen.79475

The wavefield of Lamb waves is yielded by the feature of plate-like structures. And many defects imaging techniques and intelligent recognition algorithms have been developed for defects location, sizing and recognition through analyzing the parameters of received Lamb waves signals including the arrival time, attenuation, amplitude and phase, etc. In this chapter, we give a briefly review about the defects imaging techniques and the intelligent recognition algorithms. Considering the available parameters of Lamb waves signals and the setting of detection/monitoring systems, we roughly divide the defect location and sizing techniques into four categories, including the sparse array imaging techniques, the tomography techniques, the compact array techniques, and full wavefield imaging techniques. The principle of them is introduced. Meanwhile, the intelligent recognition techniques based on various of intelligent recognition algorithms that have been widely used to analyze Lamb waves signals in the research of defect recognition are reviewed, including the support vector machine, Bayesian methodology, and the neural

Keywords: Lamb waves, plate, defect imaging techniques, intelligent detection algorithm,

The propagation characteristic of Lamb waves is yielded by the state of plate-like structures. Defect scattering waveforms are generated as the interaction between Lamb waves and

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Evaluation: Part B-Defects Imaging and Recognition


**Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part B-Defects Imaging and Recognition Techniques** Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part B-Defects Imaging and Recognition Techniques

DOI: 10.5772/intechopen.79475

Zenghua Liu and Honglei Chen Zenghua Liu and Honglei Chen

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79475

#### Abstract

[97] Roy S, Lonkar K, Janapati V, Chang FK. A novel physics-based temperature compensation model for structural health monitoring using ultrasonic guided waves. Structural

[98] Fendzi C, Rebillat M, Mechbal N, Guskov M, Coffignal G. A data driven temperature compensation approach for structural health monitoring using Lamb waves. Structural

[99] Liu GQ, Xiao YC, Zhang H, Ren GX. Baseline signal reconstruction for temperature compensation in Lamb wave-based damage detection. Sensors. 2016;16:1273. DOI: 10.3390/

[100] Dao PB, Staszewski WJ. Lamb wave based structural damage detection using cointegration and fractal signal processing. Mechanical Systems and Signal Processing. 2014;49:285-301.

Health Monitoring. 2014;13:321-342. DOI: 10.1177/1475921714522846

Health Monitoring. 2016;15:525-540. DOI: 10.1177/1475921716650997

s16081273

DOI: 10.1016/j.ymssp.2014.04.011

86 Structural Health Monitoring from Sensing to Processing

The wavefield of Lamb waves is yielded by the feature of plate-like structures. And many defects imaging techniques and intelligent recognition algorithms have been developed for defects location, sizing and recognition through analyzing the parameters of received Lamb waves signals including the arrival time, attenuation, amplitude and phase, etc. In this chapter, we give a briefly review about the defects imaging techniques and the intelligent recognition algorithms. Considering the available parameters of Lamb waves signals and the setting of detection/monitoring systems, we roughly divide the defect location and sizing techniques into four categories, including the sparse array imaging techniques, the tomography techniques, the compact array techniques, and full wavefield imaging techniques. The principle of them is introduced. Meanwhile, the intelligent recognition techniques based on various of intelligent recognition algorithms that have been widely used to analyze Lamb waves signals in the research of defect recognition are reviewed, including the support vector machine, Bayesian methodology, and the neural networks.

Keywords: Lamb waves, plate, defect imaging techniques, intelligent detection algorithm, structural integrity evaluation

## 1. Introduction

The propagation characteristic of Lamb waves is yielded by the state of plate-like structures. Defect scattering waveforms are generated as the interaction between Lamb waves and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

defects, and that may be contained in received Lamb waves signals during the Lamb waves structural integrity evaluation. To clearly show out the state of the structures, many kinds of defect imaging and recognition techniques are proposed for analyzing the change of the signal parameters based on the settings of detection/monitoring systems during the past decades. In laboratory and practical field applications of Lamb waves based structure integrity evaluation, the detection/monitoring systems have two basic setting strategies. Firstly, Lamb waves signals are emitted and sensed at relatively small number of spatially distributed position by transducers that have the same or different transduction mechanisms. These positions are maybe distributed in sparse (adjacent transducer spacing is larger than the largest wavelength of signals) or compact (adjacent transducer spacing is shorter than the shortest wavelength of signals) array forms. Collaborative with different signal excitation and detection strategies, signal processing techniques are developed for integrity detection/monitoring in the whole structure. The other strategy is a full-scale scanning of the surface of structures with laser ultrasonic systems, air-coupled scanning systems, to obtain the full wavefield of Lamb waves. On the basis of the above detection/monitoring system setting strategies, Lamb waves signals used for damage detection/monitoring are obtained. Then, signal processing techniques are adopted to analyze the change of signal parameters to extract the damage information such as the amplitudes, velocity, phase, frequency, etc. Finally, defect influence maps and intelligent recognition models that indicating defect information are achieved with imaging and recognition techniques.

imaging technique [1, 2] and the hyperbola imaging technique [3] are ToF imaging algorithms and map the amplitude information of scattering signals to elliptical trajectory and hyperbola

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xj � <sup>x</sup> � �<sup>2</sup> <sup>þ</sup> yj � <sup>y</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xj � <sup>x</sup> � �<sup>2</sup> <sup>þ</sup> yj � <sup>y</sup>

In the process, the previously recorded baseline data are subtracted from the field-sensing signals. Then, the pixel intensity is determined by calculating the amplitude information contained in the combined backward signals. Both of the algorithms have full summation form

where N is the number of transducers, sij is the amplitude information of scattering signals, tij is the arrival time of scattering signals. The quality of image produced improves rapidly with

The window-modulated ellipse imaging algorithm is proposed in Ref. [4]. Many auxiliary signal processing techniques are developed for enhancing the imaging performance, such as the scattering signal normalization to eliminate the different path sensitivity to damage and extract damage information with the complex Morlet wavelet coefficient [5], the temperature effect compensation technique to ensure the detection quality [6], consideration of the velocity

Tomography technique works with specific designed transducer array to reconstruct a physical quantity in a cross-sectional area by analyzing Lamb waves attenuation, velocity, and mode conversion from the projection of the quantity in all directions. There are three classical transducer configuration existed in tomographic detection, parallel tomography, fan beam tomography, and crosshole tomography [9]. Figure 1 plots the typical spatial distributions of transducers working with different tomography mechanisms in which the parallel array working with a parallel tomography at 0�, circular array working with fan beam tomography at 0�, and square array working with crosshole tomography are shown in Figure 1(a), (b) and (c), respectively. In the parallel array, the transducers are scanned along parallel lines. Once the pitch-catch measurements for each ray in an individual orientation have been taken, the sample is rotated by a fixed amount and the measurement is repeated. The ray density is

directionality [2], and damage information extraction with statistical method [7, 8].

� �<sup>2</sup>

� �<sup>2</sup>

sij tij½ � <sup>x</sup>; <sup>y</sup> � �, ð Þ Full summation

sij tij½ � <sup>x</sup>; <sup>y</sup> � �, Full multiplicaton � � ,

=cg, Elliptical trajectory � �

http://dx.doi.org/10.5772/intechopen.79475

<sup>=</sup>cg, Hyperbola trajecory � � ;

(1)

89

(2)

trajectory, respectively. Their calculation formulas are expressed as

þ

�

! r

! r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

and full multiplication form and can be expressed as

1 N2 X N

8 >>>>><

>>>>>:

1 N2 Y N

i¼1

i¼1

X N

<sup>j</sup>¼<sup>1</sup>, <sup>i</sup>6¼<sup>j</sup>

Y N

<sup>j</sup>¼<sup>1</sup>, <sup>i</sup>6¼<sup>j</sup>

I xð Þ¼ ; y

the increase of the transducer number.

2.2. Tomography techniques

<sup>2</sup> <sup>þ</sup> yi � <sup>y</sup> � �<sup>2</sup> <sup>q</sup>

<sup>2</sup> <sup>þ</sup> yi � <sup>y</sup> � �<sup>2</sup> <sup>q</sup>

ð Þ xi � x

ð Þ xi � x

tij ¼

8 >>>>><

>>>>>:

In this chapter, the defect imaging techniques and intelligent recognition techniques are briefly reviewed. Considering the settings of detection/monitoring system, we roughly divide the defect imaging algorithms into four categories: spare array imaging techniques, tomography techniques, compact array imaging techniques, and full wavefield imaging techniques. The basic principle of them is introduced in Section 2. In Section 3, the intelligent recognition techniques used to process Lamb waves signals and defect feature recognition are introduced. Finally, a short summary and conclusion are provided.

## 2. Defect imaging techniques

When a set of Lamb waves signals are received at spatially distributed positions, the techniques map the received time-domain signals that have or have not been processed with the signal optimization techniques into a 2D or 3D space-domain based on the ToF or beam directivity for defect location (sizing are termed the defect imaging techniques). Considering the distribution of the signal received position, we roughly divide these techniques into four categories: sparse array imaging techniques, tomography techniques, compact array imaging techniques, and full wavefield imaging techniques.

## 2.1. Sparse array imaging techniques

In a sparse array, the adjacent transducers are far separated from each other that provide higher coverage with fewer transducers at the cost of imaging resolution. Discrete ellipse imaging technique [1, 2] and the hyperbola imaging technique [3] are ToF imaging algorithms and map the amplitude information of scattering signals to elliptical trajectory and hyperbola trajectory, respectively. Their calculation formulas are expressed as

$$t\_{\vec{\eta}} = \begin{cases} \left(\sqrt{\left(\mathbf{x}\_{i} - \mathbf{x}\right)^{2} + \left(\mathbf{y}\_{i} - \mathbf{y}\right)^{2}} + \sqrt{\left(\mathbf{x}\_{\vec{\eta}} - \mathbf{x}\right)^{2} + \left(\mathbf{y}\_{j} - \mathbf{y}\right)^{2}}\right) / c\_{\mathcal{S}^{\prime}} & \text{(Elliptic trajectory)}\\ \left(\sqrt{\left(\mathbf{x}\_{i} - \mathbf{x}\right)^{2} + \left(\mathbf{y}\_{i} - \mathbf{y}\right)^{2}} - \sqrt{\left(\mathbf{x}\_{\vec{\eta}} - \mathbf{x}\right)^{2} + \left(\mathbf{y}\_{j} - \mathbf{y}\right)^{2}}\right) / c\_{\mathcal{S}^{\prime}} & \text{(Hyperbola trajectory)} \end{cases}, \tag{1}$$

In the process, the previously recorded baseline data are subtracted from the field-sensing signals. Then, the pixel intensity is determined by calculating the amplitude information contained in the combined backward signals. Both of the algorithms have full summation form and full multiplication form and can be expressed as

$$I(\mathbf{x}, y) = \begin{cases} \frac{1}{N^2} \sum\_{i=1}^{N} \sum\_{j=1, j \neq j}^{N} s\_{ij}(t\_{\vec{\eta}}[\mathbf{x}, y]), & \text{(Full summation)}\\ \frac{1}{N^2} \prod\_{i=1}^{N} \prod\_{j=1, j \neq j}^{N} s\_{ij}(t\_{\vec{\eta}}[\mathbf{x}, y]), & \text{(Full multiplication)} \end{cases} \tag{2}$$

where N is the number of transducers, sij is the amplitude information of scattering signals, tij is the arrival time of scattering signals. The quality of image produced improves rapidly with the increase of the transducer number.

The window-modulated ellipse imaging algorithm is proposed in Ref. [4]. Many auxiliary signal processing techniques are developed for enhancing the imaging performance, such as the scattering signal normalization to eliminate the different path sensitivity to damage and extract damage information with the complex Morlet wavelet coefficient [5], the temperature effect compensation technique to ensure the detection quality [6], consideration of the velocity directionality [2], and damage information extraction with statistical method [7, 8].

#### 2.2. Tomography techniques

defects, and that may be contained in received Lamb waves signals during the Lamb waves structural integrity evaluation. To clearly show out the state of the structures, many kinds of defect imaging and recognition techniques are proposed for analyzing the change of the signal parameters based on the settings of detection/monitoring systems during the past decades. In laboratory and practical field applications of Lamb waves based structure integrity evaluation, the detection/monitoring systems have two basic setting strategies. Firstly, Lamb waves signals are emitted and sensed at relatively small number of spatially distributed position by transducers that have the same or different transduction mechanisms. These positions are maybe distributed in sparse (adjacent transducer spacing is larger than the largest wavelength of signals) or compact (adjacent transducer spacing is shorter than the shortest wavelength of signals) array forms. Collaborative with different signal excitation and detection strategies, signal processing techniques are developed for integrity detection/monitoring in the whole structure. The other strategy is a full-scale scanning of the surface of structures with laser ultrasonic systems, air-coupled scanning systems, to obtain the full wavefield of Lamb waves. On the basis of the above detection/monitoring system setting strategies, Lamb waves signals used for damage detection/monitoring are obtained. Then, signal processing techniques are adopted to analyze the change of signal parameters to extract the damage information such as the amplitudes, velocity, phase, frequency, etc. Finally, defect influence maps and intelligent recognition models that indicating defect information are achieved with imaging and recogni-

In this chapter, the defect imaging techniques and intelligent recognition techniques are briefly reviewed. Considering the settings of detection/monitoring system, we roughly divide the defect imaging algorithms into four categories: spare array imaging techniques, tomography techniques, compact array imaging techniques, and full wavefield imaging techniques. The basic principle of them is introduced in Section 2. In Section 3, the intelligent recognition techniques used to process Lamb waves signals and defect feature recognition are introduced.

When a set of Lamb waves signals are received at spatially distributed positions, the techniques map the received time-domain signals that have or have not been processed with the signal optimization techniques into a 2D or 3D space-domain based on the ToF or beam directivity for defect location (sizing are termed the defect imaging techniques). Considering the distribution of the signal received position, we roughly divide these techniques into four categories: sparse array imaging techniques, tomography techniques, compact array imaging

In a sparse array, the adjacent transducers are far separated from each other that provide higher coverage with fewer transducers at the cost of imaging resolution. Discrete ellipse

Finally, a short summary and conclusion are provided.

techniques, and full wavefield imaging techniques.

2. Defect imaging techniques

88 Structural Health Monitoring from Sensing to Processing

2.1. Sparse array imaging techniques

tion techniques.

Tomography technique works with specific designed transducer array to reconstruct a physical quantity in a cross-sectional area by analyzing Lamb waves attenuation, velocity, and mode conversion from the projection of the quantity in all directions. There are three classical transducer configuration existed in tomographic detection, parallel tomography, fan beam tomography, and crosshole tomography [9]. Figure 1 plots the typical spatial distributions of transducers working with different tomography mechanisms in which the parallel array working with a parallel tomography at 0�, circular array working with fan beam tomography at 0�, and square array working with crosshole tomography are shown in Figure 1(a), (b) and (c), respectively. In the parallel array, the transducers are scanned along parallel lines. Once the pitch-catch measurements for each ray in an individual orientation have been taken, the sample is rotated by a fixed amount and the measurement is repeated. The ray density is

is the path number of the pitch-catch transducers numbered as i and j, respectively, Rij

are reviewed in [17].

IFBPð Þ¼ x; y

tion direction over the image plane.

ð<sup>2</sup><sup>π</sup> 0

projection method and (b) situation of the ith path crossing the specimen.

ðþ<sup>∞</sup> -∞

QθðÞ¼ t

Fð Þ ω; θ e

ðþ<sup>∞</sup> �∞

Fð Þ ω; θ e

where IFBP(x,y) is the pixel value in the imaging zone, F(ω,θ) is the spatial Fourier transform of a line integral of the attenuation f(x,y) in a polar coordinate system o-θ, Qθ(t) is called a filtered projection because it represents a spatial frequency filtering operation, in which the filter response is |ω|. Every point (x,y) in the image plane is contributed by a value Qθ(t) from all direction θ. For a given direction θ, the function Qθ(t) is a constant on the line AB, where t is fixed as shown in Figure 2(a). This is equivalent to saying that the filtered projection function Qθ(t), which is obtained from angle θ and position t, is back-projected along the initial projec-

Figure 2. Principle of fan beam projection and algebraic reconstruction technique. (a) Principle of the filtered back-

expressed as

related to both the distance from point (x, y) to the two transducers for excitation (xi, yi) and sensing (xj, yj) and the distance between the two transducers, β controls the size of the ellipse and β > 1. If β is too small, then artifacts will be introduced. If it is too large, the resolution will be lost. Usually, β is setting around 1.05 [16]. The technique for relative relationship calculation algorithms can be used to acquire the value of r, such as correlation coefficient method, time reversal method, baseline subtraction method, etc. More damage index calculation methods

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

Filtered back-projection (FBP) combines the back-projection and the filter based on the Radon transform and Fourier slice theorem. Only with a circular sensor array, FBP method has efficiency of reconstruction and incomplete datasets, and unfortunately is sensitive to noise. It is essential to form a complete set of projections from many directions. Its formulas can be

<sup>i</sup>2πωð Þ <sup>x</sup>cosθþysin<sup>θ</sup> <sup>ω</sup>dωd<sup>θ</sup> <sup>¼</sup>

i2πωt

ðπ 0

Qθð Þt dθ, (6)

j j ω dω, (7)

http://dx.doi.org/10.5772/intechopen.79475

<sup>n</sup>ð Þ x; y is

91

Figure 1. Typical spatial distributions of transducers working with different tomography mechanisms. (a) Parallel array working with a parallel tomography at 0�, (b) circular array working with fan beam tomography at 0�, and (c) square array working with crosshole tomography.

uniform for parallel projection tomography within the scanning region that is critical to the quality of the reconstruction. Crosshole configuration is a fast and practical alternative to the parallel-projection scheme in which transducers surround the detection zone to improve the ray density. The classical tomographic image reconstruction algorithms have the probabilistic reconstruction algorithms, transform methods, and iteration-based algorithms.

