**Operational Modal Analysis of Super Tall Buildings by a Bayesian Approach**

Feng-Liang Zhang and Yan-Chun Ni

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68397

#### Abstract

[18] Jiang SF, Wu SY, Dong LQ. A time-domain structural damage detection method based on improved multiparticle swarm coevolution optimization algorithm. Mathematical Prob-

[19] Shi ZY, Law SS, Zhang LM. Structural damage localization from modal strain energy

[20] Koh CG, Perry MJ. Structural Identification and Damage Detection using Genetic Algo-

[21] Ma SL, Jiang SF, Weng LQ. Two-stage damage identification based on modal strain energy and revised particle swarm optimization. International J of Structural Stability and Dynam-

change. Journal of Sound and Vibration. 1998;218(5):825–844

rithms. London, UK: Structures and Infrastructures Series; 2010

lems in Engineering. 2014;2014(2):77–85

64 Structural Health Monitoring - Measurement Methods and Practical Applications

ics. 2014;14(5):1440005

Structural health monitoring (SHM) has attracted increasing attention in the past few decades. It aims at monitoring the existing structures based on data acquired by different sensor networks. Modal identification is usually the first step in SHM, and it aims at identifying the modal parameters mainly including natural frequency, damping ratio and mode shape. Three different field tests can be used to collect data for modal identification, among which, ambient vibration test is the most convenient and economical one since it does not require to measure input information. This chapter will focus on the operational modal analysis (OMA), i.e. ambient modal identification of four super tall buildings by a Bayesian approach. A fast frequency domain Bayesian fast fourier transform (FFT) approach will be introduced for OMA. In addition to the most probable value (MPV) of modal parameters, the associated posterior uncertainty will be also investigated analytically. The field tests will be presented and the difficulties encountered will be discussed. Some basic dynamic characteristics will be investigated and discussed. The studies will provide baseline properties of these super tall buildings and provide a reference for future condition assessments.

Keywords: structural health monitoring, operational modal analysis, ambient vibration test, super tall buildings, posterior uncertainty, Bayesian method

#### 1. Introduction

Structural health monitoring has attracted increasing attention in the past few decades [1–3]. In the past decade, much more super tall buildings have been constructed and most of them were instrumented structural health monitoring (SHM) systems, for example, Canton Tower with the height of 610 m, on which more than 700 sensors were installed to form a sophisticated long-term SHM systems [3, 4]; Burj Khalifa, the tallest building in the world with the height of

© 2017 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.

828 m, on which an integrated real-time SHM system was instrumented [5]; Shanghai Tower with the height of 632 m and so on. Some super tall buildings are still under construction, such as Pingan International Financial Center with a height of 660 m, Shenzhen, China; Wuhan Greenland Center with a height of 636 m, Wuhan, China; Kingdom Tower with the height of 1007 m, Jeddah, Saudi Arabia. These systems play an important role in monitoring the structural conditions and making an assessment when extreme events happen. For some super tall buildings, although their heights are also more than 300 m, no long-term SHM systems were installed. Some short-term monitoring was also carried out [6, 7], for example, Building A with the height of 310 m, Hong Kong; Building B with the height of 320 m, Hong Kong; International Finance Centre with the height of 416 m, Hong Kong; etc. When some typhoons came, vibration data were collected to investigate the dynamic characteristics of these buildings.

For these super tall buildings, the monitoring of acceleration response plays an important role since the dynamic characteristics mainly including natural frequencies, damping ratios and modes shapes can be determined. They are the typical characteristics of the structures and will remain unchanged if there is no significant damage and can be used for model updating, damage detection and SHM [8–10]. The natural frequencies can help to find potential vibration problem, e.g. resonance, and then some measures can be designed to alleviate them. The damping ratio can affect the vibration level and energy dissipation capability of the structure. In the structure designing, this quantity is usually set to be constant, e.g., 5%. However, in reality, it can be affected by many factors, for example, vibration amplitude. Therefore, knowing damping ratio can better assess the structural response and provides a reference in the structural design. The mode shapes can reflect the stiffness and mass distribution and the boundary conditions of objective structures, whose change across extreme events can be used for damage detection and SHM.

To obtain the modal parameters, modal identification needs to be carried out using structural response. Acceleration and velocity data are commonly used for modal identification. There are three main ways to collect structural responses, which are free vibration test, forced vibration test and ambient vibration test. The first one is to collect structural response when the structure is under free vibration dominantly. However, for the structures in civil engineering, it is usually difficult for them to vibrate freely. The second one is to collect structural response when given some known excitation during the test. This method can improve the vibration level and provide a high signal to noise ratio for the structural response. However, to produce forced vibration, special equipment such as a high payload shaker is required. This makes the test expensive and some unexpected damage may be caused if the equipment cannot be well controlled. The third one, compared with the former two tests, is more convenient and economical since no additional excitations are required. The excitations are mainly from the ambient loading, e.g. wind, traffic loading, human walking, environmental noise, and so on. For this test, it requires high quality sensors with a lower noise level to improve the signal to noise ratio. If the noise level is too high, the modal parameters identified may have higher uncertainty.

Ambient modal identification, also called operational modal analysis (OMA), can be used to obtain the modal parameters using ambient vibration data [11]. The excitation is usually assumed to be stochastic stationary. Many methods have been developed for OMA, for example, stochastic subspace identification (SSI) [12], peak-picking (PP), and frequency domain decomposition (FDD) [13]. In addition to these non-Bayesian methods, a series of Bayesian methods have been developed [14–15], for example, Bayesian spectral density approach, Bayesian time domain method, and Bayesian fast fourier transform (FFT) approach. Recently, a fast Bayesian FFT method has been developed based on Bayesian FFT approach [16–20]. It has been extended to forced vibration data [21], free vibration data [22–23], and so on. This method views modal identification as an inference problem where the probability is taken as a measure for the relative plausibility of outcomes given a model of the structure and measured data. Both the most probable value (MPV) and the associated posterior uncertainty can be determined, making it possible to assess the accuracy of the identified modal parameters.

Based on the technique of OMA, many super tall buildings have been studied, for example, Canton Tower, super tall buildings in Hong Kong, and so on. This chapter presents the work on OMA of four different super tall buildings, including two super tall buildings in Hong Kong, Canton Tower and Shanghai Tower. It is organized as follows. In Section 2, the fast Bayesian FFT method will be introduced and it will be used for the latter study in the MPV and the associated posterior uncertainty. In Section 3, the OMA of two super tall buildings in Hong Kong will be presented. The data were collected during different strong wind events. The amplitudedependence behaviour of modal parameters was investigated. In Section 4, Canton Tower was studied using the data collected during one day's measurement by the SHM system installed. In Section 5, Shanghai Tower, the second tallest building in the world until now, was investigated by ambient vibration tests in different stages. Finally, the summary is given in Section 6.

#### 2. Fast Bayesian FFT method

828 m, on which an integrated real-time SHM system was instrumented [5]; Shanghai Tower with the height of 632 m and so on. Some super tall buildings are still under construction, such as Pingan International Financial Center with a height of 660 m, Shenzhen, China; Wuhan Greenland Center with a height of 636 m, Wuhan, China; Kingdom Tower with the height of 1007 m, Jeddah, Saudi Arabia. These systems play an important role in monitoring the structural conditions and making an assessment when extreme events happen. For some super tall buildings, although their heights are also more than 300 m, no long-term SHM systems were installed. Some short-term monitoring was also carried out [6, 7], for example, Building A with the height of 310 m, Hong Kong; Building B with the height of 320 m, Hong Kong; International Finance Centre with the height of 416 m, Hong Kong; etc. When some typhoons came, vibration data were collected to investigate the dynamic characteristics of these buildings.

66 Structural Health Monitoring - Measurement Methods and Practical Applications

For these super tall buildings, the monitoring of acceleration response plays an important role since the dynamic characteristics mainly including natural frequencies, damping ratios and modes shapes can be determined. They are the typical characteristics of the structures and will remain unchanged if there is no significant damage and can be used for model updating, damage detection and SHM [8–10]. The natural frequencies can help to find potential vibration problem, e.g. resonance, and then some measures can be designed to alleviate them. The damping ratio can affect the vibration level and energy dissipation capability of the structure. In the structure designing, this quantity is usually set to be constant, e.g., 5%. However, in reality, it can be affected by many factors, for example, vibration amplitude. Therefore, knowing damping ratio can better assess the structural response and provides a reference in the structural design. The mode shapes can reflect the stiffness and mass distribution and the boundary conditions of objective structures,

To obtain the modal parameters, modal identification needs to be carried out using structural response. Acceleration and velocity data are commonly used for modal identification. There are three main ways to collect structural responses, which are free vibration test, forced vibration test and ambient vibration test. The first one is to collect structural response when the structure is under free vibration dominantly. However, for the structures in civil engineering, it is usually difficult for them to vibrate freely. The second one is to collect structural response when given some known excitation during the test. This method can improve the vibration level and provide a high signal to noise ratio for the structural response. However, to produce forced vibration, special equipment such as a high payload shaker is required. This makes the test expensive and some unexpected damage may be caused if the equipment cannot be well controlled. The third one, compared with the former two tests, is more convenient and economical since no additional excitations are required. The excitations are mainly from the ambient loading, e.g. wind, traffic loading, human walking, environmental noise, and so on. For this test, it requires high quality sensors with a lower noise level to improve the signal to noise ratio. If the noise level is too high,

Ambient modal identification, also called operational modal analysis (OMA), can be used to obtain the modal parameters using ambient vibration data [11]. The excitation is usually assumed to be stochastic stationary. Many methods have been developed for OMA, for example, stochastic subspace identification (SSI) [12], peak-picking (PP), and frequency domain decomposition (FDD) [13]. In addition to these non-Bayesian methods, a series of Bayesian

whose change across extreme events can be used for damage detection and SHM.

the modal parameters identified may have higher uncertainty.

#### 2.1. Bayesian method for single setup

A fast Bayesian FFT approach is employed to identify the modal properties of the instrumented building using the recorded ambient vibration data in a single setup. The theory is briefly described here. The reader is referred to Ref. [14] for the original formulation and to Refs. [11, 16–18] for a recently developed fast algorithm that allows practical implementation.

The measured acceleration data are assumed to consist of the structural ambient vibration signal and prediction error

$$
\ddot{\mathbf{y}}\_j = \ddot{\mathbf{x}}\_j + \mathbf{e}\_j \tag{1}
$$

where x€<sup>j</sup> ∈R<sup>n</sup> and e<sup>j</sup> ∈ Rn (j = 1,2,…, N), respectively, denote the theoretical structural acceleration response and the prediction error, n measured degrees of freedom (DOFs), N the sampling points number. The FFT of the collected data y€<sup>j</sup> is given by

$$\mathcal{F}\_k = \sqrt{\frac{2\Delta t}{N}} \sum\_{j=1}^{N} \ddot{\mathbf{y}}\_j \exp\left[-2\pi \mathbf{i} \frac{(k-1)(j-1)}{N}\right] \tag{2}$$

in which i <sup>2</sup> ¼ �1, <sup>Δ</sup><sup>t</sup> the sampling interval, <sup>k</sup> <sup>¼</sup> <sup>1</sup>, …, Nq with Nq <sup>¼</sup> int½N=2� þ <sup>1</sup>, int½:� the integer part.

Let θ denote the targeted modal parameters, including f <sup>i</sup> , ζi, ϕ<sup>i</sup> , i ¼ 1, …, m (m is the number of modes), where fi and ζ<sup>i</sup> denote, respectively, the natural frequency and damping ratio of the i-th mode, and <sup>ϕ</sup><sup>i</sup> <sup>∈</sup> Rn is the <sup>i</sup>-th mode shape vector; <sup>S</sup>∈Rm�<sup>m</sup>, Se, the (symmetric) power spectral density (PSD) of modal forces and the PSD of prediction error, respectively.

Let <sup>Z</sup><sup>k</sup> ¼ ½ReFk; ImFk� <sup>∈</sup>R<sup>2</sup><sup>n</sup> denote the real and imaginary parts of the FFT data at fk, where f<sup>k</sup> is the FFT frequency abscissa. When performing the modal identification, the FFT data in a selected frequency band are used and they are denoted by fZkg. Based on Bayes' theorem, the posterior probability density function (PDF) of θ can be expressed as

$$p(\boldsymbol{\Theta}|\{\mathbf{Z}\_{k}\}) \propto p(\boldsymbol{\Theta})p(\{\mathbf{Z}\_{k}\}|\boldsymbol{\Theta}) \tag{3}$$

in which p(θ) denotes the prior PDF. The prior information is assumed to be uniform, and so the posterior PDF can be taken to be proportional to the 'likelihood function' pðfZkgjθÞdirectly. The 'most probable value' (MPV) of θ can be obtained by maximizing pðfZkgjθÞ.

