Piezoelectric wafer active sensors (PWAS) Disc specimens (DS)

3 RT EMIS recording after high temperatures RT EMIS recording after MD fabrication

5 RT EMI recording after low temperatures RT EMI recording after low temperatures

7 RT EMIS recording after high temperatures RT EMIS recording after high temperatures

9 RT EMIS recording after irradiation RT EMIS recording after irradiation

70C

+100, +125, and +150C

to the EMIS signature.

1 Initial RT EMIS recording of 38 PWAS (26 of them was bonded on the aluminum disc)

2 Tests and EMIS recording at high temperatures for 5 PWAS: +50/+200C, step: +25C

4 Tests and EMIS recording at low temperatures

6 Tests and EMIS recording at high temperatures for 5 PWAS: +50/+150C, step: +25C

8 Irradiation tests and EMIS recording for 2 PWAS

Table 4. Tests summary – Second stage of complex tests.

for 5 PWAS: 25, 50, 70C

at 3.71 Gy/h

A reference database is created at the beginning of the tests; for example, see Figure 6. The strategy of the program was that, in the first stage of tests, the PWASs and DSs were tested using simultaneous environmental factors that are specific to outer space, see Figure 7, the case of disc specimen 127 [25]. Then, to characterize the influence of each factor on the EMIS signature, in the second phase the tests were developed with harsh environmental factors acting successively instead of simultaneously [28], see Table 4.

Figure 6. The experimental reference RT for the EMIS method: The signature of the health status of the structure.

Figure 7. Summary of EMI measurements on S127 disc specimen, without simulated crack.

The effects of harsh environment on PWAS. After performing the tests according to the protocols in Tables 2 and 3, it is noted that the resonance frequencies on the EMIS PWAS graphs are constantly moving from left to right when temperatures drop from high (+150C) to cryogenic values (70C), as shown in Figure 8a. After completion of the tests at extreme temperatures, measurements were again made at RT.

A compensation technique [26, 28], in fact, a horizontal displacement of graphs, was used to obtain graphs in Figure 8b. As far as irradiations are concerned, they cause insignificant changes to EMIS signatures (Figure 8c). Thus, we can conclude that EMIS signature changes caused by environmental factors are reversible and consequently do not characterize real damage. The real damages are those of mechanical origin, which produce irreversible changes to the EMIS signature.

The effects on pristine DS. The EMIS behavior at extreme temperatures was analyzed on a set of 4 DS. Initially, the EMIS graph at RT (+25C) was recorded. Next, tests at low temperatures,


Table 4. Tests summary – Second stage of complex tests.

complete dose for a mission on Mars is 110 mGy/year, which means a dose of about 15 μGy/h; (b) the highest absorbed doses determined by the Pioneer probes 10 and 11 were 15 kGy, and 4.3 kGy, respectively. Consequently, the dose rate determined by the gamma 5000 irradiation chamber has been considered as acceptable. The absorbed dose of 23.5 kGy corresponded to 5 h exposure at the measured dose of 4.7 kGy/h. The usual vacuum in the outer space is 10<sup>14</sup> Pa. Vacuum pressures below 10<sup>1</sup> Pa were obtained by using a tritium manifold, a high-vacuum plant containing a vacuum pump type TSH-171E Pfeiffer, and pressure vacuum controllers type TPG 262 Pfeiffer.

A reference database is created at the beginning of the tests; for example, see Figure 6. The strategy of the program was that, in the first stage of tests, the PWASs and DSs were tested using simultaneous environmental factors that are specific to outer space, see Figure 7, the case of disc specimen 127 [25]. Then, to characterize the influence of each factor on the EMIS signature, in the second phase the tests were developed with harsh environmental factors

Figure 6. The experimental reference RT for the EMIS method: The signature of the health status of the structure.

Figure 7. Summary of EMI measurements on S127 disc specimen, without simulated crack.

acting successively instead of simultaneously [28], see Table 4.

126 Structural Health Monitoring from Sensing to Processing

Figure 8. EMIS PWAS signatures: (a) synoptic graph of temperature cycling; (b) initial and after temperature cycling, both at RT, compensated values; and (c) initial and after irradiation tests, both at RT.

0, 25, 50, and 70C were performed. When returning at the RT, T1, (+22.4C), it is noticed that the EMIS chart overlaps the initial one. After that, experiments at high temperatures up to +150C, with a chosen step of 25C, followed. When DS is brought to RT, T2 (+23.6C), it can be seen that EMIS returns to its original form, see Figure 9a.

Results similar to those of the PWAS case were also obtained in the case of 2 DS. The measurements were performed according to protocols before irradiation, during irradiation and after irradiation at RT, with the conclusion that the radiation does not produce splittings of the resonance peaks, but only negligible displacements of the peaks (Figure 9b), of the order of dozens of ohms.

## 5.2. The effects of the mechanical damages on PWAS and DS EMIS signature

Mechanical damages affect the EMIS signature in a well-defined way, namely causing the resonance peaks to split. This phenomenon intensifies in direct proportion to the decrease in distance from the PWAS center. Harsh environmental factors produce only displacements of resonance peaks and variations of amplitude on the EMIS signature, all practically reversible. (Figure 3).

A major tests result to propose a new, simple and effective approach to identifying mechanical damage. This approach allows the algorithmic distinction between real, mechanical damage

Figure 10. (a) Changes in EMIS signature, without damage versus damage (at 7 and 25 mm); (b) EMIS signature remains

Qualification of PWAS-Based SHM Technology for Space Applications

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129

Figure 11 shows one of the multiple recordings done in the time domain with SLDV. The DS 138, without damage and with arc type defect at 15 mm, is scanned at a frequency of 78.4 Hz, see a 2D and a 3D representation. The position of the laser-cut slit is marked as a red peak. The displacement is given in nanometers depending on time [ms] (vibration measured in the z-direction, perpendicular to the disc, takes also negative values). The graph refers to a vibration of a specific point on the surface of the disk otherwise indicated in the picture. It can be seen that the concentric circles are uniformly distributed on the surface of the plate when there is no damage to disturb the wave propagation. In the case with the laser made damage, the amplitudes of the waves in the vicinity of the fabricated crack are much higher than all the other points of the disk producing distinct peak in the EMIS signature. Figure 12 shows the use of SLDV for records in the frequency domain. For the same DS 138, a 3D

Figure 11. Recordings in time domain done with SLDV on DS 138: (a)disc without damage 2D representation; (b) DS with

arc type defect at 15 mm—2D; (c) disc without damage 3D; and (d) DS with arc type defect at 15 mm—3D.

and false damage, and caused by the harsh environmental factors.

5.3. Entropy method for damage detection and prediction

unchanged for different DS without damage.

image of the vibration at a frequency of 49.56 kHz is shown.

The EMIS graphs in Figure 10a show, by comparison with the graph in Figure 10b, and the impact of the damages on the spectrogram. Of course, this impact is more pronounced when the damage is closer to the PWAS center and is manifested mainly as splittings of resonance peaks in new peaks. This observation generated the idea of developing a method of identifying mechanical damage as well as of dissociating the mechanical damage from the so-called false damage, that induced by environmental factors [31].

Therefore, based on experimental observations, the splitting of resonance peaks on the EMIS signature will be associated with the occurrence of a mechanical deterioration. Instead, the effects of harsh environmental conditions are limited only to reversible movements of resonance peaks with amplitude changes; if the temperatures do not exceed certain limits, the amplitudes are practically reversible, and returning to EMIS signatures in the case of RT. More insignificant are the modifications made on the EMIS graphs by irradiation specific to outer space.

Figure 9. EMIS signature changes for a DS due to: (a) temperatures cycling; (b) irradiation.

Figure 10. (a) Changes in EMIS signature, without damage versus damage (at 7 and 25 mm); (b) EMIS signature remains unchanged for different DS without damage.

A major tests result to propose a new, simple and effective approach to identifying mechanical damage. This approach allows the algorithmic distinction between real, mechanical damage and false damage, and caused by the harsh environmental factors.

## 5.3. Entropy method for damage detection and prediction

0, 25, 50, and 70C were performed. When returning at the RT, T1, (+22.4C), it is noticed that the EMIS chart overlaps the initial one. After that, experiments at high temperatures up to +150C, with a chosen step of 25C, followed. When DS is brought to RT, T2 (+23.6C), it can be

Results similar to those of the PWAS case were also obtained in the case of 2 DS. The measurements were performed according to protocols before irradiation, during irradiation and after irradiation at RT, with the conclusion that the radiation does not produce splittings of the resonance peaks, but only negligible displacements of the peaks (Figure 9b), of the order of

Mechanical damages affect the EMIS signature in a well-defined way, namely causing the resonance peaks to split. This phenomenon intensifies in direct proportion to the decrease in distance from the PWAS center. Harsh environmental factors produce only displacements of resonance peaks and variations of amplitude on the EMIS signature, all practically reversible. (Figure 3).

The EMIS graphs in Figure 10a show, by comparison with the graph in Figure 10b, and the impact of the damages on the spectrogram. Of course, this impact is more pronounced when the damage is closer to the PWAS center and is manifested mainly as splittings of resonance peaks in new peaks. This observation generated the idea of developing a method of identifying mechanical damage as well as of dissociating the mechanical damage from the so-called false

Therefore, based on experimental observations, the splitting of resonance peaks on the EMIS signature will be associated with the occurrence of a mechanical deterioration. Instead, the effects of harsh environmental conditions are limited only to reversible movements of resonance peaks with amplitude changes; if the temperatures do not exceed certain limits, the amplitudes are practically reversible, and returning to EMIS signatures in the case of RT. More insignificant are

the modifications made on the EMIS graphs by irradiation specific to outer space.

Figure 9. EMIS signature changes for a DS due to: (a) temperatures cycling; (b) irradiation.

5.2. The effects of the mechanical damages on PWAS and DS EMIS signature

seen that EMIS returns to its original form, see Figure 9a.

128 Structural Health Monitoring from Sensing to Processing

damage, that induced by environmental factors [31].

dozens of ohms.

Figure 11 shows one of the multiple recordings done in the time domain with SLDV. The DS 138, without damage and with arc type defect at 15 mm, is scanned at a frequency of 78.4 Hz, see a 2D and a 3D representation. The position of the laser-cut slit is marked as a red peak. The displacement is given in nanometers depending on time [ms] (vibration measured in the z-direction, perpendicular to the disc, takes also negative values). The graph refers to a vibration of a specific point on the surface of the disk otherwise indicated in the picture. It can be seen that the concentric circles are uniformly distributed on the surface of the plate when there is no damage to disturb the wave propagation. In the case with the laser made damage, the amplitudes of the waves in the vicinity of the fabricated crack are much higher than all the other points of the disk producing distinct peak in the EMIS signature. Figure 12 shows the use of SLDV for records in the frequency domain. For the same DS 138, a 3D image of the vibration at a frequency of 49.56 kHz is shown.

Figure 11. Recordings in time domain done with SLDV on DS 138: (a)disc without damage 2D representation; (b) DS with arc type defect at 15 mm—2D; (c) disc without damage 3D; and (d) DS with arc type defect at 15 mm—3D.

Figure 12. Recordings in frequency domain done with SLDV on DS 138 with mechanical damage; next is given the EMI signature of the disk.

The pattern of vibration in the presence and in the vicinity of the crack shows clear disorder. From here and from the paper [31] came the idea of exploiting the entropy concept in identifying the damage. Thus, an entropy method for damage detection and the prediction was proposed [28, 32]. Since the possible use of SLDV is very costly, we propose a simple method that uses the EMIS global signature. The proposed method can successfully substitute a possible but very expensive use of SLDV that should provide mode shapes for obtaining the global EMIS signature.

Consider the discretized system Re Zð Þ ð Þ ω<sup>i</sup> ∶ ¼ Ri, ω<sup>i</sup> ∈ ω<sup>a</sup> ½ � ; ω<sup>b</sup> , Ri ≥ 0,i ¼ 1, …, n described by the probabilities P ¼ p1; p2;…; pn � �. The complex information contained in EMIS signature measurements, respectively, in Re Zð Þ ð Þ ω data, is firstly processed in sizes assimilable as probabilities, pi <sup>≥</sup> 0, <sup>i</sup> <sup>¼</sup> <sup>1</sup>, …, n and <sup>P</sup><sup>n</sup> <sup>i</sup>¼<sup>1</sup> pi <sup>¼</sup> <sup>1</sup>

$$p\_i \colon = \frac{\operatorname{Re}(Z(\omega\_i))}{\sum\_{i=1}^{n} \operatorname{Re}(Z(\omega\_i))} \colon = \frac{R\_i}{\mathbb{C}} \tag{5}$$

Cu<sup>∶</sup> <sup>¼</sup> <sup>X</sup><sup>n</sup>

<sup>i</sup> <sup>þ</sup> <sup>R</sup>dk i

Cdk<sup>∶</sup> <sup>¼</sup> <sup>X</sup><sup>n</sup>

pi,udk <sup>¼</sup> Ru

Xn i¼1

> Xn i¼1 Ru <sup>i</sup> <sup>þ</sup> <sup>R</sup>dk i � �log2 <sup>R</sup><sup>u</sup>

Ru <sup>i</sup> <sup>þ</sup> <sup>R</sup>dk i <sup>C</sup><sup>u</sup> <sup>þ</sup> <sup>C</sup><sup>d</sup><sup>1</sup> log2 <sup>R</sup><sup>u</sup>

H Pð Þ¼� ; udk

1 <sup>C</sup><sup>u</sup> <sup>þ</sup> <sup>C</sup>dk � �log2<sup>n</sup>

undamaged u DS, and so on up to ud<sup>4</sup> (Table 5).

–32 601 0.826 0.850 0.851 0.904 0.905 0.079 –42.5 651 0.771 0.821 0.805 0.882 0.876 0.108 –53 601 0.821 0.819 0.830 0.880 0.904 0.071 –68 1001 0.774 0.811 0.798 0.855 0.882 0.095 –81.5 551 0.762 0.804 0.811 0.884 0.830 0.095 92.5–98.5 601 0.714 0.799 0.790 0.829 0.833 0.117

Table 6. Influence of radiations on EMIS signature, type "u" DS [28].

Table 5. Entropy values for disc specimens DS: u vs. u (uu), u vs. d<sup>1</sup> (ud1), …, u vs. d<sup>4</sup> (ud4) [28].

–31 121 0.7601 0.7602 0.0001 –41 121 0.7571 0.7576 0.0005 –53 121 0.6721 0.6783 0.0062 –67 121 0.7275 0.7295 0.0020 –81.5 121 0.7437 0.7450 0.0013 –97 121 0.7173 0.7183 0.0010

H Pð Þ¼� ; udk

1 log2n P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> Ru i¼1 Ru

<sup>i</sup> <sup>þ</sup> <sup>R</sup>dk i � � <sup>∶</sup> <sup>¼</sup> Ru

> i¼1 Rdk

The relationship (7) gives the entropy, or complexity, or the disorder modifications on the EMIS signatures, of the undamaged u DS in relation with himself, in short uu. We continue with the increased entropy ud<sup>1</sup> of damaged DS having the damage at a distance 45 mm, d1, versus

From exploring the results in Table 5, it is noticeable that the PWAS active sensor senses the disorder caused by damage with satisfactory efficiency if this damage is located at a distance close to the sensor center, in this case at distances of 15–7 mm. This conclusion is useful for the

Frequency (kHz) n for summation uu ud1 ud2 ud3 ud4 Averaged entropy ud3 + ud4 increasing vs. uu

Frequency (kHz) n for summation Before irradiation During irradiation Entropy increasing

<sup>i</sup> <sup>þ</sup> <sup>R</sup>dk i � � � log2 <sup>C</sup><sup>u</sup> <sup>þ</sup> <sup>C</sup>dk � � � � " #

> <sup>i</sup> <sup>þ</sup> Rdk i

<sup>i</sup> (8)

<sup>i</sup> (10)

Cu <sup>þ</sup> <sup>C</sup>dk (9)

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131

<sup>i</sup> <sup>þ</sup> <sup>R</sup>dk i

Qualification of PWAS-Based SHM Technology for Space Applications

� � ! � <sup>C</sup><sup>u</sup> <sup>þ</sup> <sup>C</sup>dk � �log2 <sup>C</sup><sup>u</sup> <sup>þ</sup> <sup>C</sup>dk � � " # (11)

The normalized entropy of the set P is measured as:

$$H(P) = -\frac{\sum\_{i=1}^{n} p\_i \log\_2 p\_i}{\log\_2 n} \tag{6}$$

The disorder produced in EMIS signature by the mechanical damage will be analyzed based on the investigative capacity of PWAS. This can be deducted from graphs recorded in Figure 3, where we find the EMIS signatures of undamaged DS, noted "u," of the DS in which the damage is located at the distance d<sup>1</sup> = 45 mm, noted "d1", and so on, for the DS "d2", "d3", "d4". This calculation is carried out on frequency intervals ωaj ; ωbj h i, where certain resonance frequencies are present. Define

$$H(P, \mu u) = -\frac{\sum\_{i=1}^{n} p\_i \log\_2 p\_i}{\log\_2 n} = -\frac{\sum\_{i=1}^{n} \frac{2R\_i^u}{\mathcal{L}\mathcal{C}^u} \log\_2 \frac{2R\_i^u}{\mathcal{L}\mathcal{C}^u}}{\log\_2 n}$$

$$H(P, \mu u) = -\frac{1}{\log\_2 n} \left[ \frac{R\_1^u}{\mathcal{C}^u} \left( \log\_2 R\_1^u - \log\_2 \mathcal{C}^u \right) - \frac{R\_2^u}{\mathcal{C}^u} \left( \log\_2 R\_2^u - \log\_2 \mathcal{C}^u \right) - \dots - \frac{R\_n^u}{\mathcal{C}^u} \left( \log\_2 R\_n^u - \log\_2 \mathcal{C}^u \right) \right] \qquad (7)$$

$$H(P, \mu u) = -\frac{1}{\mathcal{C}^u \log\_2 n} \left( \sum\_{i=1}^n R\_i^u \log\_2 R\_i^u - \mathcal{C}^u \log\_2 \mathcal{C}^u \right)$$

Qualification of PWAS-Based SHM Technology for Space Applications http://dx.doi.org/10.5772/intechopen.78034 131

$$\mathbb{C}^{\mu} := \sum\_{i=1}^{n} \mathbb{R}\_{i}^{\mu} \tag{8}$$

$$p\_{i,ud\_k} = \frac{R\_i^u + R\_i^{d\_k}}{\sum\_{i=1}^n \left(R\_i^u + R\_i^{d\_k}\right)} := \frac{R\_i^u + R\_i^{d\_k}}{\mathbb{C}^u + \mathbb{C}^{d\_k}}\tag{9}$$

$$\mathbb{C}^{d\_k} := \sum\_{i=1}^n \mathbb{R}\_i^{d\_k} \tag{10}$$

$$H(\mathcal{P}, \boldsymbol{u}d\_k) = -\frac{1}{\log\_2 n} \left[ \sum\_{i=1}^n \frac{R\_i^u + R\_i^{d\_k}}{\mathbb{C}^u + \mathbb{C}^{d\_i}} \left( \log\_2 \left( R\_i^u + R\_i^{d\_k} \right) - \log\_2 \left( \mathbb{C}^u + \mathbb{C}^{d\_k} \right) \right) \right]$$

$$H(\mathcal{P}, \boldsymbol{u}d\_k) = -\frac{1}{\left( \mathbb{C}^u + \mathbb{C}^{d\_k} \right) \log\_2 n} \left[ \left( \sum\_{i=1}^n \left( R\_i^u + R\_i^{d\_k} \right) \log\_2 \left( R\_i^u + R\_i^{d\_k} \right) \right) - \left( \mathbb{C}^u + \mathbb{C}^{d\_k} \right) \log\_2 \left( \mathbb{C}^u + \mathbb{C}^{d\_k} \right) \right] \tag{11}$$

The relationship (7) gives the entropy, or complexity, or the disorder modifications on the EMIS signatures, of the undamaged u DS in relation with himself, in short uu. We continue with the increased entropy ud<sup>1</sup> of damaged DS having the damage at a distance 45 mm, d1, versus undamaged u DS, and so on up to ud<sup>4</sup> (Table 5).

From exploring the results in Table 5, it is noticeable that the PWAS active sensor senses the disorder caused by damage with satisfactory efficiency if this damage is located at a distance close to the sensor center, in this case at distances of 15–7 mm. This conclusion is useful for the


Table 5. Entropy values for disc specimens DS: u vs. u (uu), u vs. d<sup>1</sup> (ud1), …, u vs. d<sup>4</sup> (ud4) [28].


Table 6. Influence of radiations on EMIS signature, type "u" DS [28].

The pattern of vibration in the presence and in the vicinity of the crack shows clear disorder. From here and from the paper [31] came the idea of exploiting the entropy concept in identifying the damage. Thus, an entropy method for damage detection and the prediction was proposed [28, 32]. Since the possible use of SLDV is very costly, we propose a simple method that uses the EMIS global signature. The proposed method can successfully substitute a possible but very expensive use of SLDV that should provide mode shapes for obtaining the

Figure 12. Recordings in frequency domain done with SLDV on DS 138 with mechanical damage; next is given the EMI

Consider the discretized system Re Zð Þ ð Þ ω<sup>i</sup> ∶ ¼ Ri, ω<sup>i</sup> ∈ ω<sup>a</sup> ½ � ; ω<sup>b</sup> , Ri ≥ 0,i ¼ 1, …, n described by

measurements, respectively, in Re Zð Þ ð Þ ω data, is firstly processed in sizes assimilable as prob-

Re Zð Þ ð Þ ω<sup>i</sup>

<sup>i</sup>¼<sup>1</sup> Re Zð Þ ð Þ <sup>ω</sup><sup>i</sup>

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> pi

The disorder produced in EMIS signature by the mechanical damage will be analyzed based on the investigative capacity of PWAS. This can be deducted from graphs recorded in Figure 3, where we find the EMIS signatures of undamaged DS, noted "u," of the DS in which the damage is located at the distance d<sup>1</sup> = 45 mm, noted "d1", and so on, for the DS "d2", "d3",

> 2 <sup>C</sup><sup>u</sup> log2R<sup>u</sup>

> > Xn i¼1 Ru <sup>i</sup> log2R<sup>u</sup>

n

H Pð Þ¼�

<sup>i</sup>¼<sup>1</sup> pi <sup>¼</sup> <sup>1</sup>

pi <sup>∶</sup> <sup>¼</sup> <sup>P</sup>

"d4". This calculation is carried out on frequency intervals ωaj

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> pi log2pi log2<sup>n</sup> ¼ �

<sup>C</sup><sup>u</sup>log2<sup>n</sup>

<sup>1</sup> � log2C<sup>u</sup> � � � <sup>R</sup><sup>u</sup>

H Pð Þ¼� ; uu

H Pð Þ¼� ; uu <sup>1</sup>

The normalized entropy of the set P is measured as:

� �. The complex information contained in EMIS signature

<sup>∶</sup> <sup>¼</sup> Ri

log2pi

P<sup>n</sup> i¼1 2R<sup>u</sup> i <sup>2</sup>C<sup>u</sup> log2

<sup>n</sup> � log2C<sup>u</sup> � � � �

!

log2n

<sup>i</sup> � <sup>C</sup><sup>u</sup>log2C<sup>u</sup>

<sup>2</sup> � log2C<sup>u</sup> � � � … � <sup>R</sup><sup>u</sup>

<sup>C</sup> (5)

, where certain resonance

(7)

log2<sup>n</sup> (6)

; ωbj h i

> 2Ru i 2Cu

> > n <sup>C</sup><sup>u</sup> log2Ru

global EMIS signature.

signature of the disk.

the probabilities P ¼ p1; p2;…; pn

130 Structural Health Monitoring from Sensing to Processing

abilities, pi <sup>≥</sup> 0, <sup>i</sup> <sup>¼</sup> <sup>1</sup>, …, n and <sup>P</sup><sup>n</sup>

frequencies are present. Define

log2n

Ru 1 Cu log2R<sup>u</sup>

H Pð Þ¼� ; uu <sup>1</sup>


the irradiation tests and to Dr. Cristian Rugina from Institute of Solid Mechanics of the

Qualification of PWAS-Based SHM Technology for Space Applications

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133

Department of Systems, INCAS – National Institute for Aerospace Research "Elie Carafoli",

[1] Farrar CR, Worden K. An introduction to structural health monitoring. Philosophical

[2] Kinet D, Megret P, Goossen KW, Qiu L, Heider D, Caucheteur C. Fiber Bragg grating sensors toward structural health monitoring in composite materials: Challenges and solu-

[3] Ferdinand P. The evolution of optical fiber sensors technologies during the 35 last year and their applications in structural health monitoring. In: 7th European Workshop on

[4] Zagrai A, Doyle D, Gigineishvili V, Brown J, Gardenier H, Arritt B. Piezolectric wafer active sensor structural health monitoring of space structures. Journal of Intelligent Mate-

[5] Ursu I, Giurgiutiu V, Toader A. Towards spacecraft applications of structural health

[6] Toader A, Ursu I, Enciu D. New advances in space SHM project. INCAS Bulletin. 2015;

[7] Caimmi F, Bruggi M, Mariani S, Bendiscioli P. Towards the development of a MEMSbased health monitoring system for lightweight structures. In: International Electronic

Structural Health Monitoring, La Cité, Nantes, France; July 8–11, 2014

Romanian Academy, Bucharest, for FEM applied to DS.