The probabilistic reconstruction algorithms (PRAs) are processed with the probabilistic statistical techniques to analyze the difference among the parameters for all the rays, including the ToF, waveforms, and energy [10]. The PRA has the flexibility in array geometry selection that can realize good reconstruction quality in fast speed. In the analysis, the ray theory needs to satisfy two validity criteria: the geometry size of the defect must be larger than the wavelength and larger than the width of the Fresnel zone. The waveform overlapping caused by reflection echoes of multidefects may make the TOF calculation inaccurate and fail the ray theory. The probabilistic inspection of damage (RAPID) [11, 12] method is a typical PRA that has been studied in Lamb waves based structure integrity evaluation in which variable shape factor is used for irregular shape defect imaging [13]. Keulen et al. [14] introduced the damage progression history into RAPID for composite structure detection. Sheen et al. [15] modified the shape factor, β, of RAPID algorithm to quantify a defect area. The expressions of the RAPID algorithm are

$$I\_{\text{RAPID}}(\mathbf{x}, \mathbf{y}) = \sum\_{n=1}^{N} \left( 1 - \rho\_n^{ij}(\mathbf{x}, \mathbf{y}) \right) \mathcal{W}\_n \left[ R\_n^{ij}(\mathbf{x}, \mathbf{y}) \right],\tag{3}$$

$$\mathcal{W}\_n\left[\mathcal{R}\_n^{ij}(\mathbf{x},y)\right] = \begin{cases} 1 - \frac{\mathcal{R}\_n^{ij}(\mathbf{x},y)}{\beta}, & \mathcal{R}\_n^{ij}(\mathbf{x},y) \le \beta \\\ 0 & \mathcal{R}\_n^{ij}(\mathbf{x},y) > \beta \end{cases} \tag{4}$$

$$R\_n^{ij}(\mathbf{x}, \mathbf{y}) = \frac{\sqrt{(\mathbf{x}\_i - \mathbf{x})^2 + \left(\mathbf{y}\_i - \mathbf{y}\right)^2} + \sqrt{\left(\mathbf{x}\_j - \mathbf{x}\right)^2 + \left(\mathbf{y}\_j - \mathbf{y}\right)^2}}{\sqrt{\left(\mathbf{x}\_i - \mathbf{x}\_j\right)^2 + \left(\mathbf{y}\_i - \mathbf{y}\_j\right)^2}} - 1,\tag{5}$$

where IRAPIDð Þ x; y is the pixel value in the imaging zone, r is the zero-lag cross correlation between the baseline data and the received signals, Wn is the weighted distribution function, n is the path number of the pitch-catch transducers numbered as i and j, respectively, Rij <sup>n</sup>ð Þ x; y is related to both the distance from point (x, y) to the two transducers for excitation (xi, yi) and sensing (xj, yj) and the distance between the two transducers, β controls the size of the ellipse and β > 1. If β is too small, then artifacts will be introduced. If it is too large, the resolution will be lost. Usually, β is setting around 1.05 [16]. The technique for relative relationship calculation algorithms can be used to acquire the value of r, such as correlation coefficient method, time reversal method, baseline subtraction method, etc. More damage index calculation methods are reviewed in [17].

Filtered back-projection (FBP) combines the back-projection and the filter based on the Radon transform and Fourier slice theorem. Only with a circular sensor array, FBP method has efficiency of reconstruction and incomplete datasets, and unfortunately is sensitive to noise. It is essential to form a complete set of projections from many directions. Its formulas can be expressed as

uniform for parallel projection tomography within the scanning region that is critical to the quality of the reconstruction. Crosshole configuration is a fast and practical alternative to the parallel-projection scheme in which transducers surround the detection zone to improve the ray density. The classical tomographic image reconstruction algorithms have the probabilistic

Figure 1. Typical spatial distributions of transducers working with different tomography mechanisms. (a) Parallel array working with a parallel tomography at 0�, (b) circular array working with fan beam tomography at 0�, and (c) square

The probabilistic reconstruction algorithms (PRAs) are processed with the probabilistic statistical techniques to analyze the difference among the parameters for all the rays, including the ToF, waveforms, and energy [10]. The PRA has the flexibility in array geometry selection that can realize good reconstruction quality in fast speed. In the analysis, the ray theory needs to satisfy two validity criteria: the geometry size of the defect must be larger than the wavelength and larger than the width of the Fresnel zone. The waveform overlapping caused by reflection echoes of multidefects may make the TOF calculation inaccurate and fail the ray theory. The probabilistic inspection of damage (RAPID) [11, 12] method is a typical PRA that has been studied in Lamb waves based structure integrity evaluation in which variable shape factor is used for irregular shape defect imaging [13]. Keulen et al. [14] introduced the damage progression history into RAPID for composite structure detection. Sheen et al. [15] modified the shape factor, β, of RAPID

reconstruction algorithms, transform methods, and iteration-based algorithms.

algorithm to quantify a defect area. The expressions of the RAPID algorithm are

N

<sup>1</sup> � <sup>r</sup>ij

<sup>n</sup>ð Þ <sup>x</sup>; <sup>y</sup> � �Wn Rij

<sup>n</sup>ð Þ x; y <sup>β</sup> , Rij

þ

� �<sup>2</sup> <sup>þ</sup> yi � yj

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0 , Rij

<sup>n</sup>ð Þ x; y ≤ β

,

<sup>n</sup>ð Þ x; y > β

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xj � <sup>x</sup> � �<sup>2</sup> <sup>þ</sup> yj � <sup>y</sup> � �<sup>2</sup> <sup>r</sup>

� �<sup>2</sup> <sup>r</sup> � <sup>1</sup>, (5)

<sup>n</sup>ð Þ <sup>x</sup>; <sup>y</sup> � �, (3)

(4)

n¼1

8 ><

>:

xi � xj

where IRAPIDð Þ x; y is the pixel value in the imaging zone, r is the zero-lag cross correlation between the baseline data and the received signals, Wn is the weighted distribution function, n

<sup>n</sup>ð Þ <sup>x</sup>; <sup>y</sup> � � <sup>¼</sup> <sup>1</sup> � Rij

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup> <sup>þ</sup> yi � <sup>y</sup> � �<sup>2</sup> <sup>q</sup>

<sup>I</sup>RAPIDð Þ¼ <sup>x</sup>; <sup>y</sup> <sup>X</sup>

ð Þ xi � x

Wn Rij

Rij <sup>n</sup>ð Þ¼ x; y

array working with crosshole tomography.

90 Structural Health Monitoring from Sensing to Processing

$$I\_{\rm FBP}(\mathbf{x}, y) = \int\_0^{2\pi} \int\_{\rm \tau^\infty}^{+\infty} F(\omega, \theta) e^{j2\pi\omega(\mathbf{x}\cos\theta + y\sin\theta)} \omega d\omega d\theta = \int\_0^\pi Q\_\theta(t) d\theta,\tag{6}$$

$$Q\_{\theta}(t) = \int\_{-\infty}^{+\infty} F(\omega, \theta) e^{j2\pi\omega t} |\omega| d\omega,\tag{7}$$

where IFBP(x,y) is the pixel value in the imaging zone, F(ω,θ) is the spatial Fourier transform of a line integral of the attenuation f(x,y) in a polar coordinate system o-θ, Qθ(t) is called a filtered projection because it represents a spatial frequency filtering operation, in which the filter response is |ω|. Every point (x,y) in the image plane is contributed by a value Qθ(t) from all direction θ. For a given direction θ, the function Qθ(t) is a constant on the line AB, where t is fixed as shown in Figure 2(a). This is equivalent to saying that the filtered projection function Qθ(t), which is obtained from angle θ and position t, is back-projected along the initial projection direction over the image plane.

Figure 2. Principle of fan beam projection and algebraic reconstruction technique. (a) Principle of the filtered backprojection method and (b) situation of the ith path crossing the specimen.

The key to FBP tomographic image is the Fourier slice theorem that relates the measured projection data to the 2D Fourier transform of the object cross section. Wright et al. [18] used the FBP technique to image defects in isotropic and anisotropic plates of different materials using air-coupled Lamb wave tomography. Mokhtari et al. [19] proposed a polygon reconstruction technique for polygonal damage shape reconstruction. First, the projections (Radon transform) of the damaged region are generated from a small number of angles with the aid of beamforming method. Then, the damaged region is modeled by a polygon, which its optimal number of vertices is estimated using the minimum description length principle. Finally, using the polygon reconstruction technique, the coordinates of the vertices are determined. While in practice, it is not possible to measure a large number of projections in FBP that may induce the aliasing distortions by insufficiency of the input data, necessary for the transform-based techniques to produce highly accurate results. Researchers developed the interpolated FBP in which interpolations with respect to sample angle and projection angle based on limit measurements are used to generate the required projection data for the number of sampled grid values necessary for displaying a well-balanced reconstructed image. Meanwhile, it should constrain the projection data at a source point to zero when using the interpolation, rather than using extrapolation to generate projection data. Figure 2(a) plots the principle of the filtered back-projection method [20]. The formula, Ifan\_FBPð Þ x; y , of the fan beam-based FBP can be expressed as

$$I\_{\text{fan\\_FBP}}(\mathbf{x}, y) = \frac{2\pi}{M} \sum\_{i=1}^{M} \frac{Q\_{\beta i}(\boldsymbol{\gamma})}{L^2(\mathbf{x}, y, \beta\_i)},\tag{8}$$

attenuation coefficient for i

frequency dependent.

to j

th path in j

used in each step, and an iteration consists of m steps.

xk,<sup>0</sup> <sup>¼</sup> xk

xkþ<sup>1</sup> <sup>¼</sup> xk,m

xk,i <sup>¼</sup> xk,i�<sup>1</sup> <sup>þ</sup> <sup>λ</sup><sup>k</sup>

th grid. Here, m represents the number of paths and n represents the number of grids.

bi � ai

ai k k<sup>2</sup> 2

Though compared with the FBP technique, ART has many advantages including better noise tolerance and better handling of the insufficiently distributed projection datasets that are induced by the spare and nonuniformly distributed projection data, it has slow speed due to iteration process. Wang et al. [22] used the ART to locate and quantify the corrosion damage at the edge of holes. In order to make the tomographic image describe the real condition of the damage, a homogenization method was designed to make the image smoother. Improved tomograms as a result of ART consider the anisotropic and attenuation characteristics of composite plates [23]. The technique based on the similarity theory is the simultaneous iterative reconstruction technique (SIRT). Malyarenko et al. [24] described the basic principle of SIRT for Lamb waves tomography that working with travel time data. In the research, the bend ray routines of a moderately scattered wavefiled was transformed into straight routines with a ray bending correction technique. The output image from the present straight ray algorithm serves as an input background for the ray tracing routine. The curved-ray ART then reconstructs the updated image and feed the next iteration until the desired quality or asymptotic behavior is observed. Miller et al. [25] used SIRT to process the multiple-mode Lamb wave signals for feature extraction of corrosion thinning for autonomous classification of flaw severity. This technique also termed diffraction tomography (DT) technique incorporates scattering effect into tomographic algorithms in order to improve the image quality and resolution. Mode conversion frequency occurs on defect boundaries, and dispersion makes all quantities

Figure 3 plots the stages of accuracy thickness mapping tomography algorithms. Inhomogeneity objects are as small as 5% of the background; multiple scattering can introduce severe distortions in multicomponent objects [26]. The hybrid algorithm for robust breast ultrasound tomography (HARBUT) uses the low-resolution bent-ray tomography algorithm as the background for DT [27] in which bent-ray tomography can be applied initially to obtain a lowresolution estimate of the velocity field; this then forms the background for the DT method using the technique outlined above. Meanwhile, the subtraction is not necessary to obtain a

xk,i�<sup>1</sup>

In the ART, a weight matrix is constructed as a rectangular array whose size is equal to the number of paths multiplied by the number of grids. From the projections (measured data) and the weight matrix (created from sensor locations and ray geometry), the field value that maps the state of the inspection zone (correlation coefficient) is obtained using the ART method. The iterative solution to the reconstruction problem in ART is constructed by Ladas and Deveaney [21]. The iteration operation of Eq. (9) is expressed as Eq. (12) [23] in which one equation is

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

th grid, and the Lij represents the real length for i

, i ¼ 1, 2, ⋯, m

th projected

93

http://dx.doi.org/10.5772/intechopen.79475

(12)

where Qβi(nα) is the filtered projection along the fan, M is the number of projections, and L is the distance from the transmitter to the point (x,y). β<sup>i</sup> is the i th projection angle and γ is the angle of the fan beam ray passing through the point (x,y).

The algebraic reconstruction technique (ART) starts from an initial guess for the reconstructed object and then performs a sequence of iterative grid projections and correction backprojections until the reconstruction has converged. Its formulae are expressed in Eqs. (9)–(11).

$$A\_{i \times j} \times \mathbf{x}\_{j \times 1} = b\_{i \times 1} \tag{9}$$

$$b\_{i \times 1} = \int\_{\S} X(i, j) dl\_{ij} \tag{10}$$

$$
\begin{pmatrix} b\_1 \\ \vdots \\ b\_i \\ \vdots \\ b\_m \end{pmatrix} = k \begin{pmatrix} L\_{11} & \cdots & L\_{1j} & \cdots & L\_{1n} \\ \vdots & & \vdots & & \vdots \\ L\_{i1} & \cdots & L\_{ij} & & L\_{mj} \\ \vdots & & \vdots & & \vdots \\ L\_{m1} & \cdots & L\_{mj} & \cdots & L\_{mn} \end{pmatrix} \begin{pmatrix} \mathbf{x}\_1 \\ \vdots \\ \mathbf{x}\_i \\ \vdots \\ \mathbf{x}\_m \end{pmatrix} \tag{11}
$$

where Ai�<sup>j</sup> represents the weight of i th path in j th grid, x represents the image results for each cell, and bi � <sup>1</sup> represents the change of signal feature (correlation) for each path. X(i,j) is the attenuation coefficient for i th path in j th grid, and the Lij represents the real length for i th projected to j th grid. Here, m represents the number of paths and n represents the number of grids.

The key to FBP tomographic image is the Fourier slice theorem that relates the measured projection data to the 2D Fourier transform of the object cross section. Wright et al. [18] used the FBP technique to image defects in isotropic and anisotropic plates of different materials using air-coupled Lamb wave tomography. Mokhtari et al. [19] proposed a polygon reconstruction technique for polygonal damage shape reconstruction. First, the projections (Radon transform) of the damaged region are generated from a small number of angles with the aid of beamforming method. Then, the damaged region is modeled by a polygon, which its optimal number of vertices is estimated using the minimum description length principle. Finally, using the polygon reconstruction technique, the coordinates of the vertices are determined. While in practice, it is not possible to measure a large number of projections in FBP that may induce the aliasing distortions by insufficiency of the input data, necessary for the transform-based techniques to produce highly accurate results. Researchers developed the interpolated FBP in which interpolations with respect to sample angle and projection angle based on limit measurements are used to generate the required projection data for the number of sampled grid values necessary for displaying a well-balanced reconstructed image. Meanwhile, it should constrain the projection data at a source point to zero when using the interpolation, rather than using extrapolation to generate projection data. Figure 2(a) plots the principle of the filtered back-projection method [20]. The formula, Ifan\_FBPð Þ x; y , of the fan beam-based FBP can be

Ifan\_FBPð Þ¼ x; y

the distance from the transmitter to the point (x,y). β<sup>i</sup> is the i

angle of the fan beam ray passing through the point (x,y).

92 Structural Health Monitoring from Sensing to Processing

b1 ⋮ bi ⋮ bm 1

0

BBBBBB@

CCCCCCA ¼ k

0

BBBBBB@

where Ai�<sup>j</sup> represents the weight of i

2π M X M

where Qβi(nα) is the filtered projection along the fan, M is the number of projections, and L is

The algebraic reconstruction technique (ART) starts from an initial guess for the reconstructed object and then performs a sequence of iterative grid projections and correction backprojections until the reconstruction has converged. Its formulae are expressed in Eqs. (9)–(11).

> L<sup>11</sup> ⋯ L1<sup>j</sup> ⋯ L1<sup>n</sup> ⋮ ⋮⋮ Li<sup>1</sup> ⋯ Lij Lmj ⋮ ⋮⋮ Lm<sup>1</sup> ⋯ Lmj ⋯ Lmn

bi�<sup>1</sup> ¼ ð j

th path in j

cell, and bi � <sup>1</sup> represents the change of signal feature (correlation) for each path. X(i,j) is the

i¼1

Qβ<sup>i</sup>ð Þ γ <sup>L</sup><sup>2</sup> <sup>x</sup>; <sup>y</sup>; <sup>β</sup><sup>i</sup>

� � , (8)

Ai�<sup>j</sup> � xj�<sup>1</sup> ¼ bi�<sup>1</sup> (9)

x1 ⋮ xi ⋮ xm

1

0

BBBBBB@

CCCCCCA

X ið Þ ; j dlij (10)

1

CCCCCCA

th grid, x represents the image results for each

th projection angle and γ is the

(11)

expressed as

In the ART, a weight matrix is constructed as a rectangular array whose size is equal to the number of paths multiplied by the number of grids. From the projections (measured data) and the weight matrix (created from sensor locations and ray geometry), the field value that maps the state of the inspection zone (correlation coefficient) is obtained using the ART method. The iterative solution to the reconstruction problem in ART is constructed by Ladas and Deveaney [21]. The iteration operation of Eq. (9) is expressed as Eq. (12) [23] in which one equation is used in each step, and an iteration consists of m steps.

$$\begin{aligned} \mathbf{x}^{k,0} &= \mathbf{x}^k\\ \mathbf{x}^{k,i} &= \mathbf{x}^{k,i-1} + \lambda\_k \frac{b\_i - a^i \mathbf{x}^{k,i-1}}{||a^i||\_2^2}, \ i = 1, 2, \cdots, m \\ \mathbf{x}^{k+1} &= \mathbf{x}^{k,m} \end{aligned} \tag{12}$$

Though compared with the FBP technique, ART has many advantages including better noise tolerance and better handling of the insufficiently distributed projection datasets that are induced by the spare and nonuniformly distributed projection data, it has slow speed due to iteration process. Wang et al. [22] used the ART to locate and quantify the corrosion damage at the edge of holes. In order to make the tomographic image describe the real condition of the damage, a homogenization method was designed to make the image smoother. Improved tomograms as a result of ART consider the anisotropic and attenuation characteristics of composite plates [23]. The technique based on the similarity theory is the simultaneous iterative reconstruction technique (SIRT). Malyarenko et al. [24] described the basic principle of SIRT for Lamb waves tomography that working with travel time data. In the research, the bend ray routines of a moderately scattered wavefiled was transformed into straight routines with a ray bending correction technique. The output image from the present straight ray algorithm serves as an input background for the ray tracing routine. The curved-ray ART then reconstructs the updated image and feed the next iteration until the desired quality or asymptotic behavior is observed. Miller et al. [25] used SIRT to process the multiple-mode Lamb wave signals for feature extraction of corrosion thinning for autonomous classification of flaw severity. This technique also termed diffraction tomography (DT) technique incorporates scattering effect into tomographic algorithms in order to improve the image quality and resolution. Mode conversion frequency occurs on defect boundaries, and dispersion makes all quantities frequency dependent.