When N is large and Δt is small, the FFT can be shown to be asymptotically independent at different frequencies and follows a Gaussian distribution [14]. Therefore, pðfZkgjθÞ can be expressed as

$$p(\{\mathbf{Z}\_k\}|\mathbf{\Theta}) = \prod\_k \frac{1}{(2\pi)^n (\det \mathbf{C}\_k)^{1/2}} \exp\left[ -\frac{1}{2} \mathbf{Z}\_k^T \mathbf{C}\_k^{-1} \mathbf{Z}\_k \right] \tag{4}$$

in which det(.) denotes the determinant, C<sup>k</sup> the covariance matrix of Z<sup>k</sup> given by

$$\mathbf{C}\_{k} = \frac{1}{2} \begin{bmatrix} \mathbf{O} & \\ & \mathbf{O} \end{bmatrix} \begin{bmatrix} \text{Re}\mathbf{H}\_{k} & -\text{Im}\mathbf{H}\_{k} \\ \text{Im}\mathbf{H}\_{k} & \text{Re}\mathbf{H}\_{k} \end{bmatrix} \begin{bmatrix} \mathbf{O}^{T} & \\ & \mathbf{O}^{T} \end{bmatrix} + \frac{\mathbf{S}\_{\varepsilon}}{2} \mathbf{I}\_{2n} \tag{5}$$

and <sup>I</sup>2<sup>n</sup> <sup>∈</sup>R<sup>2</sup><sup>n</sup> denotes the identity matrix, <sup>Φ</sup> ¼ ½ϕ1, <sup>ϕ</sup>2, …, <sup>ϕ</sup>m�<sup>∈</sup> Rn�<sup>m</sup> the mode shape matrix, H<sup>k</sup> ∈R<sup>m</sup>�<sup>m</sup> the transfer matrix, and its (i, j) element can be given by

$$\mathbf{H}\_{k}(\mathbf{i}, \mathbf{j}) = \mathbf{S}\_{i\uparrow} \Big[ \left( \boldsymbol{\beta}\_{\vec{k}}^{2} - \mathbf{1} \right) + \mathbf{2} \mathbf{i} \zeta\_{\vec{\eta}} \boldsymbol{\beta}\_{\vec{k}} \Big]^{-1} \Big[ \left( \boldsymbol{\beta}\_{\vec{\beta}}^{2} - \mathbf{1} \right) - \mathbf{2} \mathbf{i} \zeta\_{\vec{\eta}} \boldsymbol{\beta}\_{\vec{\eta}} \Big]^{-1} \tag{6}$$

and βik ¼ f <sup>i</sup> =fk; fi is the natural frequency of the i-th mode; Sij is the cross spectral density between the i-th and j-th modal excitation. The first and second term in Eq. (5) represent the contribution from the modal response and the prediction error, respectively.

Theoretically, the modal parameters can be determined by maximizing the posterior PDF. However, there are some computational difficulties. To develop an efficient algorithm, a fast algorithm was developed, and it allows the MPV and the associated posterior uncertainty to be obtained efficiently [16–18].

#### 2.2. Bayesian method for multiple setups

In full-scale ambient tests, usually there are a large number of DOFs to be measured, but the number of available sensors is often limited. In this part, a fast Bayesian method for modal identification of well separated modes incorporating data from multiple setups will be presented. For the details of this part, please refer to [11, 19, 20].

Assume that in a selected frequency band, there is only one contributing mode and ϕ ∈ Rn denotes the global mode shape containing all the DOFs of interest. To relate the ϕ to the mode shape in a given setup covering a possibly different set of DOFs, the selection matrix in Setup i <sup>ð</sup><sup>i</sup> <sup>¼</sup> <sup>1</sup>, …, nsÞ, <sup>L</sup><sup>i</sup> <sup>∈</sup>Rni�<sup>n</sup> will be defined and ni denotes the number of measured DOFs in Setup i. In Setup i, the (j,k) entry of L<sup>i</sup> is set to 1 when DOF k is measured by the j-th channel, and it is equal to zero for the other situations. The theoretical mode shape confined to the measured DOFs in Setup i can be given by <sup>ϕ</sup><sup>i</sup> <sup>¼</sup> <sup>L</sup>i<sup>ϕ</sup> <sup>∈</sup> Rni . The modal parameters to be identified are defined as

$$\Theta = [\![f\_{i'} \zeta\_{i'} \operatorname{S}\_{i'} \operatorname{S}\_{\acute{e}i} : \operatorname{i} = 1, \dots, n\_{\diamond} \operatorname{qp} \in \mathbb{R}^n] \in \mathbb{R}^{4n\_{\diamond} + n} \tag{7}$$

in which f <sup>i</sup> , ζi, Si, Seiði ¼ 1, …, nsÞ denote the modal parameters in Setup i.

Let Z<sup>ð</sup>i<sup>Þ</sup> <sup>k</sup> ¼ ½ReFik; ImFik�<sup>∈</sup> <sup>R</sup><sup>2</sup>ni ði ¼ 1, …, nsÞ denote the FFT data at frequency fk in the i-th setup; <sup>D</sup><sup>i</sup> ¼ fZ<sup>ð</sup>i<sup>Þ</sup> <sup>k</sup> g denote the FFT data in a selected frequency band in Setup i and D ¼ fD<sup>i</sup> : i ¼ 1, …, nsg denote the FFT data in all the setups. Assuming the data in different setups are independent, based on Bayes' Theorem, given the data in all setups, the posterior PDF of θ is given by

$$p(\boldsymbol{\Theta}|\mathcal{D}) \propto p(\{D\_1, D\_2, \dots, D\_{n\_\*}\}|\mathcal{G}) = p(D\_1|\mathcal{G})p(D\_2|\mathcal{G})\dots p(D\_{n\_\*}|\mathcal{G})\tag{8}$$

Note that pðDijθÞ is independent with the modal parameters in other setups, and so pðDijθÞ ¼ pðDijf <sup>i</sup> , ζi, Si, Sei, ϕ<sup>i</sup> Þ. Eq. (8) can be given by

$$p(\boldsymbol{\Theta}|\mathcal{D}) \propto \prod\_{i=1}^{n\_{\boldsymbol{\epsilon}}} p(\mathcal{D}\_i|\boldsymbol{f}\_{i^{\boldsymbol{\epsilon}}} \zeta\_{i\boldsymbol{\epsilon}} \operatorname{S}\_{i\boldsymbol{\epsilon}} \operatorname{S}\_{\boldsymbol{\epsilon}i\boldsymbol{\epsilon}} \operatorname{q}\_i) \tag{9}$$

Similar to above section, pðDijf <sup>i</sup> , ζi, Si, Sei, ϕ<sup>i</sup> Þ is asymptotically a Gaussian distribution, with negative log-likelihood function (NLLF)

$$L\_i(\boldsymbol{\Theta}\_i) = \frac{1}{2} \sum\_k \left[ \ln \det \mathbf{C}\_{ik}(\boldsymbol{\Theta}\_i) + \mathbf{Z}\_k^{(i)T} \mathbf{C}\_{ik}(\boldsymbol{\Theta}\_i)^{-1} \mathbf{Z}\_k^{(i)} \right] \tag{10}$$

in which θ<sup>i</sup> ¼ ff <sup>i</sup> , ζi, Si, Sei, ϕ<sup>i</sup> g and

Let θ denote the targeted modal parameters, including f <sup>i</sup>

68 Structural Health Monitoring - Measurement Methods and Practical Applications

<sup>p</sup>ðfZkgjθÞ ¼ <sup>Y</sup>

<sup>C</sup><sup>k</sup> <sup>¼</sup> <sup>1</sup> 2 Φ k

Φ

H<sup>k</sup> ∈R<sup>m</sup>�<sup>m</sup> the transfer matrix, and its (i, j) element can be given by

<sup>H</sup>kði, jÞ ¼ Sij <sup>β</sup><sup>2</sup>

ð2πÞ n ðdetCkÞ

in which det(.) denotes the determinant, C<sup>k</sup> the covariance matrix of Z<sup>k</sup> given by

� � ReH<sup>k</sup> �ImH<sup>k</sup>

ik � <sup>1</sup> � � <sup>þ</sup> <sup>2</sup>iζiβik � ��<sup>1</sup> β<sup>2</sup>

contribution from the modal response and the prediction error, respectively.

expressed as

and βik ¼ f <sup>i</sup>

obtained efficiently [16–18].

2.2. Bayesian method for multiple setups

density (PSD) of modal forces and the PSD of prediction error, respectively.

posterior probability density function (PDF) of θ can be expressed as

, ζi, ϕ<sup>i</sup>

pðθjfZkgÞ∝ pðθÞpðfZkgjθÞ ð3Þ

modes), where fi and ζ<sup>i</sup> denote, respectively, the natural frequency and damping ratio of the i-th mode, and <sup>ϕ</sup><sup>i</sup> <sup>∈</sup> Rn is the <sup>i</sup>-th mode shape vector; <sup>S</sup>∈Rm�<sup>m</sup>, Se, the (symmetric) power spectral

Let <sup>Z</sup><sup>k</sup> ¼ ½ReFk; ImFk� <sup>∈</sup>R<sup>2</sup><sup>n</sup> denote the real and imaginary parts of the FFT data at fk, where f<sup>k</sup> is the FFT frequency abscissa. When performing the modal identification, the FFT data in a selected frequency band are used and they are denoted by fZkg. Based on Bayes' theorem, the

in which p(θ) denotes the prior PDF. The prior information is assumed to be uniform, and so the posterior PDF can be taken to be proportional to the 'likelihood function' pðfZkgjθÞdirectly.

When N is large and Δt is small, the FFT can be shown to be asymptotically independent at different frequencies and follows a Gaussian distribution [14]. Therefore, pðfZkgjθÞ can be

<sup>1</sup>=<sup>2</sup> exp � <sup>1</sup>

2 Zk <sup>T</sup>C<sup>k</sup> �1 Zk

� �

Φ<sup>T</sup> � �

jk � 1 � �

=fk; fi is the natural frequency of the i-th mode; Sij is the cross spectral density

þ Se 2

� 2iζjβjk h i�<sup>1</sup>

1

ImH<sup>k</sup> ReH<sup>k</sup> � � Φ<sup>T</sup>

and <sup>I</sup>2<sup>n</sup> <sup>∈</sup>R<sup>2</sup><sup>n</sup> denotes the identity matrix, <sup>Φ</sup> ¼ ½ϕ1, <sup>ϕ</sup>2, …, <sup>ϕ</sup>m�<sup>∈</sup> Rn�<sup>m</sup> the mode shape matrix,

between the i-th and j-th modal excitation. The first and second term in Eq. (5) represent the

Theoretically, the modal parameters can be determined by maximizing the posterior PDF. However, there are some computational difficulties. To develop an efficient algorithm, a fast algorithm was developed, and it allows the MPV and the associated posterior uncertainty to be

In full-scale ambient tests, usually there are a large number of DOFs to be measured, but the number of available sensors is often limited. In this part, a fast Bayesian method for modal

The 'most probable value' (MPV) of θ can be obtained by maximizing pðfZkgjθÞ.