The authors declare that they have no conflict of interest.

\*Address all correspondence to: enciu.daniela@incas.ro

Transactions of the Royal Society A. 2007;365:303-315

Ioan Ursu, Mihai Tudose and Daniela Enciu\*

tions. Sensors. 2014;14:7394-7419

rial Systems and Structures. 2010;21:921-940

monitoring. INCAS Bulletin. 2012;4(4):111-124

Conference on Sensors and Applications; 1–16 June, 2014

Conflict of interest

Author details

Bucharest, Romania

7(1):65-80

References

Table 7. Influence of temperature (after compensation) on EMIS signature, type "u" DS [28].

implementation of a SHM system, which should ensure an optimized distribution of monitoring sensors on the surface of the structure.

The fact that irradiation taken separately produces an insignificant change in the EMIS signature is attested in Table 6. If a compensation technique is considered and applied as in [26], the same conclusion applies to extreme temperature tests, see Table 7.

## 6. Conclusions

A first conclusion of descriptions and analysis made in this book chapter is that the cumulative impact of severe conditions of temperature and radiation has not generated decommissioning of PWAS sensors, thus confirming the survivability and sustainability of EMIS PWAS based SHM technology, as the first step towards de space vehicles transfer.

A second conclusion is that the splitting phenomenon of resonance peaks on EMIS signature can be associated with the occurrence of mechanical damage, making possible the clear dissociation of the changes determined by the harsh environmental conditions (temperatures and radiations). They are reduced mainly to reversible displacements of the resonance frequencies, with resonance amplitudes modifications, but if the temperatures do not cross certain limits, the amplitudes and frequencies return to those of RT case. Regarding radiations, they do not affect the EMIS graph.

## Acknowledgements

The support from National Authority for Scientific Research and Innovation (ANCSI), for Star Space SHM project code ID 188/2012, and for NUCLEU Program project code 18-036/1 PN, "Complex mechatronic systems for procedures of launching systems recovery with active structural health monitoring," is thankfully acknowledged. During these programs, a large amount of experimental data was obtained that ultimately grounded the results and conclusions presented above.

Finally, we express our gratitude to Dr. Cristian Postolache from Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering-IFIN-HH, Bucharest, for developing the irradiation tests and to Dr. Cristian Rugina from Institute of Solid Mechanics of the Romanian Academy, Bucharest, for FEM applied to DS.

## Conflict of interest

The authors declare that they have no conflict of interest.

## Author details

implementation of a SHM system, which should ensure an optimized distribution of monitor-

Frequency [kHz] n for summation RT 150C Entropy increasing

27–30 301 0.754 0.771 0.017 36.5–39.5 301 0.759 0.764 0.005 48–51.5 351 0.808 0.809 0.001 60.5–64.5 401 0.779 0.779 0.000 74–79 501 0.715 0.728 0.013

Table 7. Influence of temperature (after compensation) on EMIS signature, type "u" DS [28].

The fact that irradiation taken separately produces an insignificant change in the EMIS signature is attested in Table 6. If a compensation technique is considered and applied as in [26], the

A first conclusion of descriptions and analysis made in this book chapter is that the cumulative impact of severe conditions of temperature and radiation has not generated decommissioning of PWAS sensors, thus confirming the survivability and sustainability of EMIS PWAS based

A second conclusion is that the splitting phenomenon of resonance peaks on EMIS signature can be associated with the occurrence of mechanical damage, making possible the clear dissociation of the changes determined by the harsh environmental conditions (temperatures and radiations). They are reduced mainly to reversible displacements of the resonance frequencies, with resonance amplitudes modifications, but if the temperatures do not cross certain limits, the amplitudes and frequencies return to those of RT case. Regarding radiations, they do not

The support from National Authority for Scientific Research and Innovation (ANCSI), for Star Space SHM project code ID 188/2012, and for NUCLEU Program project code 18-036/1 PN, "Complex mechatronic systems for procedures of launching systems recovery with active structural health monitoring," is thankfully acknowledged. During these programs, a large amount of experimental data was obtained that ultimately grounded the results and conclu-

Finally, we express our gratitude to Dr. Cristian Postolache from Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering-IFIN-HH, Bucharest, for developing

ing sensors on the surface of the structure.

132 Structural Health Monitoring from Sensing to Processing

6. Conclusions

affect the EMIS graph.

Acknowledgements

sions presented above.

same conclusion applies to extreme temperature tests, see Table 7.

SHM technology, as the first step towards de space vehicles transfer.

Ioan Ursu, Mihai Tudose and Daniela Enciu\*

\*Address all correspondence to: enciu.daniela@incas.ro

Department of Systems, INCAS – National Institute for Aerospace Research "Elie Carafoli", Bucharest, Romania

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[26] Ursu I, Enciu D, Toader A. Towards structural health monitoring of space vehicles. Air-

[27] Ursu I, Toader A, Enciu D, Stefanescu DM. Advanced measurements in star space project on structural health monitoring. Proceedings of XXI IMEKO World Congress. 2015:2084-

[28] Enciu D, Ursu I, Toader A. New results concerning SHM technology qualification for transfer on space vehicles, Structural Control and Health Monitoring. 2017;24(10):e1992.

[29] Rugina C, Giurgiutiu V, Ursu I, Toader A. Finite element analysis of the electromechanical impedance method on aluminum plates in SHM. Proceedings of AEROSPATIAL 2014,

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[32] Enciu D, Ursu I, Tudose M. Complex method for online identification of mechanical damages using the electromechanical impedance spectroscopy, avoiding the false diagnosis. OSIM Patent no. RO131152B1/29.12.2017. Gold Medal and the Special Prize from the Turkish Patent and Trademark Office for the patent no. RO131152B1/29.12.2017 awarded at the 46th Edition of the International Invention Salon held at Geneva, Switzerland; 11–15

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[14] Rugina C, Enciu D, Tudose M. Numerical and experimental study of circular disc electromechanical impedance spectroscopy signature changes due to structural damage and sensor degradation. Structural Health Monitoring - an International Journal. 2015;14(6):

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663-681


**Chapter 7**

Provisional chapter

**Condition Monitoring of Wind Turbine Structures**

DOI: 10.5772/intechopen.78727

This chapter presents a fault detection method through uni- and multivariate hypothesis testing for wind turbine (WT) faults. A data-driven approach is used based on supervisory control and data acquisition (SCADA) data. First, using a healthy WT data set, a model is constructed through multiway principal component analysis (MPCA). Afterward, given a WT to be diagnosed, its data are projected into the MPCA model space. Since the turbulent wind is a random process, the dynamic response of the WT can be considered as a stochastic process, and thus, the acquired SCADA measurements are treated as a random process. The objective is to determine whether the distribution of the multivariate random samples that are obtained from the WT to be diagnosed (healthy or not) is related to the distribution of the baseline. To this end, a test for the equality of population means is performed in both the univariate and the multivariate cases. Ultimately, the test results establish whether the WT is healthy or faulty. The performance of the proposed method is validated using an advanced benchmark that comprehends a 5-MW WT subject to

Keywords: condition monitoring, wind turbines, principal component analysis,

The wind energy cost depends strongly on the performance of the condition monitoring system. Advance in this area would decrease downtime periods, extend the WT lifetime, and ultimately reduce the operation and maintenance (O&M) costs, which is one of the main

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

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

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

Condition Monitoring of Wind Turbine Structures

**through Univariate and Multivariate Hypothesis**

through Univariate and Multivariate Hypothesis

**Testing**

Testing

Francesc Pozo and Yolanda Vidal

Francesc Pozo and Yolanda Vidal

http://dx.doi.org/10.5772/intechopen.78727

Abstract

hypothesis testing

1. Introduction

Additional information is available at the end of the chapter

various actuators and sensor faults of different types.

challenges in wind energy as stated in "20% Wind Energy by 2030" [1].

Additional information is available at the end of the chapter

#### **Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing** Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

DOI: 10.5772/intechopen.78727

Francesc Pozo and Yolanda Vidal Francesc Pozo and Yolanda Vidal

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

http://dx.doi.org/10.5772/intechopen.78727

#### Abstract

This chapter presents a fault detection method through uni- and multivariate hypothesis testing for wind turbine (WT) faults. A data-driven approach is used based on supervisory control and data acquisition (SCADA) data. First, using a healthy WT data set, a model is constructed through multiway principal component analysis (MPCA). Afterward, given a WT to be diagnosed, its data are projected into the MPCA model space. Since the turbulent wind is a random process, the dynamic response of the WT can be considered as a stochastic process, and thus, the acquired SCADA measurements are treated as a random process. The objective is to determine whether the distribution of the multivariate random samples that are obtained from the WT to be diagnosed (healthy or not) is related to the distribution of the baseline. To this end, a test for the equality of population means is performed in both the univariate and the multivariate cases. Ultimately, the test results establish whether the WT is healthy or faulty. The performance of the proposed method is validated using an advanced benchmark that comprehends a 5-MW WT subject to various actuators and sensor faults of different types.

Keywords: condition monitoring, wind turbines, principal component analysis, hypothesis testing

## 1. Introduction

The wind energy cost depends strongly on the performance of the condition monitoring system. Advance in this area would decrease downtime periods, extend the WT lifetime, and ultimately reduce the operation and maintenance (O&M) costs, which is one of the main challenges in wind energy as stated in "20% Wind Energy by 2030" [1].

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

Usually, condition monitoring comprises different systems (vibration analysis, oil monitoring, etc. [2]) for different parts and different types of faults and makes use of expensive specific sensors that must be installed in the WT. Therefore, the advance in fault detection systems that only make use of already available data from the turbine SCADA system and comprehend different parts and different types of faults is promising (since no additional sensors or data acquisition devices are needed). The SCADA signals provide rich information on the WT performance; thus, with appropriate algorithms, they can be used effectively for condition monitoring, prognostics, and remaining useful life prediction of WTs [3]. There are some success stories about using SCADA data for condition monitoring. For example, Ruiz et al. presented a machine learning approach [4], Zaher and McArthur proposed to use the combination of abnormal detection and data-trending techniques encapsulated in a multiagent framework [5], Pozo and Vidal proposed a fault detection system based on principal component analysis [6].

In this work, following the enhanced benchmark challenge for wind turbine fault detection proposed in [7], a set of eight realistic fault scenarios are considered to develop a WT condition monitoring strategy that combines a SCADA data-driven baseline model—reference pattern obtained from the healthy wind turbine—based on MPCA in combination with uni- and multivariate hypothesis testing. Previous works using MPCA and hypothesis testing to detect structural damage [8] work under the hypothesis of guided waves. That is, the vibration (guided wave) induced to the structure is known and always the same. However, in this work, the vibration is induced by the changeful wind. The used benchmark comprehends different types of faults of a 5-MW WT given by the FAST simulator [9], which has been accepted by the scientific community and is widely used for WT-related research, e.g., [10–12].

The chapter is organized as follows. Section 2 briefly recalls the WT benchmark model. In Section 3, the condition monitoring strategy is stated. Simulation results are discussed in Section 4. Finally, conclusions are drawn in Section 5.

## 2. Wind turbine benchmark model

The used benchmark model is proposed in [7]. It covers a 5-MW three-bladed, variable speed WT modeled with the FAST simulator, detailed actuator and sensor models, as well as the different fault descriptions. For a complete description of the benchmark, please see reference [7]. Here, a short review is given to introduce the used notation.

τ\_rð Þþ t αgcτrðÞ¼ t αgcτcð Þt (1)

fa,m m/s2

http://dx.doi.org/10.5772/intechopen.78727

139

ss,m m/s2

fa,m m/s2

ss,m m/s2

fa,m m/s2

ss,m m/s2

PeðÞ¼ t ηgωgð Þt τrð Þt (2)

where τ<sup>r</sup> and τ<sup>c</sup> are the real generator torque and its reference (given by the controller), respectively. In the numerical simulations, αgc ¼ 50, see [13]. Moreover, the power produced

These sensors are representative of the types of sensors that are available on an MW-scale commercial wind turbine.

Reference wind turbine Magnitude Rated power 5 MW Number of blades 3 Rotor/hub diameter 126, 3 m Hub height 90 m

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

Cut-in, rated, and cut-out wind speed 3, 11:4, and 25 m/s Rated generator speed (ωng) 1173:7 rpm

Gearbox ratio 97

Number Sensor type Symbol Units Generated electrical power Pe,m kW Rotor speed ωr,m rad/s Generator speed ωg,m rad/s Generator torque τc,m Nm First pitch angle β1,m � Second pitch angle β2,m � Third pitch angle β3,m �

8 Fore-aft acceleration at tower bottom a<sup>b</sup>

9 Side-to-side acceleration at tower bottom a<sup>b</sup>

10 Fore-aft acceleration at mid-tower a<sup>m</sup>

11 Side-to-side acceleration at mid-tower a<sup>m</sup>

12 Fore-aft acceleration at tower top a<sup>t</sup>

13 Side-to-side acceleration at tower top a<sup>t</sup>

where η<sup>g</sup> is the efficiency of the generator and ω<sup>g</sup> is the generator speed. In the numerical

by the generator, Peð Þt , is given by (see [7]):

Table 2. Assumed available measurements.

Table 1. WT properties.

experiments, η<sup>g</sup> ¼ 0:98 is used, see [7].

The specifications of the 5-MW reference WT is documented in [13]. This model has been used as a reference by research teams throughout the world to standardize baseline on- and offshore wind turbine specifications. The wind turbine typical features are given in Table 1, and the assumed available SCADA data are given in Table 2. This work copes with the so-called full load region of operation. In order to run the simulations, turbulent wind data sets that cover this region have been generated with TurbSim [14], see Figure 1.

The generator-converter system can be approximated by a first-order ordinary differential equation, see [7], which is given by:


#### Table 1. WT properties.

Usually, condition monitoring comprises different systems (vibration analysis, oil monitoring, etc. [2]) for different parts and different types of faults and makes use of expensive specific sensors that must be installed in the WT. Therefore, the advance in fault detection systems that only make use of already available data from the turbine SCADA system and comprehend different parts and different types of faults is promising (since no additional sensors or data acquisition devices are needed). The SCADA signals provide rich information on the WT performance; thus, with appropriate algorithms, they can be used effectively for condition monitoring, prognostics, and remaining useful life prediction of WTs [3]. There are some success stories about using SCADA data for condition monitoring. For example, Ruiz et al. presented a machine learning approach [4], Zaher and McArthur proposed to use the combination of abnormal detection and data-trending techniques encapsulated in a multiagent framework [5], Pozo and

Vidal proposed a fault detection system based on principal component analysis [6].

scientific community and is widely used for WT-related research, e.g., [10–12].

conclusions are drawn in Section 5.

138 Structural Health Monitoring from Sensing to Processing

equation, see [7], which is given by:

2. Wind turbine benchmark model

[7]. Here, a short review is given to introduce the used notation.

cover this region have been generated with TurbSim [14], see Figure 1.

In this work, following the enhanced benchmark challenge for wind turbine fault detection proposed in [7], a set of eight realistic fault scenarios are considered to develop a WT condition monitoring strategy that combines a SCADA data-driven baseline model—reference pattern obtained from the healthy wind turbine—based on MPCA in combination with uni- and multivariate hypothesis testing. Previous works using MPCA and hypothesis testing to detect structural damage [8] work under the hypothesis of guided waves. That is, the vibration (guided wave) induced to the structure is known and always the same. However, in this work, the vibration is induced by the changeful wind. The used benchmark comprehends different types of faults of a 5-MW WT given by the FAST simulator [9], which has been accepted by the

The chapter is organized as follows. Section 2 briefly recalls the WT benchmark model. In Section 3, the condition monitoring strategy is stated. Simulation results are discussed in Section 4. Finally,

The used benchmark model is proposed in [7]. It covers a 5-MW three-bladed, variable speed WT modeled with the FAST simulator, detailed actuator and sensor models, as well as the different fault descriptions. For a complete description of the benchmark, please see reference

The specifications of the 5-MW reference WT is documented in [13]. This model has been used as a reference by research teams throughout the world to standardize baseline on- and offshore wind turbine specifications. The wind turbine typical features are given in Table 1, and the assumed available SCADA data are given in Table 2. This work copes with the so-called full load region of operation. In order to run the simulations, turbulent wind data sets that

The generator-converter system can be approximated by a first-order ordinary differential


These sensors are representative of the types of sensors that are available on an MW-scale commercial wind turbine.

Table 2. Assumed available measurements.

$$
\dot{\tau}\_r(t) + \alpha\_{\text{gt}} \tau\_r(t) = \alpha\_{\text{gt}} \tau\_c(t) \tag{1}
$$

where τ<sup>r</sup> and τ<sup>c</sup> are the real generator torque and its reference (given by the controller), respectively. In the numerical simulations, αgc ¼ 50, see [13]. Moreover, the power produced by the generator, Peð Þt , is given by (see [7]):

$$P\_{\varepsilon}(t) = \eta\_{\mathcal{g}} \omega\_{\mathcal{g}}(t) \tau\_r(t) \tag{2}$$

where η<sup>g</sup> is the efficiency of the generator and ω<sup>g</sup> is the generator speed. In the numerical experiments, η<sup>g</sup> ¼ 0:98 is used, see [7].

Figure 1. Wind speed signal with turbulence intensity set to 10%.

Each of the three pitch actuators is modeled as a closed loop transfer function between the pitch angle, βð Þs , and its reference βrð Þs :

$$\frac{\beta(\mathbf{s})}{\beta\_r(\mathbf{s})} = \frac{\omega\_n^2}{\mathbf{s}^2 + 2\xi\omega\_n\mathbf{s} + \omega\_n^2} \tag{3}$$

3. Condition monitoring (CM) strategy

model created in (i), and

WT,

should be detected.

The overall CM strategy is based on a three-tier framework:

iii. the final decision is based on both univariate and multivariate HT.

3.1. The wind as a source for the excitation: the need for a new paradigm

i. a multiway PCA (MPCA) model is built with the data that are collected from a healthy

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

http://dx.doi.org/10.5772/intechopen.78727

141

ii. when a new WT has to be diagnosed, the SCADA data are projected using the MPCA

In general, vibration-based structural health monitoring (SHM) is based on the fact that an alteration or difference in physical properties due to damage or structural change will motivate changes in dynamical responses that may be detected. Figure 2 represents this paradigm in the sense that a healthy structure is excited according to a prescribed signal to build a pattern. Afterward, the structure that has to be diagnosed is affected by exactly the same signal, where the response is measured, processed, and finally compared with the previous pattern. The strategy presented in Figure 2 is known as "guided waves in structures for SHM" [15].

In the present chapter, the field of application is wind turbines and a realistic scenario is to consider that the excitation comes from the wind turbulence. The wind turbulence cannot be controlled and it is always different. Therefore, the paradigm of guided waves in WT for SHM as in Figure 2 cannot be considered. In this case, when the source of the excitation cannot be previously prescribed, a new paradigm is needed, as represented in Figure 3. The foundation of the new paradigm is that, even with a constantly different excitation, the CM strategy based on MPCA and univariate and multivariate HT will be able to disclose some hidden damage, misbehavior, or fault. To sum up, the fundamental idea behind the CM strategy is the hypothesis that a variation in the overall behavior of the WT, even with an unprescribed excitation,

Figure 2. Vibration-based SHM is based on the fact that an alteration or difference in physical properties due to damage

or structural change will motivate changes in dynamical responses that may be detected.

where ξ is the damping ratio and ω<sup>n</sup> the natural frequency that takes the fault-free values ξ ¼ 0:6 and ω<sup>n</sup> ¼ 11:11 rad/s, see [7].

The fault detection benchmark considers different types of faults at different components (sensors and actuators), as described in Table 3.


Table 3. Fault scenarios.

## 3. Condition monitoring (CM) strategy

Each of the three pitch actuators is modeled as a closed loop transfer function between the

where ξ is the damping ratio and ω<sup>n</sup> the natural frequency that takes the fault-free values

The fault detection benchmark considers different types of faults at different components

F1 Pitch actuator Change in dynamics: high air content in oil

F2 Pitch actuator Change in dynamics: pump wear F3 Pitch actuator Change in dynamics: hydraulic leakage F4 Torque actuator Offset (offset value equal to 2000 Nm) F5 Generator speed sensor Scaling (gain factor equal to 1:2) F6 Pitch angle sensor Stuck (fixed value equal to 5�) F7 Pitch angle sensor Stuck (fixed value equal to 10�) F8 Pitch angle sensor Scaling (gain factor equal to 1:2)

n s<sup>2</sup> þ 2ξωns þ ω<sup>2</sup>

n

(3)

<sup>β</sup>rð Þ<sup>s</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup>

βð Þs

Fault Type Description

pitch angle, βð Þs , and its reference βrð Þs :

140 Structural Health Monitoring from Sensing to Processing

Figure 1. Wind speed signal with turbulence intensity set to 10%.

ξ ¼ 0:6 and ω<sup>n</sup> ¼ 11:11 rad/s, see [7].

Table 3. Fault scenarios.

(sensors and actuators), as described in Table 3.

The overall CM strategy is based on a three-tier framework:


## 3.1. The wind as a source for the excitation: the need for a new paradigm

In general, vibration-based structural health monitoring (SHM) is based on the fact that an alteration or difference in physical properties due to damage or structural change will motivate changes in dynamical responses that may be detected. Figure 2 represents this paradigm in the sense that a healthy structure is excited according to a prescribed signal to build a pattern. Afterward, the structure that has to be diagnosed is affected by exactly the same signal, where the response is measured, processed, and finally compared with the previous pattern. The strategy presented in Figure 2 is known as "guided waves in structures for SHM" [15].

In the present chapter, the field of application is wind turbines and a realistic scenario is to consider that the excitation comes from the wind turbulence. The wind turbulence cannot be controlled and it is always different. Therefore, the paradigm of guided waves in WT for SHM as in Figure 2 cannot be considered. In this case, when the source of the excitation cannot be previously prescribed, a new paradigm is needed, as represented in Figure 3. The foundation of the new paradigm is that, even with a constantly different excitation, the CM strategy based on MPCA and univariate and multivariate HT will be able to disclose some hidden damage, misbehavior, or fault. To sum up, the fundamental idea behind the CM strategy is the hypothesis that a variation in the overall behavior of the WT, even with an unprescribed excitation, should be detected.

Figure 2. Vibration-based SHM is based on the fact that an alteration or difference in physical properties due to damage or structural change will motivate changes in dynamical responses that may be detected.