Figure 3 plots the stages of accuracy thickness mapping tomography algorithms. Inhomogeneity objects are as small as 5% of the background; multiple scattering can introduce severe distortions in multicomponent objects [26]. The hybrid algorithm for robust breast ultrasound tomography (HARBUT) uses the low-resolution bent-ray tomography algorithm as the background for DT [27] in which bent-ray tomography can be applied initially to obtain a lowresolution estimate of the velocity field; this then forms the background for the DT method using the technique outlined above. Meanwhile, the subtraction is not necessary to obtain a

Lamb waves through corrosion defects and an iterative inverse model to reconstruct the corrosion profile. The aim of the tomography is to reconstruct the object function, which is a mathematical representation of the defect and is formulated in terms of velocity. The FWI algorithm proceeds from a starting velocity model to refine the velocity model in order to reduce the residual wavefield between the predicted data by the current model and the observed data from FE simulations or experiments. The predicted data are obtained by using frequency-domain finite difference method. It overcomes the limitation imposed by ignoring crucial low-frequency effects in travel time tomography. The FWI can obtain a resolution of around 0.7 wavelengths for defects with smooth depth variations from the acoustic modeling data, and about 1.52.0 wavelengths from the elastic modeling data. The defect abrupt change in the wall thickness has been shown to decrease the reconstruction error of small defects compared to the smoothly varying thickness, for larger defects with sharper change in thickness, they are more likely to lead to overestimation in depth [29]. FWI allows higher order diffraction and scattering to be considered in its numerical solver, thus it has the potential to

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achieve more accurate inversion results, especially when multiple defects exist.

Phase array (PA) technique and the synthetic aperture (SA) technique are widely performed based on the compact arrays in which the spacing between the adjacent transducers is shorter than the wavelength. Figure 4 plots the typical compact arrays used for Lamb waves based structure integrity evaluation, such as the linear-phased arrays, circular, square, spiral, and star-shaped arrays [30]. During detection or monitoring, when one of the transducers used as actuator, Lamb waves signals are captured by all the rest transducers, then next transducer is chosen and used as actuator and capture the signal data until all the transducers have been

Figure 4. Typical compact arrays used for Lamb waves based structure integrity evaluation. (a) Linear, (b) cross-shaped,

2.3. Compact array imaging techniques

(c) rectangular, (d) star-shaped, (e) circular, and (f) spiral.

Figure 3. Stages of accuracy thickness mapping tomography algorithms. (a) HARBUT. (b) FWI algorithm.

good reconstruction, simplifying the process and avoiding these errors. The object function in HARBUT is divided into two components, the known background component O<sup>b</sup> and the perturbation component Oδ. Since there is no need to run forward models, the speed of the algorithm is also improved. While the traditional HARBUT relies on having a sufficiently accurate background reconstruction that should satisfy the Born approximation assumption, iterating HARBUT uses an existing HARBUT reconstruction as the background for another HARBUT stage in place of bent-ray tomography, as illustrated in Figure 3(a). At each step, O<sup>b</sup> becomes more accurate, minimizing O<sup>δ</sup> and allowing HARBUT to produce more accurate velocity maps. Through iteration operation of the HARBUT, small and high contrast defects are successfully imaged. A Gaussian filter is used to smooth the background before the next iteration, which is a form of regularization. This filter aims to remove as many of the artifacts from each iteration as possible, while maintaining the true reconstruction values. Full waveform inversion (FWI) technique is first developed in geophysics for seismic wave imaging in which the process also based on a serious of iteration operation. Rao et al. [28] introduced the FWI in Lamb waves tomography for corrosion mapping. The stages for FWI algorithm is plotted in Figure 3(b) in which a numerical forward model is used to predict the scattering of Lamb waves through corrosion defects and an iterative inverse model to reconstruct the corrosion profile. The aim of the tomography is to reconstruct the object function, which is a mathematical representation of the defect and is formulated in terms of velocity. The FWI algorithm proceeds from a starting velocity model to refine the velocity model in order to reduce the residual wavefield between the predicted data by the current model and the observed data from FE simulations or experiments. The predicted data are obtained by using frequency-domain finite difference method. It overcomes the limitation imposed by ignoring crucial low-frequency effects in travel time tomography. The FWI can obtain a resolution of around 0.7 wavelengths for defects with smooth depth variations from the acoustic modeling data, and about 1.52.0 wavelengths from the elastic modeling data. The defect abrupt change in the wall thickness has been shown to decrease the reconstruction error of small defects compared to the smoothly varying thickness, for larger defects with sharper change in thickness, they are more likely to lead to overestimation in depth [29]. FWI allows higher order diffraction and scattering to be considered in its numerical solver, thus it has the potential to achieve more accurate inversion results, especially when multiple defects exist.

#### 2.3. Compact array imaging techniques

good reconstruction, simplifying the process and avoiding these errors. The object function in HARBUT is divided into two components, the known background component O<sup>b</sup> and the perturbation component Oδ. Since there is no need to run forward models, the speed of the algorithm is also improved. While the traditional HARBUT relies on having a sufficiently accurate background reconstruction that should satisfy the Born approximation assumption, iterating HARBUT uses an existing HARBUT reconstruction as the background for another HARBUT stage in place of bent-ray tomography, as illustrated in Figure 3(a). At each step, O<sup>b</sup> becomes more accurate, minimizing O<sup>δ</sup> and allowing HARBUT to produce more accurate velocity maps. Through iteration operation of the HARBUT, small and high contrast defects are successfully imaged. A Gaussian filter is used to smooth the background before the next iteration, which is a form of regularization. This filter aims to remove as many of the artifacts from each iteration as possible, while maintaining the true reconstruction values. Full waveform inversion (FWI) technique is first developed in geophysics for seismic wave imaging in which the process also based on a serious of iteration operation. Rao et al. [28] introduced the FWI in Lamb waves tomography for corrosion mapping. The stages for FWI algorithm is plotted in Figure 3(b) in which a numerical forward model is used to predict the scattering of

Figure 3. Stages of accuracy thickness mapping tomography algorithms. (a) HARBUT. (b) FWI algorithm.

94 Structural Health Monitoring from Sensing to Processing

Phase array (PA) technique and the synthetic aperture (SA) technique are widely performed based on the compact arrays in which the spacing between the adjacent transducers is shorter than the wavelength. Figure 4 plots the typical compact arrays used for Lamb waves based structure integrity evaluation, such as the linear-phased arrays, circular, square, spiral, and star-shaped arrays [30]. During detection or monitoring, when one of the transducers used as actuator, Lamb waves signals are captured by all the rest transducers, then next transducer is chosen and used as actuator and capture the signal data until all the transducers have been

Figure 4. Typical compact arrays used for Lamb waves based structure integrity evaluation. (a) Linear, (b) cross-shaped, (c) rectangular, (d) star-shaped, (e) circular, and (f) spiral.

used for Lamb waves emitting. Through analysis of the amplitudes and phase parameters of the received Lamb waves signals, the imaging is performed in a polar coordinate system where each pixel can be defined with its angular position and the distance from the center.

Total focusing method (TFM), also named as delay-and-sum algorithm, is processed with the amplitude information of signals. Using steered and possibly focused beam improves angular resolution in ultrasonic image but it requires scanning of the full structure. It is sensitive to the wavefield profile, signal-to-noise ratio (SNR), and the dispersion nature of Lamb waves [31]. Meanwhile, TFM suffers from large side lobes that result from overlapping echoes that result in the back-propagation. Adaptive imaging methods [32], where the weights are adjusted for each pixel, can offer a significant improvement to the side lobe behavior of TFM. Vector total focusing method, phase coherence factor (PCF), and the sign coherence factor (SCF) use signal phase information to perform the correction action and defect location. Besides achieving the main goal, these methods obtain improvements in lateral resolution and SNR. Implementation of the SCF technique is quite straight forward, operating in real-time, and can be added to any virtually existing beam former to improve the resolution [33]. Compared with amplitudebased imaging techniques, such as the TFM, the phase information-based techniques are no sensitive to Lamb waves dispersion. For enhancing the defect imaging performance, many imaging combination strategies are proposed, including the combination of the TFM and various polarity images or SCF for enhancing damage detection [34–36], the combination of the TFM, and the multiapodization polarity (MAP) technique [36, 37]. The formulas of the TFM and the SCF algorithms are expressed in Eqs. (13) and (14), respectively.

$$I\_{\rm TFM}(\mathbf{x}, y) = \frac{1}{N^2} \sum\_{i=1}^{N} \sum\_{j=1}^{N} a\_{i\bar{j}} \mu\_{i\bar{j}}(\tau\_{i\bar{j}}(\mathbf{x}, y)),\tag{13}$$

the signals are acquired through searching an array steering vectors that is orthogonal to the noise subspace. The MUSIC algorithm can provide the location or the direction-of-arrival of the active sources in the field with its high spatial resolution capability. Han et al. [40] used the timefrequency MUSIC [41] beamforming procedure to eliminate the effects of the direct excitation signals and the boundary-reflected wave signals. It is better than TFM for adjacent defect imaging when the signal-to-noise ratio is lower than 20dB [42]. Figure 5 plots the comparison of

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Decomposition of the time-reversal operator (DORT) refocuses the wave energy back on multiple scatters, even for those that are neither small nor perfectly resolved. The whole DORT process is described in detail in Ref. [43]. DORT algorithm has the capability of individually imaging these scatters by back-propagating the eigenvectors obtained from eigenvalue decomposition of the time-reversal operator, providing separate information about each scatterer. When the scatterers are relatively large compared to the excitation wavelength, a single scatterer may generate multiple significant eigenvalues. In this case, the back-propagation of the eigenvectors can provide a certain amount of information about the relatively large scatterers. Time-reversal multiple signal classification algorithm was originally proposed by Schmidt [44]. Lehman and Devaney [45] developed a combined DORT and MUSIC algorithm, termed DORT-MUSIC, to image multiple buried cylinders in the seismo-acoustic application. He et al. [46] adopted the DORT-MUSIC in space-frequency domain for separating imaging from both the actuator-to-damage and the sensor-to-damage. The dispersion, multimode, and multireflection nature of Lamb waves have serious influence on the imaging performance of

the flow chart of the MVDR and the MUSIC algorithm.

DORT, MUSIC, and DORT-MUSIC.

Figure 5. Comparison of the flow chart of the MVDR and the MUSIC algorithm.

where N is the number of a linear array, aij corresponds to an apodization applied to individual elements to control some characteristics of the acoustic beam, such as main lobe width and side lobe levels, uij(t) is the amplitude time domain data from all transmitter and receiver j; τij(x, y) is the ToF from the transmitter i to the receiver j and passes the point (x, y).

$$I\_{\rm SCF}(\mathbf{x}, \mathbf{z}) = 1 - \sigma, \quad \sigma^2 = 1 - \left[ \frac{1}{N^2} \sum\_{i=1}^N \sum\_{l=1}^N b\_{\vec{\eta}}(\mathbf{r}\_{\vec{\eta}}(\mathbf{x}, \mathbf{z})) \right]^2, \quad b\_{\vec{\eta}}(t) = \begin{cases} -1 & \text{, if } v\_{\vec{\eta}}(t) < 0 \\\ 1 & \text{, if } v\_{\vec{\eta}}(t) \ge 0 \end{cases}, \tag{14}$$

where σ is the standard deviation of the polarity bij(t) of the aperture data; bij(t) is the polarity or algebraic sign of the aperture data.

Minimum variance distortionless response (MVDR), also known as Capon's method, divides the signals into several subspaces. It can minimize the mean output power of the noise and interference. Their weights are determined by finding the vector to suppress undesired modes and incident angles [38]. One challenge associated with MVDR imaging is sensitive to the assumed look direction, which depends upon possibly unknown scattering characteristics [33].

Through adding a diagonal loading term, αI, to S \_ ð Þ ω , to obtain a non-singular S \_ ð Þ ω , in which α is proportional to the power of the received signals [39]. The incident angle and wavenumber of the signals are acquired through searching an array steering vectors that is orthogonal to the noise subspace. The MUSIC algorithm can provide the location or the direction-of-arrival of the active sources in the field with its high spatial resolution capability. Han et al. [40] used the timefrequency MUSIC [41] beamforming procedure to eliminate the effects of the direct excitation signals and the boundary-reflected wave signals. It is better than TFM for adjacent defect imaging when the signal-to-noise ratio is lower than 20dB [42]. Figure 5 plots the comparison of the flow chart of the MVDR and the MUSIC algorithm.

used for Lamb waves emitting. Through analysis of the amplitudes and phase parameters of the received Lamb waves signals, the imaging is performed in a polar coordinate system where

Total focusing method (TFM), also named as delay-and-sum algorithm, is processed with the amplitude information of signals. Using steered and possibly focused beam improves angular resolution in ultrasonic image but it requires scanning of the full structure. It is sensitive to the wavefield profile, signal-to-noise ratio (SNR), and the dispersion nature of Lamb waves [31]. Meanwhile, TFM suffers from large side lobes that result from overlapping echoes that result in the back-propagation. Adaptive imaging methods [32], where the weights are adjusted for each pixel, can offer a significant improvement to the side lobe behavior of TFM. Vector total focusing method, phase coherence factor (PCF), and the sign coherence factor (SCF) use signal phase information to perform the correction action and defect location. Besides achieving the main goal, these methods obtain improvements in lateral resolution and SNR. Implementation of the SCF technique is quite straight forward, operating in real-time, and can be added to any virtually existing beam former to improve the resolution [33]. Compared with amplitudebased imaging techniques, such as the TFM, the phase information-based techniques are no sensitive to Lamb waves dispersion. For enhancing the defect imaging performance, many imaging combination strategies are proposed, including the combination of the TFM and various polarity images or SCF for enhancing damage detection [34–36], the combination of the TFM, and the multiapodization polarity (MAP) technique [36, 37]. The formulas of the

each pixel can be defined with its angular position and the distance from the center.

TFM and the SCF algorithms are expressed in Eqs. (13) and (14), respectively.

is the ToF from the transmitter i to the receiver j and passes the point (x, y).

i¼1

X N

bij <sup>τ</sup>ijð Þ <sup>x</sup>; <sup>z</sup> � � " #<sup>2</sup>

where σ is the standard deviation of the polarity bij(t) of the aperture data; bij(t) is the polarity

Minimum variance distortionless response (MVDR), also known as Capon's method, divides the signals into several subspaces. It can minimize the mean output power of the noise and interference. Their weights are determined by finding the vector to suppress undesired modes and incident angles [38]. One challenge associated with MVDR imaging is sensitive to the assumed look direction, which depends upon possibly unknown scattering characteristics [33].

\_

is proportional to the power of the received signals [39]. The incident angle and wavenumber of

J¼1

N2 X N

ISCFð Þ¼ <sup>x</sup>; <sup>z</sup> <sup>1</sup> � <sup>σ</sup>, <sup>σ</sup><sup>2</sup> <sup>¼</sup> <sup>1</sup> � <sup>1</sup>

96 Structural Health Monitoring from Sensing to Processing

or algebraic sign of the aperture data.

Through adding a diagonal loading term, αI, to S

1 N2 X N

i¼1

where N is the number of a linear array, aij corresponds to an apodization applied to individual elements to control some characteristics of the acoustic beam, such as main lobe width and side lobe levels, uij(t) is the amplitude time domain data from all transmitter and receiver j; τij(x, y)

X N

aijuij <sup>τ</sup>ijð Þ <sup>x</sup>; <sup>y</sup> � �, (13)

, bijðÞ¼ <sup>t</sup> �<sup>1</sup> , if vijð Þ<sup>t</sup> <sup>&</sup>lt; <sup>0</sup>

�

ð Þ ω , to obtain a non-singular S

<sup>1</sup> , if vijð Þ<sup>t</sup> <sup>≥</sup> <sup>0</sup> ,

\_

ð Þ ω , in which α

(14)

J¼1

ITFMð Þ¼ x; y

Decomposition of the time-reversal operator (DORT) refocuses the wave energy back on multiple scatters, even for those that are neither small nor perfectly resolved. The whole DORT process is described in detail in Ref. [43]. DORT algorithm has the capability of individually imaging these scatters by back-propagating the eigenvectors obtained from eigenvalue decomposition of the time-reversal operator, providing separate information about each scatterer. When the scatterers are relatively large compared to the excitation wavelength, a single scatterer may generate multiple significant eigenvalues. In this case, the back-propagation of the eigenvectors can provide a certain amount of information about the relatively large scatterers. Time-reversal multiple signal classification algorithm was originally proposed by Schmidt [44]. Lehman and Devaney [45] developed a combined DORT and MUSIC algorithm, termed DORT-MUSIC, to image multiple buried cylinders in the seismo-acoustic application. He et al. [46] adopted the DORT-MUSIC in space-frequency domain for separating imaging from both the actuator-to-damage and the sensor-to-damage. The dispersion, multimode, and multireflection nature of Lamb waves have serious influence on the imaging performance of DORT, MUSIC, and DORT-MUSIC.

Figure 5. Comparison of the flow chart of the MVDR and the MUSIC algorithm.