, i ¼ 1, …, m (m is the number of

ð4Þ

ð6Þ

I2<sup>n</sup> ð5Þ

$$\mathbf{C}\_{ik}(\boldsymbol{\Theta}\_{i}) = \frac{S\_{i}D\_{ik}}{2} \begin{bmatrix} \boldsymbol{\upmu}\_{i}\boldsymbol{\upmu}\_{i}^{T} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{\upmu}\_{i}\boldsymbol{\upmu}\_{i}^{T} \end{bmatrix} + \frac{S\_{ei}}{2}\mathbf{I}\_{2n} \tag{11}$$

is the theoretical covariance matrix of the FFT data at the k-th frequency abscissa in Setup i, in which

$$D\_{\vec{k}}(f\_{\vec{\nu}}\zeta\_i) = \left[ (\mathcal{J}\_{\vec{\text{ik}}}^2 - 1)^2 + (2\zeta\_i\beta\_{\vec{\text{ik}}})^2 \right]^{-1} \tag{12}$$

with βik ¼ f <sup>i</sup> =fk. Consequently,

$$p(\boldsymbol{\Theta}|\mathcal{D}) \propto \exp\left(-L(\boldsymbol{\Theta})\right) \tag{13}$$

in which

$$L(\Theta) = \sum\_{i=1}^{n\_s} L\_i(\Theta\_i) \tag{14}$$

Similar to the case in single setup in Section 2.1., there are some computational difficulties. For the purpose of developing a fast computational procedure, it is found detCik and C�<sup>1</sup> ik can be analysed and obtained in a more manageable form. As a result (proof omitted here), the overall NLLF can be reformulated as

$$\begin{aligned} L(\boldsymbol{\Theta}) &= -(\ln 2) \sum\_{i=1}^{n\_s} n\_i \mathbf{N}\_{fi} + \sum\_{i=1}^{n\_s} (n\_i - 1) \mathbf{N}\_{fi} \ln \mathbf{S}\_{ci} \\ &+ \sum\_{i=1}^{n\_s} \sum\_{k} \ln(\mathbf{S}\_i \mathbf{D}\_{ik} \|\mathbf{L}\_i \mathbf{q}\|^2 + \mathbf{S}\_{ci}) + \sum\_{i=1}^{n\_s} \mathbf{S}\_{ci}^{-1} d\_i - \mathbf{q}^T \mathbf{A}(\mathbf{q}) \mathbf{q} \end{aligned} \tag{15}$$

where

$$\mathbf{A}(\boldsymbol{\varrho}) = \sum\_{i=1}^{n\_s} \mathbf{S}\_{ei}^{-1} \sum\_{k} (\|\mathbf{L}\_i \boldsymbol{\varrho}\|\|^2 + \frac{\mathbf{S}\_{ei}}{\mathbf{S}\_i D\_{ik}})^{-1} \mathbf{L}\_i^T \mathbf{D}\_{ik} \mathbf{L}\_i \in \mathbb{R}^{n \times n} \tag{16}$$

$$\mathbf{D}\_{\vec{k}} = \mathbf{Re}\mathcal{F}\_{\vec{k}}\mathbf{Re}\mathcal{F}\_{\vec{k}}{}^{T} + \mathbf{Im}\mathcal{F}\_{\vec{k}}\mathbf{Im}\mathcal{F}\_{\vec{k}}{}^{T} \in \mathbb{R}^{n \times n\text{-}i} \tag{17}$$

$$d\_{\vec{l}} = \sum\_{\vec{k}} (\mathbf{Re} \mathcal{F}\_{\vec{k}} \, ^T \mathbf{Re} \mathcal{F}\_{\vec{k}} + \mathbf{Im} \mathcal{F}\_{\vec{k}} \, ^T \mathbf{Im} \mathcal{F}\_{\vec{k}}) \tag{18}$$

Based on Eq. (15), an iterative scheme for the full set of solution of modal parameters can be developed, which makes the identification of modal parameters very efficiently even for a large number of measured DOFs. The associated posterior uncertainties can be calculated by the analytical formulas without resorting to finite difference. Details can be found in Refs. [19, 20].

#### 3. Two super tall buildings in Hong Kong

Buildings A and B are two super tall buildings in Hong Kong. Building A is 310 m tall, 50 m by 50 m in plan, which is a tabular concrete building with a central core wall system. Building B is 320 m tall, 50 m � 50 m in plan, whose lateral structural resistance is provided by two outrigger trusses with core walls near the centre and mega columns at the corner. Figure 1 shows the mode Operational Modal Analysis of Super Tall Buildings by a Bayesian Approach http://dx.doi.org/10.5772/intechopen.68397 71

Figure 1. Mode shapes of Buildings A and B identified under normal wind.

Dikðf <sup>i</sup>

70 Structural Health Monitoring - Measurement Methods and Practical Applications

=fk. Consequently,

overall NLLF can be reformulated as

þ Xns i¼1

LðθÞ ¼ �ðln 2Þ

X k

<sup>A</sup>ðϕÞ ¼ <sup>X</sup>ns

3. Two super tall buildings in Hong Kong

i¼1 S�<sup>1</sup> ei X k

di <sup>¼</sup> <sup>X</sup> k

Dik ¼ ReFikReFik

ðReFik

with βik ¼ f <sup>i</sup>

in which

where

[19, 20].

, <sup>ζ</sup>iÞ¼ ðβ<sup>2</sup>

ik � 1Þ

<sup>L</sup>ðθÞ ¼ <sup>X</sup>ns

the purpose of developing a fast computational procedure, it is found detCik and C�<sup>1</sup>

niNf i <sup>þ</sup>Xns

ðkLiϕk<sup>2</sup> <sup>þ</sup>

lnðSiDikkLiϕk<sup>2</sup> <sup>þ</sup> SeiÞ þXns

Xns i¼1

i¼1

Similar to the case in single setup in Section 2.1., there are some computational difficulties. For

analysed and obtained in a more manageable form. As a result (proof omitted here), the

i¼1

ðni � 1ÞNf iln Sei

i¼1 S�<sup>1</sup>

Sei SiDik Þ �1 LT

<sup>T</sup> <sup>þ</sup> ImFikImFik

<sup>T</sup>ReFik <sup>þ</sup> ImFik

Based on Eq. (15), an iterative scheme for the full set of solution of modal parameters can be developed, which makes the identification of modal parameters very efficiently even for a large number of measured DOFs. The associated posterior uncertainties can be calculated by the analytical formulas without resorting to finite difference. Details can be found in Refs.

Buildings A and B are two super tall buildings in Hong Kong. Building A is 310 m tall, 50 m by 50 m in plan, which is a tabular concrete building with a central core wall system. Building B is 320 m tall, 50 m � 50 m in plan, whose lateral structural resistance is provided by two outrigger trusses with core walls near the centre and mega columns at the corner. Figure 1 shows the mode

<sup>2</sup> þ ð2ζiβik<sup>Þ</sup> <sup>2</sup> h i�<sup>1</sup>

pðθjDÞ∝ exp ð�LðθÞÞ ð13Þ

ei di � <sup>ϕ</sup><sup>T</sup>AðϕÞ<sup>ϕ</sup>

LiðθiÞ ð14Þ

<sup>i</sup> <sup>D</sup>ikL<sup>i</sup> <sup>∈</sup> Rn�<sup>n</sup> <sup>ð</sup>16<sup>Þ</sup>

<sup>T</sup> <sup>∈</sup>Rni�ni <sup>ð</sup>17<sup>Þ</sup>

<sup>T</sup>ImFikÞ ð18<sup>Þ</sup>

ð12Þ

ik can be

ð15Þ

shapes of the first three modes of Buildings A and B. They were identified based on ambient data by placing four tri-axial accelerometers at four corners on the roof. The two numbers near to the mode name are the natural frequency and damping ratio, respectively. For Building B, due to connection to a neighbouring building, the principal modal directions do not align with the building sides.

Figure 2 shows the sensor layout inside the rooms on the roof of the buildings, and the sensor locations were kept the same for all the typhoon events. The vibration data investigated were measured during two typhoon events (namely, Typhoon Goni and Koppu) and two monsoon events (MS1 and MS2). Typhoon Goni attacked Hong Kong during 4–6 August 2009. The wind speed changed between 22 and 60 km/hr. One month later, Typhoon Koppu attacked Hong Kong. Koppu travelled faster than Goni. The wind speed changed between 25 and 120 km/hr. Typhoon Koppu provides much more information due to large structural vibrations in the current study. The MS1 visited during 4–7 January 2010. The wind speed changed between 15 and 50 km/hr. The MS2 visited in December 2010. The wind speed ranged between 12 and 45 km/ hr. The wind speeds in the two monsoon events are significantly lower than those in the typhoon events. The typhoon events can provide information for large amplitude vibration study, while the monsoon events can provide information in the low to moderate wind speed regime.

The recorded acceleration data are used for identifying the modal parameters of the structures by the Bayesian method. For the purpose that the loading and the response can be modelled as stationary stochastic process, the whole time history is divided into non-overlapping time windows of 30 minutes. Figure 3 shows the singular value (SV) spectra of the first half hour data of Building A during Typhoon Koppu. Six modes below 1 Hz can be observed while the

(a) Building A (b) Building B

Figure 2. Equipment used during strong wind event.

Figure 3. Root singular value spectra, 30-minute acceleration data, Building A.

first two modes are closely spaced. Similarly, in Building B, whose SV spectra is omitted here, there are also six modes below 1 Hz and the first two modes are closely spaced modes. The closely spaced modes may be due to their square-shaped floor plan of Buildings A and B. The first three modes are investigated including the first two translational modes and the first torsional mode.

Table 1 shows the modal parameters for Building A. The MPV of modal parameters and the corresponding posterior coefficient of variations (c.o.v.) are provided in the table. The posterior c.o.v.s of the natural frequencies are all less than 1%, which are much smaller than those of the damping ratio or the PSD of modal force. The posterior uncertainty of the damping ratio governs the data length requirement and with 30 minutes of data its c. o.v. is about 30%, showing a moderate level of accuracy. Similar investigation to Building B is also performed.

Next, the correlation between the identified natural frequencies and damping ratios with the vibration amplitude calculated based on Ref. [6] is investigated. Figures 4 and 5, respectively, show the MPV of natural frequencies and damping ratios versus the modal vibration rootmean-square (RMS) for Buildings A and B. The results for all time windows in four different events are plotted in the figure. A circle, a cross and a triangle denote the results for Typhoon Goni, Typhoon Koppu and MS2, respectively, in Building A, while for Building B, a cross and a


Table 1. Summary of identified modal properties, building A, first 30 minutes in Koppu.

first two modes are closely spaced. Similarly, in Building B, whose SV spectra is omitted here, there are also six modes below 1 Hz and the first two modes are closely spaced modes. The closely spaced modes may be due to their square-shaped floor plan of Buildings A and B. The first three modes are investigated including the first two translational modes and the first

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(a) Building A (b) Building B

Frequency (Hz)

Table 1 shows the modal parameters for Building A. The MPV of modal parameters and the corresponding posterior coefficient of variations (c.o.v.) are provided in the table. The posterior c.o.v.s of the natural frequencies are all less than 1%, which are much smaller than those of the damping ratio or the PSD of modal force. The posterior uncertainty of the damping ratio governs the data length requirement and with 30 minutes of data its c. o.v. is about 30%, showing a moderate level of accuracy. Similar investigation to Building

torsional mode.

10-7

10-6

10-5

[g/sqrt(Hz)]

10-4

**Mode1**

Figure 2. Equipment used during strong wind event.

**[**

**Mode2**

72 Structural Health Monitoring - Measurement Methods and Practical Applications

**]** [ ]

Figure 3. Root singular value spectra, 30-minute acceleration data, Building A.

**Mode3**

10-3

B is also performed.

Figure 4. Identified modal frequency and damping ratio versus modal RMS of Building A (o: Goni; �: Koppu; ⊳: MS2).

Figure 5. Identified modal frequency and damping ratio versus modal RMS of Building B (: Koppu, ⊳: MS1).

triangle, respectively, denote the result for Typhoon Koppu and MS1. In the figures, each point is centred at the MPV with an error bar covering +/– one posterior standard derivation of the modal parameter. It is obvious from that the scatter in the MPV is significantly larger than those implied by the error bars, indicating some systematic dependence on the vibration amplitude.

There is an inverse trend between the natural frequency and the RMS value of the modal response, regardless of mode and building. Due to a season effect, the identified natural frequencies in Koppu () (in summer) are not the same with those in MS1 (⊳) (in winter) at low modal RMS. The natural frequency tends to decrease with the increase of modal RMS. One possible reason is the loosening of friction joints at sufficiently high vibration levels, which results in the reduction of stiffness. The right column of Figures 4 and 5 shows a positive correlation between the damping ratio and RMS. Compared to that in the frequencies, the scatter is much bigger. The scatter in these figures can be due to limited identification precision, modelling error in the damping mechanism, modelling error in stationarity, unknown amplitude-dependence mechanism, etc. For the more detailed information of the study about the two super tall buildings, please refer to [6].

#### 4. Canton Tower

The Canton Tower as shown in Figure 6 situated in Guangzhou, China, is a super tall structure with a height of 610 m. It is composed of two tube-like structures, i.e., a reinforced concrete inner structure and a steel outer structure with concrete-filled-tube (CFT) columns.

The SHM system deployed on the Canton Tower is composed by more than 700 sensors, including anemometers, accelerometers, fibre optic strain and temperature sensors, global position system, and so on [24, 25]. Among them, 20 uni-axial accelerometers are installed on eight different cross-sections of the inner structure. On cross-sections 4 and 8, four accelerometers are instrumented at two locations for bi-axial measurement; while on each of the other cross-sections, two sensors are installed at two locations for uni-axial measurement. Sensors 01, 03, 05, 07, 08, 11, 13, 15, 17, 18 are deployed to collect the structural response in the shortaxis direction, while sensors 02, 04, 06, 09, 10, 12, 14, 16, 19, 20 measure the structural response in the long-axis direction. The frequency range of accelerometers is DC to 50 Hz and amplitude range is 2 g. The 24-hour acceleration data were collected from 18:00, 20th January 2010 to 18:00, 21st January 2010 under normal wind condition. The sampling frequencies of acceleration are set to be 50 Hz.