ð Þ <sup>x</sup><sup>11</sup> <sup>x</sup><sup>12</sup> <sup>⋯</sup> <sup>x</sup>1<sup>L</sup> <sup>x</sup><sup>21</sup> <sup>x</sup><sup>22</sup> <sup>⋯</sup> <sup>x</sup>2<sup>L</sup> <sup>⋯</sup> xn<sup>1</sup> xn<sup>2</sup> <sup>⋯</sup> xnL <sup>∈</sup> <sup>R</sup>nL (4)

∈ℳ<sup>n</sup>�<sup>L</sup>ð Þ R (5)

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143

where the real number xij, i ¼ 1, …, n, j ¼ 1, …, L corresponds to the measure of the sensor at time ð Þ ð Þ i � 1 L þ ð Þ j � 1 Δ seconds. These collected data can be arranged in matrix form as follows:

where ℳ<sup>n</sup>�<sup>L</sup>ð Þ R is the vector space of n � L matrices over R. It is worth noting that n is the number of rows of the matrix in Eq. (5) and L is the number of columns of the same matrix. The effect on the overall performance of the condition monitoring strategy on the choice of n and L

Let us assume that the SCADA data are now collected from N ∈ℕ sensors also during the same period of time. In this case, the collected data, for each sensor, can be organized in a matrix as in Eq. (5). Subsequently, all the collected data coming from the whole set of sensors

<sup>11</sup> ⋯ x<sup>2</sup>

<sup>i</sup><sup>1</sup> ⋯ x<sup>2</sup>

<sup>n</sup><sup>1</sup> ⋯ x<sup>2</sup>

j⋯jvð Þ <sup>N</sup>�<sup>1</sup> <sup>L</sup>þ<sup>1</sup>∣⋯∣vN�<sup>L</sup> |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} X<sup>N</sup>

<sup>i</sup> <sup>¼</sup> <sup>X</sup>ð Þ <sup>i</sup>; : <sup>∈</sup> <sup>R</sup><sup>N</sup>�L, i <sup>¼</sup> <sup>1</sup>, …, n represents the measurements from all the sen-

⋮ ⋮ ⋱⋮ ⋮ ⋱⋮ ⋱⋮ ⋱⋮

⋮ ⋮ ⋱⋮ ⋮ ⋱⋮ ⋱⋮ ⋱⋮

sensor. Matrix X∈ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R —where ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R is the vector space of n � ð Þ N � L matrices over R—contains the measures from N sensors at nL discretization instants. Consequently,

sors at time instants ð Þ ð Þ i � 1 L þ ð Þ j � 1 Δ seconds, j ¼ 1, …, L. Equivalently, each column vector

The objective of the subsequent analysis is to build the MPCA model, that is, the square orthogonal matrix P∈ℳð Þ� <sup>N</sup>�<sup>L</sup> ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R that has to be used to transform or project the original

vj <sup>¼</sup> <sup>X</sup>ð Þ :; <sup>j</sup> <sup>∈</sup> <sup>R</sup>n, j <sup>¼</sup> <sup>1</sup>, …, N � <sup>L</sup> represents measurements from sensor number <sup>j</sup>

instants ð Þ ð Þ i � 1 L þ ð Þ j � 1 Δ seconds, 1 ¼ 1, …, n, where d e� is the ceiling function.

<sup>1</sup><sup>L</sup> ⋯ x<sup>N</sup>

iL ⋯ x<sup>N</sup>

nL ⋯ x<sup>N</sup>

1 CA <sup>11</sup> ⋯ xN

<sup>i</sup><sup>1</sup> ⋯ xN

<sup>n</sup><sup>1</sup> ⋯ xN

1L

1

CCCCCCCCA

(6)

iL

nL

ij in the matrix represents the number of

L l m at time

1

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

CCCCCCA

x<sup>11</sup> x<sup>12</sup> ⋯ x1<sup>L</sup> ⋮ ⋮ ⋱⋮ xi<sup>1</sup> xi<sup>2</sup> ⋯ xiL ⋮ ⋮ ⋱⋮ xn<sup>1</sup> xn<sup>2</sup> ⋯ xnL

0

BBBBBB@

are concatenated and disposed in a matrix X∈ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> as follows:

<sup>12</sup> ⋯ x<sup>1</sup>

<sup>i</sup><sup>2</sup> ⋯ x<sup>1</sup>

<sup>n</sup><sup>2</sup> ⋯ x<sup>1</sup>

<sup>¼</sup> <sup>X</sup><sup>1</sup> <sup>X</sup><sup>2</sup> <sup>⋯</sup> <sup>X</sup><sup>N</sup> � �∈ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ <sup>R</sup>

data matrix X according to the following matrix-to-matrix product:

jvLþ<sup>1</sup>∣⋯∣v2<sup>L</sup> |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} X2

<sup>1</sup><sup>L</sup> x<sup>2</sup>

iL x<sup>2</sup>

nL x<sup>2</sup>

is thoroughly analyzed on [21].

X ¼

0 B@

each row vector xT

x1 <sup>11</sup> x<sup>1</sup>

0

BBBBBBBB@

x1 <sup>i</sup><sup>1</sup> x<sup>1</sup>

x1 <sup>n</sup><sup>1</sup> x<sup>1</sup>

¼ v1∣v2∣⋯∣vL |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} X1

where the superindex <sup>k</sup> <sup>¼</sup> <sup>1</sup>, …, N of each element <sup>x</sup><sup>k</sup>

Figure 3. The key idea behind the new paradigm of the detection strategy is the assumption that a change in the behavior of the overall system, even with a different excitation, has to be detected.

However, in our application, the only available excitation of the wind turbines is the wind turbulence. Therefore, guided waves in wind turbines for SHM as in Figure 2 cannot be considered as a realistic scenario. In spite of that, the new paradigm described in Figure 3 is based on the fact that, even with different wind turbulence, the fault detection strategy based on PCA and statistical multivariate hypothesis testing will be able to detect some damage, fault, or misbehavior. More precisely, the key idea behind the detection strategy is the assumption that a change in the behavior of the overall system, even with a different excitation, has to be detected. Section 4 includes the simulation results of the proposed CM strategy that validates this hypothesis.

## 3.2. Data-driven baseline modeling based on MPCA

Multiway principal component analysis (MPCA) is a natural extension of classical principal component analysis (PCA) to manage data in multidimensional arrays [16, 17]. A conventional two-dimensional data matrix can be treated as a two-way array, where experiments and variables (or discretization instant times) form the two different ways. Frequently, this arrangement has to be extended to multiway arrays, particularly if several sensors—in different experimental trials—are gathering data at different time instants. Consequently, MPCA is equivalent to the application of standard PCA to an unfolded version of the initial multiway array.

Westerhuis et al. [18] propose six different ways of unfolding a three-way data matrix. Besides, in [18], a critical analysis of several aspects of the treatment of multiway data is provided, including how the matrix is unfolded, but also mean-centering and scaling with respect to the effects on the analysis of batch data. Ruiz et al. [19] assign one of the first six letters of the alphabet to each one of the six different ways of unfolding. In this chapter, as well as in [6, 8, 20, 21], we have considered the so-called type E. However, we will present the collected SCADA data arranged in an already unfolded matrix.

The MPCA modeling starts by measuring, from a healthy wind turbine, a sensor during ð Þ nL � 1 Δ seconds, where Δ is the sampling time and n, L∈ℕ. The discretized measures of the sensor are a real vector

$$(\mathbf{x}\_{11} \; \mathbf{x}\_{12} \; \cdots \; \mathbf{x}\_{1L} \; \mathbf{x}\_{21} \; \mathbf{x}\_{22} \; \cdots \; \mathbf{x}\_{2L} \; \cdots \; \mathbf{x}\_{n1} \; \mathbf{x}\_{n2} \; \cdots \; \mathbf{x}\_{nL}) \in \mathbb{R}^{nL} \tag{4}$$

where the real number xij, i ¼ 1, …, n, j ¼ 1, …, L corresponds to the measure of the sensor at time ð Þ ð Þ i � 1 L þ ð Þ j � 1 Δ seconds. These collected data can be arranged in matrix form as follows:

$$\begin{pmatrix} \mathbf{x}\_{11} & \mathbf{x}\_{12} & \cdots & \mathbf{x}\_{1L} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{x}\_{i1} & \mathbf{x}\_{i2} & \cdots & \mathbf{x}\_{iL} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{x}\_{n1} & \mathbf{x}\_{n2} & \cdots & \mathbf{x}\_{nL} \end{pmatrix} \in \mathcal{A}\_{n \times L}(\mathbb{R}) \tag{5}$$

where ℳ<sup>n</sup>�<sup>L</sup>ð Þ R is the vector space of n � L matrices over R. It is worth noting that n is the number of rows of the matrix in Eq. (5) and L is the number of columns of the same matrix. The effect on the overall performance of the condition monitoring strategy on the choice of n and L is thoroughly analyzed on [21].

However, in our application, the only available excitation of the wind turbines is the wind turbulence. Therefore, guided waves in wind turbines for SHM as in Figure 2 cannot be considered as a realistic scenario. In spite of that, the new paradigm described in Figure 3 is based on the fact that, even with different wind turbulence, the fault detection strategy based on PCA and statistical multivariate hypothesis testing will be able to detect some damage, fault, or misbehavior. More precisely, the key idea behind the detection strategy is the assumption that a change in the behavior of the overall system, even with a different excitation, has to be detected. Section 4 includes the simulation results of the proposed CM strategy that vali-

Figure 3. The key idea behind the new paradigm of the detection strategy is the assumption that a change in the behavior

Multiway principal component analysis (MPCA) is a natural extension of classical principal component analysis (PCA) to manage data in multidimensional arrays [16, 17]. A conventional two-dimensional data matrix can be treated as a two-way array, where experiments and variables (or discretization instant times) form the two different ways. Frequently, this arrangement has to be extended to multiway arrays, particularly if several sensors—in different experimental trials—are gathering data at different time instants. Consequently, MPCA is equivalent to the application of standard PCA to an unfolded version of the initial multiway

Westerhuis et al. [18] propose six different ways of unfolding a three-way data matrix. Besides, in [18], a critical analysis of several aspects of the treatment of multiway data is provided, including how the matrix is unfolded, but also mean-centering and scaling with respect to the effects on the analysis of batch data. Ruiz et al. [19] assign one of the first six letters of the alphabet to each one of the six different ways of unfolding. In this chapter, as well as in [6, 8, 20, 21], we have considered the so-called type E. However, we will present the collected

The MPCA modeling starts by measuring, from a healthy wind turbine, a sensor during ð Þ nL � 1 Δ seconds, where Δ is the sampling time and n, L∈ℕ. The discretized measures of the

dates this hypothesis.

sensor are a real vector

array.

3.2. Data-driven baseline modeling based on MPCA

of the overall system, even with a different excitation, has to be detected.

142 Structural Health Monitoring from Sensing to Processing

SCADA data arranged in an already unfolded matrix.

Let us assume that the SCADA data are now collected from N ∈ℕ sensors also during the same period of time. In this case, the collected data, for each sensor, can be organized in a matrix as in Eq. (5). Subsequently, all the collected data coming from the whole set of sensors are concatenated and disposed in a matrix X∈ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> as follows:

$$\mathbf{X} = \begin{pmatrix} \mathbf{x}\_{11}^1 & \mathbf{x}\_{12}^1 & \cdots & \mathbf{x}\_{1L}^1 & \mathbf{x}\_{11}^2 & \cdots & \mathbf{x}\_{1L}^2 & \cdots & \mathbf{x}\_{1L}^N & \cdots & \mathbf{x}\_{1L}^N \\ \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \mathbf{x}\_{11}^1 & \mathbf{x}\_{12}^1 & \cdots & \mathbf{x}\_{1L}^1 & \mathbf{x}\_{11}^2 & \cdots & \mathbf{x}\_{1L}^2 & \cdots & \mathbf{x}\_{11}^N & \cdots & \mathbf{x}\_{1L}^N \\ \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \mathbf{x}\_{n1}^1 & \mathbf{x}\_{n2}^1 & \cdots & \mathbf{x}\_{nL}^1 & \mathbf{x}\_{n1}^2 & \cdots & \mathbf{x}\_{nL}^2 & \cdots & \mathbf{x}\_{n1}^N & \cdots & \mathbf{x}\_{nL}^N \end{pmatrix} \tag{6}$$

$$= \left( \underbrace{\underbrace{\mathbf{v}\_1 \mathbf{v}\_2 \cdots \mathbf{v}\_L}\_{\mathbf{x}^0} \underbrace{\mathbf{v}\_{L+1} \cdots \mathbf{v}\_{2L}}\_{\mathbf{x}^2} \cdot \cdots \underbrace{\mathbf{v}\_{(N-1)L+1} \cdots \mathbf{v}\_{NL}}\_{\mathbf{x}^0} \right) \tag{7}$$

$$= \left( \mathbf{X}^1 \quad \mathbf{X}^2 \quad \cdots \quad \mathbf{X}^N \right) \in \mathcal{A}\_{n \times (N \cup \lfloor \varepsilon \rfloor)} \left( \mathbb{R} \right)$$

where the superindex <sup>k</sup> <sup>¼</sup> <sup>1</sup>, …, N of each element <sup>x</sup><sup>k</sup> ij in the matrix represents the number of sensor. Matrix X∈ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R —where ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R is the vector space of n � ð Þ N � L matrices over R—contains the measures from N sensors at nL discretization instants. Consequently, each row vector xT <sup>i</sup> <sup>¼</sup> <sup>X</sup>ð Þ <sup>i</sup>; : <sup>∈</sup> <sup>R</sup><sup>N</sup>�L, i <sup>¼</sup> <sup>1</sup>, …, n represents the measurements from all the sensors at time instants ð Þ ð Þ i � 1 L þ ð Þ j � 1 Δ seconds, j ¼ 1, …, L. Equivalently, each column vector vj <sup>¼</sup> <sup>X</sup>ð Þ :; <sup>j</sup> <sup>∈</sup> <sup>R</sup>n, j <sup>¼</sup> <sup>1</sup>, …, N � <sup>L</sup> represents measurements from sensor number <sup>j</sup> L l m at time instants ð Þ ð Þ i � 1 L þ ð Þ j � 1 Δ seconds, 1 ¼ 1, …, n, where d e� is the ceiling function.

The objective of the subsequent analysis is to build the MPCA model, that is, the square orthogonal matrix P∈ℳð Þ� <sup>N</sup>�<sup>L</sup> ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R that has to be used to transform or project the original data matrix X according to the following matrix-to-matrix product:

$$\mathbf{T} = \mathbf{X}\mathbf{P} \in \mathcal{A}\_{n \times (N \cdot L)}(\mathbb{R}),\tag{7}$$

μk <sup>j</sup> <sup>¼</sup> <sup>1</sup> n Xn i¼1 xk

<sup>j</sup> is the arithmetic mean of the measures placed at the same column. In this case, then,

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

<sup>k</sup> is defined as in Eq. (9) using μ<sup>k</sup> as in Eq. (8). It is worth noting that the only difference

ij � � is scaled and centered according to the MCGS strategy described in

Xn i¼1

j

xk ij � <sup>μ</sup><sup>k</sup> j

� � <sup>¼</sup> <sup>0</sup> (15)

<sup>X</sup>�<sup>T</sup>X� <sup>∈</sup>ℳð Þ� <sup>N</sup>�<sup>L</sup> ð Þ <sup>N</sup>�<sup>L</sup> ð Þ <sup>R</sup> (16)

ij n o , i <sup>¼</sup> <sup>1</sup>, …, n, j <sup>¼</sup> <sup>1</sup>, …, L, k <sup>¼</sup> <sup>1</sup>, …, N: (17)

between the expressions in Eqs. (10) and (12) is how the elements in matrix <sup>X</sup> <sup>¼</sup> xk

Eq. (12), the average value of each column vector in the scaled matrix X� can be calculated as

Xn i¼1 xk ij ! � <sup>n</sup>μ<sup>k</sup>

" #

<sup>j</sup> � <sup>n</sup>μ<sup>k</sup> j

Taking advantage of the fact that the scaled matrix X� is a mean-centered matrix, the variancecovariance matrix can be straightforwardly computed as a matrix-to-matrix product of X� and its transpose, divided by n � 1, where n is the number of rows of matrix X in Eq. (6). More precisely,

Clearly, GS and MCGS are not the only ways to center and scale data. For instance, feature scaling, also known as unity-based normalization, can also be considered. In this case, data are centered with respect to the minimum value and scaled with respect to the range of the set, that is,

However, to easily compute the variance-covariance matrix in the CM strategy that we present in this chapter, the mean-centered group scaling (MCGS) is the method that we have selected

xk ij � <sup>μ</sup><sup>k</sup> j <sup>σ</sup><sup>k</sup> <sup>¼</sup> <sup>1</sup> nσ<sup>k</sup>

<sup>¼</sup> <sup>1</sup> nσ<sup>k</sup>

> <sup>¼</sup> <sup>1</sup> <sup>n</sup>σ<sup>k</sup> <sup>n</sup>μ<sup>k</sup>

CX� <sup>¼</sup> <sup>1</sup> n � 1

ij � � is centered and scaled—using MCGS—to define a modified matrix <sup>X</sup>� <sup>¼</sup>

<sup>q</sup> , i <sup>¼</sup> <sup>1</sup>, …, n, j <sup>¼</sup> <sup>1</sup>,…, L, k <sup>¼</sup> <sup>1</sup>, …, N: (12)

where μ<sup>k</sup>

matrix <sup>X</sup> <sup>¼</sup> <sup>x</sup><sup>k</sup>

ij � � as

When matrix <sup>X</sup> <sup>¼</sup> xk

x~k ij ≔ xk

max xk

ij � min <sup>x</sup><sup>k</sup> ij n o

ij n o � min xk

�xk ij <sup>≔</sup> xk

> 1 n Xn i¼1 �xk ij <sup>¼</sup> <sup>1</sup> n Xn i¼1

ij � <sup>μ</sup><sup>k</sup> j ffiffiffiffiffi σ2 k

<sup>X</sup>MCGS <sup>¼</sup> �x<sup>k</sup>

where σ<sup>2</sup>

ij, j ¼ 1, …, L, (11)

http://dx.doi.org/10.5772/intechopen.78727

ij � � are centered.

(14)

145

� � (13)

where the shape of the variance-covariance matrix of matrix T in Eq. (7) is diagonal.

In the proposed approach in this chapter, the model defined in matrix P in Eq. (7) is based only on measures that come from a healthy wind turbine. Posteriorly, data from the current WT to diagnose will be projected using the matrix-to-matrix multiplication also defined in Eq. (7). However, a different procedure can be considered, particularly, when the goal is not just to detect a damage or a fault but to classify it. In the latter case, matrix X in Eq. (6) should contain measures from a WT in its healthy state but also in all the possible fault scenarios. This way, the generated model in matrix P in Eq. (7) contains all the possible states of the structure.

#### 3.2.1. Centering and scaling: group scaling (GS) vs. mean-centered group scaling (MCGS)

Considering that the data stored in matrix X are affected by a changing wind turbulence, come from different sensors, and could have different magnitudes and scales, some kind of preprocessing step is required to rescale the data [22, 23]. According to Westerhuis et al. [18], the way this preprocessing step is carried out may affect the overall performance of the CM strategy. In the present chapter, we present two possible choices that have some common core. These two alternatives are as follows:


In the former case (GS), both the arithmetic mean and the variance of all measurements of the sensor are used. More precisely, for k ¼ 1, 2, …, N, we define

$$\mu^k = \frac{1}{nL} \sum\_{i=1}^n \sum\_{j=1}^L \mathbf{x}\_{ij\prime}^k \tag{8}$$

$$
\sigma\_k^2 = \frac{1}{nL} \sum\_{i=1}^n \sum\_{j=1}^L \left( \mathbf{x}\_{ij}^k - \boldsymbol{\mu}^k \right)^2 \tag{9}
$$

where μ<sup>k</sup> and σ<sup>2</sup> <sup>k</sup> are the arithmetic mean and the variance of the whole set of elements in matrix X<sup>k</sup> , respectively. In this case, matrix <sup>X</sup> <sup>¼</sup> xk ij � � is centered and scaled—using GS—to define a modified matrix <sup>X</sup> <sup>¼</sup> <sup>X</sup>GS <sup>¼</sup> <sup>x</sup><sup>k</sup> ij � � as

$$\check{\mathbf{x}}\_{ij}^{k} \coloneqq \frac{\mathbf{x}\_{ij}^{k} - \mu^{k}}{\sqrt{\sigma\_{k}^{2}}}, \quad i = 1, \dots, n, \quad j = 1, \dots, L, \ k = 1, \dots, N. \tag{10}$$

In the latter case (MCGS), the arithmetic of all measurements of the sensor at the same column is considered in the normalization. More precisely, for k ¼ 1, 2, …, N, we define

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing http://dx.doi.org/10.5772/intechopen.78727 145

$$\mu\_{\dot{j}}^k = \frac{1}{n} \sum\_{i=1}^n \mathbf{x}\_{i\dot{\nu}}^k \quad \dot{j} = 1, \dots, L,\tag{11}$$

where μ<sup>k</sup> <sup>j</sup> is the arithmetic mean of the measures placed at the same column. In this case, then, matrix <sup>X</sup> <sup>¼</sup> <sup>x</sup><sup>k</sup> ij � � is centered and scaled—using MCGS—to define a modified matrix <sup>X</sup>� <sup>¼</sup> <sup>X</sup>MCGS <sup>¼</sup> �x<sup>k</sup> ij � � as

T ¼ XP ∈ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R , (7)

where the shape of the variance-covariance matrix of matrix T in Eq. (7) is diagonal.

3.2.1. Centering and scaling: group scaling (GS) vs. mean-centered group scaling (MCGS)

Considering that the data stored in matrix X are affected by a changing wind turbulence, come from different sensors, and could have different magnitudes and scales, some kind of preprocessing step is required to rescale the data [22, 23]. According to Westerhuis et al. [18], the way this preprocessing step is carried out may affect the overall performance of the CM strategy. In the present chapter, we present two possible choices that have some common core.

In the former case (GS), both the arithmetic mean and the variance of all measurements of the

X L

j¼1

In the latter case (MCGS), the arithmetic of all measurements of the sensor at the same column

X L

ij, (8)

is centered and scaled—using GS—to

(9)

j¼1 xk

xk ij � <sup>μ</sup><sup>k</sup> � �<sup>2</sup>

<sup>k</sup> are the arithmetic mean and the variance of the whole set of elements in

<sup>q</sup> , i <sup>¼</sup> <sup>1</sup>, …, n, j <sup>¼</sup> <sup>1</sup>,…, L, k <sup>¼</sup> <sup>1</sup>, …, N: (10)

ij � �

<sup>μ</sup><sup>k</sup> <sup>¼</sup> <sup>1</sup> nL Xn i¼1

ij � � as

is considered in the normalization. More precisely, for k ¼ 1, 2, …, N, we define

of the structure.