Synthetic aperture focusing technique (SAFT) focuses the acoustic field along the 1D linear array toward the location of scatterer based on the angular and the distance information. It is first proposed for body waves defect detection. Sicard et al. [47] presented an F-SAFT algorithm for Lamb waves imaging in which the dispersion nature of Lamb waves is considered. Furthermore, multidefects detection in an isotropic plate was realized. Other algorithms for far-field defect imaging based on the wavenumber analysis have the spatial-wavenumber filter (SWF) [48–50] and wavenumber filtering algorithm [51]. Ren and Qiu [49, 52] proposed a scanning spatial-wavenumber filter-based diagnostic imaging method for online characterization of multi-impact event. The procession does not rely on any modeled or measured wavenumber response. The formulae of SCFT and the SWF are expressed as Eqs. (15)–(18), respectively.

$$I\_{\rm SFT}(\mathbf{x},d) = \text{ifft}\left(\sum\_{f \in \Omega} \mathbf{s}(k\_x, d, f)\right), \text{ s}(k\_x, d, f) = \text{fft}(\mathbf{u}(\mathbf{x}, t)) \exp\left(2\pi d \overline{\sqrt{\left(c\_p(f \times 2h)/2\right)}}^2 - k\_x^2\right), \tag{15}$$

$$I\_{\rm SWF}(k, t\_r) = \sum \left| u(\mathbf{x}, t\_r) \otimes \phi(\mathbf{x}) \right| = \sum \left| 4\pi^2 A(t\_r) \delta(k - k\_4 \cos \theta\_a) \delta(k - k\_4 \cos \theta) \right|, \tag{16}$$

$$A(t\_r) = \mu(t\_r)e^{i\omega t\_r}e^{-i\mathbf{k}\_al\_a},\tag{17}$$

of damage size estimation [56, 57]. Mode separation can be performed similarly for reflection

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

The imaging techniques based on time-domain signal process have the integral mean value (IMV), the root mean square (RMS), and the weighted root mean square (WRMS) [59] that can

> ðt2 t1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

where u(t) is the received signals at n points. For a discrete signal ur=u(tr) sampled at n points with time intervals Δt, following relation can be written as uk=u(tk), tk=t1+(k-1)Δt, Δt=(t2-t1)/ (n-1), k=1,2,…,n. w(t) is a weighting factor, which decreases the importance of the time samples closer to the beginning of the sampling process and increases the importance of the samples closer to its end. t<sup>1</sup> and t<sup>2</sup> denote the beginning and the end of the sampling process, respectively. The weighting factor wk=k (m=1), the importance (weight) of particular time samples, increases linearly with time t; this importance (weight) increases as a square function of time t

The effectiveness of the applied algorithms is strongly dependent on the calculation parameters (weighting factor and time window), excitation frequency, and damage types. The extension of the time window leads to the increase in differences in the WRMS values between the damaged and undamaged areas. The constant weighting factors do not provide efficient results due to the high influence of the incident wave at excitation point. The statistical analysis of the calculated WRMS values was adopted to successfully supplement the visual assessment

The multidimensional Fourier transform maps the time-space domain signals into the frequency-wavenumber domain and realizes defect imaging; the formula of the transform can

where u(x,y,t) is the full wavefield data; a and b are the coordinates of the window function in x and y dimension; W is the window with various of types, including rectangle window, Gauss window, and Hanning window. For a Hanning window with a diameter of Dr, W can be

u xð Þ ; y; t W xð Þ � a; y � b e

ðt2 t1 u tð Þ<sup>2</sup> h idt <sup>s</sup>

u tð Þdt <sup>≈</sup> <sup>1</sup> n Xn k¼1

≈

≈

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n Xn k¼1

� � <sup>s</sup>

1 n Xn k¼1

wk <sup>¼</sup> w tð Þ¼ <sup>k</sup> km, m <sup>≥</sup> <sup>0</sup> (22)

u2 k

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� � <sup>s</sup>

wku<sup>2</sup> k

uk, (19)

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99

�<sup>i</sup>ð Þ <sup>ω</sup>tþkxxþkyy dydxdt, (23)

, (20)

, (21)

t<sup>2</sup> � t<sup>1</sup>

ðt2 t1 w tð Þu tð Þ<sup>2</sup> h idt <sup>s</sup>

1 t<sup>2</sup> � t<sup>1</sup>

1 t<sup>2</sup> � t<sup>1</sup>

<sup>2</sup> (m=2).

IMVð Þ¼ u tð Þ <sup>1</sup>

RMSð Þ¼ u tð Þ

WRMSð Þ¼ u tð Þ

when the weighting factor is wk=k

of the defect imaging [60].

I ω; kx; ky � � <sup>¼</sup> ð∞ �∞ ð∞ �∞ ð∞ �∞

be expressed as

expressed as

separation [58].

be expressed as Eqs. (19)–(22), respectively.

$$\phi(\mathbf{x}) = \left[ e^{\vec{\mathbf{k}}\_{\mathbf{u}} \mathbf{x}\_1 \cos \theta}, e^{\vec{\mathbf{k}}\_{\mathbf{u}} \mathbf{x}\_2 \cos \theta}, \dots, e^{\vec{\mathbf{k}}\_{\mathbf{u}} \mathbf{x}\_m \cos \theta}, \dots, e^{\vec{\mathbf{k}}\_{\mathbf{u}} \mathbf{x}\_M \cos \theta} \right], \tag{18}$$

where ISCFT is the imaging result of SAFT, u(x,t) is the spatial response acquired by the linear array, d is the propagation distance, kx is the wavenumber in x direction; ISWF is the imaging result of the SWF, u(x,tr) is the response acquired at time tr, ⊗ indicates the convolution operation, ϕ(x) is the original spatial-wavenumber filter, a is the number of the transducer, θa, la are the angle and the distance of the damage respectively, ka is the wavenumber at direction θa.

#### 2.4. Full wavefield imaging techniques

With the aid of the laser ultrasonic system, the strategy used for capturing the full propagation wavefield relies on experiment settings in which one transducer at a fixed position and the second transducer as a movable point, actuator-sensor synchronization and signal registration at one point, in a repetitive manner at various locations. The time delay is introduced between consecutive wave excitations in order to wait until the wave fully attenuates. Researchers adopted the compressive sensing algorithm [53, 54] or combined binary search and compressed sensing [55] to improve the efficiency of full wavefield data acquisition. Once timespace wavefield data are acquired, data analysis can be implemented in time-space domain and frequency-wavenumber domain. The original signal process techniques are used for studying the amplitude information to observe the wave reflection with the root mean square and cumulative kinetic energy methods. Moreover, advanced signal processing techniques with 2D Fourier transform [44], such as wavenumber filtering, frequency-wavenumber analysis, space-frequency-wavenumber analysis, local wavenumber domain analysis, give the possibility of damage size estimation [56, 57]. Mode separation can be performed similarly for reflection separation [58].

Synthetic aperture focusing technique (SAFT) focuses the acoustic field along the 1D linear array toward the location of scatterer based on the angular and the distance information. It is first proposed for body waves defect detection. Sicard et al. [47] presented an F-SAFT algorithm for Lamb waves imaging in which the dispersion nature of Lamb waves is considered. Furthermore, multidefects detection in an isotropic plate was realized. Other algorithms for far-field defect imaging based on the wavenumber analysis have the spatial-wavenumber filter (SWF) [48–50] and wavenumber filtering algorithm [51]. Ren and Qiu [49, 52] proposed a scanning spatial-wavenumber filter-based diagnostic imaging method for online characterization of multi-impact event. The procession does not rely on any modeled or measured wavenumber response. The formulae of SCFT and the SWF are expressed as Eqs. (15)–(18),

A, skð Þ¼ <sup>x</sup>; d; f fft u x ð Þ ð Þ ; t exp 2πdi

<sup>i</sup>ωtr e

ikaxmcos<sup>θ</sup>;…;e ikaxMcos<sup>θ</sup> � �, (18)

� <sup>¼</sup> <sup>X</sup> <sup>4</sup>π<sup>2</sup>

ikax2cos<sup>θ</sup>; …;e

where ISCFT is the imaging result of SAFT, u(x,t) is the spatial response acquired by the linear array, d is the propagation distance, kx is the wavenumber in x direction; ISWF is the imaging result of the SWF, u(x,tr) is the response acquired at time tr, ⊗ indicates the convolution operation, ϕ(x) is the original spatial-wavenumber filter, a is the number of the transducer, θa, la are the

With the aid of the laser ultrasonic system, the strategy used for capturing the full propagation wavefield relies on experiment settings in which one transducer at a fixed position and the second transducer as a movable point, actuator-sensor synchronization and signal registration at one point, in a repetitive manner at various locations. The time delay is introduced between consecutive wave excitations in order to wait until the wave fully attenuates. Researchers adopted the compressive sensing algorithm [53, 54] or combined binary search and compressed sensing [55] to improve the efficiency of full wavefield data acquisition. Once timespace wavefield data are acquired, data analysis can be implemented in time-space domain and frequency-wavenumber domain. The original signal process techniques are used for studying the amplitude information to observe the wave reflection with the root mean square and cumulative kinetic energy methods. Moreover, advanced signal processing techniques with 2D Fourier transform [44], such as wavenumber filtering, frequency-wavenumber analysis, space-frequency-wavenumber analysis, local wavenumber domain analysis, give the possibility

A tð Þ¼ <sup>r</sup> u tð Þ<sup>r</sup> e

angle and the distance of the damage respectively, ka is the wavenumber at direction θa.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f 2 cpð Þ <sup>f</sup> � <sup>2</sup><sup>h</sup> <sup>=</sup><sup>2</sup> � �<sup>2</sup> � <sup>k</sup>

vuut

�ikala , (17)

A tð Þ<sup>r</sup> <sup>δ</sup>ð Þ <sup>k</sup> � kacosθ<sup>a</sup> <sup>δ</sup>ð Þ <sup>k</sup> � kacos<sup>θ</sup> � � �

0 @

2 x

�, (16)

1 A,

(15)

respectively.

<sup>I</sup>SCFTð Þ¼ <sup>x</sup>; <sup>d</sup> ifft <sup>X</sup>

ISWFð Þ¼ k; tr

f ∈ Ω

98 Structural Health Monitoring from Sensing to Processing

2.4. Full wavefield imaging techniques

0 @

s kð Þ <sup>x</sup>; d; f

ϕð Þ¼ x e

1

<sup>X</sup> u xð Þ ; tr <sup>⊗</sup> <sup>ϕ</sup>ð Þ<sup>x</sup> � � �

ikax1cos<sup>θ</sup>;e

The imaging techniques based on time-domain signal process have the integral mean value (IMV), the root mean square (RMS), and the weighted root mean square (WRMS) [59] that can be expressed as Eqs. (19)–(22), respectively.

$$\text{IMV}(\boldsymbol{\mu}(t)) = \frac{1}{t\_2 - t\_1} \int\_{t\_1}^{t\_2} \boldsymbol{\mu}(t)dt \approx \frac{1}{n} \sum\_{k=1}^{n} \boldsymbol{\mu}\_{k\prime} \tag{19}$$

$$\text{RMS}(\mu(t)) = \sqrt{\frac{1}{t\_2 - t\_1} \int\_{t\_1}^{t\_2} \left[ \mu(t)^2 \right] dt} \approx \sqrt{\frac{1}{n} \sum\_{k=1}^n \left[ \mu\_k^2 \right]} \tag{20}$$

$$\text{WRMS}(u(t)) = \sqrt{\frac{1}{t\_2 - t\_1} \int\_{t\_1}^{t\_2} \left[ w(t)u(t)^2 \right] dt} \approx \sqrt{\frac{1}{n} \sum\_{k=1}^n \left[ w\_k u\_k^2 \right]} \,\tag{21}$$

$$w\_k = w(t\_k) = k^m, m \ge 0 \tag{22}$$

where u(t) is the received signals at n points. For a discrete signal ur=u(tr) sampled at n points with time intervals Δt, following relation can be written as uk=u(tk), tk=t1+(k-1)Δt, Δt=(t2-t1)/ (n-1), k=1,2,…,n. w(t) is a weighting factor, which decreases the importance of the time samples closer to the beginning of the sampling process and increases the importance of the samples closer to its end. t<sup>1</sup> and t<sup>2</sup> denote the beginning and the end of the sampling process, respectively. The weighting factor wk=k (m=1), the importance (weight) of particular time samples, increases linearly with time t; this importance (weight) increases as a square function of time t when the weighting factor is wk=k <sup>2</sup> (m=2).

The effectiveness of the applied algorithms is strongly dependent on the calculation parameters (weighting factor and time window), excitation frequency, and damage types. The extension of the time window leads to the increase in differences in the WRMS values between the damaged and undamaged areas. The constant weighting factors do not provide efficient results due to the high influence of the incident wave at excitation point. The statistical analysis of the calculated WRMS values was adopted to successfully supplement the visual assessment of the defect imaging [60].

The multidimensional Fourier transform maps the time-space domain signals into the frequency-wavenumber domain and realizes defect imaging; the formula of the transform can be expressed as

$$I(\omega, k\_x, k\_y) = \int\_{-\infty}^{\infty} \int\_{-\infty}^{\infty} \int\_{-\infty}^{\infty} u(\mathbf{x}, y, t) \mathcal{W}(\mathbf{x} - a, y - b) e^{-i \left(at + k\_x x + k\_y y\right)} dy d\mathbf{x} dt,\tag{23}$$

where u(x,y,t) is the full wavefield data; a and b are the coordinates of the window function in x and y dimension; W is the window with various of types, including rectangle window, Gauss window, and Hanning window. For a Hanning window with a diameter of Dr, W can be expressed as

$$W(\mathbf{x}, y) = \begin{cases} 0.5 \left[ 1 - \cos \left( 2\pi \frac{\sqrt{\mathbf{x}^2 + y^2}}{D\_r} \right) \right] & \text{if } \sqrt{\mathbf{x}^2 + y^2} \le 0.5 D\_r \\\ 0 & \text{otherwise} \end{cases} \tag{24}$$

The wavenumber adaptive image filtering is introduced in reference [61] and further expanded in reference [62] in which the data are transformed from Cartesian coordinates to polar coordinates. In the frequency-wavenumber domain, the filtering is applied to separate the different modes or forward and backward waves, as shown in Eq. (25).

$$
\bar{S}(\omega, k\_r; \Theta\_i) = I(\omega, k\_r; \Theta\_i) W(k\_r, \omega), \tag{25}
$$

are adopted for feature extraction, including dynamic wavelet fingerprinting, wavelet transform (CWT, DWT, and wavelet packet decomposition), and statistical features [70]. While the processing of the feature extraction with these techniques may be very time consuming [71] and cannot ensure the feature data are optimally suitable for mapping the state of structures. Additionally, overtrain may be induced with the available dataset for these methods. So, many techniques have been developed to optimize the feature extraction process. The principal component analysis (PCA) is one of the most widely used linear mapping techniques for feature reduction [72, 73]. Nonlinear mapping techniques reduce dimensionality following the criterion which minimizes the difference between interpoint distances of the initial and detection/monitoring feature space, including Sammon mapping, self-organizing maps, and the generative topographic maps [74]. In the following part of this section, we focus on the introduction of the pattern recognition model that attracted relatively more attention in structure integrity evaluation, such as support vector machine,

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101

Support vector machine (SVM) is a supervised learning classifier that uses a kernel function to form a hypothesis space in a high-dimensional feature space for linear and nonlinear classification. The principle schematic diagram of support vector machine is plotted in Figure 6. The kernel function may be a linear, polynomial, sigmoid, or custom kernels. Given a set of training examples that are belonging to two categories, an SVM training algorithm builds a model that assigns the examples to one category or the other. In this case, the SVM is a nonprobabilistic binary linear classifier that is not common in practical application. For nonlinear classification and regression problems, the input data are mapped to another linearly separable space using a nonlinear kernel function ϕ and the normal linear SVM. The least squares support vector machine (LS-SVM) is an improved variant of SVM. It can increase the convergence rate for complex problems [75]. The general formula of the LS-SVM

Figure 6. Principle schematic diagram of support vector machine. (a) Linearly separable space with linear function and

Bayesian methodology, and neural networks.

3.1. Support vector machine

can be expressed as

(b) linearly separable space with nonlinear function.

where <sup>S</sup><sup>~</sup> <sup>ω</sup>; kr ð Þ ; <sup>θ</sup><sup>l</sup> is the separating waves in frequency-wavenumber domain, <sup>I</sup>(ω,kr;θi) is the frequency-wavenumber result of the u(t,r;θ) in polar coordinates; θ<sup>i</sup> is the specific angle index; W(kr,ω) is a 2D window function operating as a filter in frequency-wavenumber domain.

Finally, the filtered data are successively transformed back to the time domain in polar coordinates and Cartesian coordinates.

Harley et al. [63] presented a baseline-free, model-driven, statistical damage detection, and imaging framework for guided waves measured from partial wavefield scans in which the sparse wavenumber analysis, sparse wavenumber synthesis, and data-fitting optimization to accurately model damage-free wavefield data. Kudela et al. [64] combined the time-distance mapping technique and novel Lamb waves focusing technique to realize crack detection. Meanwhile, the temperature effect is compensated by using the temperature-dependent dispersion curve. Pai et al. [65] presented a dynamics-based methodology for accurate damage inspection of thin-walled structures by combining a boundary effect evaluation method for space-wavenumber analysis of measured operational deflection shapes and a conjugate-pair decomposition method for time-frequency analysis of time traces of measured points. Li et al. [66] proposed a correlation filtering-based matching pursuit signal processing approach to realize precise value of time of flight and locating and sizing the delamination in composite beams. Through analysis, the reflection intensity of Lamb waves from an elliptical damage realized defect sizing [67]. Perelli et al. [68] combined the wavelet packet transform and frequency warping to generate a sparse decomposition of the acquired dispersive signal. Tofeldt et al. [69] presented a 2D array and wide-frequency bandwidth technique for Lamb waves phase velocity imaging. Through a discrete Fourier transform, a spectral estimate is obtained for the 2D array in the frequency-phase velocity domain. The variation of the phase velocity is then mapped using a stepwise movement of the 2D array within the complete measurement domain.

## 3. Intelligent recognition techniques

There are mainly two steps for defect recognition in structure integrity evaluation, i.e., feature extraction and classifier design. Time-frequency and time-scale analysis techniques are adopted for feature extraction, including dynamic wavelet fingerprinting, wavelet transform (CWT, DWT, and wavelet packet decomposition), and statistical features [70]. While the processing of the feature extraction with these techniques may be very time consuming [71] and cannot ensure the feature data are optimally suitable for mapping the state of structures. Additionally, overtrain may be induced with the available dataset for these methods. So, many techniques have been developed to optimize the feature extraction process. The principal component analysis (PCA) is one of the most widely used linear mapping techniques for feature reduction [72, 73]. Nonlinear mapping techniques reduce dimensionality following the criterion which minimizes the difference between interpoint distances of the initial and detection/monitoring feature space, including Sammon mapping, self-organizing maps, and the generative topographic maps [74]. In the following part of this section, we focus on the introduction of the pattern recognition model that attracted relatively more attention in structure integrity evaluation, such as support vector machine, Bayesian methodology, and neural networks.

#### 3.1. Support vector machine

W xð Þ¼ ; y

100 Structural Health Monitoring from Sensing to Processing

nates and Cartesian coordinates.

measurement domain.

3. Intelligent recognition techniques

8 ><

>:

0:5 1 � cos 2π

different modes or forward and backward waves, as shown in Eq. (25).

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>x</sup><sup>2</sup> <sup>þ</sup> <sup>y</sup><sup>2</sup> <sup>p</sup> Dr

0 otherwise

if ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>x</sup><sup>2</sup> <sup>þ</sup> <sup>y</sup><sup>2</sup> <sup>p</sup> <sup>≤</sup> <sup>0</sup>:5Dr

<sup>S</sup><sup>~</sup> <sup>ω</sup>; kr ð Þ¼ ; <sup>θ</sup><sup>i</sup> <sup>I</sup> <sup>ω</sup>; kr ð Þ ; <sup>θ</sup><sup>i</sup> W kr ð Þ ; <sup>ω</sup> , (25)

:

(24)

" # !