As the last example, the 24-hour data were separated into 48 time windows with 30 minutes for each window. Figure 7 shows the root PSD spectra of the structural responses of a typical

Figure 6. Overview of Canton Tower.

triangle, respectively, denote the result for Typhoon Koppu and MS1. In the figures, each point is centred at the MPV with an error bar covering +/– one posterior standard derivation of the modal parameter. It is obvious from that the scatter in the MPV is significantly larger than those implied by the error bars, indicating some systematic dependence on the vibration

Figure 5. Identified modal frequency and damping ratio versus modal RMS of Building B (: Koppu, ⊳: MS1).

74 Structural Health Monitoring - Measurement Methods and Practical Applications

There is an inverse trend between the natural frequency and the RMS value of the modal response, regardless of mode and building. Due to a season effect, the identified natural frequencies in Koppu () (in summer) are not the same with those in MS1 (⊳) (in winter) at low modal RMS. The natural frequency tends to decrease with the increase of modal RMS. One possible reason is the loosening of friction joints at sufficiently high vibration levels, which results in the reduction of stiffness. The right column of Figures 4 and 5 shows a positive correlation between the damping ratio and RMS. Compared to that in the frequencies, the scatter is much bigger. The scatter in these figures can be due to limited identification precision, modelling error in the damping mechanism, modelling error in stationarity, unknown amplitude-dependence mechanism, etc. For the more detailed information of the study about

amplitude.

the two super tall buildings, please refer to [6].

Figure 7. Power spectral density for a typical 30-minute window.

time window. Fifteen peaks can be observed below 2.0 Hz. The first mode is less than 0.1 Hz, and it is the foundational mode of the Canton Tower. In the operational modal analysis by the Fast Bayesian FFT method, all the 15 modes are identified. Table 2 shows the identified modal parameters of the 15 modes. From the second to the ninth column, every two columns are considered as one group with first denoting the MPV and second denoting the associated posterior c.o.v. The c.o.v. of modal frequencies are quite small (less than 0.5%), implying that the MPVs are quite accurate. The damping ratios for this structure are small and only those of the first and fourth modes are higher than 1%. This is consistent with the results obtained in Ref. [24]. The posterior uncertainty of damping ratios is relatively high in comparison with that


f: modal frequency; ζ: damping ratio; S: PSD of modal force; Se: PSD of prediction error.

Table 2. Identified modal parameters and the associated posterior uncertainty.

of modal frequencies, with an order of magnitude of a few tens' percent. The PSD of modal force and PSD of prediction error are all related to the excitation environment. The c.o.v. of the former is apparently larger than the c.o.v. of the latter.

Figures 8 and 9 show the identified mode shapes of the fifteen modes projected in short- and long-axis directions, respectively. As aforementioned, on cross-sections 4 and 8, four accelerometers were deployed for bi-axial measurement at two plane locations. With this information, the torsional behaviour of these modes can be investigated. From the mode shapes identified (omitted here), although the mode shapes of some modes in Figures 8 and 9 are similar when projected in short- or long-axis direction, they are different in top view, i.e. Modes 6, 10, 12, 15 exhibit a significant torsional behaviour.

Figure 8. Identified mode shapes for the first 15 modes projected in short-axis direction.

time window. Fifteen peaks can be observed below 2.0 Hz. The first mode is less than 0.1 Hz, and it is the foundational mode of the Canton Tower. In the operational modal analysis by the Fast Bayesian FFT method, all the 15 modes are identified. Table 2 shows the identified modal parameters of the 15 modes. From the second to the ninth column, every two columns are considered as one group with first denoting the MPV and second denoting the associated posterior c.o.v. The c.o.v. of modal frequencies are quite small (less than 0.5%), implying that the MPVs are quite accurate. The damping ratios for this structure are small and only those of the first and fourth modes are higher than 1%. This is consistent with the results obtained in Ref. [24]. The posterior uncertainty of damping ratios is relatively high in comparison with that

1 Bending 0.094 0.37 1.20 32.5 1.64 17.5 5.56 3.21 2 Bending 0.138 0.18 0.48 39.9 0.92 17.3 3.49 3.50 3 Bending 0.366 0.08 0.26 32.5 0.30 10.9 1.49 2.28 4 Bending 0.424 0.07 0.21 35.7 0.05 17.1 2.25 3.28 5 Bending 0.475 0.05 0.12 41.6 0.88 11.8 1.77 2.58 6 Torsion 0.506 0.04 0.10 46.4 0.05 21.5 8.83 4.00 7 Bending 0.522 0.07 0.27 29.1 0.19 15.6 2.52 3.01 8 Bending 0.796 0.05 0.23 23.2 0.08 7.8 0.81 1.61 9 Bending 0.966 0.06 0.36 17.5 0.06 7.6 0.65 1.50 10 Combined 1.151 0.03 0.13 26.8 0.01 11.7 0.63 2.35 11 Bending 1.191 0.03 0.11 29.1 0.01 12.9 0.84 2.53 12 Torsion 1.250 0.03 0.11 27.6 0.01 9.8 0.66 1.94 13 Bending 1.388 0.05 0.33 16.0 0.05 8.4 0.50 1.63 14 Bending 1.643 0.04 0.22 16.7 0.07 6.4 0.51 1.33 15 Combined 1.946 0.08 0.74 11.6 0.09 10.3 0.62 1.53

10-6

Figure 7. Power spectral density for a typical 30-minute window.

Structural Health Monitoring - Measurement Methods and Practical Applications

Mode Characteristics f (Hz) COV (%) ζ (%) COV (%) S (μg<sup>2</sup>

f: modal frequency; ζ: damping ratio; S: PSD of modal force; Se: PSD of prediction error.

Table 2. Identified modal parameters and the associated posterior uncertainty.

10-5

[g/ÖHz]

10-4

10-3

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Root PSD

/Hz) COV (%) Se (μg2

/Hz) COV (%)

Frequency [Hz]

Figure 9. Identified mode shapes for the first 15 modes projected in long-axis direction.

To verify the results identified by the Fast Bayesian FFT method, the enhanced FDD method is used to identify the modal parameters using the same data. Table 3 shows the identified modal frequencies and damping ratios. The identified modal frequencies for different modes are consistent with their counterparts identified by the Fast Bayesian FFT method. However, there is a larger discrepancy for the damping ratios. A noticeable difference can be observed between the two groups of results, implying that high uncertainty exists in the identified damping ratios, as shown by the large posterior c.o.v. of damping ratios obtained by the Fast Bayesian FFT method. For the more detailed information of the study about Canton Tower, please refer to [4].


Table 3. Modal parameters identified by enhanced FDD method.

#### 5. Shanghai Tower

The Shanghai Tower (Figure 10) is a 124-story 632 m high super tall structure, situated in Lujiazui, Shanghai, China. The structure has eight electromechanical floor zones with six two-storey outrigger trusses together with eight boxy space circular trusses set along these different zones. It has a mega frame-tube-outrigger lateral resistant system, where the mega frame is composed by the boxy space circular truss and the giant column. To monitor the structural condition of the super tall building, an SHM system was instrumented on this structure. Many kinds of sensors were installed including accelerometers, temperature sensors, GPS, etc. A series of field vibration tests were conducted to investigate its modal parameters.

Figure 10. Overview of the building.

To verify the results identified by the Fast Bayesian FFT method, the enhanced FDD method is used to identify the modal parameters using the same data. Table 3 shows the identified modal frequencies and damping ratios. The identified modal frequencies for different modes are consistent with their counterparts identified by the Fast Bayesian FFT method. However, there is a larger discrepancy for the damping ratios. A noticeable difference can be observed between the two groups of results, implying that high uncertainty exists in the identified damping ratios, as shown by the large posterior c.o.v. of damping ratios obtained by the Fast Bayesian FFT method. For the more detailed information of the study about Canton Tower,

Mode Modal frequency (Hz) Damping ratio (%)

 0.094 2.48 0.138 1.33 0.366 0.46 0.424 0.32 0.475 0.29 0.506 0.28 0.522 0.43 0.796 0.46 0.965 0.64 1.151 0.16 1.191 0.16 1.250 0.16 1.390 0.34 1.642 0.27 1.948 0.86

78 Structural Health Monitoring - Measurement Methods and Practical Applications

The Shanghai Tower (Figure 10) is a 124-story 632 m high super tall structure, situated in Lujiazui, Shanghai, China. The structure has eight electromechanical floor zones with six two-storey outrigger trusses together with eight boxy space circular trusses set along these different zones. It has a mega frame-tube-outrigger lateral resistant system, where the mega frame is composed by the boxy space circular truss and the giant column. To monitor the structural condition of the super tall building, an SHM system was instrumented on this structure. Many kinds of sensors were installed including accelerometers, temperature sensors, GPS, etc. A series of field vibration tests were conducted to investigate its modal

please refer to [4].

5. Shanghai Tower

Table 3. Modal parameters identified by enhanced FDD method.

parameters.

#### 5.1. Field vibration tests in different stages

From April 2012 to December 2014, to study the modal parameters during construction, 15 ambient vibration tests were carried out over a period of two and a half years. Table 4 shows the time to carry out the field test corresponding to the number of floors constructed. Two different locations were measured in each test. They were at the top of a core tube and the top of composite slabs after completion of concrete pouring. A series of finite element models (FEMs) (built by ETABS) of the first eight construction stages were also developed to perform comparison. The measured structures and the FEM model are shown in Figure 11.

When the main structure was finished, one field test was conducted to measure different corners of the tube to investigate the dynamic characteristics of a typical floor. For the convenience of sensor alignment and cables arrangement, 101th floor was selected since only the shear walls were constructed on this floor. It was planned to measure nine locations bi-axially,


Table 4. Measurement information.

Figure 11. Overview of buildings in different stages and finite element models, field test on a typical floor.

which are shown in Figure 12. It includes one location at the centre and the locations in the eight corners. With the help of core walls, sensor alignment was finished in half an hour.

In this test, only four uniaxial sensors were available, and so to finish the whole measurement, multiple setups were designed. Two reference channels were put in Location 1 to provide common information for mode shapes assembling and they were kept unchanged during the whole measurement. Based on the number of sensors and locations, eight different setups were

Figure 12. Setup plan.

arranged. The plans for these setups can be found in Ref. [26]. Forty minutes are required at least for each setup. Thirty minutes were used for data collection and the remaining 10 minutes were used for roving the sensor. It covered 10 am to 7 pm during a working day to finish the whole measurement with the sampling frequency of 2048 Hz. For the convenience of analysis, the measured data were decimated to a sampling frequency of 64 Hz.

#### 5.2. Data analysis

which are shown in Figure 12. It includes one location at the centre and the locations in the eight corners. With the help of core walls, sensor alignment was finished in half an hour.

Figure 11. Overview of buildings in different stages and finite element models, field test on a typical floor.

80 Structural Health Monitoring - Measurement Methods and Practical Applications

Figure 12. Setup plan.

In this test, only four uniaxial sensors were available, and so to finish the whole measurement, multiple setups were designed. Two reference channels were put in Location 1 to provide common information for mode shapes assembling and they were kept unchanged during the whole measurement. Based on the number of sensors and locations, eight different setups were Using the data collected in different construction stages, the variations of modal parameters were investigated. In each test, 20 minutes data in the Location 2 were analysed. Figure 13 provides the identified results of natural frequencies and damping ratios for Modes 1 and 2. The MPV is denoted by a dot, while 2 posterior standard deviations were expressed by an error bar. The MPV of natural frequencies decreases with the number of floors and the increasing speed tends to be stable after the main structure was finished. The posterior uncertainty of the natural frequency is small, and so the decrease of the natural frequency with the number of floors constructed is due to the structural height instead of identification error since the error bars among neighbouring setups have no overlap. For the damping ratios, the MPVs are all around or less than 1% and no obvious trend can be observed with the structural height. The posterior uncertainty of damping ratios is relatively large, which can be seen in Figure 13.

The identified results of the first two modes and the corresponding ones obtained from the FEM are shown in Figure 14. From the figure, it is seen that the two group results were consistent with each other, which implies that the influence of the increase of structural height

Figure 13. Modal parameters in different construction stages.

Figure 14. Comparison between the identified results and FEM results. (a) Mode 1 and (b) Mode 2.

on the reduction of natural frequency is reasonable. No obvious problem from the point of view of this modal parameter can be observed during construction.