These two alternatives are as follows:

144 Structural Health Monitoring from Sensing to Processing

ii. mean-centered group scaling (MCGS).

define a modified matrix <sup>X</sup> <sup>¼</sup> <sup>X</sup>GS <sup>¼</sup> <sup>x</sup><sup>k</sup>

xk ij <sup>≔</sup> xk

sensor are used. More precisely, for k ¼ 1, 2, …, N, we define

σ2 <sup>k</sup> <sup>¼</sup> <sup>1</sup> nL Xn i¼1

, respectively. In this case, matrix <sup>X</sup> <sup>¼</sup> xk

ij � <sup>μ</sup><sup>k</sup> ffiffiffiffiffi σ2 k

i. group scaling (GS) and

where μ<sup>k</sup> and σ<sup>2</sup>

matrix X<sup>k</sup>

In the proposed approach in this chapter, the model defined in matrix P in Eq. (7) is based only on measures that come from a healthy wind turbine. Posteriorly, data from the current WT to diagnose will be projected using the matrix-to-matrix multiplication also defined in Eq. (7). However, a different procedure can be considered, particularly, when the goal is not just to detect a damage or a fault but to classify it. In the latter case, matrix X in Eq. (6) should contain measures from a WT in its healthy state but also in all the possible fault scenarios. This way, the generated model in matrix P in Eq. (7) contains all the possible states

$$\check{\mathbf{x}}\_{ij}^{k} \coloneqq \frac{\mathbf{x}\_{ij}^{k} - \mu\_{j}^{k}}{\sqrt{\sigma\_{k}^{2}}}, \quad \mathbf{i} = \mathbf{1}, \dots, n, \quad j = 1, \dots, L, \ k = 1, \dots, N. \tag{12}$$

where σ<sup>2</sup> <sup>k</sup> is defined as in Eq. (9) using μ<sup>k</sup> as in Eq. (8). It is worth noting that the only difference between the expressions in Eqs. (10) and (12) is how the elements in matrix <sup>X</sup> <sup>¼</sup> xk ij � � are centered. When matrix <sup>X</sup> <sup>¼</sup> xk ij � � is scaled and centered according to the MCGS strategy described in Eq. (12), the average value of each column vector in the scaled matrix X� can be calculated as

$$\frac{1}{n}\sum\_{i=1}^{n}\check{\mathbf{x}}\_{ij}^{k} = \frac{1}{n}\sum\_{i=1}^{n}\frac{\mathbf{x}\_{ij}^{k} - \mu\_{j}^{k}}{\sigma^{k}} = \frac{1}{n\sigma^{k}}\sum\_{i=1}^{n}\left(\mathbf{x}\_{ij}^{k} - \mu\_{j}^{k}\right) \tag{13}$$

$$=\frac{1}{n\sigma^{k}}\left[\left(\sum\_{i=1}^{n}\mathbf{x}\_{ij}^{k}\right)-n\mu\_{j}^{k}\right] \tag{14}$$

$$=\frac{1}{n\sigma^k}\left(n\mu\_j^k - n\mu\_j^k\right) = 0\tag{15}$$

Taking advantage of the fact that the scaled matrix X� is a mean-centered matrix, the variancecovariance matrix can be straightforwardly computed as a matrix-to-matrix product of X� and its transpose, divided by n � 1, where n is the number of rows of matrix X in Eq. (6). More precisely,

$$\mathbf{C}\check{\mathbf{X}} = \frac{1}{n-1}\check{\mathbf{X}}^T\check{\mathbf{X}} \in \mathcal{A}\_{(N:L)\times(N:L)}(\mathbb{R})\tag{16}$$

Clearly, GS and MCGS are not the only ways to center and scale data. For instance, feature scaling, also known as unity-based normalization, can also be considered. In this case, data are centered with respect to the minimum value and scaled with respect to the range of the set, that is,

$$\tilde{\mathbf{x}}\_{\vec{ij}}^{k} \coloneqq \frac{\mathbf{x}\_{\vec{ij}}^{k} - \min\left\{ \mathbf{x}\_{\vec{ij}}^{k} \right\}}{\max\left\{ \mathbf{x}\_{\vec{ij}}^{k} \right\} - \min\left\{ \mathbf{x}\_{\vec{ij}}^{k} \right\}}, \ i = 1, \dots, n, \ j = 1, \dots, L, \ k = 1, \dots, N. \tag{17}$$

However, to easily compute the variance-covariance matrix in the CM strategy that we present in this chapter, the mean-centered group scaling (MCGS) is the method that we have selected for the centering and scaling. In order to not to use the baroque notation X throughout the rest of this chapter, this centered and scaled matrix is redesignated as X, without the breve sign.

The MPCA model is described by the latent vectors

$$\mathbf{p}\_{j'} \cdot \mathbf{j} = \mathbf{1}, \ldots, \mathbf{N} \cdot \mathbf{L} \tag{18}$$

3.3. HT-based condition monitoring

Y ¼

ij � � similar to the one in Eq. (12):

�yk ij <sup>≔</sup> yk

<sup>Y</sup>� <sup>¼</sup> �<sup>y</sup> k

where σ<sup>2</sup>

<sup>k</sup> and μ<sup>k</sup>

y1 <sup>11</sup> y<sup>1</sup>

0

BBBBBBBBBBBB@

0 B@ y1 <sup>i</sup><sup>1</sup> y<sup>1</sup>

y1 <sup>ν</sup><sup>1</sup> y<sup>1</sup>

<sup>¼</sup> <sup>Y</sup><sup>1</sup> <sup>Y</sup><sup>2</sup>

¼ w1∣w2∣⋯∣wL |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} Y1

> ij � <sup>μ</sup><sup>k</sup> j ffiffiffiffiffi σ2 k

structure to diagnose, the scores related to each row vector

where matrix P^ is the reduced MPCA model in Eq. (27).

are computed using a vector-to-matrix product:

r

t <sup>i</sup> <sup>¼</sup> <sup>r</sup>

As said in Section 3.2, the MPCA model is based only on measures that come from a healthy wind turbine. Posteriorly, data from the current WT to diagnose—and subjected to a different wind turbulence—are gathered from as many sensors as in the modeling phase described in Section 3.2 and during a period of time, ð Þ νL � 1 Δ seconds, which is not necessarily equal.

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

1L⋯yN

iL⋯yN i1⋯y<sup>N</sup> iL

νL⋯yN

jwLþ<sup>1</sup>∣⋯∣w2<sup>L</sup> |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} Y2

It should be noted that ν∈ℕ (the number of rows of matrix Y) does not necessarily need to match the natural number n, which represents the number of rows of matrix X in Eq. (6). However, the number of columns, represented by the natural number N � L, must agree.

The collected data in matrix Y in Eq. (28) are first centered and scaled to form a matrix

previously calculated in Eqs. (9) and (11), respectively, with respect to X in Eq. (6). After the preprocessing step, that is, centering and scaling the raw data collected from the current

<sup>i</sup> � <sup>P</sup>^ <sup>∈</sup> <sup>R</sup><sup>ℓ</sup>

11⋯yN 1L 1

CCCCCCCCCCCCA

j⋯jwð Þ <sup>N</sup>�<sup>1</sup> <sup>L</sup>þ<sup>1</sup>∣⋯∣wN�<sup>L</sup> |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Y<sup>N</sup>

<sup>q</sup> , i <sup>¼</sup> <sup>1</sup>, …, <sup>ν</sup>, j <sup>¼</sup> <sup>1</sup>, …, L, k <sup>¼</sup> <sup>1</sup>, …, N, (29)

<sup>i</sup> <sup>¼</sup> <sup>Y</sup>� ð Þ <sup>i</sup>; : <sup>∈</sup> <sup>R</sup><sup>N</sup>�L, i <sup>¼</sup> <sup>1</sup>, …, <sup>ν</sup> (30)

, i ¼ 1, …, ν (31)

<sup>j</sup> are the values of the variance and the arithmetic mean that have been

∈ℳ<sup>ν</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ R

1 CA

http://dx.doi.org/10.5772/intechopen.78727

(28)

147

ν1⋯yN νL

These new data are arranged in a new matrix Y in a similar way as in Eq. (6):

⋮ ⋮⋱⋮⋮⋱⋮⋱⋮⋱⋮

⋮ ⋮⋱⋮⋮⋱⋮⋱⋮⋱⋮

<sup>⋯</sup>Y<sup>N</sup> � � <sup>∈</sup>ℳ<sup>n</sup>�ð Þ <sup>N</sup>�<sup>L</sup> ð Þ <sup>R</sup>

12⋯y<sup>1</sup> 1Ly<sup>2</sup> 11⋯y<sup>2</sup>

i2⋯y<sup>1</sup> iLy<sup>2</sup> i1⋯y<sup>2</sup>

ν2⋯y<sup>1</sup> νLy<sup>2</sup> ν1⋯y<sup>2</sup>

also known as eigenvector or proper vectors, and the latent roots

$$A\_{\dot{\jmath}\prime} \quad j = 1, \ldots, N \cdot L,\tag{19}$$

also known as eigenvalues or proper values, of the variance-covariance matrix CX as follows:

$$\mathbf{C}\_{\mathbf{X}}\mathbf{P} = \mathbf{P}\Lambda\tag{20}$$

where

$$\mathbf{P} = \left( p\_1 | p\_2 | \cdots | p\_{N \cdot L} \right) \in \mathcal{A}\_{N \cdot L \times N \cdot L} (\mathbb{R}) \tag{21}$$

$$
\Lambda = \left(\Lambda\_{\vec{\eta}}\right) \in \mathcal{A}\_{N \cdot L \times N \cdot L}(\mathbb{R}) \tag{22}
$$

and

$$
\Lambda\_{\vec{\eta}} = \lambda\_{\vec{\eta}} \quad \vec{\jmath} = 1, \ldots, N \cdot L \tag{23}
$$

$$
\Lambda\_{i\dot{j}} = 0, \quad \text{i.j} = 1, \ldots, N \cdot L, \quad \text{i} \neq \text{j} \tag{24}
$$

The latent vectors and latent roots in Eqs. (21) and (23) are arranged in descending order with respect to the absolute values of the latent roots, that is,

$$|\lambda\_i| \ge |\lambda\_{i+1}| \quad i = 1, \dots, N \cdot L - 1 \tag{25}$$

The latent vector p1—corresponding to the largest latent root λ<sup>1</sup> (in absolute value)—is called the first principal component (PC). Likewise, the latent vector p2—corresponding to the second largest latent root λ<sup>2</sup> (in absolute value)—is called the second principal component. Equivalently, the latent vector pj , j ¼ 1, ⋯, N � L—corresponding to the latent root λj—is called the j�th principal component.

Matrix T in Eq. (7) represents the transformed or projected matrix onto the principal component space and it is also known as score matrix.

When, for the sake of dimensionality reduction, a decreased number of principal components are considered:

$$
\ell < N \cdot L,\tag{26}
$$

a reduced multiway PCA model is then assembled:

$$P = \left(p\_1|p\_2|\cdots|p\_\ell\right) \in \mathcal{A}\_{N \cdot L \times \ell}(\mathbb{R}).\tag{27}$$

#### 3.3. HT-based condition monitoring

for the centering and scaling. In order to not to use the baroque notation X throughout the rest of this chapter, this centered and scaled matrix is redesignated as X, without the breve sign.

also known as eigenvalues or proper values, of the variance-covariance matrix CX as follows:

The latent vectors and latent roots in Eqs. (21) and (23) are arranged in descending order with

The latent vector p1—corresponding to the largest latent root λ<sup>1</sup> (in absolute value)—is called the first principal component (PC). Likewise, the latent vector p2—corresponding to the second largest latent root λ<sup>2</sup> (in absolute value)—is called the second principal component. Equiva-

Matrix T in Eq. (7) represents the transformed or projected matrix onto the principal compo-

When, for the sake of dimensionality reduction, a decreased number of principal components

P ¼ p1jp2j⋯jp<sup>ℓ</sup>

, j ¼ 1, …, N � L, (18)

λj, j ¼ 1, …, N � L, (19)

CXP ¼ PΛ (20)

<sup>∈</sup>ℳ<sup>N</sup>�L�N�<sup>L</sup>ð Þ <sup>R</sup> (21)

Λjj ¼ λj, j ¼ 1, …, N � L (23)

Λij ¼ 0, i, j ¼ 1, …, N � L, i 6¼ j (24)

∣λi∣ ≥ ∣λ<sup>i</sup>þ<sup>1</sup>∣, i ¼ 1, …, N � L � 1 (25)

, j ¼ 1, ⋯, N � L—corresponding to the latent root λj—is called the

<sup>ℓ</sup> <sup>&</sup>lt; <sup>N</sup> � L, (26)

<sup>∈</sup>ℳ<sup>N</sup>�L�<sup>ℓ</sup>ð Þ <sup>R</sup> : (27)

<sup>∈</sup>ℳ<sup>N</sup>�L�N�<sup>L</sup>ð Þ <sup>R</sup> (22)

pj

<sup>P</sup> <sup>¼</sup> <sup>p</sup>1jp2j⋯jpN�<sup>L</sup>

Λ ¼ Λij

also known as eigenvector or proper vectors, and the latent roots

The MPCA model is described by the latent vectors

146 Structural Health Monitoring from Sensing to Processing

respect to the absolute values of the latent roots, that is,

nent space and it is also known as score matrix.

a reduced multiway PCA model is then assembled:

lently, the latent vector pj

j�th principal component.

are considered:

where

and

As said in Section 3.2, the MPCA model is based only on measures that come from a healthy wind turbine. Posteriorly, data from the current WT to diagnose—and subjected to a different wind turbulence—are gathered from as many sensors as in the modeling phase described in Section 3.2 and during a period of time, ð Þ νL � 1 Δ seconds, which is not necessarily equal. These new data are arranged in a new matrix Y in a similar way as in Eq. (6):

$$\mathbf{Y} = \begin{pmatrix} y\_{11}^1 & y\_{12}^1 \cdots y\_{1L}^1 y\_{11}^2 \cdots y\_{1L}^2 \cdots y\_{1L}^N \cdots y\_{1L}^N \\ \vdots & \vdots \ddots \vdots \ddots \vdots \vdots \ddots \vdots \vdots \\ y\_{i1}^1 & y\_{i2}^1 \cdots y\_{iL}^2 y\_{i1}^2 \cdots y\_{iL}^N \cdots y\_{i1}^N \cdots y\_{iL}^N \\ \vdots & \vdots \ddots \vdots \vdots \ddots \vdots \vdots \ddots \vdots \\ \vdots & \vdots \ddots \vdots \vdots \ddots \vdots \vdots \ddots \vdots \\ y\_{i1}^1 & y\_{i2}^1 \cdots y\_{iL}^1 y\_{i1}^2 \cdots y\_{iL}^N \cdots y\_{iL}^N \cdots y\_{iL}^N \end{pmatrix} \in \mathcal{A}\_{\nu \times (N,L)}(\mathbb{R}) \tag{28}$$
 
$$= \left( \underbrace{w\_1 |w\_2| \cdots |w\_L| \underbrace{w\_{L+1}| \cdots |w\_{2L}|}\_{\mathbf{Y}^2} \cdots \underbrace{|w\_{(N-1)L+1}| \cdots |w\_{NL}|}\_{\mathbf{Y}^N} \right)$$
 
$$= \left( \mathbf{Y}^1 \quad \mathbf{Y}^2 \cdots \mathbf{Y}^N \right) \in \mathcal{A}\_{n \times (N,L)}(\mathbb{R})$$

It should be noted that ν∈ℕ (the number of rows of matrix Y) does not necessarily need to match the natural number n, which represents the number of rows of matrix X in Eq. (6). However, the number of columns, represented by the natural number N � L, must agree.

The collected data in matrix Y in Eq. (28) are first centered and scaled to form a matrix <sup>Y</sup>� <sup>¼</sup> �<sup>y</sup> k ij � � similar to the one in Eq. (12):

$$\check{y}\_{ij}^{k} \coloneqq \frac{y\_{ij}^{k} - \mu\_{j}^{k}}{\sqrt{\sigma\_{k}^{2}}}, \quad i = 1, \dots, \nu, \quad j = 1, \dots, L, \ k = 1, \dots, N,\tag{29}$$

where σ<sup>2</sup> <sup>k</sup> and μ<sup>k</sup> <sup>j</sup> are the values of the variance and the arithmetic mean that have been previously calculated in Eqs. (9) and (11), respectively, with respect to X in Eq. (6). After the preprocessing step, that is, centering and scaling the raw data collected from the current structure to diagnose, the scores related to each row vector

$$r^i = \check{\mathbf{Y}}(i, :) \in \mathbb{R}^{N \cdot L}, \ i = 1, \ldots, \nu \tag{30}$$

are computed using a vector-to-matrix product:

$$t^i = r^i \cdot \hat{\mathbf{P}} \in \mathbb{R}^l, \ i = 1, \ldots, \nu \tag{31}$$

where matrix P^ is the reduced MPCA model in Eq. (27).

Let us consider the canonical basis

$$\{\mathbf{e}\_1, \mathbf{e}\_2, \dots, \mathbf{e}\_\ell\} \subset \mathbb{R}^\ell \tag{32}$$

three-dimensional baseline sample (left) and the other is referred to faults 1, 4, and 7 (right). In a classic application of the PCA strategy in the field of SHM, the scores allow a separation, clustering, or visual grouping [24]. However, in this case, it can be clearly monitored in Figure 4 (right) that a clustering, visual grouping, or separation cannot be performed. Therefore, more powerful and reliable tools are needed to be able to detect a fault in the WT.

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

http://dx.doi.org/10.5772/intechopen.78727

149

In structural health monitoring or condition monitoring applications, the final decision on whether the structure, the actuator and/or the sensor is healthy or not should not depend on graphical approaches. One of the most common approaches to reliable indicators of damage or faults is the use of the powerful machinery of statistical hypothesis testing. The differences in this kind of strategies rely on what is the subject of the test and, of course, how the raw data collected by the sensors are arranged and preprocessed. For instance, in Zugasti et al. [25] the damage detection is based on testing for significant changes in the parameter vector of an AutoRegressive model. A comprehensive three-tier modular structural health monitoring framework is proposed by Hackell et al. [26] where the hypothesis testing is used to declare decision boundaries, control charts, and ROC curves with the ultimate goal of distinguishing between healthy and potentially damaged data on an operational wind turbine. A somehow different approach is presented by Ng et al. [27] that includes a vehicle health monitoring system where several univariate hypothesis tests are considered in parallel. Again in the field of structural health monitoring or condition monitoring of wind turbines, a recent work by Tsiapoki et al. [28] where damage and ice detection is based on data normalization, feature

The use of univariate hypothesis testing as a key element for structural health monitoring or condition monitoring has been increasing in the last years as a reliable method. Variations of these univariate HT for multiple indicators include the use of univariate HT in parallel, that is, testing for each component of a parameter vector rather than testing for the whole multidimensional parameter vector. The first approach for the detection of structural changes using a multivariate hypothesis testing has been proposed by Pozo et al. [8]. One of the key results in the work [8] is that multivariate HTs allow to get better results in damage or fault detection that just univariate test. One interesting example presented in the work by Pozo et al. [8] shows

> H<sup>0</sup> : μc,i ¼ μh,i H<sup>1</sup> : μc,i 6¼ μh,i

H<sup>0</sup> : μ<sup>c</sup> ¼ μ<sup>h</sup> H<sup>1</sup> : μ<sup>c</sup> 6¼ μ<sup>h</sup>

<sup>c</sup> ¼ μc, <sup>1</sup> μc, <sup>2</sup> ⋯ μc, <sup>5</sup> 

<sup>h</sup> ¼ μh, <sup>1</sup> μh, <sup>2</sup> ⋯ μh, <sup>5</sup>

(39)

(37)

(38)

that, for a given level of significance α, five independent univariate hypothesis

where i ¼ 1, 2, …, 5 lead to a wrong decision while the single multivariate HT

μT

μT

extraction and hypothesis testing (HT).

where

of the <sup>ℓ</sup>�dimensional real vector space <sup>R</sup><sup>ℓ</sup> .

Given a row vector r<sup>i</sup> as in Eq. (30), the real number

$$t\_1^i = t^i \cdot \mathbf{e}\_1 \in \mathbb{R} \tag{33}$$

is called the first score. Likewise, the scalar

$$t\_2^i = t^i \cdot \mathbf{e}\_2 \in \mathbb{R} \tag{34}$$

is called the second score. In general, the scalar

$$t^i\_j = t^i \cdot \mathbf{e}\_j \in \mathbb{R} \tag{35}$$

is called the score associated with the principal component pj , j <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup> or, simply, score <sup>j</sup>.

t

In addition, an s�dimensional vector as can be built if more than one score is considered at the same time. Indeed,

$$\mathbf{t}\_s^i = \begin{bmatrix} t\_1^i & t\_2^i & \cdots & t\_s^i \end{bmatrix}^T \in \mathbb{R}^s, \quad s \le \ell. \tag{36}$$

#### 3.3.1. Scores as a random sample

As said in Section 3.1, the excitation of the WT comes from a changing turbulent wind. Somehow, this turbulent wind can be viewed as a random signal. Therefore, the response of the WT can be also viewed as a random process and so the measurements in the row vector r<sup>i</sup> in Eq. (30). As a consequence, the vector t <sup>i</sup> receives this random nature and it can be observed as an ℓ-dimensional random vector to construct the statistical approach in this chapter. As a motivating example, in Figure 4, two three-dimensional samples are represented: one is the

Figure 4. Baseline sample (left) and sample from the wind turbine to be diagnosed (right).

three-dimensional baseline sample (left) and the other is referred to faults 1, 4, and 7 (right). In a classic application of the PCA strategy in the field of SHM, the scores allow a separation, clustering, or visual grouping [24]. However, in this case, it can be clearly monitored in Figure 4 (right) that a clustering, visual grouping, or separation cannot be performed. Therefore, more powerful and reliable tools are needed to be able to detect a fault in the WT.

In structural health monitoring or condition monitoring applications, the final decision on whether the structure, the actuator and/or the sensor is healthy or not should not depend on graphical approaches. One of the most common approaches to reliable indicators of damage or faults is the use of the powerful machinery of statistical hypothesis testing. The differences in this kind of strategies rely on what is the subject of the test and, of course, how the raw data collected by the sensors are arranged and preprocessed. For instance, in Zugasti et al. [25] the damage detection is based on testing for significant changes in the parameter vector of an AutoRegressive model. A comprehensive three-tier modular structural health monitoring framework is proposed by Hackell et al. [26] where the hypothesis testing is used to declare decision boundaries, control charts, and ROC curves with the ultimate goal of distinguishing between healthy and potentially damaged data on an operational wind turbine. A somehow different approach is presented by Ng et al. [27] that includes a vehicle health monitoring system where several univariate hypothesis tests are considered in parallel. Again in the field of structural health monitoring or condition monitoring of wind turbines, a recent work by Tsiapoki et al. [28] where damage and ice detection is based on data normalization, feature extraction and hypothesis testing (HT).

The use of univariate hypothesis testing as a key element for structural health monitoring or condition monitoring has been increasing in the last years as a reliable method. Variations of these univariate HT for multiple indicators include the use of univariate HT in parallel, that is, testing for each component of a parameter vector rather than testing for the whole multidimensional parameter vector. The first approach for the detection of structural changes using a multivariate hypothesis testing has been proposed by Pozo et al. [8]. One of the key results in the work [8] is that multivariate HTs allow to get better results in damage or fault detection that just univariate test. One interesting example presented in the work by Pozo et al. [8] shows that, for a given level of significance α, five independent univariate hypothesis

$$\begin{aligned} \mu\_0 &: & \mu\_{\mathbf{c},i} = \mu\_{\mathbf{h},i} \\ H\_1 &: & \mu\_{\mathbf{c},i} \neq \mu\_{\mathbf{h},i} \end{aligned} \tag{37}$$

where i ¼ 1, 2, …, 5 lead to a wrong decision while the single multivariate HT

$$\begin{aligned} \mu\_0 &: & \mu\_{\rm c} = \mu\_{\rm h} \\ H\_1 &: & \mu\_{\rm c} \neq \mu\_{\rm h} \end{aligned} \tag{38}$$

where

Let us consider the canonical basis

148 Structural Health Monitoring from Sensing to Processing

of the <sup>ℓ</sup>�dimensional real vector space <sup>R</sup><sup>ℓ</sup>

is called the first score. Likewise, the scalar

is called the second score. In general, the scalar

same time. Indeed,

3.3.1. Scores as a random sample

in Eq. (30). As a consequence, the vector t

is called the score associated with the principal component pj

t i <sup>s</sup> ¼ t i <sup>1</sup> t i <sup>2</sup> ⋯ t i s

Figure 4. Baseline sample (left) and sample from the wind turbine to be diagnosed (right).

Given a row vector r<sup>i</sup> as in Eq. (30), the real number

.

t i <sup>1</sup> ¼ t

t i <sup>2</sup> ¼ t

t i <sup>j</sup> ¼ t

In addition, an s�dimensional vector as can be built if more than one score is considered at the

As said in Section 3.1, the excitation of the WT comes from a changing turbulent wind. Somehow, this turbulent wind can be viewed as a random signal. Therefore, the response of the WT can be also viewed as a random process and so the measurements in the row vector r<sup>i</sup>

as an ℓ-dimensional random vector to construct the statistical approach in this chapter. As a motivating example, in Figure 4, two three-dimensional samples are represented: one is the

∈ R<sup>s</sup>

<sup>T</sup>

f g <sup>e</sup>1; <sup>e</sup>2;…; <sup>e</sup><sup>ℓ</sup> <sup>⊂</sup> <sup>R</sup><sup>ℓ</sup> (32)

<sup>i</sup> � <sup>e</sup><sup>1</sup> <sup>∈</sup> <sup>R</sup> (33)

<sup>i</sup> � <sup>e</sup><sup>2</sup> <sup>∈</sup> <sup>R</sup> (34)

<sup>i</sup> � <sup>e</sup><sup>j</sup> <sup>∈</sup> <sup>R</sup> (35)

<sup>i</sup> receives this random nature and it can be observed

, j <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup> or, simply, score <sup>j</sup>.