The wavenumber adaptive image filtering is introduced in reference [61] and further expanded in reference [62] in which the data are transformed from Cartesian coordinates to polar coordinates. In the frequency-wavenumber domain, the filtering is applied to separate the

where <sup>S</sup><sup>~</sup> <sup>ω</sup>; kr ð Þ ; <sup>θ</sup><sup>l</sup> is the separating waves in frequency-wavenumber domain, <sup>I</sup>(ω,kr;θi) is the frequency-wavenumber result of the u(t,r;θ) in polar coordinates; θ<sup>i</sup> is the specific angle index; W(kr,ω) is a 2D window function operating as a filter in frequency-wavenumber domain.

Finally, the filtered data are successively transformed back to the time domain in polar coordi-

Harley et al. [63] presented a baseline-free, model-driven, statistical damage detection, and imaging framework for guided waves measured from partial wavefield scans in which the sparse wavenumber analysis, sparse wavenumber synthesis, and data-fitting optimization to accurately model damage-free wavefield data. Kudela et al. [64] combined the time-distance mapping technique and novel Lamb waves focusing technique to realize crack detection. Meanwhile, the temperature effect is compensated by using the temperature-dependent dispersion curve. Pai et al. [65] presented a dynamics-based methodology for accurate damage inspection of thin-walled structures by combining a boundary effect evaluation method for space-wavenumber analysis of measured operational deflection shapes and a conjugate-pair decomposition method for time-frequency analysis of time traces of measured points. Li et al. [66] proposed a correlation filtering-based matching pursuit signal processing approach to realize precise value of time of flight and locating and sizing the delamination in composite beams. Through analysis, the reflection intensity of Lamb waves from an elliptical damage realized defect sizing [67]. Perelli et al. [68] combined the wavelet packet transform and frequency warping to generate a sparse decomposition of the acquired dispersive signal. Tofeldt et al. [69] presented a 2D array and wide-frequency bandwidth technique for Lamb waves phase velocity imaging. Through a discrete Fourier transform, a spectral estimate is obtained for the 2D array in the frequency-phase velocity domain. The variation of the phase velocity is then mapped using a stepwise movement of the 2D array within the complete

There are mainly two steps for defect recognition in structure integrity evaluation, i.e., feature extraction and classifier design. Time-frequency and time-scale analysis techniques Support vector machine (SVM) is a supervised learning classifier that uses a kernel function to form a hypothesis space in a high-dimensional feature space for linear and nonlinear classification. The principle schematic diagram of support vector machine is plotted in Figure 6. The kernel function may be a linear, polynomial, sigmoid, or custom kernels. Given a set of training examples that are belonging to two categories, an SVM training algorithm builds a model that assigns the examples to one category or the other. In this case, the SVM is a nonprobabilistic binary linear classifier that is not common in practical application. For nonlinear classification and regression problems, the input data are mapped to another linearly separable space using a nonlinear kernel function ϕ and the normal linear SVM. The least squares support vector machine (LS-SVM) is an improved variant of SVM. It can increase the convergence rate for complex problems [75]. The general formula of the LS-SVM can be expressed as

Figure 6. Principle schematic diagram of support vector machine. (a) Linearly separable space with linear function and (b) linearly separable space with nonlinear function.

$$y(\mathbf{x}) = w^T \phi(\mathbf{x}) + b,\tag{26}$$

detection/monitoring. A multivariate regression model is proposed to correlate damage features, the phase change, and normalized amplitude, to the actual crack size [81]. It is a baseline crack size quantification model can also use for more general and complex structures. Prior distributions of model parameters are obtained using the coupon test data. The posterior distribution of the parameters and the posterior distribution of θ in a multivariate regression model are expressed as Eq. (28). A multilevel Bayesian framework is proposed for identifying the position and the effective mechanical properties of the damaged layers in composite laminates [82] in which the framework is initially applied to a set of synthetic signals with increasing levels of noise and complexity. He et al. [83] employed the Bayesian model to determine the crack number, and then, the Bayesian statistical framework was used to identify the crack parameters and the associated uncertainties in beam-like structures. The proposed method is able to accurately identify the number, locations, and sizes of the cracks, and is robust under measurement

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

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103

Bayesian imaging method (BIM) is used to build the likelihood function using the differences between the model predictions and the field observations. The structure is discretized into many small cells, and each cell is assigned an associated probability of damage, such as the location and size. Next, the overall posterior distribution of the parameters can be obtained by combining the prior information about the parameters. The marginal posterior distribution of each parameter is estimated by the samples generated using the Markov-Chain Monte-Carlo method. Given the parameter samples, the probability of damage in each cell is computed using the ratio of the number of samples falling into each cell to the total number of samples. Following the damage probability distribution can be used to construct an image that directly represents the damage location and size. Peng et al. [84] presented a Bayesian imaging technique to simultaneously estimate damage location and size, as well as the corresponding uncertainty bounds. Neerukatti et al. [85] used a sequential Bayesian technique to combine a physics-based damage prognosis model with a data-driven probabilistic damage localization approach for effective damage localization and prognosis in complex metallic structures. Sohn et al. [86] proposed an instantaneous damage diagnosis based on the concepts of time reversal acoustics and consecutive outlier analysis to minimize damage misclassification without rely-

Gaussian mixture model (GMM) is a probability static method for characterizing uncertainties based on unsupervised learning. This method organizes itself according to the nature of the input data with probability distributions without any prior knowledge. The GMM has the advantages of better robustness of uncertainties and high efficiency with lower computational complexity with a relatively small number of model parameters. PCA is used to reduce the dimensions of the extracted multistatistical characteristic parameters of the excited Lamb waves, then training the damage identification system using the GMM [73]. Several statistical characteristic parameters, including the root mean square (RMS), variance, skewness, kurtosis, peak-to-peak (PPK), and K-factor, are extracted as the input for the GMM-processed Lamb wave-based identification model. Qiu et al. [72] proposed an online updating Gaussian mixture model (GMM), for aircraft wings par damage evaluation under time-varying boundary

conditions in which the formulas are expressed as Eqs. (29) and (30).

noise.

ing on past baseline data.

where the term <sup>ϕ</sup>(�) is a nonlinear mapping function, <sup>w</sup> <sup>∈</sup> Rn and <sup>b</sup><sup>∈</sup> <sup>R</sup> are the mode parameters.

SVM is a robust classifier in the existence of noise and more computational efficient than artificial neural network (ANN) [76]. Das et al. [77] developed an one-class SVM algorithm to characterize and classify different damage states in composite laminates by measuring the change in the signature of the Lamb waves that propagates through the anisotropic media under forced excitations. Park et al. [78] used SVM to enhance the damage identification with the extracted damage features. In the study, multifeatures were extracted for mapping the state of structures, including TOF, the root mean square deviations (RMSD) of the impedances, and wavelet coefficients (WC) of Lamb waves. Then, in Ref. [79], the same authors proposed a twostep support vector machine (SVM) classifier for railroad track damage identification that forms optimal separable hyperplanes. In the study, a two-dimensional damage feature space was built with the root mean square deviations (RMSD) of impedance signatures and the sum of square of wavelet coefficients for maximum energy mode of guided waves. In the process, the damage detection was accomplished by the first step-SVM, and damage classification was carried out by the second step-SVM. Sun et al. [80] adopted genetic algorithm to optimize the LS-SVM parameters in which normalized amplitude, phase change, and correlation coefficient were proposed to build the damage features.

#### 3.2. Bayesian methodology

The Bayes' theorem combines a prior belief and the observation regarding the related parameters through the likelihood function to update the distribution of the interested parameters in which the model parameters u can be updated using the observation data θ, as expressed as

$$
\sigma(u) \propto p(u)p(\theta|u),\tag{27}
$$

where p(u) is the prior distribution of the model parameters u that can be a vector for multiple parameters. p(θ|u) is the likelihood function. q(u) is the posterior distribution of updated parameter u.

$$q(\theta|\mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_n) \propto p(\theta) \left(\frac{1}{\sqrt{2\pi}\sigma\_\varepsilon}\right)^n \times \exp\left\{-\frac{1}{2} \sum\_{i=1}^n \left[\frac{\mathbf{x}\_i - M(\theta)}{\sigma\_\varepsilon}\right]^2\right\},\tag{28}$$

where M(θ) is a parameterized model describing the relationship between the signal features and damage information. σ<sup>ε</sup> is the standard deviation of the error term. The posterior distribution of each parameter is estimated by the samples generated with the Markov-Chain Monte-Carlo method.

Bayesian methodology is a probabilistic detection technique that has the ability to consider the uncertainties such as measurement uncertainty, and model parameter uncertainty in damage detection/monitoring. A multivariate regression model is proposed to correlate damage features, the phase change, and normalized amplitude, to the actual crack size [81]. It is a baseline crack size quantification model can also use for more general and complex structures. Prior distributions of model parameters are obtained using the coupon test data. The posterior distribution of the parameters and the posterior distribution of θ in a multivariate regression model are expressed as Eq. (28). A multilevel Bayesian framework is proposed for identifying the position and the effective mechanical properties of the damaged layers in composite laminates [82] in which the framework is initially applied to a set of synthetic signals with increasing levels of noise and complexity. He et al. [83] employed the Bayesian model to determine the crack number, and then, the Bayesian statistical framework was used to identify the crack parameters and the associated uncertainties in beam-like structures. The proposed method is able to accurately identify the number, locations, and sizes of the cracks, and is robust under measurement noise.

y xð Þ¼ wTϕð Þþ <sup>x</sup> b, (26)

q uð Þ∝p uð Þpð Þ θju , (27)

xi � Mð Þ θ σε

, (28)

� �<sup>2</sup> ( )

where the term <sup>ϕ</sup>(�) is a nonlinear mapping function, <sup>w</sup> <sup>∈</sup> Rn and <sup>b</sup><sup>∈</sup> <sup>R</sup> are the mode parame-

SVM is a robust classifier in the existence of noise and more computational efficient than artificial neural network (ANN) [76]. Das et al. [77] developed an one-class SVM algorithm to characterize and classify different damage states in composite laminates by measuring the change in the signature of the Lamb waves that propagates through the anisotropic media under forced excitations. Park et al. [78] used SVM to enhance the damage identification with the extracted damage features. In the study, multifeatures were extracted for mapping the state of structures, including TOF, the root mean square deviations (RMSD) of the impedances, and wavelet coefficients (WC) of Lamb waves. Then, in Ref. [79], the same authors proposed a twostep support vector machine (SVM) classifier for railroad track damage identification that forms optimal separable hyperplanes. In the study, a two-dimensional damage feature space was built with the root mean square deviations (RMSD) of impedance signatures and the sum of square of wavelet coefficients for maximum energy mode of guided waves. In the process, the damage detection was accomplished by the first step-SVM, and damage classification was carried out by the second step-SVM. Sun et al. [80] adopted genetic algorithm to optimize the LS-SVM parameters in which normalized amplitude, phase change, and correlation coefficient

The Bayes' theorem combines a prior belief and the observation regarding the related parameters through the likelihood function to update the distribution of the interested parameters in which the model parameters u can be updated using the observation data θ, as expressed as

where p(u) is the prior distribution of the model parameters u that can be a vector for multiple parameters. p(θ|u) is the likelihood function. q(u) is the posterior distribution of updated

where M(θ) is a parameterized model describing the relationship between the signal features and damage information. σ<sup>ε</sup> is the standard deviation of the error term. The posterior distribution of each parameter is estimated by the samples generated with the Markov-Chain

Bayesian methodology is a probabilistic detection technique that has the ability to consider the uncertainties such as measurement uncertainty, and model parameter uncertainty in damage

� exp � <sup>1</sup>

2 Xn i¼1

ffiffiffiffiffiffi <sup>2</sup><sup>π</sup> <sup>p</sup> σε � �<sup>n</sup>

ters.

were proposed to build the damage features.

102 Structural Health Monitoring from Sensing to Processing

<sup>q</sup>ð Þ <sup>θ</sup>jx1; <sup>x</sup>2;…; xn <sup>∝</sup>pð Þ <sup>θ</sup> <sup>1</sup>

3.2. Bayesian methodology

parameter u.

Monte-Carlo method.

Bayesian imaging method (BIM) is used to build the likelihood function using the differences between the model predictions and the field observations. The structure is discretized into many small cells, and each cell is assigned an associated probability of damage, such as the location and size. Next, the overall posterior distribution of the parameters can be obtained by combining the prior information about the parameters. The marginal posterior distribution of each parameter is estimated by the samples generated using the Markov-Chain Monte-Carlo method. Given the parameter samples, the probability of damage in each cell is computed using the ratio of the number of samples falling into each cell to the total number of samples. Following the damage probability distribution can be used to construct an image that directly represents the damage location and size. Peng et al. [84] presented a Bayesian imaging technique to simultaneously estimate damage location and size, as well as the corresponding uncertainty bounds. Neerukatti et al. [85] used a sequential Bayesian technique to combine a physics-based damage prognosis model with a data-driven probabilistic damage localization approach for effective damage localization and prognosis in complex metallic structures. Sohn et al. [86] proposed an instantaneous damage diagnosis based on the concepts of time reversal acoustics and consecutive outlier analysis to minimize damage misclassification without relying on past baseline data.

Gaussian mixture model (GMM) is a probability static method for characterizing uncertainties based on unsupervised learning. This method organizes itself according to the nature of the input data with probability distributions without any prior knowledge. The GMM has the advantages of better robustness of uncertainties and high efficiency with lower computational complexity with a relatively small number of model parameters. PCA is used to reduce the dimensions of the extracted multistatistical characteristic parameters of the excited Lamb waves, then training the damage identification system using the GMM [73]. Several statistical characteristic parameters, including the root mean square (RMS), variance, skewness, kurtosis, peak-to-peak (PPK), and K-factor, are extracted as the input for the GMM-processed Lamb wave-based identification model. Qiu et al. [72] proposed an online updating Gaussian mixture model (GMM), for aircraft wings par damage evaluation under time-varying boundary conditions in which the formulas are expressed as Eqs. (29) and (30).

$$\phi\left(f\_r|\mu,\Sigma\right) = \sum\_{i=1}^{\mathcal{C}} w\_i \phi\_i\left(f\_r|\mu\_i,\Sigma\_i\right),\tag{29}$$

network, the forward and the backward principles are plotted in Figure 7(a), (b) and (c), respectively. There exists three types of nodes including input nodes, hidden nodes, and output nodes. Except the input layer out, there is a transfer function in each node to transfer input data to the connected nodes in the adjacent layout. The typical transfer function used in a neural network classifier has the unit step (threshold), sigmoid, piecewise linear, and Gaussian. The training of neutral networks consists of the forward propagation and the backward propagation. In the forward propagation process, the input nodes take the feature date into the model. The information is presented as activation values, where each node is given a value, the higher value, the greater activation. Based on the weights, inhibition or excitation, and transfer functions, the activation value is passed from node to node. The activation values at each node are summed. Then, the value is modified based on its transfer function. The activation flows through the network, through hidden layers, until it reaches the output nodes. Then, the difference between the output value and actual value (error) modified with the backward propagation process with gradient descent algorithm until satisfy a stop threshold. The diagnostic efficiency and precision are highly dependent on the network architecture [87]. The traditional artificial neural networks (ANNs) have been adopted in defect recognition such as welding defects [88], delamination in composite structures [89], and composite plates structural health monitoring [90]. De Fenza et al. [91] combined the ANN and the probability ellipse method to determine the location and degree

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Benefiting from the flexible configuration of neural networks, researcher developed many kinds of neural networks used in structure integrity evaluation. Probabilistic neural network (PNN) combines the Bayes decision strategy with the Parzen nonparametric estimator of the probability density functions in which the interpretation of the neural network is in the form of a probability density function. An accepted norm for decision strategies used to classify patterns is that they minimize the "expected risk." Park et al. [92] adopted the PNN and SVM to online monitoring the state of jointed plates in which the extracted damage feature that constructed with the ToF and the wavelet coefficient obtained from wavelet transforms of Lamb wave signals. Kohonen neural network (KNN) has two layers, input layer and output layer, and is used for honeycomb sandwich and carbon fiber composite structures studied in which the amount of neuron in input layer is determined by input vector dimensions [93]. The neurons of output layer layout form a 2D plane. In regression neural networks for pattern recognition, a trained network produces large errors when some parts of the test pattern are not found in the training pattern. The weight-range selection (WRS) method has a supervised multilayer perceptron operating with one hidden layer of neurons and trained using a backpropagation algorithm to eliminate the large errors induced by the case a test pattern not found in the training set [94]. Anaya et al. [95] adopted an artificial immune system (AIS) and the notion of affinity was used for the sake of damage detection and used a fuzzy c-means algorithm is used for damage classification of an aircraft skin panel. Compared with standard Lamb waves based methods, there is no need to directly analyze the complex time-domain traces containing overlapping, multimodal, and dispersive wave propagation. Other kinds of neural networks that have been studied in nondestructive testing have the recurrent neural network (RNN) [96], deep learning network (DLN), and convolutional neural network (CNN).

of defects in aluminum and composite plates.

$$\phi\_i(\boldsymbol{f}\_r|\boldsymbol{\mu}\_i, \boldsymbol{\Sigma}\_i) = \frac{1}{\left(2\pi\right)^{d/2}} \exp\left\{-\frac{1}{2} \left(\boldsymbol{f}\_r - \boldsymbol{\mu}\_i\right)^T \sum\_{i}^{-1} \left(\boldsymbol{f}\_r - \boldsymbol{\mu}\_i\right)\right\},\tag{30}$$

where f={f1,f2,…,fk} is a random sample set composed by k independent random samples. fr denotes a d-dimensional sample in the sample set, where fr={f1,f2,…,fd} <sup>T</sup> and r=1,2,….,k, μi, Σ<sup>i</sup> and wi are the mean, the covariance matrix and the mixture weight of the i th Gaussian component, respectively, and i=1,2, …C, C is the number of Gaussian components, ϕi(fr|μi, Σi) is the probability density of each Gaussian component is a d-dimensional Gaussian function.