Next, the data of the field test in a typical floor will be investigated. Figure 15 plots the PSD spectra of the data in Setup 1. Eight obvious peaks can be observed from 0 to 1 Hz. The numbers near to each peak indicate the potential modes. There are two closely spaced modes (Modes 1 and 2) whose mode shapes can be predicted by the FEM model to be two transitional modes in x- and y-directions of the building, respectively. Therefore, to use the proposed multiple setups algorithm, the data in x- and y-directions were analysed separately to obtain the mode shapes. For Mode 3 to Mode 8, they can be taken as well separated, and so they are identified directly using the collected data.

The mode shapes of the first three identified modes were shown in Figure 16. Modes 1 and 2 are, respectively, two translational modes along the x- and y-directions. The third mode is a torsional mode and its torsion centre is at the centre of the tube. The mode shapes of Modes 4–6 are similar to Modes 1–3. Modes 7 and 8 (omitted here) are also, respectively, the two translational modes in the x- and y-directions. From the mode shapes, it is observed that although this super building was designed in a novelty manner, the mode shapes of the first eight modes are still all regular,

Figure 15. PSD spectrum of the data in Setup 1: (a) PSD spectra and (b) SVD spectra.

Operational Modal Analysis of Super Tall Buildings by a Bayesian Approach http://dx.doi.org/10.5772/intechopen.68397 83

Figure 16. Identified mode shapes: Mode 1, Mode 2, and Mode 3.

i.e. two translational modes and then one torsional mode. Table 5 gives the averaged posterior c. o.v. and the sample c.o.v. (=sample standard derivation/sample mean) of identified modal parameters for the first eight modes among different setups. The posterior c.o.v. tends to be larger than the sample c.o.v., while their orders of magnitude are still similar. These two quantities are well consistent with each other, although they can, respectively, reflect Bayesian and frequentist perspectives. For the more detailed information of the study about Shanghai Tower, please refer to [26].


Table 5. Posterior c.o.v. and sample c.o.v..

#### 6. Conclusion

on the reduction of natural frequency is reasonable. No obvious problem from the point of

Next, the data of the field test in a typical floor will be investigated. Figure 15 plots the PSD spectra of the data in Setup 1. Eight obvious peaks can be observed from 0 to 1 Hz. The numbers near to each peak indicate the potential modes. There are two closely spaced modes (Modes 1 and 2) whose mode shapes can be predicted by the FEM model to be two transitional modes in x- and y-directions of the building, respectively. Therefore, to use the proposed multiple setups algorithm, the data in x- and y-directions were analysed separately to obtain the mode shapes. For Mode 3 to Mode 8, they can be taken as well separated, and so they are

The mode shapes of the first three identified modes were shown in Figure 16. Modes 1 and 2 are, respectively, two translational modes along the x- and y-directions. The third mode is a torsional mode and its torsion centre is at the centre of the tube. The mode shapes of Modes 4–6 are similar to Modes 1–3. Modes 7 and 8 (omitted here) are also, respectively, the two translational modes in the x- and y-directions. From the mode shapes, it is observed that although this super building was designed in a novelty manner, the mode shapes of the first eight modes are still all regular,

view of this modal parameter can be observed during construction.

82 Structural Health Monitoring - Measurement Methods and Practical Applications

Figure 15. PSD spectrum of the data in Setup 1: (a) PSD spectra and (b) SVD spectra.

Figure 14. Comparison between the identified results and FEM results. (a) Mode 1 and (b) Mode 2.

identified directly using the collected data.

This chapter presents the work on the operational modal analysis of four super tall buildings including two super tall buildings situated in Hong Kong, Canton Tower and Shanghai Tower. A fast Bayesian method is used to perform the OMA. It is found that the Bayesian method can be well applied into these four field structures. The natural frequencies of the first fundamental mode of these four buildings are around 0.1 Hz, while the damping ratios are all around 1%. In addition to the most probable values of modal parameters, the associated posterior uncertainties are also investigated. The posterior c.o.v. of natural frequencies are usually small, indicating the identification of this quantity is accurate, while that of damping ratios are obviously larger than the natural frequencies. This is consistent with the common finding. The investigation in this chapter provides a reference for future OMA of super tall buildings, and the Fast Bayesian FFT method is a robust method having the potential to be used in other field structures.

### Acknowledgements

The work in this paper was partly supported by grants from National Natural Science Foundation of China through Grant 51508413 and 51508407, Shanghai Pujiang Program (Grant No.: 15PJ1408600) and Fundamental Research Funds for the Central Universities (Grant No.:20161143).

#### Author details

Feng-Liang Zhang and Yan-Chun Ni\*

\*Address all correspondence to: yanchunni@gmail.com

College of Civil Engineering, Tongji University, Shanghai, China

#### References


[9] Au SK, Zhang FL. Fundamental two-stage formulation for Bayesian system identification, Part I: General theory. Mechanical Systems and Signal Processing. 2016;66:31–42

Acknowledgements

Author details

References

Feng-Liang Zhang and Yan-Chun Ni\*

Monitoring. 2003;2(3):257–267

itoring. 2009;16:73–98

(10):1675–1687

2012;101:12–23

314–336

and Performance. 2016;12(3):289–311

\*Address all correspondence to: yanchunni@gmail.com

84 Structural Health Monitoring - Measurement Methods and Practical Applications

College of Civil Engineering, Tongji University, Shanghai, China

The work in this paper was partly supported by grants from National Natural Science Foundation of China through Grant 51508413 and 51508407, Shanghai Pujiang Program (Grant No.: 15PJ1408600) and Fundamental Research Funds for the Central Universities (Grant No.:20161143).

[1] Chang PC, Flatau A, Liu SC. Health monitoring of civil infrastructure. Structural Health

[2] Van der Auweraer H, Peeters B. International research projects on structural health

[3] Ni YQ, Xia Y, Liao WX, Ko JM. Technology innovation in developing the structural health monitoring system for Guangzhou New TV Tower. Structural Control and Health Mon-

[4] Zhang FL, Ni YQ, Ni YC, Wang YW. Operational modal analysis of Canton Tower by a fast frequency domain Bayesian method. Smart Structures and Systems. 2016;17(2):209-230 [5] Kijewski-Correa T, Kwon DK, Kareem A, Bentz A, Guo Y, Bobby A, Abdelrazaq A. Smartsync: An integrated real-time structural health monitoring and structural identification system for tall buildings. Journal of Structural Engineering, ASCE. 2013;139

[6] Au SK, Zhang FL, To P. Field observations on modal properties of two tall buildings under strong wind. Journal of Wind Engineering and Industrial Aerodynamics.

[7] Li QS, Yi J. Monitoring of dynamic behaviour of super-tall buildings during typhoons. Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design

[8] Lam HF, Hu J, Yang JH. Bayesian operational modal analysis and Markov chain Monte Carlo-based model updating of a factory building. Engineering Structures. 2017;132:

monitoring: An overview. Structural Health Monitoring. 2003;2(4):341–358


## **Mooring Integrity Management: Novel Approaches Towards** *In Situ* **Monitoring**

Ángela Angulo, Graham Edwards, Slim Soua and Tat-Hean Gan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68386

#### **Abstract**

[24] Chen WH, Lu ZR, Lin W, Chen SH, Ni YQ, Xia Y, Liao WY. Theoretical and experimental modal analysis of the Guangzhou New TV Tower. Engineering Structures. 2011;33:3628–

[25] Ni YQ, Xia Y, Lin W, Chen WH, Ko JM. SHM benchmark for high-rise structures: A reduced-order finite element model and field measurement data. Smart Structures and

[26] Zhang FL, Xiong HB, Shi WX, et al. Structural health monitoring of Shanghai Tower during different stages using a Bayesian approach. Structural Control and Health Moni-

3646

Systems. 2012;10(4):411–426

86 Structural Health Monitoring - Measurement Methods and Practical Applications

toring. 2016;23(11):1366–1384

The recent dramatic fluctuations in oil and gas prices are forcing operators to look at radically new ways of maintaining the integrity of their structures. Moreover, the life of old structures has to be extended. This includes the replacement of expensive periodic in-service inspections with cost-efficient structural health monitoring (SHM) with permanently installed sensors. Mooring chains for floating offshore installations, typically designed for a 25-year service life, are loaded in fatigue in a seawater environment. There is no industry consensus on failure mechanisms or even defect initiation that mooring chains may incur. Moorings are safety-critical areas, which by their nature are hazardous to inspect. Close visual inspection in the turret is usually too hazardous for divers, yet is not possible with remotely operated vehicles (ROVs), because of limited access. Conventional non-destructive techniques (NDTs) are used to carry out inspections of mooring chains in the turret of floating production storage and offloading (FPSO) units. Although successful at detecting and assessing the fatigue cracks, the hazardous nature of the operation calls for remote techniques that can be applied continuously to identify damage initiation and progress. Appropriate replacement plans must enhance current strategies by implementing real-time data retrofit.

**Keywords:** mooring chain, structural integrity, structural health monitoring, acoustic emission, guided wave, crack growth

#### **1. Introduction**

As offshore exploration and production goes further afield and into deeper waters, more offshore operations, e.g. oil and gas operations [1], are conducted from floating platforms moored to the seabed by chains. Mooring lines are safety-critical systems on offshore floating

© 2017 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.

and semi-submersible platforms. The lines are often subject to immense environmental and structural forces from currents, waves and hurricanes. Other forces arise from impact with the seabed, abrasion, increased drag by accumulation of marine organisms and salt water corrosion. Failure of one or more of these mooring lines can result in disastrous and economic consequences for safety, the environment and production.

Periodic inspection of chain systems is mandatory [2] for safety and early detection of faults and is usually performed either through:


An advantage of in-water inspection being carried out *in situ* is that it is easy to identify which parts of the chain have been in the wear zone, i.e. in the thrash zone and at the fairlead. This is normally more difficult to determine for long lengths of chain inspected on the quayside [3]. However, the most important advantage of in-water inspection is that it can be carried out during the daily production by the facility with minimal stoppage time, hence excluding the need to decommission and the cost to business through lost production.

Currently, the volumetric non-destructive testing (NDT) used in the offshore industrial sector cannot be deployed underwater with the same efficiency without radical adaptation of the technology. In general, current in-water testing techniques have intrinsic issues with probability of detection that are amplified when applied underwater; hence, their use on mooring chains requires highly specialised procedures. This is limited:


These limitations compromise the capability for early detection of faults, resulting in periodic failures. For example, between 1980 and 2001, the HSE reported [4] that a drilling semi-submersible in the North Sea can expect to experience a mooring failure (anchor dragging, breaking of mooring lines, loss of anchor, winch failures) once every 4.7 operating years, a production semi-submersible once every 9 years and a floating production storage and offloading (FPSO) installation once every 8.8 years, due to failure to detect defects in the chain.

Consequently, reliance must be placed on in-air inspection, resulting in disruption to the daily operations and substantial economic loss for the operating companies, as the production structures require partial/full de-commissioning during the inspection period (**Figure 1**).

and semi-submersible platforms. The lines are often subject to immense environmental and structural forces from currents, waves and hurricanes. Other forces arise from impact with the seabed, abrasion, increased drag by accumulation of marine organisms and salt water corrosion. Failure of one or more of these mooring lines can result in disastrous and economic

Periodic inspection of chain systems is mandatory [2] for safety and early detection of faults

• an in-air (outside the water) process that necessitates the removal of the chain for inspection at the surface. Although common practice with movable jack-up drilling rigs, for example, it is not possible with fixed production systems except by taking the system

An advantage of in-water inspection being carried out *in situ* is that it is easy to identify which parts of the chain have been in the wear zone, i.e. in the thrash zone and at the fairlead. This is normally more difficult to determine for long lengths of chain inspected on the quayside [3]. However, the most important advantage of in-water inspection is that it can be carried out during the daily production by the facility with minimal stoppage time, hence excluding the

Currently, the volumetric non-destructive testing (NDT) used in the offshore industrial sector cannot be deployed underwater with the same efficiency without radical adaptation of the technology. In general, current in-water testing techniques have intrinsic issues with probability of detection that are amplified when applied underwater; hence, their use on mooring chains

• NDT diver-inspections are in general not a favoured option due to health and safety issues, inconsistency of results and an inherent depth limitation and risk, e.g. when checking the

• standalone robotic systems are too large and cumbersome for practical offshore operations. They are not able to inspect the chains in the thrash zone or near the chain fairleads;

• tethered remotely operated vehicles (ROVs) that use both mechanical and optical calliper systems have met with limited success primarily due to their method of deployment on the chain, i.e. they need in-water diver supervision as they have the potential to be knocked out

These limitations compromise the capability for early detection of faults, resulting in periodic failures. For example, between 1980 and 2001, the HSE reported [4] that a drilling semi-submersible in the North Sea can expect to experience a mooring failure (anchor dragging, breaking of mooring lines, loss of anchor, winch failures) once every 4.7 operating years, a production semi-submersible once every 9 years and a floating production storage and offloading (FPSO)

of true positioning and must be recalibrated between successive measurements.

installation once every 8.8 years, due to failure to detect defects in the chain.

consequences for safety, the environment and production.