, s ≤ ℓ: (36)

$$\begin{aligned} \boldsymbol{\mu}\_{\rm c}^{T} &= \begin{bmatrix} \boldsymbol{\mu}\_{\rm c,1} & \boldsymbol{\mu}\_{\rm c,2} & \cdots & \boldsymbol{\mu}\_{\rm c,5} \end{bmatrix} \\ \boldsymbol{\mu}\_{\rm h}^{T} &= \begin{bmatrix} \boldsymbol{\mu}\_{\rm h,1} & \boldsymbol{\mu}\_{\rm h,2} & \cdots & \boldsymbol{\mu}\_{\rm h,5} \end{bmatrix} \end{aligned} \tag{39}$$

is able to correctly classify the structure. This example shows that multivariate HT is even more reliable than univariate HT. However, these benefits come at a price, in the sense that in order to apply the multivariate HT, the statistical distribution of the data must be multinormal. Of course, it may happen that five sets of 50 samples

$$N\left\{\mathbf{x}\_1^i, \mathbf{x}\_2^i, \dots, \mathbf{x}\_{50}^i\right\} \succ N(\mu\_i, \sigma\_i), \quad i = 1, 2, \dots, 5 \tag{40}$$

are normally distributed, while the sample vector

$$\{\mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_{50}\} \not\sim \mathcal{N}(\mu, \Sigma),\tag{41}$$

Let us define

where

then construct the following test:

δμ ¼ μ<sup>X</sup> � μ<sup>Y</sup> (45)

http://dx.doi.org/10.5772/intechopen.78727

H<sup>0</sup> : δμ ¼ 0 versus (46)

H<sup>1</sup> : δμ 6¼ 0 (47)

� � and <sup>N</sup> <sup>μ</sup>Y; <sup>σ</sup><sup>Y</sup>

WS ↣t<sup>r</sup> (49)

<sup>5</sup>, (50)

� � and the

(48)

151

(51)

as the difference between these two mean values. Since we want to know if the distribution of

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

where the null hypothesis H<sup>0</sup> is "the sample of the WT to be diagnosed is distributed as the baseline sample" and the alternative hypothesis H<sup>1</sup> is "the sample of the WT to be diagnosed is not distributed as the baseline sample." In other words, if the result of the test is that H<sup>0</sup> is accepted, the current WT is categorized as healthy. Otherwise, if H<sup>0</sup> is rejected in favor of H1,

Given the assumptions of normality and considering that the two variances are not necessarily equal, the test for the equality of mean is based on the so-called Welch-Satterthwaite method [29], which is outlined below for the sake of completeness. If two random samples of size n and

WS <sup>¼</sup> <sup>X</sup> � <sup>Y</sup> � � <sup>þ</sup> <sup>μ</sup><sup>X</sup> � <sup>μ</sup><sup>Y</sup>

s2 X <sup>n</sup> <sup>þ</sup> <sup>s</sup><sup>2</sup> Y ν � �<sup>2</sup>

S<sup>2</sup> is the sample variance as a random variable, s<sup>2</sup> is the variance of a sample, X, Y are the

<sup>t</sup>obs <sup>¼</sup> <sup>x</sup> � <sup>y</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 X <sup>n</sup> <sup>þ</sup> <sup>s</sup><sup>2</sup> Y ν r� �

where x, y is the mean of a particular sample. The quantity tobs is the fault indicator. We can

s2 <sup>X</sup> ð Þ <sup>=</sup><sup>n</sup> <sup>2</sup> <sup>n</sup>�<sup>1</sup> <sup>þ</sup> <sup>s</sup><sup>2</sup>

The magnitude of the test statistic using Welch-Satterthwaite method is defined as

� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S2 X <sup>n</sup> <sup>þ</sup> <sup>S</sup><sup>2</sup> Y ν r� �

> <sup>Y</sup> ð Þ <sup>=</sup><sup>ν</sup> <sup>2</sup> ν�1

these two samples is related, this leads to a test of the hypothesis

this would indicate the presence of some faults in the WT.

ν, respectively, are taken from two normal distributions N μX; σ<sup>X</sup>

population variances are unknown and not necessarily equal, the random variable

can be approximated with a t-distribution with r degrees of freedom (DOF), that is

r ¼

sample mean as a random variable, and b c� is the standard floor function.

where

$$\mathbf{x}\_{j} = \begin{bmatrix} \mathbf{x}\_{j}^{1} & \mathbf{x}\_{j}^{2} & \cdots & \mathbf{x}\_{j}^{5} \end{bmatrix}^{T}, \quad j = 1, \ldots, 50 \tag{42}$$

and Σ is the variance-covariance matrix, is not multinormally distributed.

#### 3.3.2. Univariate case: testing for the equality of means

In this section, we present how a fault is detected in the WT using univariate HT. To this end, first we have to define what we consider our baseline. Given a principal component <sup>j</sup> <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup>, the baseline sample is the set of real numbers τ<sup>i</sup> j n o <sup>i</sup>¼1,…,n defined by

$$\pi\_j^i \coloneqq \left( \mathbf{X}(i, :) \cdot \widehat{\mathbf{P}} \right)(j) = \mathbf{X}(i, :) \cdot \widehat{\mathbf{P}} \cdot \mathbf{e}\_{j\prime} \quad i = 1, \ldots, n,\tag{43}$$

where e<sup>j</sup> is the j-th vector of the canonical basis in Eq. (32), P is the MPCA model defined in Eq. (27), and X is the centered and scaled matrix of the collected data from a healthy WT as in Eq. (6). Similarly, and given a principal component <sup>j</sup> <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup>, the sample of the current WT to diagnose is defined as the set of ν real numbers

$$\left\{ t\_{\dagger}^{i} \right\}\_{i=1,\ldots,\nu} \tag{44}$$

as defined in Eq. (35).

Before the univariate HT is applied, the following assumptions must be made:


It is worth mentioning that the variances of these two samples are not supposed to be necessary equal.

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing http://dx.doi.org/10.5772/intechopen.78727 151

Let us define

is able to correctly classify the structure. This example shows that multivariate HT is even more reliable than univariate HT. However, these benefits come at a price, in the sense that in order to apply the multivariate HT, the statistical distribution of the data must be multinormal.

; σ<sup>i</sup>

� �, i <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, <sup>5</sup> (40)

, j ¼ 1, …, 50 (42)

f g <sup>x</sup>1; <sup>x</sup>2;…; <sup>x</sup><sup>50</sup> <sup>=</sup>↣<sup>N</sup> <sup>μ</sup>;<sup>Σ</sup> � �, (41)

Of course, it may happen that five sets of 50 samples

150 Structural Health Monitoring from Sensing to Processing

are normally distributed, while the sample vector

3.3.2. Univariate case: testing for the equality of means

the baseline sample is the set of real numbers τ<sup>i</sup>

τi

diagnose is defined as the set of ν real numbers

j n o

i j n o

as defined in Eq. (35).

i. the baseline sample τ<sup>i</sup>

ii. the random sample t

sary equal.

where

xi <sup>1</sup>; xi <sup>2</sup>;…; x<sup>i</sup> 50 � �↣<sup>N</sup> <sup>μ</sup><sup>i</sup>

<sup>x</sup><sup>j</sup> <sup>¼</sup> <sup>x</sup><sup>1</sup>

<sup>j</sup> <sup>≔</sup> <sup>X</sup>ð Þ� <sup>i</sup>; : <sup>P</sup><sup>b</sup> � �

<sup>j</sup> x<sup>2</sup>

and Σ is the variance-covariance matrix, is not multinormally distributed.

<sup>j</sup> ⋯ x<sup>5</sup> j

In this section, we present how a fault is detected in the WT using univariate HT. To this end, first we have to define what we consider our baseline. Given a principal component <sup>j</sup> <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup>,

where e<sup>j</sup> is the j-th vector of the canonical basis in Eq. (32), P is the MPCA model defined in Eq. (27), and X is the centered and scaled matrix of the collected data from a healthy WT as in Eq. (6). Similarly, and given a principal component <sup>j</sup> <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup>, the sample of the current WT to

It is worth mentioning that the variances of these two samples are not supposed to be neces-

t i j n o

Before the univariate HT is applied, the following assumptions must be made:

distributed with unknown mean μ<sup>X</sup> and unknown variance σ<sup>2</sup>

distribution with unknown mean μ<sup>Y</sup> and unknown variance σ<sup>2</sup>

i¼1,…,ν

j n o

<sup>i</sup>¼1,…,n defined by

ðÞ¼ j Xð Þ� i; : Pb � ej, i ¼ 1, …, n, (43)

<sup>i</sup>¼1,…,<sup>ν</sup> (44)

<sup>X</sup> and

Y.

<sup>i</sup>¼1,…,n is a random sample of a random variable (RV) normally

in Eq. (44) of the current WT to diagnose follows a normal

h i<sup>T</sup>

$$
\delta\mu = \mu\_X - \mu\_Y \tag{45}
$$

as the difference between these two mean values. Since we want to know if the distribution of these two samples is related, this leads to a test of the hypothesis

$$H\_0: \quad \delta\mu = 0 \text{ versus} \tag{46}$$

$$H\_1: \quad \delta\mu \neq 0\tag{47}$$

where the null hypothesis H<sup>0</sup> is "the sample of the WT to be diagnosed is distributed as the baseline sample" and the alternative hypothesis H<sup>1</sup> is "the sample of the WT to be diagnosed is not distributed as the baseline sample." In other words, if the result of the test is that H<sup>0</sup> is accepted, the current WT is categorized as healthy. Otherwise, if H<sup>0</sup> is rejected in favor of H1, this would indicate the presence of some faults in the WT.

Given the assumptions of normality and considering that the two variances are not necessarily equal, the test for the equality of mean is based on the so-called Welch-Satterthwaite method [29], which is outlined below for the sake of completeness. If two random samples of size n and ν, respectively, are taken from two normal distributions N μX; σ<sup>X</sup> � � and <sup>N</sup> <sup>μ</sup>Y; <sup>σ</sup><sup>Y</sup> � � and the population variances are unknown and not necessarily equal, the random variable

$$\mathcal{W}\mathcal{F} = \frac{\left(\overline{X} - \overline{Y}\right) + \left(\mu\_X - \mu\_Y\right)}{\sqrt{\left(\frac{S\_X^2}{n} + \frac{S\_Y^2}{\nu}\right)}}\tag{48}$$

can be approximated with a t-distribution with r degrees of freedom (DOF), that is

$$\mathcal{W}\mathcal{G} \hookrightarrow \mathfrak{t}\_{\rho} \tag{49}$$

where

$$\rho = \left\lfloor \frac{\left(\frac{s\_\chi^2}{n} + \frac{s\_\chi^2}{\nu}\right)^2}{\left(\frac{s\_\chi^2/n\right)^2}{n-1} + \frac{\left(s\_\chi^2/\nu\right)^2}{\nu-1}} \right\rfloor \tag{50}$$

S<sup>2</sup> is the sample variance as a random variable, s<sup>2</sup> is the variance of a sample, X, Y are the sample mean as a random variable, and b c� is the standard floor function.

The magnitude of the test statistic using Welch-Satterthwaite method is defined as

$$t\_{\rm obs} = \frac{\overline{x} - \overline{y}}{\sqrt{\left(\frac{s\_\chi^2}{n} + \frac{s\_Y^2}{\nu}\right)}}\tag{51}$$

where x, y is the mean of a particular sample. The quantity tobs is the fault indicator. We can then construct the following test:

$$|t\_{\rm obs}| \le t^{\star} \quad \Rightarrow \quad \textbf{Accept}\ \ H\_0 \tag{52}$$

other words, if the result of the test is that H<sup>0</sup> is accepted, the current WT is categorized as healthy. Otherwise, if H<sup>0</sup> is rejected in favor of H1, this would indicate the presence of some

Condition Monitoring of Wind Turbine Structures through Univariate and Multivariate Hypothesis Testing

In this case, the multivariate test is based on Hotelling's T<sup>2</sup> statistic and it is outlined below.

<sup>↣</sup> ð Þ <sup>υ</sup> � <sup>1</sup> <sup>s</sup> υ � s

where Fs,υ�<sup>s</sup> denotes an RV with an F-distribution with s and υ � s DOF, X is the sample vector

<sup>n</sup> S∈ℳ<sup>s</sup>�<sup>s</sup>ð Þ R is the estimated variance-covariance matrix of X.

<sup>S</sup>�<sup>1</sup> <sup>x</sup> � <sup>μ</sup><sup>h</sup>

<sup>υ</sup>�<sup>s</sup> <sup>F</sup>s,υ�<sup>s</sup>ð Þ <sup>α</sup> (the WT is classified as not healthy) and

<sup>υ</sup>�<sup>s</sup> <sup>F</sup>s,υ�<sup>s</sup>ð Þ <sup>α</sup> (the WT is classified as healthy).

The results of the CM strategies presented in Sections 3.3.2 and 3.3.3 are organized into three subsections. The absolute value of samples that are correctly identified and the absolute number of false alarms and missing faults are included in Section 4.1. Sections 4.2 and 4.3 show the results, not as absolute values but as a percentage. More precisely, the sensitivity and the specificity are both comprised in Section 4.2, including the false-negative (FNR) and the

<sup>S</sup>�<sup>1</sup> <sup>X</sup> � <sup>μ</sup><sup>h</sup>

� � (56)

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153

Fs,υ�s, (57)

� �, (58)

Fs,υ�<sup>s</sup>ðÞ ) α Accept H0, (59)

Fs,υ�<sup>s</sup>ðÞ ) α Accept H1, (60)

ℙðFs,υ�<sup>s</sup> > Fs,υ�<sup>s</sup>ð Þ α Þ ¼ α, (61)

When an MRS of size <sup>υ</sup>∈<sup>ℕ</sup> is taken from an MVND Ns <sup>μ</sup>h; � � <sup>P</sup> , the RV

<sup>T</sup><sup>2</sup> <sup>¼</sup> <sup>υ</sup> <sup>X</sup> � <sup>μ</sup><sup>h</sup> � �<sup>T</sup>

T2

obs ¼ υ x � μ<sup>h</sup> � �<sup>T</sup>

where Fs,υ�<sup>s</sup>ð Þ α is the upper 100 ð Þ α th percentile of the Fs,υ�<sup>s</sup> distribution, that is,

where ℙ is a probability measure and α is the level of significance for the test. To sum up,

t 2

and is the fault indicator. We can then construct the following test:

obs <sup>≤</sup> ð Þ <sup>υ</sup> � <sup>1</sup> <sup>s</sup> υ � s

obs <sup>&</sup>gt; ð Þ <sup>υ</sup> � <sup>1</sup> <sup>s</sup> υ � s

t 2

t 2

2 obs <sup>&</sup>gt; ð Þ <sup>υ</sup>�<sup>1</sup> <sup>s</sup>

> 2 obs <sup>≤</sup> ð Þ <sup>υ</sup>�<sup>1</sup> <sup>s</sup>

faults in the WT.

is distributed as

mean as a MRV, and <sup>1</sup>

i. H<sup>0</sup> is rejected if t

ii. H<sup>0</sup> is accepted if t

4. Simulation results

The value of the test statistic is defined as

$$|t\_{\rm obs}| > t^{\star} \quad \Rightarrow \quad \text{Accept } H\_1 \tag{53}$$

where t <sup>⋆</sup> is such that

$$P\left(t\_{\rho} \ge t^{\star}\right) = \frac{\alpha}{2},\tag{54}$$

where α is the level of significance for the test. To sum up,


#### 3.3.3. Multivariate case: testing a multivariate mean vector

In Section 3.3.2, for each principal component <sup>j</sup> <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup>, a test for the equality of means is performed. This means that for a single sample of the current structure to diagnose, we obtain ℓ decisions on whether the structure is healthy or not. In the present section, more than one principal component will be considered jointly thus defining a vector. Therefore, a test for the plausibility of a value for a normal population mean vector will be performed.

As in Section 3.3.2, the objective of this work is to determine whether the distribution of the multivariate random samples that are obtained from the WT to be diagnosed (healthy or not) is connected to the distribution of the baseline.

Let us define s ∈ℕ as the number of PCs that are considered at the same time. Before the multivariate HT is applied, the following assumptions must be made:


In this case, opposite to what we have assumed in Section 3.3.2, both multivariate random variables have the same known variance-covariance matrix.

Similarly as in Section 3.3.2, the question that arises here is whether a given s-dimensional vector <sup>μ</sup><sup>c</sup> is a reasonable value for the mean of an MVND Ns <sup>μ</sup>h; � � <sup>P</sup> . This leads to the following test of the hypothesis

$$\begin{aligned} H\_0: \quad \mu\_\mathrm{c} &= \mu\_\mathrm{h} \quad \text{versus} \\ H\_1: \quad \mu\_\mathrm{c} &\neq \mu\_\mathrm{h'} \end{aligned} \tag{55}$$

where H<sup>0</sup> is "the MRS of the WT to be diagnosed is distributed as the baseline projection" and H<sup>1</sup> is "the MRS of the WT to be diagnosed is not distributed as the baseline projection." In other words, if the result of the test is that H<sup>0</sup> is accepted, the current WT is categorized as healthy. Otherwise, if H<sup>0</sup> is rejected in favor of H1, this would indicate the presence of some faults in the WT.

In this case, the multivariate test is based on Hotelling's T<sup>2</sup> statistic and it is outlined below. When an MRS of size <sup>υ</sup>∈<sup>ℕ</sup> is taken from an MVND Ns <sup>μ</sup>h; � � <sup>P</sup> , the RV

$$\mathbf{T}^2 = \upsilon \left(\overline{\mathbf{X}} - \boldsymbol{\mu}\_{\mathrm{h}}\right)^T \mathbf{S}^{-1} \left(\overline{\mathbf{X}} - \boldsymbol{\mu}\_{\mathrm{h}}\right) \tag{56}$$

is distributed as

tobs j j ≤ t

tobs j j > t

where α is the level of significance for the test. To sum up,

3.3.3. Multivariate case: testing a multivariate mean vector

connected to the distribution of the baseline.

P t<sup>r</sup> ≥ t <sup>⋆</sup> � � <sup>¼</sup> <sup>α</sup>

<sup>⋆</sup> (the WT is classified as not healthy) and

<sup>⋆</sup> (the WT is classified as healthy).

In Section 3.3.2, for each principal component <sup>j</sup> <sup>¼</sup> <sup>1</sup>, …, <sup>ℓ</sup>, a test for the equality of means is performed. This means that for a single sample of the current structure to diagnose, we obtain ℓ decisions on whether the structure is healthy or not. In the present section, more than one principal component will be considered jointly thus defining a vector. Therefore, a test for the

As in Section 3.3.2, the objective of this work is to determine whether the distribution of the multivariate random samples that are obtained from the WT to be diagnosed (healthy or not) is

Let us define s ∈ℕ as the number of PCs that are considered at the same time. Before the

i. the baseline projection is a multivariate random sample (MRS) of a multivariate random variable (MRV) following a multivariate normal distribution (MVND) with known population mean vector <sup>μ</sup><sup>h</sup> <sup>∈</sup> <sup>R</sup><sup>s</sup> and known variance-covariance matrix <sup>P</sup>∈ℳ<sup>s</sup>�<sup>s</sup>ð Þ <sup>R</sup> and ii. the multivariate random sample of the WT to be diagnosed also follows an MVND with unknown multivariate mean vector <sup>μ</sup><sup>c</sup> <sup>∈</sup> <sup>R</sup><sup>s</sup> and known variance-covariance matrix

In this case, opposite to what we have assumed in Section 3.3.2, both multivariate random

Similarly as in Section 3.3.2, the question that arises here is whether a given s-dimensional vector <sup>μ</sup><sup>c</sup> is a reasonable value for the mean of an MVND Ns <sup>μ</sup>h; � � <sup>P</sup> . This leads to the

H<sup>0</sup> : μ<sup>c</sup> ¼ μ<sup>h</sup> versus

where H<sup>0</sup> is "the MRS of the WT to be diagnosed is distributed as the baseline projection" and H<sup>1</sup> is "the MRS of the WT to be diagnosed is not distributed as the baseline projection." In

<sup>H</sup><sup>1</sup> : <sup>μ</sup><sup>c</sup> 6¼ <sup>μ</sup>h, (55)

plausibility of a value for a normal population mean vector will be performed.

multivariate HT is applied, the following assumptions must be made:

variables have the same known variance-covariance matrix.

where t

<sup>⋆</sup> is such that

152 Structural Health Monitoring from Sensing to Processing

i. H<sup>0</sup> is rejected if tobs j j > t

ii. H<sup>0</sup> is accepted if tobs j j ≤ t

<sup>P</sup>∈ℳ<sup>s</sup>�<sup>s</sup>ð Þ <sup>R</sup> .

following test of the hypothesis

<sup>⋆</sup> ) Accept <sup>H</sup><sup>0</sup> (52)

<sup>⋆</sup> ) Accept <sup>H</sup><sup>1</sup> (53)

<sup>2</sup> , (54)

$$T^2 \mapsto \frac{(\upsilon - 1)s}{\upsilon - s} F\_{s, \upsilon - s\nu} \tag{57}$$

where Fs,υ�<sup>s</sup> denotes an RV with an F-distribution with s and υ � s DOF, X is the sample vector mean as a MRV, and <sup>1</sup> <sup>n</sup> S∈ℳ<sup>s</sup>�<sup>s</sup>ð Þ R is the estimated variance-covariance matrix of X.

The value of the test statistic is defined as

$$t\_{\rm obs}^2 = \nu \left(\overline{\mathbf{x}} - \mu\_{\rm h}\right)^T \mathbf{S}^{-1} \left(\overline{\mathbf{x}} - \mu\_{\rm h}\right),\tag{58}$$

and is the fault indicator. We can then construct the following test:

$$\mathbf{h}\_{\text{obs}}^2 \le \frac{(\boldsymbol{\nu} - \mathbf{1})\mathbf{s}}{\boldsymbol{\nu} - \mathbf{s}} \mathbf{F}\_{\text{s}, \boldsymbol{\nu} - \mathbf{s}}(\boldsymbol{a}) \quad \Rightarrow \quad \text{Accept} \ H\_0 \tag{59}$$

$$\mathbf{f}\_{\text{obs}}^2 > \frac{(\upsilon - 1)\mathbf{s}}{\upsilon - \mathbf{s}} \mathbf{F}\_{\text{s}, \upsilon - \mathbf{s}}(\mathbf{a}) \quad \Rightarrow \text{ Accept } H\_1 \tag{60}$$

where Fs,υ�<sup>s</sup>ð Þ α is the upper 100 ð Þ α th percentile of the Fs,υ�<sup>s</sup> distribution, that is,

$$\mathbb{P}(\mathcal{F}\_{s,v-s} > \mathcal{F}\_{s,v-s}(\alpha)) = \alpha,\tag{61}$$

where ℙ is a probability measure and α is the level of significance for the test. To sum up,


## 4. Simulation results

The results of the CM strategies presented in Sections 3.3.2 and 3.3.3 are organized into three subsections. The absolute value of samples that are correctly identified and the absolute number of false alarms and missing faults are included in Section 4.1. Sections 4.2 and 4.3 show the results, not as absolute values but as a percentage. More precisely, the sensitivity and the specificity are both comprised in Section 4.2, including the false-negative (FNR) and the false-positive rates (FPR). Besides, the true rate of both false negatives and false positives are contained in Section 4.3.