#### 3.3. Neural networks

Neutral network is comprised of layouts that are built with artificial neurons, termed nodes. These nodes in the adjacent layers are connected to each other with various of strengths (weights). The high weights value indicates a strong connection; vice versa, it is a weak connection. Figure 7 shows the principle diagram of a three-layer neutral network in which the three-layer neural

Figure 7. Principle diagram of a three-layer neural network. (a) Three-layer neural network, (b) forward, and (c) backward.

network, the forward and the backward principles are plotted in Figure 7(a), (b) and (c), respectively. There exists three types of nodes including input nodes, hidden nodes, and output nodes. Except the input layer out, there is a transfer function in each node to transfer input data to the connected nodes in the adjacent layout. The typical transfer function used in a neural network classifier has the unit step (threshold), sigmoid, piecewise linear, and Gaussian. The training of neutral networks consists of the forward propagation and the backward propagation. In the forward propagation process, the input nodes take the feature date into the model. The information is presented as activation values, where each node is given a value, the higher value, the greater activation. Based on the weights, inhibition or excitation, and transfer functions, the activation value is passed from node to node. The activation values at each node are summed. Then, the value is modified based on its transfer function. The activation flows through the network, through hidden layers, until it reaches the output nodes. Then, the difference between the output value and actual value (error) modified with the backward propagation process with gradient descent algorithm until satisfy a stop threshold. The diagnostic efficiency and precision are highly dependent on the network architecture [87]. The traditional artificial neural networks (ANNs) have been adopted in defect recognition such as welding defects [88], delamination in composite structures [89], and composite plates structural health monitoring [90]. De Fenza et al. [91] combined the ANN and the probability ellipse method to determine the location and degree of defects in aluminum and composite plates.

<sup>ϕ</sup> <sup>f</sup> <sup>r</sup>jμ; <sup>Σ</sup> � � <sup>¼</sup> <sup>X</sup>

ð Þ 2π

denotes a d-dimensional sample in the sample set, where fr={f1,f2,…,fd}

ϕ<sup>i</sup> f <sup>r</sup>jμ<sup>i</sup>

104 Structural Health Monitoring from Sensing to Processing

3.3. Neural networks

ward.

; Σ<sup>i</sup> � � <sup>¼</sup> <sup>1</sup> C

i¼1

where f={f1,f2,…,fk} is a random sample set composed by k independent random samples. fr

component, respectively, and i=1,2, …C, C is the number of Gaussian components, ϕi(fr|μi, Σi) is the probability density of each Gaussian component is a d-dimensional Gaussian function.

Neutral network is comprised of layouts that are built with artificial neurons, termed nodes. These nodes in the adjacent layers are connected to each other with various of strengths (weights). The high weights value indicates a strong connection; vice versa, it is a weak connection. Figure 7 shows the principle diagram of a three-layer neutral network in which the three-layer neural

Figure 7. Principle diagram of a three-layer neural network. (a) Three-layer neural network, (b) forward, and (c) back-

<sup>d</sup>=<sup>2</sup> exp � <sup>1</sup>

and wi are the mean, the covariance matrix and the mixture weight of the i

wiϕ<sup>i</sup> f <sup>r</sup>jμ<sup>i</sup>

<sup>2</sup> <sup>f</sup> <sup>r</sup> � <sup>μ</sup><sup>i</sup> � �<sup>T</sup> <sup>X</sup>�<sup>1</sup>

; Σ<sup>i</sup>

� � ( )

i

f <sup>r</sup> � μ<sup>i</sup>

� �, (29)

, (30)

<sup>T</sup> and r=1,2,….,k, μi, Σ<sup>i</sup>

th Gaussian

Benefiting from the flexible configuration of neural networks, researcher developed many kinds of neural networks used in structure integrity evaluation. Probabilistic neural network (PNN) combines the Bayes decision strategy with the Parzen nonparametric estimator of the probability density functions in which the interpretation of the neural network is in the form of a probability density function. An accepted norm for decision strategies used to classify patterns is that they minimize the "expected risk." Park et al. [92] adopted the PNN and SVM to online monitoring the state of jointed plates in which the extracted damage feature that constructed with the ToF and the wavelet coefficient obtained from wavelet transforms of Lamb wave signals. Kohonen neural network (KNN) has two layers, input layer and output layer, and is used for honeycomb sandwich and carbon fiber composite structures studied in which the amount of neuron in input layer is determined by input vector dimensions [93]. The neurons of output layer layout form a 2D plane. In regression neural networks for pattern recognition, a trained network produces large errors when some parts of the test pattern are not found in the training pattern. The weight-range selection (WRS) method has a supervised multilayer perceptron operating with one hidden layer of neurons and trained using a backpropagation algorithm to eliminate the large errors induced by the case a test pattern not found in the training set [94]. Anaya et al. [95] adopted an artificial immune system (AIS) and the notion of affinity was used for the sake of damage detection and used a fuzzy c-means algorithm is used for damage classification of an aircraft skin panel. Compared with standard Lamb waves based methods, there is no need to directly analyze the complex time-domain traces containing overlapping, multimodal, and dispersive wave propagation. Other kinds of neural networks that have been studied in nondestructive testing have the recurrent neural network (RNN) [96], deep learning network (DLN), and convolutional neural network (CNN).

## 4. Summary and conclusions

In this chapter, we divided the defects imaging techniques into four categories based on the setting of detection/monitoring system, and the basic principle of them is introduced. Three kinds of intelligent recognition techniques that have been widely studied in Lamb waves structural integrity evaluation are also reviewed.

SVM, LS-SVM, two-step SVM. Bayesian methodology realizes the observation of data estimation with the prior received data. For the Bayesian methodology, the state of structures is predicated with the prior distributions of model parameters obtained using the coupon test data. The related techniques have the multilevel Bayesian model, Bayesian imaging method, and the GMM. Among them, the GMM is a probability static method with unsupervised learning property. It has the advantages of better robustness of uncertainties and high efficiency with lower computational complexity with a relatively small number of model parameters. Neural networks are a supervise classifier based on the back-propagation algorithm to optimize the model parameters. Benefiting from the flexible configuration of neural networks, researchers developed many kinds of neural networks for structure integrity evaluation. During the past decade, ANN, PNN, KNN, CNN, etc., have been applied for on- or offline structure integrity evaluation with the extracted Lamb waves defect information. These neural networks can realize accurate defect recognition in the case they are trained with enough dataset. Meanwhile, they have low noise tolerance in field applications.

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

http://dx.doi.org/10.5772/intechopen.79475

107

This work was supported by the National Natural Science Foundation of China (Grant Nos.

We declare that we do not have any commercial or associative interest that represents a conflict

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of

[1] Liu ZH, Yu FX, Wei R, He CF, Wu B. Image fusion based on single-frequency guided wave mode signals for structural health monitoring in composite plates. Materials Evaluation.

Acknowledgements

Conflict of interest

Author details

References

Zenghua Liu\* and Honglei Chen

Technology, Beijing, China

2013;71:1434-1443

51475012, 11772014, 11527801, and 11272021).

of interest in connection with the work submitted.

\*Address all correspondence to: liuzenghua@bjut.edu.cn


SVM, LS-SVM, two-step SVM. Bayesian methodology realizes the observation of data estimation with the prior received data. For the Bayesian methodology, the state of structures is predicated with the prior distributions of model parameters obtained using the coupon test data. The related techniques have the multilevel Bayesian model, Bayesian imaging method, and the GMM. Among them, the GMM is a probability static method with unsupervised learning property. It has the advantages of better robustness of uncertainties and high efficiency with lower computational complexity with a relatively small number of model parameters. Neural networks are a supervise classifier based on the back-propagation algorithm to optimize the model parameters. Benefiting from the flexible configuration of neural networks, researchers developed many kinds of neural networks for structure integrity evaluation. During the past decade, ANN, PNN, KNN, CNN, etc., have been applied for on- or offline structure integrity evaluation with the extracted Lamb waves defect information. These neural networks can realize accurate defect recognition in the case they are trained with enough dataset. Meanwhile, they have low noise tolerance in field applications.

## Acknowledgements

4. Summary and conclusions

106 Structural Health Monitoring from Sensing to Processing

structural integrity evaluation are also reviewed.

tion, defect imaging can be enhanced.

In this chapter, we divided the defects imaging techniques into four categories based on the setting of detection/monitoring system, and the basic principle of them is introduced. Three kinds of intelligent recognition techniques that have been widely studied in Lamb waves

1. The discrete ellipse imaging algorithm, the hyperbola imaging technique, and the tomography imagine algorithms are processed in the detection/monitoring based on sparse arrays in which the spacing between the adjacent transducers is larger than the wavelength. Discrete ellipse imaging, the hyperbola imaging algorithm, and their optimal type are processed with the defect scattering signals. The pixel intensity is drawn in an elliptical trajectory and the hyperbola trajectory, respectively. Both of the algorithms are imaging with the amplitude information and sensitive to the dispersion and the SNR of signals. The imaging performance is closely related with transducer numbers and the signal resolutions. In the tomography technique, the distribution of sensing points has relative regular forms such as the parallel, square, or circular. The imaging algorithms used in the tomography have PRA algorithms, FBP-based algorithm, the ART-based algorithms, and the novel algorithms such as the HARBUT and FWI. With the dense ray in the detection, defect sizing can be realized with the tomography techniques, particularly for the HARBUT, and

2. Compact array in which the spacing of the adjacent transducers is shorter than the wavelength that with various of shapes have been developed in Lamb waves based defects imaging, including 1D linear array, 2D rectangular, circular, and spiral arrays. The defect imaging algorithms based on compact arrays have PA, SA, and the full wavefield techniques. The TFM, SCF, MVDR, MUSIC, SAFT-based imaging algorithms, and the SWF can be used for full-scale scanning of the plate and realizing defect location. The TFM is an imaging algorithm with the amplitude information that is sensitive to the dispersion nature of Lamb waves. The phase information-based algorithms, PCF, SCF, have relatively more robust imaging performance than TFM. Besides these algorithms, MVDR, MUSIC, SAFT, and SWF have the potential used for baseline-free detection. The full wavefield techniques have the ability for defect accuracy imaging by analyzing the received full wavefield data. Among them, the IMV, RMS, and WRMS are adopted to time-domain analysis for defect location and sizing. With the 2D Fourier transform, the received timespace data are mapped into frequency-wavenumber domain, and defect sizing and thinning quantification are realized through analysis of the spatial wavenumber information. Meanwhile, many optimization techniques with the added windows are adopted to separate the scattering waves in frequency-wavenumber domain for reflection waves separa-

3. SVM, Bayesian methodology, and the neural networks are three kinds of typical classifiers used in Lamb waves based structure integrity evaluation. SVM maps the input data that indicates the state of the structures into a hypothesis space with a kernel function that may be a linear, polynomial, or custom kernel. The classifiers based on SVM have the one-class

FWI has attractive performance in accuracy corrosion defect imaging.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51475012, 11772014, 11527801, and 11272021).

## Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

## Author details

Zenghua Liu\* and Honglei Chen

\*Address all correspondence to: liuzenghua@bjut.edu.cn

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China

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[79] Park S, Lee JJ, Yun CB, Inman DJ. A built-in active sensing system-based structural health monitoring technique using statistical pattern recognition. Journal of Mechanical Science and Technology. 2007;21:896-902. DOI: 10.1007/BF03027065

[91] De Fenza A, Sorrentino A, Vitiello P. Application of artificial neural networks and probability ellipse methods for damage detection using Lamb waves. Composite Structures.

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation…

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[94] Liew CK, Veidt M. Guided waves damage identification in beams with test pattern dependent series neural network systems. WSEAS Transactions on Signal Processing. 2008;4:86-96

[95] Anaya M, Tibaduiza DA, Pozo F. Detection and classification of structural changes using artificial immune systems and fuzzy clustering. International Journal of Bio-Inspired

[96] Yuan L, Yuan Y, Hernández Á, Shi L. Feature extraction for track section status classifica-

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114 Structural Health Monitoring from Sensing to Processing


**Chapter 6**

Provisional chapter

**Qualification of PWAS-Based SHM Technology for**

DOI: 10.5772/intechopen.78034

The chapter refers to the results obtained in the framework of a national research project whose novelty was that concomitant outer space constraints, namely extreme temperature variations, radiations and vacuum, were applied to structures specimens to study their effect on the structural health monitoring (SHM) technology based on piezoelectric wafer active sensors (PWAS) and electromechanical impedance spectroscopy (EMIS) method of damages detection and identification. The results, in short, concern (a) the survivability and sustainability of EMIS technique, in fact the PWAS transducers survival, in these harsh conditions and (b) the developing of a methodology to distinguish between the damages of mechanical origin, and the false ones, caused by environmental conditions, which are, basically, harmless. This has resulted by observing that the splitting phenomenon of resonance peaks on EMIS signature can be associated with the occurrence of mechanical damage, making so possible the clear dissociation of the changes determined

Keywords: lab tests, electromechanical impedance spectroscopy (EMIS), piezoelectric wafer active sensor (PWAS), outer space harsh environmental conditions, entropy, real

In the beginning, we prefer to appeal to the well-known definitions. In this book chapter, "the process of implementing a damage identification strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). […] The damage is defined as changes to the material and/or geometric properties of these systems, including changes to the boundary conditions and system connectivity, which adversely affect the

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Qualification of PWAS-Based SHM Technology for

**Space Applications**

Space Applications

Abstract

Ioan Ursu, Mihai Tudose and Daniela Enciu

Ioan Ursu, Mihai Tudose and Daniela Enciu

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

by the harsh environmental conditions.

damage versus false damage

1. Introduction

http://dx.doi.org/10.5772/intechopen.78034

#### **Qualification of PWAS-Based SHM Technology for Space Applications** Qualification of PWAS-Based SHM Technology for Space Applications

DOI: 10.5772/intechopen.78034

Ioan Ursu, Mihai Tudose and Daniela Enciu Ioan Ursu, Mihai Tudose and Daniela Enciu

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78034

#### Abstract

The chapter refers to the results obtained in the framework of a national research project whose novelty was that concomitant outer space constraints, namely extreme temperature variations, radiations and vacuum, were applied to structures specimens to study their effect on the structural health monitoring (SHM) technology based on piezoelectric wafer active sensors (PWAS) and electromechanical impedance spectroscopy (EMIS) method of damages detection and identification. The results, in short, concern (a) the survivability and sustainability of EMIS technique, in fact the PWAS transducers survival, in these harsh conditions and (b) the developing of a methodology to distinguish between the damages of mechanical origin, and the false ones, caused by environmental conditions, which are, basically, harmless. This has resulted by observing that the splitting phenomenon of resonance peaks on EMIS signature can be associated with the occurrence of mechanical damage, making so possible the clear dissociation of the changes determined by the harsh environmental conditions.

Keywords: lab tests, electromechanical impedance spectroscopy (EMIS), piezoelectric wafer active sensor (PWAS), outer space harsh environmental conditions, entropy, real damage versus false damage

## 1. Introduction

In the beginning, we prefer to appeal to the well-known definitions. In this book chapter, "the process of implementing a damage identification strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). […] The damage is defined as changes to the material and/or geometric properties of these systems, including changes to the boundary conditions and system connectivity, which adversely affect the

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

current or future performance of these systems" [1]. SHM is, properly, an on-line measurement process supposing a sensor system distributed over the monitored structure. This process is complemented by off-line analysis of damage-sensitive features from these measurements, or by an on-line analysis of damages occurrence, as shown in this contribution. SHM technology enjoys special attention over the past two to three decades. The sensors used to damage detection belong to a wide range, such as optical fiber sensors [2, 3], acoustic active and passive sensors [4–6], microelectromechanical systems (MEMS) [7], and wireless sensor systems [8]. The basic SHM methods are the method based on a modal modification of structure dynamic vibrations in a relatively low-frequency register [9] and the electromechanical method of impedance spectroscopy (EMIS) in the high-frequency register, using the active piezo sensors [10–14]. It should be added that SHM methodology has been strongly related during its development to predictive maintenance [15] and fault detection [16] techniques due to safety demands in all areas of activity, especially in aerospace applications, chemical industry, nuclear power plants, and so on. SHM methodology has its obvious relevance to the air and space industry but has become imperious for many other industries due to the increase of the productivity and quality demands (zero-defects manufacturing), cost savings together with enhanced safety, and increased availability. Of course, not all existing damages compromise the good functioning of the structure. Based on a long-time SHM process, one obtains information on the ability of the structure to perform in spite of the inevitable aging and degradation resulting from operational environments [1], with the benefit to managing the structures life prognosis and reducing life-cycle costs. SHM will be one of the major contributions for future smart structures, including space ones [17].

in SHM technology is considered [10] (see [11]). The electromechanical impedance spectrum is defined as the ratios between the applied excitation voltage V tð Þ ≔ V0sinð Þ ωt [V] and the current I tð Þ ≔ Isinð Þ ωt [A] generated by the piezoelectric effect. Where appropriate, impedance results are obtained based on an analytical relationship, or by dedicated equipment such as the HP 4194A impedance analyzer. Experimentally it has been proven that the real part, Re (Z (ω)), of the EMIS PWAS attached to the structure can be taken as an indication of the presence of damage or defects, due to the fact that this value closely follows the resonance behavior of the structure vibrating under the PWAS excitation [11]. In other words, this measured value is very sensitive to the smallest variations in the high-frequency structural dynamics at local scales (on the order of microns), which are associated with the presence of incipient damage. Of course, these changes cannot be detected by classical modal

Qualification of PWAS-Based SHM Technology for Space Applications

http://dx.doi.org/10.5772/intechopen.78034

119

3. Theoretical and experimental framework of qualification PWAS based

Although SHM will be soon, we think, a key technology in the field of space vehicles, it is surprising how few papers can be reported for the time being in this field [4, 5, 18–22]. However, it is becoming clearer that new space programs can no longer ignore the implementation of SHM technologies to monitor and test the health and performance of space structures. The safety of the crew on board and the safety of the spacecraft, especially in critical moments of launch and re-entry into the earth's atmosphere, depend on the onboard existence of a SHM system. Spatial vehicles, but also the satellites, are subject to harsh environmental conditions: strong vibrations at launching and landing, cosmic radiation (with energy up to 1.6 � <sup>10</sup>�<sup>11</sup> <sup>J</sup> (1 GeV) [23], extreme temperatures (+120�C for exposed surfaces to the Sun and �230�C for

The premise of a tests program for qualification PWAS-based SHM technology for space applications is that the changes in the EMIS signature will reflect the complex conditions in which the structures are found: overexposure to natural damage, that is, mechanical fatigue and aging, and special operating conditions in an environment defined by outer space (extreme temperatures, radiation, and vacuum). Both kinds of constraints, that is, mechanical and environmental, are to be simulated. The specific problem of the tests relates to the ability of the PWAS transducer to measure the modal behavior of the structure on which it is attached in the simulated harsh environmental conditions and with simulated mechanical damages. Consequently, a considerable amount of testing stages, EMIS records, data processing, and analytical assessments on damage identification were performed [5, 6, 24–28]. The following types of specimens were subjected to the tests: (a) PWAS STEMINC SMD07T02S412WL transducers, (b) M-bond 610 Vishay epoxy adhesive, and (c) STEMINC PWAS transducers [26] (Figure 1). The material and geometry data of the disc specimens (DS) were: A2024 aluminum alloy, with a diameter of 100 mm and a thickness of 0.8 mm. To simulate damages, in discs were processed, with laser technology, slits with 10 mm in length and 0.15 mm width, of

analysis sensors operating at lower frequencies.