88 Structural Health Monitoring - Measurement Methods and Practical Applications

• in-water inspection, which is carried out with the chain system *in situ*.

need to decommission and the cost to business through lost production.

requires highly specialised procedures. This is limited:

and is usually performed either through:

out of production;

thrash zone;

On another front, greater demand for energy in Europe [5], depletion of onshore resources and insecurity of supply from geopolitically unstable traditional areas [6], has led to a push for offshore oil and gas exploration in deep water, with substantial interest in marginal production fields. This necessitates floating production systems with massive mooring chain systems to overcome the substantial challenge for economic extraction. The reliability of inspection is dictated by three important factors [7] as follows:


**Figure 1.** From left to right: Example of wear and corrosion on a chain link from the sea-bed touch down zone, in-water inspection showing a studded chain which has lost its stud *in situ*, illustration of marine growth on long-term deployed chain, affecting optical in-water inspection, friction-induced bending.

#### **1.1. Damage mechanisms**

The life cycle of a mooring system is in excess of 20 years, and it would normally be designed to withstand '100-year period storm' conditions. A typical floating structure has 14 moorings which can amount to nearly 10 km of chain or hybrid chain and polyester rope (central section). Mooring chains are subjected to cyclical loads and therefore fatigue which can cause a chain to break well below the ultimate strength of the material. These loads are due to the hydrodynamic currents in the water, aerodynamic loads on the pulling weight of the platform, and the local conditions causing the lines to have more or less sag depending on the load direction which can render the chains almost straight with a correspondingly higher horizontal tension component and stiffness, 'freezing' [9], hence fatigue. Microscopic physical damage accumulates with continued cyclic loading until cracks form. Once the crack reaches a critical size, brittle fracture occurs, the chain will break and the mooring will fail. A single mooring line failure may cause the platform to capsize. After multiple mooring failures the platform could drift away, losing control of the well-heads, which without de-pressurising would ultimately cause the risers to rupture catastrophically.

Several field studies have found that wear and tear occur in mooring chains links much sooner than anticipated, i.e. the combined wear and corrosion rate over the years is estimated to be 0.6 mm/year which is 50% higher than the maximum values found in corrosion inspection standards, e.g. API's RP2SK, DnV's OSE301. Loss of section of chain links could be due to corrosion, non-axial friction or even sulphate-reducing bacteria (SRB) that induces pitting corrosion, etc. (**Figure 2**). Consequently, there is an urgent need to either:

• increase the frequency of in-air testing, which would cause disturbance of operations at the platforms and decommissioning at each major inspection;

**Figure 2.** Mooring line degradation and the key areas to inspect.

• or increase the reliability of in-water NDT with a method that can assess progressive wear and tear while the facilities are in operation.

#### **1.2. Innovative character of** *in situ* **monitoring in relation to the state of the art**

Mooring chain life can be significantly reduced, leading to unacceptable risk of catastrophic failure, if early damage is not detected. Chain mounted equipment is available to monitor chain tension and bending, but detection of damage caused by stress concentrations, fatigue, corrosion and fretting or combinations of these is not currently possible. The acoustic emission (AE) technique is capable of detecting cracks in mooring chains and fatigue damage. AE monitoring has shown sensitivity to crack growth during fatigue tests on chains. This chapter will describe the AE technique for detecting fatigue cracks, a procedure for applying the technique, a methodology for incorporating the AE test data with other data in the frame of a holistic approach to integrity management of moorings and a specification for an operational system.

Structural health monitoring (SHM) is the process of implementing a damage detection and characterisation strategy for engineering structures. Damage is defined as changes to the material which adversely affect its performance. The extraction of damage-sensitive features from the very large amount of sensor data normally requires sophisticated statistical analyses.

#### **2. State of the art of inspection methodologies**

**1.1. Damage mechanisms**

90 Structural Health Monitoring - Measurement Methods and Practical Applications

rupture catastrophically.

The life cycle of a mooring system is in excess of 20 years, and it would normally be designed to withstand '100-year period storm' conditions. A typical floating structure has 14 moorings which can amount to nearly 10 km of chain or hybrid chain and polyester rope (central section). Mooring chains are subjected to cyclical loads and therefore fatigue which can cause a chain to break well below the ultimate strength of the material. These loads are due to the hydrodynamic currents in the water, aerodynamic loads on the pulling weight of the platform, and the local conditions causing the lines to have more or less sag depending on the load direction which can render the chains almost straight with a correspondingly higher horizontal tension component and stiffness, 'freezing' [9], hence fatigue. Microscopic physical damage accumulates with continued cyclic loading until cracks form. Once the crack reaches a critical size, brittle fracture occurs, the chain will break and the mooring will fail. A single mooring line failure may cause the platform to capsize. After multiple mooring failures the platform could drift away, losing control of the well-heads, which without de-pressurising would ultimately cause the risers to

Several field studies have found that wear and tear occur in mooring chains links much sooner than anticipated, i.e. the combined wear and corrosion rate over the years is estimated to be 0.6 mm/year which is 50% higher than the maximum values found in corrosion inspection standards, e.g. API's RP2SK, DnV's OSE301. Loss of section of chain links could be due to corrosion, non-axial friction or even sulphate-reducing bacteria (SRB) that induces pitting

• increase the frequency of in-air testing, which would cause disturbance of operations at the

corrosion, etc. (**Figure 2**). Consequently, there is an urgent need to either:

platforms and decommissioning at each major inspection;

**Figure 2.** Mooring line degradation and the key areas to inspect.

At present, the state of the art in-water inspection techniques are not reliable; experience has shown that anomalies identified by in-water inspection can only be evaluated with true confidence by in-air inspection.

Specifically, the in-water techniques do not provide early detection of fatigue cracks in the chains and consequently provide little early warning of loss of integrity of moorings. This is mainly due to the inherent difficulties in the logistics of underwater testing and to the inability of the techniques to reach all the areas within the chain links (i.e. contact surfaces between links, marine growth). Several in-water mooring chain NDT systems have been developed with varying levels of success. The main aim for all of them has been to reduce the level of 'human overlooking/presence' in water during the test. These range from a simple diver-deployed manual caliper to prototype stand-alone, ROV-deployed system and a chain climbing robot.

The in-water testing systems mainly deal with two inspection procedures:


#### **2.1. Review of current practices**

In principle, there are two major stages to the testing of mooring chains:


Both types use several known approaches:

	- break testing on at least three links of the same chain, e.g. an applied maximum load for a period of 30 seconds without showing signs of cracking;
	- mechanical testing (tensile and impact).
	- Magnetic particle testing (MPT);
	- Penetrant testing;
	- Radiographic testing;
	- Ultrasonic testing.

It is customary to recover the mooring lines part way through their service life for periodic in-air testing, but this has four disadvantages, namely:


The current situation in the water inspection of mooring lines is accurately reflected in the HSE UK Survey of in-water inspection:

*'There is an imbalance between the critical nature of mooring systems and the attention HSE receive, i.e. embodied by the frequency and accuracy of real time testing. Currently, there is no in-water technique to check for possible fatigues, cracks and monitor the progressive cases of cracks and defects*  *in a real time manner. A new inspection system is needed, which is mostly to be of acoustical nature… It is clearly not appropriate to rely on annual in-water ROVs inspection to check if a mooring line has failed' [4].*

From the above discussion, it is clear that an early detection tool for the structural condition of mooring chains would benefit operators to minimize the lost revenue related to unplanned shutdown of offshore oil and gas, wind platforms and other offshore platforms.

#### **2.2. NDT procedures**

**2.1. Review of current practices**

In principle, there are two major stages to the testing of mooring chains:

• Invasive and destructive testing (IDT). This is usually carried out in-air and either before commissioning of a mooring system (i.e. sample testing) or after clear signs of early damage to the mooring chain (i.e. to establish causes of chain damage during its decommissioning of the chain for future chain design). The main IDT accredited checks are as follows:


• Non-destructive testing (NDT) and visual inspection. These do not affect production and can be repeated. Besides visual inspection, the main types of NDT for mooring systems are

It is customary to recover the mooring lines part way through their service life for periodic

(1) the lines may be damaged either during recovery or reinstallation, e.g. losing their studs; (2) the whole operation is expensive, since the services of anchor handling and possibly

The current situation in the water inspection of mooring lines is accurately reflected in the

*'There is an imbalance between the critical nature of mooring systems and the attention HSE receive, i.e. embodied by the frequency and accuracy of real time testing. Currently, there is no in-water technique to check for possible fatigues, cracks and monitor the progressive cases of cracks and defects* 

for a period of 30 seconds without showing signs of cracking;

i. manufacturer's quality control inspection before deployment;

ii. in-service inspection, i.e. for safety and maintenance.

92 Structural Health Monitoring - Measurement Methods and Practical Applications



(4) defects may grow between inspections.

HSE UK Survey of in-water inspection:

in-air testing, but this has four disadvantages, namely:

heading control tugs will be required for a number of days;

(3) in-air inspection will not necessarily detect all possible cracks and defects;




as follows:

Both types use several known approaches:

NDT procedures are key documents. They state which technique is to be used (in NDT terminology, a technique is a specific way of applying an NDT method), the instructions on how it is to be used, including setting up the test equipment and its calibration, the data gathering processes and how the results are to be interpreted. The interpretation must include a methodology for sentencing test signals or indications and distinguishing them from spurious or non-relevant signals. All the NDT methods suffer from a propensity for giving false-calls, where defects are 'called' only to show when examined more closely that nothing is present. Many NDT techniques fall into disrepute when there are too many false calls and for this reason, special effort will be paid to developing procedures that are less prone to error.

The development of any NDT procedure starts with an understanding of the defects being sought. The most important influencing parameters on defect sensitivity in an NDT procedure for chains are the following:


An example of a recent failure, investigation of a mooring chain link identified fretting in the contact area between the chain links (**Figure 3a**), and the propagation of one crack through the link thickness in a series of fracture faces of increasing diameter (**Figure 3b**).

In the following sections, two well-known SHM techniques have been put forward as an example of novel practices applied to this field: GUW and AE. In order to assess their application to mooring chain monitoring, both modelling and experimental methodologies and results will be described.

**Figure 3.** (a) Fretting of contact surfaces between chain links. (b) Fracture surfaces as crack propagates through chain.

#### **3. Guided ultrasonic waves approach**

A medium range ultrasonic test (MRUT) has been developed for chains that use guided ultrasonic waves (GUWs). GUWs propagate long distances along elongated objects such as pipes and cylinders, because the multiplying effects of internal reflections from the objects boundaries give rise to waves that are 'guided' and suffer relatively low energy losses. The wave modes are complex however. The so-called 'dispersion curves' (**Figure 4a**) show that as the frequency increases so does the number of wave modes. The additional wave modes increase 'noise' and have the potential to reduce test sensitivity. The high noise due to the presence of multiple GUW modes may be partly compensated with new signal processing algorithms that differentiate the higher-order modes. Alternatively, instead of relying on one ultrasound frequency in the test, the technique might involve a sweep through a range of test frequencies. Some experimental data have already been derived from chains in this way.

GUWs are used in the long-range ultrasonic testing (LRUT) of pipes. In LRUT, the transmitted wave mode from the transducer tool wrapped around the pipe is symmetrical and either longitudinal (L-wave) or torsional (T-wave). However, around chains, a symmetrical wave will become distorted by the chain curvature (**Figure 4b**) to become a flexural (F-wave). The distortion has been studied using numerical models supported by experimentation. Another option is to use Rayleigh waves instead of guided waves. These propagate along the surface only and exist at high frequencies when the frequency-thickness product is beyond a certain limit defined by the thickness of the pipe. However, Rayleigh waves are likely to be strongly affected by surface roughness.

#### **3.1. Finite element modelling**

Finite element analysis (FEA) has been used to study the complex GUW propagation around chains and therefore provide a theoretical basis for ultrasound frequency selection for chain links and to aid the optimisation of the inspection technique.

Mooring Integrity Management: Novel Approaches Towards *In Situ* Monitoring http://dx.doi.org/10.5772/intechopen.68386 95

**Figure 4.** (a) Dispersion curves for a set of GUW modes. (b) Distortion of GUW around a chain.

The modelling work was conducting using the commercially available finite element software, Abaqus. The models were linear elastic and assumed the following material properties for carbon manganese steel.