4.1. Types I and II errors

In this section, each of the 24 samples is classified as follows:

missing fault/type II error], and

Table 5. Scheme for the presentation of the results in Table 6

Score 1 Scores 1–2

Score 2 Scores 1–7

Score 3 Scores 1–12

4.2. Sensitivity and specificity

classified as such.

hypothesis test as "healthy" (accept H0) [right decision],

ii. faulty sample classified by the test as "faulty" (accept H1) [right decision],

iv. healthy sample classified as "faulty" [wrong decision/false alarm/type I error]. The results displayed in Table 6 are disposed according to the scheme in Table 5.

i. number of samples from the healthy WT (healthy sample), which were classified by the

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iii. samples from the faulty WT (faulty sample) classified as "healthy" [wrong decision/

As in [20, 30], two more statistical indicators are analyzed to assess the efficiency of the test. On the one hand, the specificity of the test is defined as the fraction of samples from the healthy structure, which are correctly classified. On the other hand, the sensitivity—or the power of the test—is defined as the fraction of samples from the faulty wind turbine that are correctly

Accept H<sup>0</sup> Correct decision Type II error (missing fault)

H<sup>0</sup> H<sup>1</sup> H<sup>0</sup> H<sup>1</sup>

Accept H<sup>1</sup> Type I error (false alarm) Correct decision

Accept H<sup>0</sup> 16 1 Accept H<sup>0</sup> 12 0 Accept H<sup>1</sup> 0 7 Accept H<sup>1</sup> 4 8

Accept H<sup>0</sup> 13 7 Accept H<sup>0</sup> 13 0 Accept H<sup>1</sup> 3 1 Accept H<sup>1</sup> 3 8

Accept H<sup>0</sup> 16 8 Accept H<sup>0</sup> 16 0 Accept H<sup>1</sup> 0 0 Accept H<sup>1</sup> 0 8

Table 6. Categorization of the samples with respect to the presence or absence of a fault and the result of the test considering the first score, the second score, and the third score (left) and scores 1–2 (jointly), scores 1–7 (jointly), and scores 1–12 (jointly) (right), when the size of the samples to diagnose is ν ¼ 50 and the level of significance is α ¼ 10%

Healthy sample (H0) Faulty sample (H1)

For the validation of the CM strategies presented in Sections 3.3.2 and 3.3.3, 24 samples of ν ¼ 50 elements each have been examined, in accordance with the following organization:

• 8 samples of a faulty WT (one sample for each one of the different fault scenarios described in Table 3) and

• 16 samples of a healthy WT.

All samples are acquired with changing wind data sets with turbulence intensity established to 10% and computed with TurbSim [14]. These wind data have the subsequent features:


Each sample of ν ¼ 50 elements comes from the measures collected during ð Þ ν � L � 1 Δ ¼ 312:4875 seconds. The values for these parameters are listed in Table 4.

We present, in Sections 4.1, 4.2, and 4.3, the results when the collected data are projected into:


In the three univariate cases, (i)–(iii), we use the test for the equality of means, while in the three multivariate cases, (iv)–(vi), we use the test for the plausibility of a value for a normal population. In both cases, the chosen level of significance is α ¼ 10%.


Table 4. The collected measures are arranged in a ν � ð Þ N � L matrix Y as in Eq. (28)

## 4.1. Types I and II errors

false-positive rates (FPR). Besides, the true rate of both false negatives and false positives are

For the validation of the CM strategies presented in Sections 3.3.2 and 3.3.3, 24 samples of ν ¼ 50 elements each have been examined, in accordance with the following organization: • 8 samples of a faulty WT (one sample for each one of the different fault scenarios described

All samples are acquired with changing wind data sets with turbulence intensity established to

Each sample of ν ¼ 50 elements comes from the measures collected during ð Þ ν � L � 1 Δ ¼

We present, in Sections 4.1, 4.2, and 4.3, the results when the collected data are projected into:

In the three univariate cases, (i)–(iii), we use the test for the equality of means, while in the three multivariate cases, (iv)–(vi), we use the test for the plausibility of a value for a normal

Parameter Symbol Magnitude

Number of rows ν 50 Number of columns L 500 Sampling time Δ 0:0125 Number of sensors N 13

10% and computed with TurbSim [14]. These wind data have the subsequent features:

contained in Section 4.3.

154 Structural Health Monitoring from Sensing to Processing

• 16 samples of a healthy WT.

i. Kaimal turbulence model,

ii. logarithmic profile wind type,

iv. a roughness factor of 0:01 m.

i. the first principal component,

ii. the second principal component, iii. the third principal component,

iii. mean speed of 18:2 m/s simulated at hub height, and

iv. the first and the second principal components, jointly,

population. In both cases, the chosen level of significance is α ¼ 10%.

Table 4. The collected measures are arranged in a ν � ð Þ N � L matrix Y as in Eq. (28)

v. the first seven principal components, jointly, and

vi. the first twelve principal components, jointly.

312:4875 seconds. The values for these parameters are listed in Table 4.

in Table 3) and

In this section, each of the 24 samples is classified as follows:


The results displayed in Table 6 are disposed according to the scheme in Table 5.

## 4.2. Sensitivity and specificity

As in [20, 30], two more statistical indicators are analyzed to assess the efficiency of the test. On the one hand, the specificity of the test is defined as the fraction of samples from the healthy structure, which are correctly classified. On the other hand, the sensitivity—or the power of the test—is defined as the fraction of samples from the faulty wind turbine that are correctly classified as such.



Table 5. Scheme for the presentation of the results in Table 6

Table 6. Categorization of the samples with respect to the presence or absence of a fault and the result of the test considering the first score, the second score, and the third score (left) and scores 1–2 (jointly), scores 1–7 (jointly), and scores 1–12 (jointly) (right), when the size of the samples to diagnose is ν ¼ 50 and the level of significance is α ¼ 10% The sensitivity and specificity of both the univariate HT and the multivariate case with respect to the 24 samples displayed in Table 8 are disposed according to the scheme in Table 7.

## 4.3. Reliability of the results

Finally, the true rate of false negatives and the true rate of false positives can be used to assess the performance of the proposed CM strategy. These two measures—closely related to Bayes' theorem [31]—are described in Table 9. On the one hand, the true rate of false negatives is the fraction of samples from the faulty WT that have been wrongly identified as healthy. On the other hand, the true rate of false positives is the fraction of sample from the healthy WT that have been wrongly identified as faulty.

The true rate of false negatives and the true rate of false positives of both the univariate HT and the multivariate case displayed in Table 10 are disposed according to the scheme in Table 9.


5. Concluding remarks

present.

tively.

Acknowledgements

already available data from the WT SCADA system.

Score 1 Scores 1–2

Score 2 Scores 1–7

Score 3 Scores 1–12

of the samples to diagnose is ν ¼ 50 and the level of significance is α ¼ 10%

average values are 24:67 and 25%, respectively.

Generalitat de Catalunya through the research project 2017 SGR 388.

A multifault detection method based on MPCA through uni- and multivariate hypothesis testing has been presented in this chapter. It is noteworthy to mention the obtained performance through the study of eight realistic different faults in different components of the WT, taking into account that the proposed strategy does not need extra sensors but only uses

Table 10. True rate of false negatives and true rate of false positives of the test considering the first score, the second score, and the third score (left) and scores 1–2 (jointly), scores 1–7 (jointly), and scores 1–12 (jointly) (right), when the size

H<sup>0</sup> H<sup>1</sup> H<sup>0</sup> H<sup>1</sup>

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157

Accept H<sup>0</sup> 0.94 0.06 Accept H<sup>0</sup> 1.00 0.00 Accept H<sup>1</sup> 0.00 1.00 Accept H<sup>1</sup> 0.33 0.67

Accept H<sup>0</sup> 0.65 0.35 Accept H<sup>0</sup> 1.00 0.00 Accept H<sup>1</sup> 0.75 0.25 Accept H<sup>1</sup> 0.27 0.73

Accept H<sup>0</sup> 0.67 0.33 Accept H<sup>0</sup> 1.00 0.00 Accept H<sup>1</sup> 0.00 0.00 Accept H<sup>1</sup> 0.00 1.00

The three main conclusions, which show the benefits of the multivariate statistical hypothesis testing in comparison with the univariate case, for WT condition monitoring, are the following:

1. Given a level of significance α ¼ 10%, when the first 12 scores are considered jointly, an accuracy of 100% is obtained, while in all the other studied cases, misclassifications are

2. Multivariate analysis leads to average values of 100% for the sensitivity and 85:33% for the specificity, while for the univariate case, the average values are 33:33 and 93:67%, respec-

3. Multivariate analysis leads to average value of the true rate of false negatives of 0% and the average value of the true rate of false positives of 20%, while for the univariate case, the

This work has been partially funded by the Spanish Ministry of Economy and Competitiveness through the research projects DPI2014-58427-C2-1-R and DPI2017-82930-C2-1-R, and by the


Table 7. Relationship between specificity and sensitivity.

Table 8. Sensitivity and specificity of the test considering the first score, the second score, and the third score (left) and scores 1–2 (jointly), scores 1–7 (jointly), and scores 1–12 (jointly) (right), when the size of the samples to diagnose is ν ¼ 50 and the level of significance is α ¼ 10%


Table 9. Relationship between the proportion of false negatives and false positives.

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Table 10. True rate of false negatives and true rate of false positives of the test considering the first score, the second score, and the third score (left) and scores 1–2 (jointly), scores 1–7 (jointly), and scores 1–12 (jointly) (right), when the size of the samples to diagnose is ν ¼ 50 and the level of significance is α ¼ 10%

## 5. Concluding remarks

The sensitivity and specificity of both the univariate HT and the multivariate case with respect to the 24 samples displayed in Table 8 are disposed according to the scheme in Table 7.

Finally, the true rate of false negatives and the true rate of false positives can be used to assess the performance of the proposed CM strategy. These two measures—closely related to Bayes' theorem [31]—are described in Table 9. On the one hand, the true rate of false negatives is the fraction of samples from the faulty WT that have been wrongly identified as healthy. On the other hand, the true rate of false positives is the fraction of sample from the healthy WT that

The true rate of false negatives and the true rate of false positives of both the univariate HT and the multivariate case displayed in Table 10 are disposed according to the scheme in Table 9.

Accept H<sup>0</sup> Specificity (1 � α) False-negative rate (γ) Accept H<sup>1</sup> False-positive rate (α) Sensitivity (1 � γ)

Accept H<sup>0</sup> 1.00 0.12 Accept H<sup>0</sup> 0.75 0.00 Accept H<sup>1</sup> 0.00 0.88 Accept H<sup>1</sup> 0.25 1.00

Accept H<sup>0</sup> 0.81 0.88 Accept H<sup>0</sup> 0.81 0.00 Accept H<sup>1</sup> 0.19 0.12 Accept H<sup>1</sup> 0.19 1.00

Accept H<sup>0</sup> 1.00 1.00 Accept H<sup>0</sup> 1.00 0.00 Accept H<sup>1</sup> 0.00 0.00 Accept H<sup>1</sup> 0.00 1.00

Table 8. Sensitivity and specificity of the test considering the first score, the second score, and the third score (left) and scores 1–2 (jointly), scores 1–7 (jointly), and scores 1–12 (jointly) (right), when the size of the samples to diagnose is ν ¼ 50

Healthy sample (H0) Faulty sample (H1)

True rate of false negatives <sup>ℙ</sup> <sup>H</sup>1jaccept <sup>H</sup><sup>0</sup>

<sup>ℙ</sup> <sup>H</sup>1jacceptH<sup>1</sup>

H<sup>0</sup> H<sup>1</sup> H<sup>0</sup> H<sup>1</sup>

Healthy sample (H0) Faulty sample (H1)

4.3. Reliability of the results

have been wrongly identified as faulty.

156 Structural Health Monitoring from Sensing to Processing

Table 7. Relationship between specificity and sensitivity.

and the level of significance is α ¼ 10%

Accept H<sup>0</sup> ℙ H0jaccept H<sup>0</sup>

Accept H<sup>1</sup> True rate of false positives ℙ H0jaccept H<sup>1</sup>

Table 9. Relationship between the proportion of false negatives and false positives.

Score 1 Scores 1–2

Score 2 Scores 1–7

Score 3 Scores 1–12

A multifault detection method based on MPCA through uni- and multivariate hypothesis testing has been presented in this chapter. It is noteworthy to mention the obtained performance through the study of eight realistic different faults in different components of the WT, taking into account that the proposed strategy does not need extra sensors but only uses already available data from the WT SCADA system.

The three main conclusions, which show the benefits of the multivariate statistical hypothesis testing in comparison with the univariate case, for WT condition monitoring, are the following:


## Acknowledgements

This work has been partially funded by the Spanish Ministry of Economy and Competitiveness through the research projects DPI2014-58427-C2-1-R and DPI2017-82930-C2-1-R, and by the Generalitat de Catalunya through the research project 2017 SGR 388.

## Abbreviations

The following abbreviations are used in this chapter:

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## Author details

Francesc Pozo\* and Yolanda Vidal

\*Address all correspondence to: francesc.pozo@upc.edu

Control, Modeling, Identification and Applications (CoDAlab), Department of Mathematics, Escola d'Enginyeria de Barcelona Est (EEBE), Universitat Politècnica de Catalunya (UPC), Barcelona, Spain

## References

Abbreviations

The following abbreviations are used in this chapter:

FAST fatigue, aerodynamics, structures, and turbulence

DOF degrees of freedom CM condition monitoring

158 Structural Health Monitoring from Sensing to Processing

FD fault detection

GS group scaling

FNR false-negative rate FPR false-positive rate

HT hypothesis testing

MCGS mean-centered group scaling

MRS multivariate random sample MRV multivariate random variable

O&M operation and maintenance PCA principal component analysis

SHM structural health monitoring

RV random variable

WT wind turbine

Francesc Pozo\* and Yolanda Vidal

Author details

Barcelona, Spain

MVND multivariate normal distribution

MPCA multiway principal component analysis

SCADA supervisory control and data acquisition

\*Address all correspondence to: francesc.pozo@upc.edu

Control, Modeling, Identification and Applications (CoDAlab), Department of Mathematics, Escola d'Enginyeria de Barcelona Est (EEBE), Universitat Politècnica de Catalunya (UPC),


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[29] Ugarte MD, Militino AF, Arnholt A. Probability and Statistics with R. Boca Raton, FL,

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[31] DeGroot MH, Schervish MJ. Probability and Statistics. London, UK: Pearson; 2012

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USA: CRC Press/Taylor & Francis Group; 2008

IEEE. 2016;104(8):1632-1646

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[27] Ng HK, Chen RH, Speyer JL. A vehicle health monitoring system evaluated experimentally on a passenger vehicle. IEEE Transactions on Control Systems Technology. 2006; 14(5):854-870

[13] Jonkman JM, Butterfield S, Musial W, Scott G. Definition of a 5-MW reference wind turbine for offshore system development, Technical Report. Golden, Colorado: National

[14] Kelley, N.; Jonkman, B. NWTC Computer-Aided Engineering Tools (Turbsim); Last mod-

[15] Ostachowicz W, Kudela P, Krawczuk M, Zak A. Guided Waves in Structures for SHM: The Time-Domain Spectral Element Method. Chichester, UK: John Wiley & Sons, Ltd; 2012

[16] Chai Y, Yang H, Zhao L. Data unfolding PCA modelling and monitoring of multiphase

[17] Ruiz M, Villez K, Sin G, Colomer J, Vanrrolleghem P. Influence of scaling and unfolding in PCA based monitoring of nutrient removing batch process. In: Fault Detection, Supervision and Safety of Technical Processes 2006. Amsterdam, The Netherlands: Elsevier; 2007.

[18] Westerhuis JA, Kourti T, MacGregor JF. Comparing alternative approaches for multivariate statistical analysis of batch process data. Journal of Chemometrics. 1999;13(3-4):397-413

[19] Ruiz M, Mujica LE, Sierra J, Pozo F, Rodellar J. Multiway principal component analysis contributions for structural damage localization. Structural Health Monitoring. 2017:

[20] Pozo F, Vidal Y. Wind turbine fault detection through principal component analysis and

[21] Pozo F, Vidal Y, Serrahima JM. On real-time fault detection in wind turbines: Sensor selection algorithm and detection time reduction analysis. Energies. 2016;9(7):520

[22] Anaya M, Tibaduiza D, Pozo F. A bioinspired methodology based on an artificial immune system for damage detection in structural health monitoring. Shock and Vibration. 2015;

[23] Anaya M, Tibaduiza DA, Pozo F. Detection and classification of structural changes using artificial immune systems and fuzzy clustering. International Journal of Bio-Inspired

measures for damage assessment in structures. Structural Health Monitoring. 2011;10(5):

[25] Zugasti E, González AG, Anduaga J, Arregui MA, Martínez F. Nullspace and autoregressive damage detection: A comparative study. Smart Materials and Structures. 2012;

[26] Häckell MW, Rolfes R, Kane MB, Lynch JP. Three-tier modular structural health monitoring framework using environmental and operational condition clustering for data

2-statistic PCA-based

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batch processes. IFAC Proceedings Volumes. 2013;46(13):569-574

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Renewable Energy Laboratory; 2009. NREL/TP-500-38060

160 Structural Health Monitoring from Sensing to Processing


**Chapter 8**

**Provisional chapter**

**Structural Health Monitoring of Bolted Joints Using**

**Structural Health Monitoring of Bolted Joints Using** 

Bolted joints are widely applied in engineering structures. Significant advantages of bolted joints are that they can be easily disassembled and the possibility to design for bearing large working load. However, in practical applications, preload loss in pre-tensioned bolts is inevitable. Reliable detection of bolt loosening is significant to ensure structural reliability and safety. In the past decades, the guided wave-based structural health monitoring (SHM) methods have been developed for the detection of bolt loosening, and considerable advancements have been made in this area. This chapter presents a review of the existing studies on bolt preload monitoring method based on guided wave. The basic principle and characteristics of the typical methods are discussed, which involve wave energy dissipation, time reversal guided wave, contact acoustic nonlinearity, and active chaotic ultrasonic excitation-based methods. In addition, this chapter presents an experimental comparison of the detection sensitivity of wave energy dissipation and time reversal method. The results show that the TR method is more sensitive to bolt loosening. **Keywords:** bolted joints, bolt-loosening monitoring, structural health monitoring,

Bolted joints are widely used in engineering structures such as aerospace and civil structures. Significant advantages of bolted joints are that they can be easily assembled and disassembled and the possibility of bearing large load. In practical applications, bolted joints are subjected to a variety of failure modes including self-loosening, slippage, shaking apart, fatigue cracks, and breaking [1]. Self-loosening is the most common issue among them due to inappropriate

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

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

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

DOI: 10.5772/intechopen.76915

**Guided Waves: A Review**

**Guided Waves: A Review**

http://dx.doi.org/10.5772/intechopen.76915

guided waves, time reversal method

**Abstract**

**1. Introduction**

Fei Du, Chao Xu, Huaiyu Ren and Changhai Yan

Fei Du, Chao Xu, Huaiyu Ren and Changhai Yan

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

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

DOI: 10.5772/intechopen.76915

Fei Du, Chao Xu, Huaiyu Ren and Changhai Yan Fei Du, Chao Xu, Huaiyu Ren and Changhai Yan

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

http://dx.doi.org/10.5772/intechopen.76915

#### **Abstract**

Bolted joints are widely applied in engineering structures. Significant advantages of bolted joints are that they can be easily disassembled and the possibility to design for bearing large working load. However, in practical applications, preload loss in pre-tensioned bolts is inevitable. Reliable detection of bolt loosening is significant to ensure structural reliability and safety. In the past decades, the guided wave-based structural health monitoring (SHM) methods have been developed for the detection of bolt loosening, and considerable advancements have been made in this area. This chapter presents a review of the existing studies on bolt preload monitoring method based on guided wave. The basic principle and characteristics of the typical methods are discussed, which involve wave energy dissipation, time reversal guided wave, contact acoustic nonlinearity, and active chaotic ultrasonic excitation-based methods. In addition, this chapter presents an experimental comparison of the detection sensitivity of wave energy dissipation and time reversal method. The results show that the TR method is more sensitive to bolt loosening.

**Keywords:** bolted joints, bolt-loosening monitoring, structural health monitoring, guided waves, time reversal method

## **1. Introduction**

Bolted joints are widely used in engineering structures such as aerospace and civil structures. Significant advantages of bolted joints are that they can be easily assembled and disassembled and the possibility of bearing large load. In practical applications, bolted joints are subjected to a variety of failure modes including self-loosening, slippage, shaking apart, fatigue cracks, and breaking [1]. Self-loosening is the most common issue among them due to inappropriate

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

preloads during installation, time varying external loads during service, or other environment factors. Bolts loosening may lead to the failure of the entire structure. Therefore, it is critical to monitor bolt preload to ensure the safety and reliability of structures.

Structural health monitoring (SHM) is generally referred to the process of acquiring and analyzing data from on-board sensors to determine the health of a structure [2]. Several SHM approaches have been reported for the detection of bolt loosening in different structural systems, such as vibration, electromechanical impedance, and guided wave-based techniques. In vibration-based techniques, global dynamic properties, like resonant frequencies, modal shapes, and frequency response functions are utilized for the detection of bolt loosening [3]. However, since an assembled structure usually comprises many bolts and joint interfaces which are known as local structural elements, global structural dynamic properties do not change significantly due to bolt preload loosening at a local position [4]. Consequently, vibration-based SHM techniques are relatively insensitive to changes in bolt preloads and thus lead to poor prognostic capability. Impedance-based techniques monitor variations in mechanical impedance due to damage, which is coupled with electrical impedance of piezoelectric transducers (PZTs) [5]. Previous studies have shown the feasibility of using impedance-based approaches for the detection of bolt loosening [6–8]. A piezoelectric transducer (PZT) is attached to a target bolt-jointed structure, and bolt preload can be identified by monitoring the change of the measured electrical impedance [7]. Although this technique is sensitive to minor changes in the bolt preload, its detection area is limited to the near field of the piezoelectric active sensor [9] and an expensive high-precision impedance analyzer with a high-sampling frequency is required [10].

the interface increases. Correspondingly, the real contact area increases as well. When a wave travels through a lap joint, only a part of the incident wave energy can be transmitted, and the other part is reflected and dissipated. Based on Hertz contact theory and the sinusoidal wavy surface model, Yang and Chang [3] establish the relationship between real contact area and contact pressure at a joint interface. Their results show that the energy of transmitted guided wave is proportional to the real contact area of joint interface which increases with bolt preload. Although the topographies of rough contact surfaces are not strictly sinusoidal and the plastic deformation of contact asperities are not considered, Yang's theoretical analysis agrees well with experimental observation. After that, the transmitted wave energy is widely used as the tightness index for bolt-loosening detection. However, based on the theory of rough contact mechanics, the real contact area at an interface reaches a saturation value when the applied contact pressure reaches a certain value [14]. Accordingly, the transmitted energy also saturates when the externally applied load reaches a certain value. In this case, the sensitivity of the transmitted

Structural Health Monitoring of Bolted Joints Using Guided Waves: A Review

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165

Nonlinear features of acoustic waves can also be extracted and linked to bolt loosening. Among approaches based on nonlinear features, contact acoustic nonlinearity (CAN) is drawing increasing attention. When the bolt is loosening and the joint is stimulated by acoustic waves or vibration under certain amplitude, joint interface undergoes a certain extent of tension and compression and it opens and closes periodically. This induces asymmetry in the contact restoration forces. Consequently, those forces cause a parametric change of stiffness and lead to structural dynamic nonlinearity, known as contact acoustic nonlinearity [15, 16]. Since the guided wave amplitude excited by a piezoelectric element is generally small, it is difficult to stimulate the nonlinearity of the structure itself. Therefore, impact modulation (IM) and vibro-acoustic modulation (VAM) are two major implementations of CAN-based modulation [17]. The major difference between them is that IM adopts an impact force to excite the natural vibration modes of the inspected structure, while VAM applies a stable vibration to the structure using a harmonic force. The essence of the modulation methods resides on the interaction of the jointed interface with a mixed excitation, like a vibration and a wave. When all the bolts in a jointed structure are fully fastened, the acquired signal spectrum exhibits two peaks at the vibration and wave frequencies, respectively. When bolts

wave energy-based damage detection strategy is reduced considerably.