SHM technology for space applications

unexposed surfaces [22]), and advanced vacuum.

various geometries, and locations.

## 2. PWAS-based SHM technology—EMIS method

The active SHM sensing techniques are based on two different approaches: transient guided waves and standing waves [12]. In such SHM processes, a piezoelectric wafer active sensor (PWAS) is required to generate elastic waves. These travel along the mechanical structure, are reflected by different structural abnormalities, or boundary edges, and they are recaptured by the same sensor in a pulse-echo configuration or by other sensors of same or different type, even passive sensors, and in pitch-catch configuration. If the structural damage or boundary edges are in the close vicinity of the active sensor, their reflections overlap the incident transient wave, and making impossible the interpretation [14]. One of the active SHM sensing techniques is based on standing waves, in the so-called EMIS method; by sweeping the frequency of the input signals to PWAS, some changes appear in the impedance measured by an impedance analyzer connected to the PWAS terminals. By monitoring the changes in the real part of the impedance function, which is most sensitive to structural changes [10], one can evaluate the integrity of the host structure.

The EMIS method uses PWAS high-frequency active sensors and bonded to the structure. The presence of damage in a neighboring zone of the sensor is signaled as its EMIS "signature," respectively, as a modification of the electromagnetic impedance spectrum Z (ω), recorded and online processed, and in principle [10–14]. The pioneering work on using EMIS in SHM technology is considered [10] (see [11]). The electromechanical impedance spectrum is defined as the ratios between the applied excitation voltage V tð Þ ≔ V0sinð Þ ωt [V] and the current I tð Þ ≔ Isinð Þ ωt [A] generated by the piezoelectric effect. Where appropriate, impedance results are obtained based on an analytical relationship, or by dedicated equipment such as the HP 4194A impedance analyzer. Experimentally it has been proven that the real part, Re (Z (ω)), of the EMIS PWAS attached to the structure can be taken as an indication of the presence of damage or defects, due to the fact that this value closely follows the resonance behavior of the structure vibrating under the PWAS excitation [11]. In other words, this measured value is very sensitive to the smallest variations in the high-frequency structural dynamics at local scales (on the order of microns), which are associated with the presence of incipient damage. Of course, these changes cannot be detected by classical modal analysis sensors operating at lower frequencies.

current or future performance of these systems" [1]. SHM is, properly, an on-line measurement process supposing a sensor system distributed over the monitored structure. This process is complemented by off-line analysis of damage-sensitive features from these measurements, or by an on-line analysis of damages occurrence, as shown in this contribution. SHM technology enjoys special attention over the past two to three decades. The sensors used to damage detection belong to a wide range, such as optical fiber sensors [2, 3], acoustic active and passive sensors [4–6], microelectromechanical systems (MEMS) [7], and wireless sensor systems [8]. The basic SHM methods are the method based on a modal modification of structure dynamic vibrations in a relatively low-frequency register [9] and the electromechanical method of impedance spectroscopy (EMIS) in the high-frequency register, using the active piezo sensors [10–14]. It should be added that SHM methodology has been strongly related during its development to predictive maintenance [15] and fault detection [16] techniques due to safety demands in all areas of activity, especially in aerospace applications, chemical industry, nuclear power plants, and so on. SHM methodology has its obvious relevance to the air and space industry but has become imperious for many other industries due to the increase of the productivity and quality demands (zero-defects manufacturing), cost savings together with enhanced safety, and increased availability. Of course, not all existing damages compromise the good functioning of the structure. Based on a long-time SHM process, one obtains information on the ability of the structure to perform in spite of the inevitable aging and degradation resulting from operational environments [1], with the benefit to managing the structures life prognosis and reducing life-cycle costs. SHM will be one of the major contributions for

The active SHM sensing techniques are based on two different approaches: transient guided waves and standing waves [12]. In such SHM processes, a piezoelectric wafer active sensor (PWAS) is required to generate elastic waves. These travel along the mechanical structure, are reflected by different structural abnormalities, or boundary edges, and they are recaptured by the same sensor in a pulse-echo configuration or by other sensors of same or different type, even passive sensors, and in pitch-catch configuration. If the structural damage or boundary edges are in the close vicinity of the active sensor, their reflections overlap the incident transient wave, and making impossible the interpretation [14]. One of the active SHM sensing techniques is based on standing waves, in the so-called EMIS method; by sweeping the frequency of the input signals to PWAS, some changes appear in the impedance measured by an impedance analyzer connected to the PWAS terminals. By monitoring the changes in the real part of the impedance function, which is most sensitive to structural changes [10], one can

The EMIS method uses PWAS high-frequency active sensors and bonded to the structure. The presence of damage in a neighboring zone of the sensor is signaled as its EMIS "signature," respectively, as a modification of the electromagnetic impedance spectrum Z (ω), recorded and online processed, and in principle [10–14]. The pioneering work on using EMIS

future smart structures, including space ones [17].

118 Structural Health Monitoring from Sensing to Processing

evaluate the integrity of the host structure.

2. PWAS-based SHM technology—EMIS method

## 3. Theoretical and experimental framework of qualification PWAS based SHM technology for space applications

Although SHM will be soon, we think, a key technology in the field of space vehicles, it is surprising how few papers can be reported for the time being in this field [4, 5, 18–22]. However, it is becoming clearer that new space programs can no longer ignore the implementation of SHM technologies to monitor and test the health and performance of space structures. The safety of the crew on board and the safety of the spacecraft, especially in critical moments of launch and re-entry into the earth's atmosphere, depend on the onboard existence of a SHM system. Spatial vehicles, but also the satellites, are subject to harsh environmental conditions: strong vibrations at launching and landing, cosmic radiation (with energy up to 1.6 � <sup>10</sup>�<sup>11</sup> <sup>J</sup> (1 GeV) [23], extreme temperatures (+120�C for exposed surfaces to the Sun and �230�C for unexposed surfaces [22]), and advanced vacuum.

The premise of a tests program for qualification PWAS-based SHM technology for space applications is that the changes in the EMIS signature will reflect the complex conditions in which the structures are found: overexposure to natural damage, that is, mechanical fatigue and aging, and special operating conditions in an environment defined by outer space (extreme temperatures, radiation, and vacuum). Both kinds of constraints, that is, mechanical and environmental, are to be simulated. The specific problem of the tests relates to the ability of the PWAS transducer to measure the modal behavior of the structure on which it is attached in the simulated harsh environmental conditions and with simulated mechanical damages. Consequently, a considerable amount of testing stages, EMIS records, data processing, and analytical assessments on damage identification were performed [5, 6, 24–28]. The following types of specimens were subjected to the tests: (a) PWAS STEMINC SMD07T02S412WL transducers, (b) M-bond 610 Vishay epoxy adhesive, and (c) STEMINC PWAS transducers [26] (Figure 1). The material and geometry data of the disc specimens (DS) were: A2024 aluminum alloy, with a diameter of 100 mm and a thickness of 0.8 mm. To simulate damages, in discs were processed, with laser technology, slits with 10 mm in length and 0.15 mm width, of various geometries, and locations.

The saying "there is nothing more practical than a good theory" is widely known. In a complex tests program with the primary focus of the experiment, it was important to know well the theoretical tools. Indeed, the experiments were based on the concept of EMIS signature, so it was also important to master the theoretical basis of the EMIS method. The graphs summarized in this chapter, to which can be added the numerical analysis in [13, 14] and [29], as well as data, are given in Table 1; show that this goal has been met. Detailed analytical solutions are presented in [11–13]. Numerical calculations and experimental validation are widely described in [13, 6, 25, 29]. We cannot fail to notice the excellent monographs [30, 12] that guided the studies and experiments presented in this chapter. As a theoretical foundation, we retain the following equations that provide frequencies of flexural (f-indexed) and, respectively, axial

(a-indexed) modes of a circular pristine disc:

0 <sup>0</sup>ð Þ λ

0 <sup>0</sup>ð Þ λ I 0

<sup>D</sup>∇<sup>4</sup><sup>w</sup> <sup>þ</sup> <sup>r</sup><sup>h</sup>

zJ0ð Þ� <sup>z</sup> ð Þ <sup>1</sup> � <sup>ν</sup> <sup>J</sup>1ð Þ¼ <sup>z</sup> <sup>0</sup>, z <sup>≔</sup> <sup>γ</sup>a, <sup>ω</sup><sup>j</sup> <sup>≔</sup> cLð Þ<sup>z</sup> j, <sup>a</sup>=a, c<sup>2</sup>

∂2 w ∂t

<sup>0</sup>ð Þ <sup>λ</sup> , <sup>ω</sup>j,f <sup>≔</sup> <sup>λ</sup><sup>2</sup>

The characteristic Eqs. (1) are obtained as solutions of the equation of motion for the transverse

<sup>∇</sup><sup>4</sup> <sup>¼</sup> <sup>∇</sup><sup>2</sup>∇2, where <sup>∇</sup><sup>2</sup> is the Laplace operator. The Eqs. (1) give natural frequencies <sup>ω</sup><sup>j</sup> associated with solutions (eigenvalues) λ<sup>j</sup> or z γ is wavenumber, γ ¼ ω=cL. J0ð Þ λ is the Bessel function of first kind and order zero, whereas I0ð Þ λ is the modified Bessel function of first kind and order zero. D is the transverse (flexural) rigidity, E is Young's modulus, h is the plate thickness, a is the plate radius, v is Poisson's ratio, and r is mass density per unit area of the plate. As already mentioned, the DS were fabricated from A2024 aluminum alloy with a diameter of 2a=100 mm and a thickness of h ¼0.8 mm. The properties of the A2024 aluminum

the experimental method are closer to the theoretical ones. The axial frequencies were noted

Hence, finally electromechanical impedance Z(ω) of a PWAS transducer bonded to disc spec-

νth (kHz) 12.57 19.69 28.38 35.67 38.63 50.51 63.95 78.97 93.95 95.57 νexp1 (kHz) 12.48 19.46 28.23 35.89 38.51 50.01 62.90 77.02 92.04 93.85 νexp2 (kHz) 12.65 19.91 28.27 28.63 35.42 37.35 38.07 38.87 49.32 50.53 63.62 77.93 90.63 93.73

Table 1. Theoretical (νth) and measured frequencies on pristine specimen (noted with νexp1) and on the arc at 15 mm

j,f

<sup>2</sup> <sup>¼</sup> <sup>0</sup>, D <sup>≔</sup> Eh<sup>3</sup>

s

ffiffiffiffiffiffiffiffiffi D rha<sup>4</sup>

, D <sup>≔</sup> Eh<sup>3</sup>

Qualification of PWAS-Based SHM Technology for Space Applications

http://dx.doi.org/10.5772/intechopen.78034

12 1 � v<sup>2</sup> ð Þ

<sup>L</sup> <sup>≔</sup> <sup>E</sup><sup>=</sup> <sup>r</sup> <sup>1</sup> � <sup>v</sup><sup>2</sup> � � � �

12 1 � <sup>v</sup><sup>2</sup> ð Þ (2)

, and ν = 0.3312. The frequencies values obtained by

(1)

121

0 <sup>0</sup>ð Þ <sup>λ</sup> <sup>¼</sup> <sup>J</sup>

J0ð Þþ λ ð Þ 1 � v λJ

I0ð Þ� λ ð Þ 1 � v λI

plates were: E= 73.146 MPa, r = 2780 kg/m3

displacement w of a plate [30]:

λ2

λ2

with an italic font.

damaged specimen (νexp2).

imen is:

Figure 1. Disc specimens (DS), geometry of damage simulation.

Disc type PWASs with a diameter of 8 mm was bonded in the center of the aluminum disc specimen with epoxy adhesive. The thickness of the adhesive layer was measured with a comparator, and was found to be between 20 and 100 μm. Figure 2 shows a disc with an arctype simulated crack damage at 7 mm from the PWAS. The geometry of the simulated cracks (0.15 mm wide and 10 mm long) is the following: crack 1 (curvature):R = 45 mm, θ = 13; crack 2:R= 25 mm, θ = 23; crack 3: R = 15 mm, θ=38; and crack 4: R = 7 mm, θ = 82. The set of records refer to either PWASs or specimens with bonded PWAS, without and with simulated damages. In Figure 2c, the experimental set-up for EMIS recording using the HP 4194A impedance analyzer is presented.

The SHM test protocol involved a lot of operations: records and processing for EMIS, extreme temperature irradiation under high-vacuum, irradiation at room temperature (RT) and atmospheric pressure, optical and acoustic microscopy, scanning laser Doppler vibrometry (SLDV). From the processing of impedance spectrum will result in the characterization of damages. This is done by scalar sizes suitable to capture the differences between the spectra caused by this damage/crack. Ideally, these values should capture only those spectral features that are directly altered by the damage, while the variations caused by normal operating conditions to be neglected.

Figure 2. (a) PWAS STEMiNC type SMD 07T02R412WL; (b) DS with simulated damage at 7 mm from the PWAS; and (c) experimental set-up for EMIS recording at RT using the HP 4194A impedance analyzer.

The saying "there is nothing more practical than a good theory" is widely known. In a complex tests program with the primary focus of the experiment, it was important to know well the theoretical tools. Indeed, the experiments were based on the concept of EMIS signature, so it was also important to master the theoretical basis of the EMIS method. The graphs summarized in this chapter, to which can be added the numerical analysis in [13, 14] and [29], as well as data, are given in Table 1; show that this goal has been met. Detailed analytical solutions are presented in [11–13]. Numerical calculations and experimental validation are widely described in [13, 6, 25, 29]. We cannot fail to notice the excellent monographs [30, 12] that guided the studies and experiments presented in this chapter. As a theoretical foundation, we retain the following equations that provide frequencies of flexural (f-indexed) and, respectively, axial (a-indexed) modes of a circular pristine disc:

Disc type PWASs with a diameter of 8 mm was bonded in the center of the aluminum disc specimen with epoxy adhesive. The thickness of the adhesive layer was measured with a comparator, and was found to be between 20 and 100 μm. Figure 2 shows a disc with an arctype simulated crack damage at 7 mm from the PWAS. The geometry of the simulated cracks (0.15 mm wide and 10 mm long) is the following: crack 1 (curvature):R = 45 mm, θ = 13; crack 2:R= 25 mm, θ = 23; crack 3: R = 15 mm, θ=38; and crack 4: R = 7 mm, θ = 82. The set of records refer to either PWASs or specimens with bonded PWAS, without and with simulated damages. In Figure 2c, the experimental set-up for EMIS recording using the HP 4194A

The SHM test protocol involved a lot of operations: records and processing for EMIS, extreme temperature irradiation under high-vacuum, irradiation at room temperature (RT) and atmospheric pressure, optical and acoustic microscopy, scanning laser Doppler vibrometry (SLDV). From the processing of impedance spectrum will result in the characterization of damages. This is done by scalar sizes suitable to capture the differences between the spectra caused by this damage/crack. Ideally, these values should capture only those spectral features that are directly altered by the damage, while the variations caused by normal operating conditions to

Figure 2. (a) PWAS STEMiNC type SMD 07T02R412WL; (b) DS with simulated damage at 7 mm from the PWAS; and

(c) experimental set-up for EMIS recording at RT using the HP 4194A impedance analyzer.

impedance analyzer is presented.

Figure 1. Disc specimens (DS), geometry of damage simulation.

120 Structural Health Monitoring from Sensing to Processing

be neglected.

$$\frac{\lambda^2 I\_0(\lambda) + (1 - \upsilon)\lambda I\_0'(\lambda)}{\lambda^2 I\_0(\lambda) - (1 - \upsilon)\lambda I\_0'(\lambda)} = \frac{I\_0'(\lambda)}{I\_0'(\lambda)}, \quad \omega\_{]\_f} := \lambda\_{,f}^2 \sqrt{\frac{D}{\rho h a^{\theta}}} \quad D := \frac{E h^3}{12(1 - \upsilon^2)}\tag{1}$$
 
$$zI\_0(z) - (1 - \upsilon)I\_1(z) = 0, \quad z := \gamma a, \quad \omega\_{\rangle} := c\_\mathsf{L}(z)\_{j,A}/a, \qquad c\_\mathsf{L}^2 := E/\left(\rho \left(1 - \upsilon^2\right)\right)$$

The characteristic Eqs. (1) are obtained as solutions of the equation of motion for the transverse displacement w of a plate [30]:

$$D\nabla^4 w + \rho h \frac{\partial^2 w}{\partial t^2} = 0, \quad D \coloneqq \frac{Eh^3}{12(1 - v^2)}\tag{2}$$

<sup>∇</sup><sup>4</sup> <sup>¼</sup> <sup>∇</sup><sup>2</sup>∇2, where <sup>∇</sup><sup>2</sup> is the Laplace operator. The Eqs. (1) give natural frequencies <sup>ω</sup><sup>j</sup> associated with solutions (eigenvalues) λ<sup>j</sup> or z γ is wavenumber, γ ¼ ω=cL. J0ð Þ λ is the Bessel function of first kind and order zero, whereas I0ð Þ λ is the modified Bessel function of first kind and order zero. D is the transverse (flexural) rigidity, E is Young's modulus, h is the plate thickness, a is the plate radius, v is Poisson's ratio, and r is mass density per unit area of the plate. As already mentioned, the DS were fabricated from A2024 aluminum alloy with a diameter of 2a=100 mm and a thickness of h ¼0.8 mm. The properties of the A2024 aluminum plates were: E= 73.146 MPa, r = 2780 kg/m3 , and ν = 0.3312. The frequencies values obtained by the experimental method are closer to the theoretical ones. The axial frequencies were noted with an italic font.