**3. Guided ultrasonic waves approach**

94 Structural Health Monitoring - Measurement Methods and Practical Applications

from chains in this way.

affected by surface roughness.

**3.1. Finite element modelling**

A medium range ultrasonic test (MRUT) has been developed for chains that use guided ultrasonic waves (GUWs). GUWs propagate long distances along elongated objects such as pipes and cylinders, because the multiplying effects of internal reflections from the objects boundaries give rise to waves that are 'guided' and suffer relatively low energy losses. The wave modes are complex however. The so-called 'dispersion curves' (**Figure 4a**) show that as the frequency increases so does the number of wave modes. The additional wave modes increase 'noise' and have the potential to reduce test sensitivity. The high noise due to the presence of multiple GUW modes may be partly compensated with new signal processing algorithms that differentiate the higher-order modes. Alternatively, instead of relying on one ultrasound frequency in the test, the technique might involve a sweep through a range of test frequencies. Some experimental data have already been derived

**Figure 3.** (a) Fretting of contact surfaces between chain links. (b) Fracture surfaces as crack propagates through chain.

GUWs are used in the long-range ultrasonic testing (LRUT) of pipes. In LRUT, the transmitted wave mode from the transducer tool wrapped around the pipe is symmetrical and either longitudinal (L-wave) or torsional (T-wave). However, around chains, a symmetrical wave will become distorted by the chain curvature (**Figure 4b**) to become a flexural (F-wave). The distortion has been studied using numerical models supported by experimentation. Another option is to use Rayleigh waves instead of guided waves. These propagate along the surface only and exist at high frequencies when the frequency-thickness product is beyond a certain limit defined by the thickness of the pipe. However, Rayleigh waves are likely to be strongly

Finite element analysis (FEA) has been used to study the complex GUW propagation around chains and therefore provide a theoretical basis for ultrasound frequency selection for chain

links and to aid the optimisation of the inspection technique.

• Density = 7830 kg/m<sup>3</sup>

The finite element mesh was refined such that there were at least eight elements per wavelength for the smallest possible wavelength in the system. The elements used were eight-node linear bricks. In order to investigate the inspection of chain links, a number of models have been generated as follows.


A chain link of diameter 110 mm was used in the analysis.

#### *3.1.1. Modelling results*

The natural frequency analyses found that both the T(0,1) and T(0,2) exist at the typical torsional GUW inspection frequencies (20–80 kHz). **Figure 5** shows the displaced shapes and distribution of von-Mises stress in the straight section of the chain link at frequencies of around 45 kHz. The von-Mises stress has been used due to it being independent of the axis system used (e.g. Cartesian or cylindrical). It is proportional to the sound energy. **Figure 5** shows the distribution of von-Mises stress across the cross-section. It can be seen that the amplitude of the T(0,1) wave mode is strongest at the outside surface whereas the T(0,2) wave mode is

**Figure 5.** (a) Von-Mises stress distribution of the T(0,1) wave mode at 44 kHz and (b) T(0,2) wave mode at 47 kHz.

subsurface. The distribution of energy may affect the ability to detect flaws in a certain location. The results indicate that T(0,1) would be best for detecting surface breaking flaws. The natural frequency model was also used to extract the displaced shapes of torsional family wave modes.

Next, a wave propagation model was used to understand the behaviour of GUW as they propagate around the bend in the chain link. One bend was modelled and the ends of the model were elongated to prevent end reflections from interfering with the signals received. A single ring of exciters was used so that the pulse would propagate in both directions.

The magnitude of the displacement after excitation of a 10-cycle 40 kHz pulse is shown in **Figure 6**. It can be seen that the signal is no longer axisymmetric after propagation around the bend. This indicates that mode conversion has occurred. Some analysis was carried out to quantify the wave modes present in the signal after propagation around the bend. A mode filtering technique was used to separate the wave modes by circumferential order [12]. Since a torsional excitation was applied, it was assumed that wave modes in the torsional family were present. **Figure 6** shows the amplitudes of the individual wave modes plotted against circumferential order. It can be seen that there is a strong F(1,2) wave mode after passing the bend while T(0,1) wave mode propagates in the other direction along the straight section. The amplitude decreases with increasing circumferential order as would be expected.

**Figure 6.** Displacement magnitude after propagation of a 10-cycle 40 kHz pulse around the bend.

Finally, a model of the whole chain link was created and a range of frequencies from 30 to 70 kHz were analysed. Excitation was applied using two rings to match the experimental work, where phasing is used to remove the wave propagating in one direction while reinforcing the wave propagating in the other. The ring spacing was 30 mm and 16 transducers around the circumference were simulated in each ring. The weld was idealised to a triangular shape with a height of 5 mm and a length of 60 mm on the opposite side of the chain from the ring. **Figure 7** shows the von-Mises stress in the chain link just after the input of a 10-cycle 30 kHz pulse. As before, it is clear that significant mode conversion has occurred.

**Figure 8** shows the predicted A-scans from each of the models. The mode filtering technique was applied so that the A-scan for individual modes could be assessed. At 30 kHz, the reflections from the weld were distinct and there is relatively little 'noise' in between, whereas at 40 and 60 kHz, the reflections are less clear and the signals caused by the pulses of ultrasound circulating the chain become evident. The algorithm that is used to eliminate signals from pulses 'going the wrong' way through the rings starts to break down for certain wavelengths, and the circulating through-transmission pulses become superimposed on the pulse-echoes. At 50 kHz, there was a lot of noise at the start of the trace. This is likely to be caused by the T(0,2) wave mode. Its cut-off is around 50 kHz and therefore it is only excited at frequencies of 50 kHz and above. However, around its cut-off frequency, it will be highly dispersive which could cause this effect.

subsurface. The distribution of energy may affect the ability to detect flaws in a certain location. The results indicate that T(0,1) would be best for detecting surface breaking flaws. The natural frequency model was also used to extract the displaced shapes of torsional family

**Figure 5.** (a) Von-Mises stress distribution of the T(0,1) wave mode at 44 kHz and (b) T(0,2) wave mode at 47 kHz.

96 Structural Health Monitoring - Measurement Methods and Practical Applications

Next, a wave propagation model was used to understand the behaviour of GUW as they propagate around the bend in the chain link. One bend was modelled and the ends of the model were elongated to prevent end reflections from interfering with the signals received. A

The magnitude of the displacement after excitation of a 10-cycle 40 kHz pulse is shown in **Figure 6**. It can be seen that the signal is no longer axisymmetric after propagation around the bend. This indicates that mode conversion has occurred. Some analysis was carried out to quantify the wave modes present in the signal after propagation around the bend. A mode filtering technique was used to separate the wave modes by circumferential order [12]. Since a torsional excitation was applied, it was assumed that wave modes in the torsional family were present. **Figure 6** shows the amplitudes of the individual wave modes plotted against circumferential order. It can be seen that there is a strong F(1,2) wave mode after passing the bend while T(0,1) wave mode propagates in the other direction along the straight section. The amplitude decreases with increasing circumferential order as would

single ring of exciters was used so that the pulse would propagate in both directions.

**Figure 6.** Displacement magnitude after propagation of a 10-cycle 40 kHz pulse around the bend.

wave modes.

be expected.

**Figure 7.** Von-Mises stress distribution in a chain link just after excitation of a 10-cycle 30 kHz pulse.

**Figure 8.** Predicted A-scan of individual wave modes for a: (a) 10-cycle 30 kHz excitation, (b) 10-cycle 40 kHz excitation, (c) 10-cycle 50 kHz excitation and (d) 10.

Finally, the model of the chain link was used to simulate a 50% cross-sectional area flaw for the 10-cycle 30 kHz case. The flaw was approximately 3 mm wide. **Figure 9** shows the layout of the model. **Figure 9** shows the predicted A-scans for individual modes. When compared with **Figure 10** it can be seen that the difference is quite noticeable indicating that detection of the presence of the 50% cross-sectional area of the flaw is possible.

#### **3.2. Methodology and laboratory experiments on chain links**

Modelling work was carried out, but under the important proviso that the test procedures used were not 'optimum'. In other words, further on-going work was/is needed on wave

**Figure 9.** Layout of model of chain link with 50% cross-sectional area loss flaw.

**Figure 10.** Predicted A-scan of individual wave modes for a 10-cycle 30 kHz excitation in a chain link with a 50% cross-sectional area loss flaw.

propagation in solid cylinders and around bends, selection of ultrasound frequency and pulse length, tool design, etc.

110 mm diameter chains were available for this work. Although this size is at the bottom of the range of chain sizes of interest to the end-users, the availability of the 110 mm diameter 3-m long solid rod on which to calibrate the A-scans was an important advantage at this stage of the study.

Eight chains were tested, two of which contained a defect by way of an EDM slot or a ground notch. The chains varied slightly from 105 to 110 mm diameter. The diameter is the diameter of the solid rod from which the chain link is forged. Once bent into shape it is welded at the ends to complete the whole link. The diameter determines the overall geometry of the chain.

Two slots were carefully placed on one of the 110-mm chain links; one on the intrados and the other on the extrados. On a second 105 mm chain, a notch on the intrados was 'grown' from 5 to 20% through-wall (**Figure 11**).

**Figure 11.** Aged chain link with slots.

Finally, the model of the chain link was used to simulate a 50% cross-sectional area flaw for the 10-cycle 30 kHz case. The flaw was approximately 3 mm wide. **Figure 9** shows the layout of the model. **Figure 9** shows the predicted A-scans for individual modes. When compared with **Figure 10** it can be seen that the difference is quite noticeable indicating that detection of

**Figure 8.** Predicted A-scan of individual wave modes for a: (a) 10-cycle 30 kHz excitation, (b) 10-cycle 40 kHz excitation,

Modelling work was carried out, but under the important proviso that the test procedures used were not 'optimum'. In other words, further on-going work was/is needed on wave

the presence of the 50% cross-sectional area of the flaw is possible.

**3.2. Methodology and laboratory experiments on chain links**

98 Structural Health Monitoring - Measurement Methods and Practical Applications

**Figure 9.** Layout of model of chain link with 50% cross-sectional area loss flaw.

(c) 10-cycle 50 kHz excitation and (d) 10.

#### *3.2.1. Guided ultrasonic waves equipment and specifications*

An important issue is whether the inspection capsule will be able to carry the instrument. There are advantages in keeping the distance between the instrument and the tool as short as possible, because noise is reduced and the signal is less attenuated.

In GUW techniques, the tool design and its performance is critical for the quality of the test results. To propagate symmetrical GUW into a pipe, the collar around the tool must apply equal pressure to all the transducers in a ring or an array.

In the present application, the transducer tool was always placed on the side of the chain opposite from the weld. Tests were performed with the transducer tool on the weld, but there was a drop in performance due to the unevenness of the surface.

The GUW frequencies were swept from 30 to 100 kHz in 5 kHz steps. The T-wave A-scans were collected over a 3-m range from the transducer and converted into ASC files for analysis.

#### *3.2.2. Experimental results*

A typical T-wave rectified A-scan is shown in **Figure 12**. It clearly shows multiple echoes from the weld on the opposite side of the chain form the tool.

The data could be grouped to show signal variation with frequency (**Figure 13**).

Closer analyses of the A-scans, however, show them to be divided into bands (see **Figure 14**):


**Figure 12.** 30 kHz T-wave A-scan from 110 mm chain link.

**Figure 13.** T-wave A-scan data collected from a defect-free chain: amplitude (mV) vs. time (ms).

These signal patterns were also observed in the finite element models. It is evident from the work here that only in the 30–40 and 70–80 kHz bands were the signals optimised. From the modelling, this appears to be a function of the ring spacing.

#### *3.2.3. Conclusion*

*3.2.1. Guided ultrasonic waves equipment and specifications*

100 Structural Health Monitoring - Measurement Methods and Practical Applications

equal pressure to all the transducers in a ring or an array.

from the weld on the opposite side of the chain form the tool.

(1) 30–40 kHz where the weld signals are clearly distinguishable;

(3) 70–80 kHz where the weld signals are again clearly resolved;

**Figure 12.** 30 kHz T-wave A-scan from 110 mm chain link.

(4) 95–100 kHz where signals cannot be distinguished from the noise.

*3.2.2. Experimental results*

possible, because noise is reduced and the signal is less attenuated.

there was a drop in performance due to the unevenness of the surface.