**Figure 1.** Guided wave transmitted across a bolted joint.

Guided wave-based damage detection techniques have been intensively developed over the last two decades [11, 12]. Due to their sensitivity to small structural damages and large sensing range [13], guided wave techniques have been increasingly used for structural health monitoring. In recent years, bolt preload detection methods using guided wave have received much interest. In this chapter, bolt preload monitoring methods based on guided waves and the relevant theories are reviewed. The objective is to understand the current technology gaps, future research directions, and areas requiring attention of the researchers. This chapter is organized as follows. Section 2 presents the theoretical backgrounds and numerical modeling approach of guided wave-based SHM methods. Then, linear feature-based detection methods are reviewed and compared in Section 3, which include wave energy dissipation methods and time reversal methods. Section 4 displays nonlinear feature-based methods including contact acoustic nonlinearity (CAN), phase shift, and chaotic ultrasonic excitation methods. Finally, conclusions are summarized in Section 5.

## **2. Theoretical basis and numerical modeling**

## **2.1. Theoretical backgrounds**

A typical bolted joint is illustrated in **Figure 1**. It can be seen that a bolted joint usually consists of one bolt, one nut, and two contact parts. From the view of a micro-scale, the joint interface can be considered to be covered with a large amount of asperities. The real contact area is the summation of the contact area of each asperity. As the bolt preload increases, the contact pressure at

**Figure 1.** Guided wave transmitted across a bolted joint.

preloads during installation, time varying external loads during service, or other environment factors. Bolts loosening may lead to the failure of the entire structure. Therefore, it is

Structural health monitoring (SHM) is generally referred to the process of acquiring and analyzing data from on-board sensors to determine the health of a structure [2]. Several SHM approaches have been reported for the detection of bolt loosening in different structural systems, such as vibration, electromechanical impedance, and guided wave-based techniques. In vibration-based techniques, global dynamic properties, like resonant frequencies, modal shapes, and frequency response functions are utilized for the detection of bolt loosening [3]. However, since an assembled structure usually comprises many bolts and joint interfaces which are known as local structural elements, global structural dynamic properties do not change significantly due to bolt preload loosening at a local position [4]. Consequently, vibration-based SHM techniques are relatively insensitive to changes in bolt preloads and thus lead to poor prognostic capability. Impedance-based techniques monitor variations in mechanical impedance due to damage, which is coupled with electrical impedance of piezoelectric transducers (PZTs) [5]. Previous studies have shown the feasibility of using impedance-based approaches for the detection of bolt loosening [6–8]. A piezoelectric transducer (PZT) is attached to a target bolt-jointed structure, and bolt preload can be identified by monitoring the change of the measured electrical impedance [7]. Although this technique is sensitive to minor changes in the bolt preload, its detection area is limited to the near field of the piezoelectric active sensor [9] and an expensive high-precision impedance analyzer with a high-sampling frequency is required [10].

Guided wave-based damage detection techniques have been intensively developed over the last two decades [11, 12]. Due to their sensitivity to small structural damages and large sensing range [13], guided wave techniques have been increasingly used for structural health monitoring. In recent years, bolt preload detection methods using guided wave have received much interest. In this chapter, bolt preload monitoring methods based on guided waves and the relevant theories are reviewed. The objective is to understand the current technology gaps, future research directions, and areas requiring attention of the researchers. This chapter is organized as follows. Section 2 presents the theoretical backgrounds and numerical modeling approach of guided wave-based SHM methods. Then, linear feature-based detection methods are reviewed and compared in Section 3, which include wave energy dissipation methods and time reversal methods. Section 4 displays nonlinear feature-based methods including contact acoustic nonlinearity (CAN), phase shift, and chaotic ultrasonic excitation methods. Finally, conclusions are summarized in Section 5.

A typical bolted joint is illustrated in **Figure 1**. It can be seen that a bolted joint usually consists of one bolt, one nut, and two contact parts. From the view of a micro-scale, the joint interface can be considered to be covered with a large amount of asperities. The real contact area is the summation of the contact area of each asperity. As the bolt preload increases, the contact pressure at

**2. Theoretical basis and numerical modeling**

**2.1. Theoretical backgrounds**

critical to monitor bolt preload to ensure the safety and reliability of structures.

164 Structural Health Monitoring from Sensing to Processing

the interface increases. Correspondingly, the real contact area increases as well. When a wave travels through a lap joint, only a part of the incident wave energy can be transmitted, and the other part is reflected and dissipated. Based on Hertz contact theory and the sinusoidal wavy surface model, Yang and Chang [3] establish the relationship between real contact area and contact pressure at a joint interface. Their results show that the energy of transmitted guided wave is proportional to the real contact area of joint interface which increases with bolt preload. Although the topographies of rough contact surfaces are not strictly sinusoidal and the plastic deformation of contact asperities are not considered, Yang's theoretical analysis agrees well with experimental observation. After that, the transmitted wave energy is widely used as the tightness index for bolt-loosening detection. However, based on the theory of rough contact mechanics, the real contact area at an interface reaches a saturation value when the applied contact pressure reaches a certain value [14]. Accordingly, the transmitted energy also saturates when the externally applied load reaches a certain value. In this case, the sensitivity of the transmitted wave energy-based damage detection strategy is reduced considerably.

Nonlinear features of acoustic waves can also be extracted and linked to bolt loosening. Among approaches based on nonlinear features, contact acoustic nonlinearity (CAN) is drawing increasing attention. When the bolt is loosening and the joint is stimulated by acoustic waves or vibration under certain amplitude, joint interface undergoes a certain extent of tension and compression and it opens and closes periodically. This induces asymmetry in the contact restoration forces. Consequently, those forces cause a parametric change of stiffness and lead to structural dynamic nonlinearity, known as contact acoustic nonlinearity [15, 16]. Since the guided wave amplitude excited by a piezoelectric element is generally small, it is difficult to stimulate the nonlinearity of the structure itself. Therefore, impact modulation (IM) and vibro-acoustic modulation (VAM) are two major implementations of CAN-based modulation [17]. The major difference between them is that IM adopts an impact force to excite the natural vibration modes of the inspected structure, while VAM applies a stable vibration to the structure using a harmonic force. The essence of the modulation methods resides on the interaction of the jointed interface with a mixed excitation, like a vibration and a wave. When all the bolts in a jointed structure are fully fastened, the acquired signal spectrum exhibits two peaks at the vibration and wave frequencies, respectively. When bolts are loosening, there would be additional frequency components around the wave frequency in the spectrum, termed as left and right sidebands. The magnitudes of the sidebands, which are determined by the intensity of CAN, can be linked quantitatively to the bolt preload [18].

In order to quantitatively describe the relation between sidebands of signal spectral features and the residual bolt preload, Zhang et al. [18] established a theoretical modeling of CAN in a joint, as shown in **Figure 2a**. The analysis based on the model demonstrates that the magnitude of the sideband is proportional linearly to the nonlinear contact stiffness *K2* which is dependent on the contact pressure at the jointed interface. The above model is a simplified model with single degree of freedom (DOF). Subsequently, Zhang et al. [19] presented a two-DOF nonlinear model to analyze the physical phenomenon of subharmonics and their generation conditions, as shown in **Figure 2b**. On this basis, analytical prediction was carried out to verify the validity of the loosening detection method for bolted joint structures using the subharmonic resonance.

#### **2.2. Numerical modeling**

To understand how guided waves interact with bolted lap joints exactly, theoretical models are essential to describe the propagation behavior of guided wave. Apparently, the above simplified single or two DOF models are not enough. Since the bolted structure is inhomogeneous in the direction of wave propagation, it cannot be modeled by analytical or semi-analytical methods. Finite element method (FEM) can be applied to a variety of complex geometries and has become the most common wave propagation analysis method. Therefore, Clayton et al. [20] established a three-dimensional finite element model of guided wave propagation in bolted joints, but interface contact was not considered in order to reduce computational cost. Then, Doyle et al. [21], and Bao and Giurgiutiu [22] used the same method to establish finite element analysis models. However, they found that these models could not reflect the variation of the guided wave under different bolt preloads. Therefore, in order to consider contact

behaviors, Bao et al. [23] added contact elements to the finite element model. The improved model can effectively reflect the variation of the guided wave under different preloads, but the wave variations and the measurement results were quite different. The main reason might be that the contact surfaces in the above models are smooth, while the real contact surfaces are rough. In 2016, Parvasi et al. [10] tried to consider rough contact surfaces in finite element model by randomly adjusting node position at the contact surfaces, as shown in **Figure 3**. The simulation results are closer to the experimental measurement results, but the mesh size (1.8 mm) of the contact area is much larger than the size of micro-asperities on rough surfaces. The above FEM models are mainly used to analyze the relationship between bolt preload and transmitted guided wave energy. Shen et al. [24] built anther 3D multiphysics transient

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**Figure 3.** Multi-physics FEM model of bolted lap joint considering rough contact surfaces [10].

**Figure 4.** Transient dynamic finite element model and frequency spectrum of simulation signal [24].

**Figure 2.** Theoretical modeling of CAN in a joint: (a) single degree of freedom [18] and (b) two degrees of freedom [19].

**Figure 3.** Multi-physics FEM model of bolted lap joint considering rough contact surfaces [10].

are loosening, there would be additional frequency components around the wave frequency in the spectrum, termed as left and right sidebands. The magnitudes of the sidebands, which are determined by the intensity of CAN, can be linked quantitatively to the bolt preload [18]. In order to quantitatively describe the relation between sidebands of signal spectral features and the residual bolt preload, Zhang et al. [18] established a theoretical modeling of CAN in a joint, as shown in **Figure 2a**. The analysis based on the model demonstrates that the magnitude

on the contact pressure at the jointed interface. The above model is a simplified model with single degree of freedom (DOF). Subsequently, Zhang et al. [19] presented a two-DOF nonlinear model to analyze the physical phenomenon of subharmonics and their generation conditions, as shown in **Figure 2b**. On this basis, analytical prediction was carried out to verify the validity of the loosening detection method for bolted joint structures using the subharmonic resonance.

To understand how guided waves interact with bolted lap joints exactly, theoretical models are essential to describe the propagation behavior of guided wave. Apparently, the above simplified single or two DOF models are not enough. Since the bolted structure is inhomogeneous in the direction of wave propagation, it cannot be modeled by analytical or semi-analytical methods. Finite element method (FEM) can be applied to a variety of complex geometries and has become the most common wave propagation analysis method. Therefore, Clayton et al. [20] established a three-dimensional finite element model of guided wave propagation in bolted joints, but interface contact was not considered in order to reduce computational cost. Then, Doyle et al. [21], and Bao and Giurgiutiu [22] used the same method to establish finite element analysis models. However, they found that these models could not reflect the variation of the guided wave under different bolt preloads. Therefore, in order to consider contact

**Figure 2.** Theoretical modeling of CAN in a joint: (a) single degree of freedom [18] and (b) two degrees of freedom [19].

which is dependent

of the sideband is proportional linearly to the nonlinear contact stiffness *K2*

**2.2. Numerical modeling**

166 Structural Health Monitoring from Sensing to Processing

behaviors, Bao et al. [23] added contact elements to the finite element model. The improved model can effectively reflect the variation of the guided wave under different preloads, but the wave variations and the measurement results were quite different. The main reason might be that the contact surfaces in the above models are smooth, while the real contact surfaces are rough. In 2016, Parvasi et al. [10] tried to consider rough contact surfaces in finite element model by randomly adjusting node position at the contact surfaces, as shown in **Figure 3**. The simulation results are closer to the experimental measurement results, but the mesh size (1.8 mm) of the contact area is much larger than the size of micro-asperities on rough surfaces.

The above FEM models are mainly used to analyze the relationship between bolt preload and transmitted guided wave energy. Shen et al. [24] built anther 3D multiphysics transient

**Figure 4.** Transient dynamic finite element model and frequency spectrum of simulation signal [24].

dynamic finite element model to analyze the relationship between CAN and bolt load, as shown in **Figure 4a**. The nonlinear higher harmonics (second-order harmonic and third-order harmonic) can be observed clearly in the simulation signal, as shown in **Figure 4b**. The simulation results also displayed that as the bolt preload increases, the ratio of the spectral amplitude at the second harmonic to that at the excitation frequency decreases.

## **3. Linear feature-based techniques**

#### **3.1. Wave energy dissipation**

Because ultrasonic wave energy through the bolt joint is strongly tied to the contact status of bolted interface, the transmitted guided wave energy is widely used as tightness index. This type of method is also known as wave energy dissipation (WED) method. In order to detect fastener integrity in thermal protection panels in space vehicles, Yang and Chang [3, 25] used the energy and attenuation speed of guided wave transmitted across jointed interface to assess preload levels and locations of loosening bolt. Subsequently, Wang et al. [26] used only the transmitted guided wave energy to monitor bolt preload. The schematic of the bolt joint monitoring system is displayed in **Figure 5**. The experimental results show that the transmitted energy is basically proportional to torque level. However, the energy does not change with bolt torque when the applied torque reaches a certain value and this is referred to as saturation phenomenon, as shown in **Figure 6a**. Similarly, Amerini and Meo [27] calculated the energy of the transmitted guided wave in frequency domain to assess the tightening state of a bolt lap joint, as shown in **Figure 6b**. Yang et al. [28] extended the WED method to composite bolted joints. With a scanning laser ultrasound system, Haynes et al. [29] acquired the full-field wave data and calculated the wave energy before and after the lap joint to monitor bolt torque levels. Unfortunately, saturation phenomena are also observed in all the above experimental studies. On the other hand, due to multi-mode, dispersion, and boundary reflection of guided waves, the response signal at a joint structure is quite complex [27]. Hence, Kędra et al. [30] investigated the effects of excitation frequency, the time range of received signal, and the position of sensor on the preload detection accuracy of the WED method. They pointed out that these parameters have to be carefully selected.

monitor the preload of L-shaped bolt joints, Jalalpour et al. [31] proposed a preload monitoring method using fast Fourier transform, cross-correlation, and fuzzy pattern recognition to process transmitted wave. Nevertheless, the fuzzy sets of torque level were limited. Montoya et al. [32] assessed the rigidity of L-shaped bolt joint using transmitted wave energy. Subsequently, Montoya et al. [33] further extended the method to bolt loosening and preload monitoring of satellite panels jointed by a right angle bracket. Their experimental results display that some measurement parameters, such as the time window of the received signal, have a significant effect on the sensitivity and repeatability of the measurement [33]. With respect to bolt-loosening monitoring in multi-bolt-jointed structures, Mita et al. [34] proposed to use support vector machine to recognize different loosening patterns. Their results show that the proposed method could identify the location and the level of preload of loosened bolts. Moreover, Liang and Yuan [35] developed a decision fusion system for multi-bolt structure, as shown in **Figure 7**. This system consists of individual classification, classifier selection, and decision fusion. The results demonstrate that the proposed method can accurately and rapidly identify the bolt loosening by analyzing the acquired wave signal.

**Figure 7.** Sensor layout and joint failure position on the specimen [35].

**Figure 6.** Results of WED methods with saturation phenomenon: (a) result from reference [26] and (b) result from

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reference [27].

The above bolt preload detection methods are limited to a flat lap joint with a single bolt. However, in real structures, bolted joints with complex geometry or multiple bolts are more common. In this case, complex signal-processing methods are always needed. In order to

**Figure 5.** Schematic of the bolt joint monitoring system [26].

dynamic finite element model to analyze the relationship between CAN and bolt load, as shown in **Figure 4a**. The nonlinear higher harmonics (second-order harmonic and third-order harmonic) can be observed clearly in the simulation signal, as shown in **Figure 4b**. The simulation results also displayed that as the bolt preload increases, the ratio of the spectral ampli-

Because ultrasonic wave energy through the bolt joint is strongly tied to the contact status of bolted interface, the transmitted guided wave energy is widely used as tightness index. This type of method is also known as wave energy dissipation (WED) method. In order to detect fastener integrity in thermal protection panels in space vehicles, Yang and Chang [3, 25] used the energy and attenuation speed of guided wave transmitted across jointed interface to assess preload levels and locations of loosening bolt. Subsequently, Wang et al. [26] used only the transmitted guided wave energy to monitor bolt preload. The schematic of the bolt joint monitoring system is displayed in **Figure 5**. The experimental results show that the transmitted energy is basically proportional to torque level. However, the energy does not change with bolt torque when the applied torque reaches a certain value and this is referred to as saturation phenomenon, as shown in **Figure 6a**. Similarly, Amerini and Meo [27] calculated the energy of the transmitted guided wave in frequency domain to assess the tightening state of a bolt lap joint, as shown in **Figure 6b**. Yang et al. [28] extended the WED method to composite bolted joints. With a scanning laser ultrasound system, Haynes et al. [29] acquired the full-field wave data and calculated the wave energy before and after the lap joint to monitor bolt torque levels. Unfortunately, saturation phenomena are also observed in all the above experimental studies. On the other hand, due to multi-mode, dispersion, and boundary reflection of guided waves, the response signal at a joint structure is quite complex [27]. Hence, Kędra et al. [30] investigated the effects of excitation frequency, the time range of received signal, and the position of sensor on the preload detection accuracy of the

WED method. They pointed out that these parameters have to be carefully selected.

The above bolt preload detection methods are limited to a flat lap joint with a single bolt. However, in real structures, bolted joints with complex geometry or multiple bolts are more common. In this case, complex signal-processing methods are always needed. In order to

tude at the second harmonic to that at the excitation frequency decreases.

**3. Linear feature-based techniques**

168 Structural Health Monitoring from Sensing to Processing

**Figure 5.** Schematic of the bolt joint monitoring system [26].

**3.1. Wave energy dissipation**

**Figure 6.** Results of WED methods with saturation phenomenon: (a) result from reference [26] and (b) result from reference [27].

monitor the preload of L-shaped bolt joints, Jalalpour et al. [31] proposed a preload monitoring method using fast Fourier transform, cross-correlation, and fuzzy pattern recognition to process transmitted wave. Nevertheless, the fuzzy sets of torque level were limited. Montoya et al. [32] assessed the rigidity of L-shaped bolt joint using transmitted wave energy. Subsequently, Montoya et al. [33] further extended the method to bolt loosening and preload monitoring of satellite panels jointed by a right angle bracket. Their experimental results display that some measurement parameters, such as the time window of the received signal, have a significant effect on the sensitivity and repeatability of the measurement [33]. With respect to bolt-loosening monitoring in multi-bolt-jointed structures, Mita et al. [34] proposed to use support vector machine to recognize different loosening patterns. Their results show that the proposed method could identify the location and the level of preload of loosened bolts. Moreover, Liang and Yuan [35] developed a decision fusion system for multi-bolt structure, as shown in **Figure 7**. This system consists of individual classification, classifier selection, and decision fusion. The results demonstrate that the proposed method can accurately and rapidly identify the bolt loosening by analyzing the acquired wave signal.

**Figure 7.** Sensor layout and joint failure position on the specimen [35].

#### **3.2. Time reversal method**

Since guided wave signals are always very complex because of multi-mode, dispersion, and scattering at any discontinuity, Fink et al. [36] extended time reversal concept (TR) to a guided wave monitoring technique. In time reversal approach, a received signal is reversed and reemitted as an excitation signal, and then a reconstruction of the input signal can be obtained at the source position. Hence, the time reversal method can effectively reduce the influences of dispersion and multi-modal of the guided wave. In recent years, time reversalbased guided wave monitoring methods have been widely applied to damage detection in various structures, such as metallic plates [37], composite plates [38–40], and rebar-reinforced concrete beams [41]. Recently, Parvasi et al. [10] proposed to use time reversal method to focus guided wave energy transmitted through bolted joint, and then the refocused amplitude peak was selected as the tightness index for preload detection. The experimental results show that the proposed tightness index increases with bolt torque. The TR method for bolt preload monitoring can be divided into four steps, which is shown in **Figure 8**. Step 1, a tone burst input e(t) is applied to transducer A, which activates wave propagation in the plate. Step 2, a wave response signal u(t) is captured by transducer B. Step 3, the recorded signal u(t) is reversed in time domain and is restimulated using transducer B. Step 4, a guided wave signal is captured by transducer A again, and the original signal is reconstructed. Finally, the reconstructed signal peak is used as the tightness index for preload detection [10]. One of the main advantages of TR method is that there is no need to take efforts to select time window of received signal as the WED method.

interface, the saturation phenomenon becomes insignificant. Huo et al. [43] studied guided wave propagation across contact interface based on fractal contact theory and finite element method. They concluded that the saturation phenomenon is linked to the plastic deformation

Until now, the difference in monitoring sensitivities of WED and TR methods is not clear. Hence, the monitoring sensitivities of the two methods are compared in this section. The experimental setup and specimens are displayed in **Figure 9**. The metallic bolted lap joint consists of two flat aluminum 2024-T3 beams, one M6 bolt, one nut, and two washers. The length of each beam is 400 mm, the width is 50 mm, and the thickness 2 mm. The normal torque is selected to be 10 Nm. A torque wrench with a resolution of 0.2 Nm is used to apply bolt preload. A data acquisition (DAQ) system NI USB-6366 with a sampling frequency of 2 MHz is used to generate wave excitation and record responses. A program is built in the LabVIEW environment to control the process of data acquisition. A high voltage amplifier PINTEK HA-400 is used to amplify the excitation signal and provides voltage to PZT actuators. In addition, the specimen is mounted on a foam support to simulate a free-free boundary condition. Two PZT patches are bonded on the specimen. The patch on the left beam, 100 mm, away from the bolt is numbered as PZT 1 PZT. Another one on the right beam, 100 mm, from

The bolt preload is evaluated by both WED and TR methods at the same time. **Figure 10** pres-

load when the preload is smaller than 6 Nm. However, an obvious saturation trend can be seen, and only the lowest 0.1-Nm torque case can be clearly identified. By contrast, *TIΩ*(TR) increases with bolt preload in the entire preload range, and the 0.1-, 2-, and 4-Nm cases can be clearly identified. On the other hand, *TIΩ*(TR) cannot be used to identify torque cases larger

(*TR*) It can be seen that *TIΩ*(WED) increases with bolt pre-

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(*TR*) especially at the early stage of bolt loosening. The

(*WED*), the WED

(*MTR*) method is better

ents the results of tightness indexes *TIΩ*(WED) and *TIΩ*(TR) obtained by *TI<sup>Ω</sup>*

than 6 Nm. It can be concluded that the detection sensitivity of TR *TIp*

(*WED*) WED method *TI<sup>Ω</sup>*

of interacting asperities under a heavy axial load.

**3.3. Comparison of TR and WED methods**

the jointed bolt is numbered as PZT 2.

and TR methods, respectively. *TI<sup>Ω</sup>*

**Figure 9.** Experimental setup and specimens.

than that of *TI<sup>Ω</sup>*

Actually, the refocused amplitude peak is strongly related to the transmitted wave energy. Hence, when bolt preload is relatively high and the real contact area does not increase with preload, the focused signal peak amplitude changes very slowly. Therefore, Tao et al. [42] experimentally investigated the saturation phenomenon of TR method for bolted preload detection. The results demonstrate that with the increase of the surface roughness of bolted

**Figure 8.** Illustration of the time reversal method in a lap jointed beam.

interface, the saturation phenomenon becomes insignificant. Huo et al. [43] studied guided wave propagation across contact interface based on fractal contact theory and finite element method. They concluded that the saturation phenomenon is linked to the plastic deformation of interacting asperities under a heavy axial load.