Hence, finally electromechanical impedance Z(ω) of a PWAS transducer bonded to disc specimen is:


Table 1. Theoretical (νth) and measured frequencies on pristine specimen (noted with νexp1) and on the arc at 15 mm damaged specimen (νexp2).

$$Z(\omega) = \frac{1}{i\omega \mathbb{C} \left(1 - k\_p^2\right)} \left\{ \left[ 1 + \frac{k\_p^2}{1 - k\_p^2} \frac{(1 + \upsilon\_a)I\_1(\varphi\_a)}{\varphi\_a I\_0(\varphi\_a) - (1 - \upsilon\_a)I\_1(\varphi\_a) - \frac{\rho}{r\_a}\chi(\omega)(1 + \upsilon\_a)I\_1(\varphi\_a)} \right] \right\}^{-1} \tag{3}$$

$$k\_p^2 \coloneqq \frac{2d\_{31}^2}{s\_{11}^E (1 - \upsilon\_a)c\_{33}^E}, \varphi\_a = \frac{\alpha r\_a}{c\_P}, c\_P \coloneqq \sqrt{\frac{1}{\rho s\_{11}^E (1 - \upsilon\_a^2)}}, \quad \chi(\omega) = k\_{\text{str}}(\omega)/k\_{\text{PWM}} $$

Relationship (3) is an analytical one. The analytical results are compared with the experimental ones. The statistics of the analytical determinations and the measurements are based on an indicator. In statistics framework, the most available definitions of damages "metrics" could be: "root mean square deviation" (RMSD), mean absolute percentage deviation (MAPD), and "correlation coefficient deviation" (CCD). Expressions of such sizes given in terms of the real

�, RMSD ¼

The symbols Z and Z<sup>0</sup> means averages in time and σ<sup>Z</sup> and σZ<sup>0</sup> represents the standard deviation. Herein, we are interested to "assess a RMS type damage metrics," both for the real fault embodied through cracks or cuts simulated on disk specimens, or to statistical evaluation of EMI changes caused by temperature or irradiation constraints on single PWAS, or DS,

The test program started with the establishment of a reference database, with RT EMIS records and processing for each PWAS and DS. It is important to note that the recorded data has been analyzed even from the beginning taking into account the impact that a PWAS improperly glued on DS has on the EMIS graphs. Figure 4 shows how an inappropriate bonding resulted

Since the EMIS signature does not always clarify the origin of the damages – mechanical or electronic, generated by fatigue and the aging of the structure or by deficiencies of sensors bonding

i

X N

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

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i

= X N

Re Z<sup>0</sup> i � � � � <sup>2</sup> 123

Reð Þ� Zi Re <sup>Z</sup><sup>0</sup>

Qualification of PWAS-Based SHM Technology for Space Applications

� � � � <sup>2</sup>

� � � Re <sup>Z</sup><sup>0</sup> h i � � , CCD <sup>¼</sup> <sup>1</sup> � CC (4)

part of the impedance, Re (Z), are the following:

Reð Þ� Zi Re <sup>Z</sup><sup>0</sup>

X N

i � � � � =Re Z<sup>0</sup>

constraints generating so-called "virtual (or false) defects".

Figure 4. EMI signature for (a) a "good" bonding and (b) a "bad" bonding.

4. Checks before complex harsh environments tests

<sup>s</sup> �

i � ��

Reð Þ� Zi Re <sup>Z</sup> � � � � � Re <sup>Z</sup><sup>0</sup>

MAPD <sup>¼</sup> <sup>X</sup>

N

CC <sup>¼</sup> <sup>1</sup> σZσZ<sup>0</sup>

in the specimen discredit.

� � � � �

kstrð Þ <sup>ω</sup> is the dynamic stiffness of PWAS bonded on disc specimen; kPWAS <sup>¼</sup> ta<sup>=</sup> ras<sup>E</sup> <sup>11</sup>ð Þ 1 � ν<sup>a</sup> � � is the PWAS stiffness; kP is the planar coupling factor; cP is the sound speed in PWAS disc; cLis the longitudinal wave speed in disc specimen; va, ra, and ha are corresponding parameters of PWAS. Finally, s<sup>E</sup> <sup>11</sup>, ε<sup>E</sup> <sup>33</sup>, and d<sup>31</sup> are recognized as PWAS compliance coefficient, dielectric permittivity and, respectively, strain constant.

The issues raised above are primarily qualitative, but at the same time, together with the results of numerical integration and with the measurements made on specimens, will show the capability and resources of the PWAS EMIS SHM technique. For example, spectrum splitting around resonance nominal frequencies of the pristine structure can be considered as an indication of the occurrence of mechanical damage in the monitored structure (Figure 3).

The numerical model used in tests program is based on the finite element method (FEM). FEM analysis allowed the study of damaged DSs [13, 14]. There was a good correlation between the analytical method and the experimental method.

The EMIS signature is calculated analytically (for regular geometric shapes, such as discs) and numerically. Table 1 shows the theoretical natural frequencies described by the analytical model (1), the measured ones corresponding to the pristine DS (noted with νexp1) and to the "arc at 45 mm from PWAS" damaged DS (νexp2).

Figure 3. Measurement records for pristine specimen versus damaged one. Changes in RT EMIS signatures for different crack locations.

Relationship (3) is an analytical one. The analytical results are compared with the experimental ones. The statistics of the analytical determinations and the measurements are based on an indicator. In statistics framework, the most available definitions of damages "metrics" could be: "root mean square deviation" (RMSD), mean absolute percentage deviation (MAPD), and "correlation coefficient deviation" (CCD). Expressions of such sizes given in terms of the real part of the impedance, Re (Z), are the following:

$$\text{MAPD} = \sum\_{N} \left| \left[ \text{Re}(\mathbf{Z}\_{i}) - \text{Re}(\mathbf{Z}\_{i}^{0}) \right] / \text{Re}(\mathbf{Z}\_{i}^{0}) \right|, \text{RMSD} = \sqrt{\sum\_{N} \left[ \text{Re}(\mathbf{Z}\_{i}) - \text{Re}(\mathbf{Z}\_{i}^{0}) \right]^{2} / \sum\_{N} \left[ \text{Re}(\mathbf{Z}\_{i}^{0}) \right]^{2}}$$

$$\text{CC} = \frac{1}{\sigma\_{2}\sigma\_{2^{0}}} \sum\_{N} \left[ \text{Re}(\mathbf{Z}\_{i}) - \text{Re}(\mathbf{Z}) \right] \times \left[ \text{Re}(\mathbf{Z}\_{i}^{0}) - \text{Re}(\mathbf{Z}^{0}) \right], \text{CCD} = 1 - \text{CC} \tag{4}$$

The symbols Z and Z<sup>0</sup> means averages in time and σ<sup>Z</sup> and σZ<sup>0</sup> represents the standard deviation. Herein, we are interested to "assess a RMS type damage metrics," both for the real fault embodied through cracks or cuts simulated on disk specimens, or to statistical evaluation of EMI changes caused by temperature or irradiation constraints on single PWAS, or DS, constraints generating so-called "virtual (or false) defects".

## 4. Checks before complex harsh environments tests

Zð Þ¼ ω

k2

PWAS. Finally, s<sup>E</sup>

crack locations.

1 iωC 1 � k

<sup>p</sup> <sup>≔</sup> <sup>2</sup>d<sup>2</sup>

sE

2 p � � <sup>1</sup> <sup>þ</sup>

122 Structural Health Monitoring from Sensing to Processing

31

<sup>11</sup>, ε<sup>E</sup>

permittivity and, respectively, strain constant.

analytical method and the experimental method.

"arc at 45 mm from PWAS" damaged DS (νexp2).

33

<sup>11</sup>ð Þ <sup>1</sup> � <sup>ν</sup><sup>a</sup> <sup>ε</sup><sup>E</sup>

k2 p 1 � k 2 p

,φ<sup>a</sup> <sup>¼</sup> <sup>ω</sup>ra cP

φaJ<sup>0</sup> φ<sup>a</sup>

, cP ≔

ð Þ 1 þ va J<sup>1</sup> φ<sup>a</sup>

<sup>33</sup>, and d<sup>31</sup> are recognized as PWAS compliance coefficient, dielectric

( ) " # �<sup>1</sup>

� � � <sup>a</sup> ra

� � � ð Þ <sup>1</sup> � va <sup>J</sup><sup>1</sup> <sup>φ</sup><sup>a</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup>

<sup>11</sup> 1 � v<sup>2</sup> a � �

the PWAS stiffness; kP is the planar coupling factor; cP is the sound speed in PWAS disc; cLis the longitudinal wave speed in disc specimen; va, ra, and ha are corresponding parameters of

The issues raised above are primarily qualitative, but at the same time, together with the results of numerical integration and with the measurements made on specimens, will show the capability and resources of the PWAS EMIS SHM technique. For example, spectrum splitting around resonance nominal frequencies of the pristine structure can be considered as an indication of the occurrence of mechanical damage in the monitored structure (Figure 3).

The numerical model used in tests program is based on the finite element method (FEM). FEM analysis allowed the study of damaged DSs [13, 14]. There was a good correlation between the

The EMIS signature is calculated analytically (for regular geometric shapes, such as discs) and numerically. Table 1 shows the theoretical natural frequencies described by the analytical model (1), the measured ones corresponding to the pristine DS (noted with νexp1) and to the

Figure 3. Measurement records for pristine specimen versus damaged one. Changes in RT EMIS signatures for different

rs<sup>E</sup>

s

kstrð Þ <sup>ω</sup> is the dynamic stiffness of PWAS bonded on disc specimen; kPWAS <sup>¼</sup> ta<sup>=</sup> ras<sup>E</sup>

� �

, χ ωð Þ¼ kstrð Þ ω =kPWAS

χ ωð Þð Þ 1 þ va J<sup>1</sup> φ<sup>a</sup>

� �

(3)

<sup>11</sup>ð Þ 1 � ν<sup>a</sup> � � is

> The test program started with the establishment of a reference database, with RT EMIS records and processing for each PWAS and DS. It is important to note that the recorded data has been analyzed even from the beginning taking into account the impact that a PWAS improperly glued on DS has on the EMIS graphs. Figure 4 shows how an inappropriate bonding resulted in the specimen discredit.

> Since the EMIS signature does not always clarify the origin of the damages – mechanical or electronic, generated by fatigue and the aging of the structure or by deficiencies of sensors bonding

Figure 4. EMI signature for (a) a "good" bonding and (b) a "bad" bonding.

on the specimen and so on, special investigative means were added. This preliminary analysis is correlated with the experimental observation that there can be slight variation of EMIS for nominally identical specimens. It was considered that possible causes of EMIS signature changes were (a) fatigue and aging of the mechanical structure due to vibration, (b) unfulfillment of an adequate bonding of PWAS to the specimen, and (c) damage of PWAS itself.

5. Describing tests protocol and results

thermostatic chamber FD 115 Binder.

Initial EMIS reading – RT

EMIS reading after each cycle – RT

5.1. The effects of the harsh environment on PWAS and DS EMIS signature

Two specimens exposed to harsh environmental conditions in the laboratory simulations are free PWAS sensors and circular plates with central bonded PWAS. EMIS was recorded both during exposure to harsh conditions, and in the intervals between these exposures, at RT, see Table 2. The technical details of the factors involved in one cycle of harsh environment exposure are presented in Table 3. The first stage of the complex test protocol stipulated five cycles of

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125

In the test program has been used special harsh environment simulation equipment, starting with the Dewar cryogenic vessel, and the convection oven with the Memmert UFE 400 digital temperature controller. Also, some of the experiments at negative temperatures were performed at INCAS in the environmental chamber INSTRON 5982, and the high temperatures in the

The test program also developed experiments at the Horia Hulubei national institute for R and D in physics and nuclear engineering-IFIN-HH, in the gamma irradiation chamber 5000 with 60-Co circular distributed sources. The details are presented in the paper [26]. The measured radiation flow was 4.7 kGy/h. Five consecutive test cycles (Table 3) were programmed to provide a full irradiation dose of 23.5 kGy. The premise of the calculations was as follows: (a) the estimated

Tested specimen Activity Amount Working time [h]

testing in harsh, space type, conditions 30 200 EMI measurement after returning to RT 30 20 EMI changes analysis 30 100

testing in harsh, space type, conditions 34 200 EMI measurement after returning to RT 34 20 EMI changes analysis 34 100

PWAS EMI measuring at RT 30 20

Disc with PWAS EMI measuring at room temperature 34 20

0.5 h <sup>196</sup> <sup>1</sup>–<sup>10</sup><sup>2</sup> 2.35 4.7

1.0 h RT — — 0.5 h +100 1–10<sup>2</sup> 2.35

Table 2. Complex testing protocol for simulation of harsh space type conditions - first stage of complex tests.

Duration Temperature (C) Vacuum (Pa) Dose per step (kGy) Dose per cycle (kGy)

Table 3. Overview of one test cycle of cumulative environmental factors: Radiation, temperature, and vacuum tests.

concomitant outer-space condition: high-temperature variation, radiation, and vacuum.

Figure 5 top shows images obtained with SAM 300, at investigating the DS 122, particularly chosen wrong, for study. One can see: cracks in PWAS (red circles) caused by unequal forces applied during the bonding process; a piece of PWAS is broken (green rectangle); areas without glue (yellow rhombs). Another device used was the digital microscope VHX 5000. The VHX is an all-in-one microscope that incorporates observation, image capture, and measurement capabilities. Figure 5 bottom shows two images of the DS 106 obtained with this device. The picture on the right is an enlarged image of the left side; a crack is shown in PWAS.

Figure 5. Top: Investigating the DS 122 with 300 scanning acoustic microscope (SAM); middle: Images obtained with digital microscope VHX 5000, DS106; and bottom: Areas of interest PWAS health monitoring.

## 5. Describing tests protocol and results

on the specimen and so on, special investigative means were added. This preliminary analysis is correlated with the experimental observation that there can be slight variation of EMIS for nominally identical specimens. It was considered that possible causes of EMIS signature changes were (a) fatigue and aging of the mechanical structure due to vibration, (b) unfulfillment of an adequate

Figure 5 top shows images obtained with SAM 300, at investigating the DS 122, particularly chosen wrong, for study. One can see: cracks in PWAS (red circles) caused by unequal forces applied during the bonding process; a piece of PWAS is broken (green rectangle); areas without glue (yellow rhombs). Another device used was the digital microscope VHX 5000. The VHX is an all-in-one microscope that incorporates observation, image capture, and measurement capabilities. Figure 5 bottom shows two images of the DS 106 obtained with this device. The picture on the right is an enlarged image of the left side; a crack is shown in PWAS.

Figure 5. Top: Investigating the DS 122 with 300 scanning acoustic microscope (SAM); middle: Images obtained with

digital microscope VHX 5000, DS106; and bottom: Areas of interest PWAS health monitoring.

bonding of PWAS to the specimen, and (c) damage of PWAS itself.

124 Structural Health Monitoring from Sensing to Processing

## 5.1. The effects of the harsh environment on PWAS and DS EMIS signature

Two specimens exposed to harsh environmental conditions in the laboratory simulations are free PWAS sensors and circular plates with central bonded PWAS. EMIS was recorded both during exposure to harsh conditions, and in the intervals between these exposures, at RT, see Table 2. The technical details of the factors involved in one cycle of harsh environment exposure are presented in Table 3. The first stage of the complex test protocol stipulated five cycles of concomitant outer-space condition: high-temperature variation, radiation, and vacuum.

In the test program has been used special harsh environment simulation equipment, starting with the Dewar cryogenic vessel, and the convection oven with the Memmert UFE 400 digital temperature controller. Also, some of the experiments at negative temperatures were performed at INCAS in the environmental chamber INSTRON 5982, and the high temperatures in the thermostatic chamber FD 115 Binder.

The test program also developed experiments at the Horia Hulubei national institute for R and D in physics and nuclear engineering-IFIN-HH, in the gamma irradiation chamber 5000 with 60-Co circular distributed sources. The details are presented in the paper [26]. The measured radiation flow was 4.7 kGy/h. Five consecutive test cycles (Table 3) were programmed to provide a full irradiation dose of 23.5 kGy. The premise of the calculations was as follows: (a) the estimated


Table 2. Complex testing protocol for simulation of harsh space type conditions - first stage of complex tests.


Table 3. Overview of one test cycle of cumulative environmental factors: Radiation, temperature, and vacuum tests.

complete dose for a mission on Mars is 110 mGy/year, which means a dose of about 15 μGy/h; (b) the highest absorbed doses determined by the Pioneer probes 10 and 11 were 15 kGy, and 4.3 kGy, respectively. Consequently, the dose rate determined by the gamma 5000 irradiation chamber has been considered as acceptable. The absorbed dose of 23.5 kGy corresponded to 5 h exposure at the measured dose of 4.7 kGy/h. The usual vacuum in the outer space is 10<sup>14</sup> Pa. Vacuum pressures below 10<sup>1</sup> Pa were obtained by using a tritium manifold, a high-vacuum plant containing a vacuum pump type TSH-171E Pfeiffer, and pressure vacuum controllers type TPG 262 Pfeiffer.

The effects of harsh environment on PWAS. After performing the tests according to the protocols in Tables 2 and 3, it is noted that the resonance frequencies on the EMIS PWAS graphs are constantly moving from left to right when temperatures drop from high (+150C) to cryogenic values (70C), as shown in Figure 8a. After completion of the tests at extreme

A compensation technique [26, 28], in fact, a horizontal displacement of graphs, was used to obtain graphs in Figure 8b. As far as irradiations are concerned, they cause insignificant changes to EMIS signatures (Figure 8c). Thus, we can conclude that EMIS signature changes caused by environmental factors are reversible and consequently do not characterize real damage. The real damages are those of mechanical origin, which produce irreversible changes

The effects on pristine DS. The EMIS behavior at extreme temperatures was analyzed on a set of 4 DS. Initially, the EMIS graph at RT (+25C) was recorded. Next, tests at low temperatures,

Initial RT EMIS recording of 26 DS; 10 of them was eliminated

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(2 DS), 25 mm (3 DS), 15 mm (3 DS), and 7 mm (2 DS)

Fabrication of arc type mechanical damages (MD): arc at 45 mm

Tests and EMIS recording at low temperatures for 4 DS: 0, 25, 50,

Tests and EMIS recording at high temperatures for 4 DS: +50, +75,

Irradiation tests and EMIS recording for 2 DS at 3.71 Gy/h

Figure 8. EMIS PWAS signatures: (a) synoptic graph of temperature cycling; (b) initial and after temperature cycling,

both at RT, compensated values; and (c) initial and after irradiation tests, both at RT.

temperatures, measurements were again made at RT.