An important issue is whether the inspection capsule will be able to carry the instrument. There are advantages in keeping the distance between the instrument and the tool as short as

In GUW techniques, the tool design and its performance is critical for the quality of the test results. To propagate symmetrical GUW into a pipe, the collar around the tool must apply

In the present application, the transducer tool was always placed on the side of the chain opposite from the weld. Tests were performed with the transducer tool on the weld, but

The GUW frequencies were swept from 30 to 100 kHz in 5 kHz steps. The T-wave A-scans were collected over a 3-m range from the transducer and converted into ASC files for analysis.

A typical T-wave rectified A-scan is shown in **Figure 12**. It clearly shows multiple echoes

Closer analyses of the A-scans, however, show them to be divided into bands (see **Figure 14**):

(2) 50–60 kHz where a signal appears between the positions of the previous weld signals;

The data could be grouped to show signal variation with frequency (**Figure 13**).

The propagation of GUW around mooring chains is extremely complex and the modelling and experiments reported here go only part of the way to explaining it. Nevertheless, T-wave propagation was proven to be sensitive to the large defects despite there being more wave modes than are present in LRUT of pipes. L-wave propagation along bars is extremely complex and only if signal processing methods can be developed to differentiate the modes might L-waves be considered for testing chains.

Also, the best resolution was obtained within certain frequency bands, evident in both the numerical modelling and the experiments.

**Figure 14.** A-scans at different frequencies from 30 to 100 kHz: amplitude (mV) vs. time (ms).

### **4. Acoustic emission approach**

Structural integrity approaches have strongly recommended monitoring mooring chains *in situ* during operation to verify mooring integrity. To more accurately assess the operational condition of in-service mooring chains, it is beneficial to investigate the next-generation of monitoring technologies and their ability to detect flaws and corrosion prior to critical failure. One promising monitoring tool for providing early warning of flaws is acoustic emission testing (AET), which has been used to successfully detect cracks in marine structures during operation.

Acoustic emissions are elastic waves that are spontaneously released by a material undergoing deformation. Acoustic emissions, or so-called 'hits' or events are the stress waves produced by the sudden internal stress redistribution of a material caused by changes in the internal structure. The stress can be hydrostatic, pneumatic, thermal or bending. Possible causes of the internal structure changes are crack initiation and growth, crack opening and closure, dislocation movements. Materials emit ultrasound when they are stressed and fail on a microscopic scale [11].

The optimum AE parameters must be estimated for each application. The appropriate selection and installation of the AE sensors is crucial for a precise data collection strategy. The data must be processed to determine crack initiation and growth and to discriminate irrelevant information.

Acoustic emissions are used to detect defects in structures both in service and during manufacture. The technique can also be used to monitor defect growth during mechanical test in the laboratory. It is an ideal method for examining the behaviour of materials deforming under load.

The difference between an AE technique and other NDT methods is the former detects active defects inside the material, while other the latter attempt to detect passive and active defects. Furthermore, AE needs only the input of one or more relatively small sensors on the surface of the structure or specimen being examined, so that the structure or specimen can be subjected to the in-service or laboratory operation, while the AE system continuously monitors the progressive damage.

The disadvantage of AE is that AE systems can only estimate qualitatively the extent of damage or size of defect. So, other NDT methods are still needed to do more exhaustive examination and provide quantitative results. Conventional ultrasonic evaluation is often used to evaluate AE indications.

#### **4.1. Finite element modelling**

Again FEA has been used to analyse the AE wave propagation along the structure. As described in section 3.1, the model is linear elastic and assumed the following material properties for carbon steel.


A chain link of diameter 76 mm was used in the analysis.

A static analysis was run with a pressure of 1000 Pa to find the equilibrium state. The force was applied on the region shown **Figure 15a** which gave the result shown in **Figure 15b**

A dynamic model was created with the same geometry and same pressure applied, but with a crack inserted at the position indicated in **Figure 16**. The shape was a segment of the circle, with a maximum depth of 10 mm. The position was at the inner side of the join between the curved section and straight section of the chain link.

Stresses from the static model were applied to the dynamic model as the initial conditions.

Two AE sensors were modelled in the dynamic model. Each was 10 mm long, 29 mm around the circumference and positioned at 146.4 mm along from the plane of the crack. They were positioned one at the top of the model (Sensor 1) and one at the bottom (Sensor 2) as shown in **Figure 17**. The outputs were requested in the local cylindrical coordinate system (*r*, *θ*, *z*).

#### *4.1.1. Modelling results*

**4. Acoustic emission approach**

102 Structural Health Monitoring - Measurement Methods and Practical Applications

a microscopic scale [11].

gressive damage.

used to evaluate AE indications.

**4.1. Finite element modelling**

• Young's modulus = 207 GPa

.

erties for carbon steel.

• Poisson's ratio = 0.3 • Density = 7830 kg/m<sup>3</sup>

Structural integrity approaches have strongly recommended monitoring mooring chains *in situ* during operation to verify mooring integrity. To more accurately assess the operational condition of in-service mooring chains, it is beneficial to investigate the next-generation of monitoring technologies and their ability to detect flaws and corrosion prior to critical failure. One promising monitoring tool for providing early warning of flaws is acoustic emission testing (AET), which

Acoustic emissions are elastic waves that are spontaneously released by a material undergoing deformation. Acoustic emissions, or so-called 'hits' or events are the stress waves produced by the sudden internal stress redistribution of a material caused by changes in the internal structure. The stress can be hydrostatic, pneumatic, thermal or bending. Possible causes of the internal structure changes are crack initiation and growth, crack opening and closure, dislocation movements. Materials emit ultrasound when they are stressed and fail on

The optimum AE parameters must be estimated for each application. The appropriate selection and installation of the AE sensors is crucial for a precise data collection strategy. The data must be processed to determine crack initiation and growth and to discriminate irrelevant information. Acoustic emissions are used to detect defects in structures both in service and during manufacture. The technique can also be used to monitor defect growth during mechanical test in the laboratory. It is an ideal method for examining the behaviour of materials deforming under load. The difference between an AE technique and other NDT methods is the former detects active defects inside the material, while other the latter attempt to detect passive and active defects. Furthermore, AE needs only the input of one or more relatively small sensors on the surface of the structure or specimen being examined, so that the structure or specimen can be subjected to the in-service or laboratory operation, while the AE system continuously monitors the pro-

The disadvantage of AE is that AE systems can only estimate qualitatively the extent of damage or size of defect. So, other NDT methods are still needed to do more exhaustive examination and provide quantitative results. Conventional ultrasonic evaluation is often

Again FEA has been used to analyse the AE wave propagation along the structure. As described in section 3.1, the model is linear elastic and assumed the following material prop-

has been used to successfully detect cracks in marine structures during operation.

The dynamic model was solved in Abaqus for a simulated time of 0.5 ms. The crack opening can be observed in **Figure 18**.

The AE wave propagation and the displacement generated by the simulated crack growing can be observed in **Figure 19**. This relates directly with the elastic waves released at the crack tip.

The (*r*, *θ*, *z*) components of the displacements at each sensor location were recorded. **Figure 20** shows the displacement amplitude at both sensors location. The time of arrival (ToA) at each sensor can be observed. Calculating the value of the ToA, parameters such as the wave velocity or the location and time of occurrence can be estimated.

#### **4.2. Methodology and experiments on chain links**

Following the FEA analysis, a mooring chain link was monitored using AE in a simulated seawater tank tensile test rig. The rig is able to apply variable tension to a single link. A notch was initially introduced into the chain. During the test, a tensile load was applied at the

**Figure 15.** (a) Area were force is applied and (b) distribution of stress along the chain.

**Figure 16.** Chain seam model view.

**Figure 17.** AE sensors location: Sensor 1 top, Sensor 2 bottom.

**Figure 18.** Crack opening model.

**Figure 19.** Elastic wave propagation model.

**Figure 20.** AE waveform for S1 and S2: displacement module vs. time.

**Figure 16.** Chain seam model view.

**Figure 18.** Crack opening model.

**Figure 19.** Elastic wave propagation model.

**Figure 17.** AE sensors location: Sensor 1 top, Sensor 2 bottom.

104 Structural Health Monitoring - Measurement Methods and Practical Applications

connection point of the chain. The location of the sensors, forces and AE sensors can be seen in **Figure 21**.

#### *4.2.1. Acoustic emission equipment and specifications*

An AE system is a multi-channel data acquisition tool consisting of parallel measurement channels and system front-end software running on an external computer. A measurement channel consists of an AE sensor, AE preamplifier and one channel of an AE signal processor card.

The tensile test rig was instrumented with three AE sensors to record the AE data during the full test. Two AE sensors (150 kHz resonance frequency) were mounted with a magnetic holder on the tank frame to serve as 'guard' sensors in order to filter external environmental noise. The principal sensor used to detect the AE activities was submerged inside the seawater mounted using a magnetic holder. This was an AE sensor with an integrated preamplifier gain of 34 dB. Its resonance frequency was 150 kHz and it had an operating range of 90–450 kHz. It was of a design suitable for wet environments and on-site monitoring of underwater

**Figure 21.** Chain set up under load with induced notch.

 installations. The sensor was operated in a passive mode during the whole loading process to detect crack initiation and crack growth.

#### *4.2.2. Experimental results*

The laboratory trials were divided in two parts: the first part lasting for 75 hours to calibrate the set-up. In the second part, the system ran continuously for 285 hours to validate the long-term inspection capability. During these two tests, the load applied on the chain was kept constant at 8 MN.

One AE feature that proved to successfully represent crack initiation and propagation is energy. During the experimental test, cumulative energy was continuously calculated and recorded. From the calibration test, the set-up was validated (**Figure 22**).

During the long-term test, AE cumulative energy vs. time illustrated a linear increase in AE activity at first (**Figure 23**); this is followed by a rapid increase of energy when crack was propagating at a large scale.

#### *4.2.3. Conclusion*

AE graphs of cumulative energy vs. time show that the mooring chain crack propagation process was captured. The results can be considered as a characteristic curve of crack growth status over time.

Through both the calibration test and long-term test, the ability of the technique to detect and process AE events in real time has been proved. Other AE signal features including duration, peak amplitude together with cumulative energy should be analysed to evaluate the crack growth process.

**Figure 22.** Cumulative energy vs. time (calibration test, 75 h).

**Figure 23.** Cumulative energy vs. time (laboratory test, 285 h).

#### **5. Final discussion**

installations. The sensor was operated in a passive mode during the whole loading process

The laboratory trials were divided in two parts: the first part lasting for 75 hours to calibrate the set-up. In the second part, the system ran continuously for 285 hours to validate the long-term inspection capability. During these two tests, the load applied on the chain was

One AE feature that proved to successfully represent crack initiation and propagation is energy. During the experimental test, cumulative energy was continuously calculated and

During the long-term test, AE cumulative energy vs. time illustrated a linear increase in AE activity at first (**Figure 23**); this is followed by a rapid increase of energy when crack was

AE graphs of cumulative energy vs. time show that the mooring chain crack propagation process was captured. The results can be considered as a characteristic curve of crack growth

Through both the calibration test and long-term test, the ability of the technique to detect and process AE events in real time has been proved. Other AE signal features including duration, peak amplitude together with cumulative energy should be analysed to evaluate the crack

recorded. From the calibration test, the set-up was validated (**Figure 22**).

to detect crack initiation and crack growth.

106 Structural Health Monitoring - Measurement Methods and Practical Applications

*4.2.2. Experimental results*

kept constant at 8 MN.

propagating at a large scale.

*4.2.3. Conclusion*

status over time.

growth process.

**Figure 22.** Cumulative energy vs. time (calibration test, 75 h).

Due to the increasing demand of structural retrofit into conventional inspection strategies, SHM is of interest to an extensive range of industries. GUW and AE are non-destructive monitoring techniques which are widely employed at present. The output of its application will be comprehensive, real-time assessment of the structural condition of industrial assets.

The primary goal of this study was to investigate the applicability of GUW and AE approaches for crack initiation, location and propagation on a mooring chain. Modelling work and experimental testing have shown indication of the active damaged regions.

Because of the inherent uncertainties present in any SHM technique, the described technologies should be applied as part of a full mooring chain structural integrity assessment. Recent developments in internet infrastructure and connectivity for monitoring and sensing present an opportunity to overcome the limitations of AE and GUW testing for continuous monitoring. In addition to the continuous data output, a risk-based integrity management strategy may also include, where available, data from periodic inspections, numerical modelling showing stress distributions or crack propagation, historic and current operations.

#### **Author details**

Ángela Angulo, Graham Edwards, Slim Soua and Tat-Hean Gan\*

\*Address all correspondence to: tat-hean.gan@twi.co.uk

TWI Ltd, Integrity management Group, Granta Park, Great Abington, Cambridge, United Kingdom

#### **References**