## **3.3. Comparison of TR and WED methods**

Until now, the difference in monitoring sensitivities of WED and TR methods is not clear. Hence, the monitoring sensitivities of the two methods are compared in this section. The experimental setup and specimens are displayed in **Figure 9**. The metallic bolted lap joint consists of two flat aluminum 2024-T3 beams, one M6 bolt, one nut, and two washers. The length of each beam is 400 mm, the width is 50 mm, and the thickness 2 mm. The normal torque is selected to be 10 Nm. A torque wrench with a resolution of 0.2 Nm is used to apply bolt preload. A data acquisition (DAQ) system NI USB-6366 with a sampling frequency of 2 MHz is used to generate wave excitation and record responses. A program is built in the LabVIEW environment to control the process of data acquisition. A high voltage amplifier PINTEK HA-400 is used to amplify the excitation signal and provides voltage to PZT actuators. In addition, the specimen is mounted on a foam support to simulate a free-free boundary condition. Two PZT patches are bonded on the specimen. The patch on the left beam, 100 mm, away from the bolt is numbered as PZT 1 PZT. Another one on the right beam, 100 mm, from the jointed bolt is numbered as PZT 2.

The bolt preload is evaluated by both WED and TR methods at the same time. **Figure 10** presents the results of tightness indexes *TIΩ*(WED) and *TIΩ*(TR) obtained by *TI<sup>Ω</sup>* (*WED*), the WED and TR methods, respectively. *TI<sup>Ω</sup>* (*TR*) It can be seen that *TIΩ*(WED) increases with bolt preload when the preload is smaller than 6 Nm. However, an obvious saturation trend can be seen, and only the lowest 0.1-Nm torque case can be clearly identified. By contrast, *TIΩ*(TR) increases with bolt preload in the entire preload range, and the 0.1-, 2-, and 4-Nm cases can be clearly identified. On the other hand, *TIΩ*(TR) cannot be used to identify torque cases larger than 6 Nm. It can be concluded that the detection sensitivity of TR *TIp* (*MTR*) method is better than that of *TI<sup>Ω</sup>* (*WED*) WED method *TI<sup>Ω</sup>* (*TR*) especially at the early stage of bolt loosening. The

**Figure 9.** Experimental setup and specimens.

**Figure 8.** Illustration of the time reversal method in a lap jointed beam.

**3.2. Time reversal method**

170 Structural Health Monitoring from Sensing to Processing

of received signal as the WED method.

Since guided wave signals are always very complex because of multi-mode, dispersion, and scattering at any discontinuity, Fink et al. [36] extended time reversal concept (TR) to a guided wave monitoring technique. In time reversal approach, a received signal is reversed and reemitted as an excitation signal, and then a reconstruction of the input signal can be obtained at the source position. Hence, the time reversal method can effectively reduce the influences of dispersion and multi-modal of the guided wave. In recent years, time reversalbased guided wave monitoring methods have been widely applied to damage detection in various structures, such as metallic plates [37], composite plates [38–40], and rebar-reinforced concrete beams [41]. Recently, Parvasi et al. [10] proposed to use time reversal method to focus guided wave energy transmitted through bolted joint, and then the refocused amplitude peak was selected as the tightness index for preload detection. The experimental results show that the proposed tightness index increases with bolt torque. The TR method for bolt preload monitoring can be divided into four steps, which is shown in **Figure 8**. Step 1, a tone burst input e(t) is applied to transducer A, which activates wave propagation in the plate. Step 2, a wave response signal u(t) is captured by transducer B. Step 3, the recorded signal u(t) is reversed in time domain and is restimulated using transducer B. Step 4, a guided wave signal is captured by transducer A again, and the original signal is reconstructed. Finally, the reconstructed signal peak is used as the tightness index for preload detection [10]. One of the main advantages of TR method is that there is no need to take efforts to select time window

Actually, the refocused amplitude peak is strongly related to the transmitted wave energy. Hence, when bolt preload is relatively high and the real contact area does not increase with preload, the focused signal peak amplitude changes very slowly. Therefore, Tao et al. [42] experimentally investigated the saturation phenomenon of TR method for bolted preload detection. The results demonstrate that with the increase of the surface roughness of bolted

**Figure 10.** Preload detection results of the WED and TR methods.

main reason is that guided waves traveled twice (from PZT1 to PZT2, and then PZT2 to PZT1) through the jointed interface in the TR technique. The interface affects the waves twice and thus makes the *TIΩ*(TR) more sensitive to the bolt preload [10].

both second-order harmonics index and sideband index to assess the tightening state of a bolted structure, and the assessment results of the two methods are similar. On the other hand, Zhang Z et al. [16] also compared the high-order harmonics and sideband methods and demonstrated that the stability of spectral sideband-based method is better. Spectral sideband can also be generated by impact modulation. Meyer and Adams [44] proposed an impact modulation-based method to detect bolt loosening in an aluminum joint. However, the sideband amplitudes are sensitive to test parameters including impact amplitude and location, probing force amplitude and frequency, and sensor location. One common disadvantage of these above spectral sideband methods is that it needs two different actuators and one sensor for each joint monitored [27]. Meanwhile, the saturation phenomena have not been completely removed, and the detec-

**Figure 11.** Preload monitoring of bolted composite joint using VAM method [17]: (a) experimental setup for VAM

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Apart from transmitted wave energy and CAN, the phase shift of guided wave has also been used for quantifying bolt torques. Zagrai et al. [45] estimated bolt torques by measuring delays of guided wave transmitted across bolt joint. Their experimental results demonstrated that bolt torque is proportional to phase shift of the guided waves, as shown in **Figure 12**.

In addition, Zagrai et al. [45] tried to explain the experiment results by acousto-elastic theory and presented a simplified theoretical approach to calculate phase shift of the propagating elastic wave. However, their approach gives approximately an order of magnitude underestimation for pulse delays. Subsequently, Doyle et al. [46, 47] further studied phase shift of guided wave propagating in a complex structure analogous to a typical satellite panel containing 49 bolt joints using an array of piezoelectric sensors sparsely distributed. The results show that the time at which this shift occurs is related to the distance between the location of loosening bolt and the primary wave propagation path. Thereby, using only two or three possible paths, it is possible to obtain a realistic estimate of the location of damage in the form of single bolt loosening [47]. On this basis, Zagrai et al. [48] tried to develop a baseline-free method utilizing

tion sensitivity still needs to be improved at the early stage of bolt loosening.

method and (b) comparison of VAM and WED methods.

**4.2. Phase shift**

## **4. Nonlinear feature-based techniques**

## **4.1. Contact acoustic nonlinearity**

Contact acoustic nonlinearity (CAN) is shown to increase with the decrease in contact load, so the second-order harmonics, subharmonic, and spectral sidebands caused by CAN have also been used for bolt preload detection. Usually, the second-order harmonic and subharmonic can be generated by a single frequency excitation, and spectral sidebands are generated by both low- and high-frequency excitations. For the second-order harmonic-based method, the ratio between the second harmonic amplitude and the carrier frequency signal amplitude provided a reliable index for bolt load assessment. Under multi-frequency excitation, the loosening/tightening index proposed is the difference in dB between the carrier frequency amplitude and a mean of the two sideband amplitudes [27]. Zhang M et al. [19] presented a subharmonic resonance method for the detection of bolt looseness, and the bolted joint was excited by a single frequency-guided wave. CAN features are more likely to be excited by adding vibration excitation. Thereby, Zhang Z et al. [17, 18] proposed a vibro-acoustic modulation (VAM)-based method and developed a sideband index for metal and composite bolted joints. The experimental setup and the corresponding detection results for composite bolted joints are shown in **Figure 11**.

In **Figure 11**, the label *β* is the sideband index in VAM method, and the label energy is the transmitted energy of Lamb waves in WED method. Zhang Z et al. [17] compared the proposed VAM method with WED-based linear method, and the results show that the proposed sideband index *β* effectively enhanced measurement sensitivity. In addition, Amerini and Meo [27] developed

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**Figure 11.** Preload monitoring of bolted composite joint using VAM method [17]: (a) experimental setup for VAM method and (b) comparison of VAM and WED methods.

both second-order harmonics index and sideband index to assess the tightening state of a bolted structure, and the assessment results of the two methods are similar. On the other hand, Zhang Z et al. [16] also compared the high-order harmonics and sideband methods and demonstrated that the stability of spectral sideband-based method is better. Spectral sideband can also be generated by impact modulation. Meyer and Adams [44] proposed an impact modulation-based method to detect bolt loosening in an aluminum joint. However, the sideband amplitudes are sensitive to test parameters including impact amplitude and location, probing force amplitude and frequency, and sensor location. One common disadvantage of these above spectral sideband methods is that it needs two different actuators and one sensor for each joint monitored [27]. Meanwhile, the saturation phenomena have not been completely removed, and the detection sensitivity still needs to be improved at the early stage of bolt loosening.

#### **4.2. Phase shift**

main reason is that guided waves traveled twice (from PZT1 to PZT2, and then PZT2 to PZT1) through the jointed interface in the TR technique. The interface affects the waves twice and

Contact acoustic nonlinearity (CAN) is shown to increase with the decrease in contact load, so the second-order harmonics, subharmonic, and spectral sidebands caused by CAN have also been used for bolt preload detection. Usually, the second-order harmonic and subharmonic can be generated by a single frequency excitation, and spectral sidebands are generated by both low- and high-frequency excitations. For the second-order harmonic-based method, the ratio between the second harmonic amplitude and the carrier frequency signal amplitude provided a reliable index for bolt load assessment. Under multi-frequency excitation, the loosening/tightening index proposed is the difference in dB between the carrier frequency amplitude and a mean of the two sideband amplitudes [27]. Zhang M et al. [19] presented a subharmonic resonance method for the detection of bolt looseness, and the bolted joint was excited by a single frequency-guided wave. CAN features are more likely to be excited by adding vibration excitation. Thereby, Zhang Z et al. [17, 18] proposed a vibro-acoustic modulation (VAM)-based method and developed a sideband index for metal and composite bolted joints. The experimental setup and the corresponding detection results for composite bolted

In **Figure 11**, the label *β* is the sideband index in VAM method, and the label energy is the transmitted energy of Lamb waves in WED method. Zhang Z et al. [17] compared the proposed VAM method with WED-based linear method, and the results show that the proposed sideband index *β* effectively enhanced measurement sensitivity. In addition, Amerini and Meo [27] developed

thus makes the *TIΩ*(TR) more sensitive to the bolt preload [10].

**4. Nonlinear feature-based techniques**

**Figure 10.** Preload detection results of the WED and TR methods.

172 Structural Health Monitoring from Sensing to Processing

**4.1. Contact acoustic nonlinearity**

joints are shown in **Figure 11**.

Apart from transmitted wave energy and CAN, the phase shift of guided wave has also been used for quantifying bolt torques. Zagrai et al. [45] estimated bolt torques by measuring delays of guided wave transmitted across bolt joint. Their experimental results demonstrated that bolt torque is proportional to phase shift of the guided waves, as shown in **Figure 12**.

In addition, Zagrai et al. [45] tried to explain the experiment results by acousto-elastic theory and presented a simplified theoretical approach to calculate phase shift of the propagating elastic wave. However, their approach gives approximately an order of magnitude underestimation for pulse delays. Subsequently, Doyle et al. [46, 47] further studied phase shift of guided wave propagating in a complex structure analogous to a typical satellite panel containing 49 bolt joints using an array of piezoelectric sensors sparsely distributed. The results show that the time at which this shift occurs is related to the distance between the location of loosening bolt and the primary wave propagation path. Thereby, using only two or three possible paths, it is possible to obtain a realistic estimate of the location of damage in the form of single bolt loosening [47]. On this basis, Zagrai et al. [48] tried to develop a baseline-free method utilizing

Clayton et al. [20] proposed a bolt preload monitoring approach combining a chaotic excitation method with ultrasonic guided waves. In this method, the chaotic signal is upconverting to an ultrasonic frequency band, and the ultrasound signal with chaotic characteristics is generated to stimulate the bolted structure. The response signal is reconstructed to analyze the phase space, and the nonlinear characteristic quantitatively representing the bolt looseness is extracted. Fasel et al. [49, 50] used similar methods to identify bolt preload in simulations and experiments on single and multi-bolt structures. Recently, based on the chaotic ultrasonic excitation method, Wu and Xu [51] take both Lyapunov dimension and the ratio of averaged local attractor variance (ALAVR) as looseness indexes, which can be used to characterize an attractor's whole features and local features. Experimental results show that ALAVR is better

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Ultrasonic guided wave is an effective technique to monitor the preload of bolts. The research status of this field is reviewed in this chapter. At present, considerable advancements have been made in this area in the past two decades. Both linear and nonlinear features of guided waves introduced by bolted joints have been used for bolt preload monitoring. In particular, the transmitted wave energy as a linear feature is the most extensively used for preload monitoring in single bolt and multi-bolt structures. For this reason, the wave energy dissipation method (WED) based on the above features is experimentally compared with time reversal method (TR). The results show that the detection sensitivity of WED method is not very good, especially at the early stage of bolt loosening, and the TR method is more sensitive to bolt loosening. Meanwhile, this chapter also reviews a variety of monitoring methods based on nonlinear features, including contact acoustic nonlinearity (CAN), phase shift caused by acoustic-elastic, and chaotic ultrasound. The above methods can improve the detection sensitivity, but there are also several disadvantages. For example, both acoustic and vibrational excitations are always required for CAN-based methods, and high-frequency sampling frequencies are required for phase shift-based method. The open areas of research, which might

**1.** Accurate and efficient numerical models should be further developed to simulate wave propagation in bolted joints. For example, acoustic-elastic are currently believed to cause the phase shift of transmitted guided-wave signal. However, the current simplified model based on acoustic-elastic cannot effectively explain the phase shift phenomenon. In the meantime, it is very difficult to consider the micro-topography of contact surfaces in FEM models now. Therefore, the establishment of a more accurate and efficient numerical model is expected to

fully study the interaction between jointed interface and guided wave theoretically.

**2.** Improving bolt preload monitoring method is still required. Although bolt preload monitoring methods such as TR and VAM methods can effectively improve the preload detection sensitivity, the detection sensitivity of these methods is not still very good at the early stage of bolt loosening. Moreover, almost all the methods currently require baseline

for bolt preload monitoring, as displayed in **Figure 13**.

need attention, are outlined as follows:

**5. Conclusions**

**Figure 12.** Guided wave signals recorded at different bolt torques: (a) full records and (b) zoomed-in segments [45].

signals of different initial phases to assess bolt loosening. Unfortunately, it does not work in structures with complicated geometries and large number of bolts. Furthermore, changes of the phase shift induced by a bolted joint are rather small and require sensitive equipment with advanced signal-processing capabilities [46]. In addition, because received guided waves are very complex, it is difficult to select the correct time window and the corresponding wave speed to calculate phase shift and the distance between wave path and damage.

#### **4.3. Chaotic ultrasonic excitation**

In addition to stimulate the nonlinear characteristics of the jointed structure, another research idea is to directly use nonlinear ultrasonic excitation. At this time, artificially introducing a nonlinear component in the ultrasonic excitation signal can be used to sensitively estimate the change of structural parameters caused by loosened bolts. Chaotic signal is a wellknown nonlinear signal, but chaotic signals generated by most well-known chaotic systems are unsuitable for guided wave monitoring which is more sensitive to small-scale damage.

**Figure 13.** Looseness indexes versus bolt preload [51]: (a) Lyapunov dimension and (b) ALAVR.

Clayton et al. [20] proposed a bolt preload monitoring approach combining a chaotic excitation method with ultrasonic guided waves. In this method, the chaotic signal is upconverting to an ultrasonic frequency band, and the ultrasound signal with chaotic characteristics is generated to stimulate the bolted structure. The response signal is reconstructed to analyze the phase space, and the nonlinear characteristic quantitatively representing the bolt looseness is extracted. Fasel et al. [49, 50] used similar methods to identify bolt preload in simulations and experiments on single and multi-bolt structures. Recently, based on the chaotic ultrasonic excitation method, Wu and Xu [51] take both Lyapunov dimension and the ratio of averaged local attractor variance (ALAVR) as looseness indexes, which can be used to characterize an attractor's whole features and local features. Experimental results show that ALAVR is better for bolt preload monitoring, as displayed in **Figure 13**.

## **5. Conclusions**

signals of different initial phases to assess bolt loosening. Unfortunately, it does not work in structures with complicated geometries and large number of bolts. Furthermore, changes of the phase shift induced by a bolted joint are rather small and require sensitive equipment with advanced signal-processing capabilities [46]. In addition, because received guided waves are very complex, it is difficult to select the correct time window and the corresponding wave speed

**Figure 12.** Guided wave signals recorded at different bolt torques: (a) full records and (b) zoomed-in segments [45].

In addition to stimulate the nonlinear characteristics of the jointed structure, another research idea is to directly use nonlinear ultrasonic excitation. At this time, artificially introducing a nonlinear component in the ultrasonic excitation signal can be used to sensitively estimate the change of structural parameters caused by loosened bolts. Chaotic signal is a wellknown nonlinear signal, but chaotic signals generated by most well-known chaotic systems are unsuitable for guided wave monitoring which is more sensitive to small-scale damage.

to calculate phase shift and the distance between wave path and damage.

**Figure 13.** Looseness indexes versus bolt preload [51]: (a) Lyapunov dimension and (b) ALAVR.

**4.3. Chaotic ultrasonic excitation**

174 Structural Health Monitoring from Sensing to Processing

Ultrasonic guided wave is an effective technique to monitor the preload of bolts. The research status of this field is reviewed in this chapter. At present, considerable advancements have been made in this area in the past two decades. Both linear and nonlinear features of guided waves introduced by bolted joints have been used for bolt preload monitoring. In particular, the transmitted wave energy as a linear feature is the most extensively used for preload monitoring in single bolt and multi-bolt structures. For this reason, the wave energy dissipation method (WED) based on the above features is experimentally compared with time reversal method (TR). The results show that the detection sensitivity of WED method is not very good, especially at the early stage of bolt loosening, and the TR method is more sensitive to bolt loosening. Meanwhile, this chapter also reviews a variety of monitoring methods based on nonlinear features, including contact acoustic nonlinearity (CAN), phase shift caused by acoustic-elastic, and chaotic ultrasound. The above methods can improve the detection sensitivity, but there are also several disadvantages. For example, both acoustic and vibrational excitations are always required for CAN-based methods, and high-frequency sampling frequencies are required for phase shift-based method. The open areas of research, which might need attention, are outlined as follows:


signals from healthy structures. Therefore, the establishment of a baseline free monitoring method with a high detection sensitivity is an important step for moving toward the goal of real-life in-service implementation.

**Author details**

, Chao Xu<sup>1</sup>

Technology, Beijing, China

**References**

\*, Huaiyu Ren<sup>2</sup>

\*Address all correspondence to: chao\_xu@nwpu.edu.cn

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and Changhai Yan<sup>2</sup>

2 Science and Technology of Space Physics Laboratory, China Academy of Launch Vehicle

Structural Health Monitoring of Bolted Joints Using Guided Waves: A Review

http://dx.doi.org/10.5772/intechopen.76915

177

[1] Peairs DM, Park G, Inman DJ. Practical issues of activating self-repairing bolted joints.

[2] ARP S. Guidelines for Implementation of Structural Health Monitoring on Fixed Wing

[3] Yang J, Chang F-K. Detection of bolt loosening in C–C composite thermal protection panels: I. Diagnostic principle. Smart Materials and Structures. 2006;**15**:581-590

[4] Todd MD, Nichols JM, Nichols CJ, Virgin LN. An assessment of modal property effectiveness in detecting bolted joint degradation: Theory and experiment. Journal of Sound

[5] Madhav AVG, Kiong SC. Application of electromechanical impedance technique for engineering structures: Review and future issues. Journal of Intelligent Material Systems

[6] Peairs DM, Inman DJ. Improving accessibility of the impedance-based structural health monitoring method. Journal of Intelligent Material Systems & Structures. 2004;**15**:129-139 [7] Mascarenas DL, Park G, Farinholt KM, Todd MD, Farrar CR. A low-power wireless sensing device for remote inspection of bolted joints. Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering. 2009;**223**:565-575 [8] Kuznetsov S, Pavelko I, Panidis T, Pavelko V, Ozolinsh I. Bolt-joint structural health monitoring by the method of electromechanical impedance. Aircraft Engineering &

[9] Zagrai A, Doyle D, Gigineishvili V, Brown J, Gardenier H, Arritt B. Piezoelectric wafer active sensor structural health monitoring of space structures. Journal of Intelligent

[10] Parvasi SM, Ho SCM, Kong Q, Mousavi R, Song G. Real time bolt preload monitoring using piezoceramic transducers and time reversal technique—A numerical study with

[11] Raghavan AC, Cesnik CES. Review of guided-wave structural health monitoring. Shock

experimental verification. Smart Materials and Structures. 2016;**25**:085015

1 School of Astronautics, Northwestern Polytechnical University, Xi'an, China

Fei Du<sup>1</sup>

**3.** Bolt-loosening detection methods considering environmental factors for multi-bolt structures should be further developed. Current research limited to a flat lap joint with a single bolt. However, bolted joints with complex structure and multiple bolts are more common in real structures. Meanwhile, little attention has been paid to preload monitoring considering environmental factors which have significant effect on guided wave monitoring. Hence, loosening detection method considering environmental factors for multi-bolt structures is also very important for realizing the application of bolt preload monitoring in real engineering structures.

## **Acknowledgements**

This study is supported by the National Natural Science Foundation of China (Grant Nos. 51705422 and 11372246). This study is also supported by China NSAF Project (Grant No. U1530139) and Fundamental Research Funds for the Central Universities (Grant No. 3102017O QD004).

## **Nomenclature**


## **Author details**

signals from healthy structures. Therefore, the establishment of a baseline free monitoring method with a high detection sensitivity is an important step for moving toward the goal

**3.** Bolt-loosening detection methods considering environmental factors for multi-bolt structures should be further developed. Current research limited to a flat lap joint with a single bolt. However, bolted joints with complex structure and multiple bolts are more common in real structures. Meanwhile, little attention has been paid to preload monitoring considering environmental factors which have significant effect on guided wave monitoring. Hence, loosening detection method considering environmental factors for multi-bolt structures is also very important for realizing the application of bolt preload monitoring in real

This study is supported by the National Natural Science Foundation of China (Grant Nos. 51705422 and 11372246). This study is also supported by China NSAF Project (Grant No. U1530139) and Fundamental Research Funds for the Central Universities (Grant No. 3102017O

of real-life in-service implementation.

176 Structural Health Monitoring from Sensing to Processing

ALAVR ratio of averaged local attractor variance

CAN contact acoustic nonlinearity

DOF degree of freedom

IM impact modulation

, K<sup>2</sup> contact stiffness

TR time reversal

TIΩ tightness index

β sideband index

PZT piezoelectric transducers

SHM structural health monitoring

VAM vibro-acoustic modulation

ΔD tightness index based on Lyapunov dimension

WED wave energy dissipation

FEM finite element method

engineering structures.

**Acknowledgements**

QD004).

K1

**Nomenclature**

Fei Du<sup>1</sup> , Chao Xu<sup>1</sup> \*, Huaiyu Ren<sup>2</sup> and Changhai Yan<sup>2</sup>

\*Address all correspondence to: chao\_xu@nwpu.edu.cn

1 School of Astronautics, Northwestern Polytechnical University, Xi'an, China

2 Science and Technology of Space Physics Laboratory, China Academy of Launch Vehicle Technology, Beijing, China

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## *Edited by Magd Abdel Wahab, Yun Lai Zhou and Nuno Manuel Mendes Maia*

Structural health monitoring (SHM) has attracted more attention during the last few decades in many engineering fields with the main aim of avoiding structural disastrous events. This aim is achieved by using advanced sensing techniques and further data processing. SHM has experienced booming advancements during recent years due to the developments in sensing techniques. The reliable operation of current, sophisticated, man-made structures drives the development of incipient reliable damage diagnosis and assessment. This book aims to illustrate the background and applications of SHM from both sensing and processing approaches. Its main objective is to summarize the advantages and disadvantages of SHM methodologies and their applications, which may provide a new perspective in understanding SHM for readers from diverse engineering fields.

Published in London, UK © 2018 IntechOpen © chombosan / iStock

Structural Health Monitoring from Sensing to Processing

Structural Health Monitoring

from Sensing to Processing

*Edited by Magd Abdel Wahab, Yun Lai Zhou* 

*and Nuno Manuel Mendes Maia*