Structure damage localization with ultrasonic guided waves based on a time–frequency method

Signal Processing 96 (2014) 21–28

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Structure damage localization with ultrasonic guided waves based on a time–frequency method Daoyi Dai, Qingbo He n Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026, PR China

a r t i c l e i n f o

abstract

Article history: Received 20 November 2012 Received in revised form 3 April 2013 Accepted 27 May 2013 Available online 7 June 2013

The ultrasonic guided wave is widely used for structure health monitoring with the sparse piezoelectric actuator/transducer array in recent decades. It is based on the principle that the damage in the structure would reflect or scatter the wave pulse and thus, the damagescattered signal could be applied as the feature signal to distinguish the damage. Precise measurement of time of the flight (TOF) of the propagating signal plays a pivotal role in structure damage localization. In this paper, a time–frequency analysis method, Wigner– Ville Distribution (WVD), is applied to calculate the TOF of signal based on its excellent time–frequency energy distribution property. The true energy distribution in the time– frequency domain is beneficial to reliably locate the position of damage. Experimental studies are demonstrated for damage localization of one-dimensional and twodimensional structures. In comparison with traditional Hilbert envelope and Gabor wavelet transform methods, the proposed WVD-based method has better performance on the accuracy and the stability of damage localization in one-dimensional structure. In addition, the proposed scheme is validated to work effectively for damage imaging of a two-dimensional structure. & 2013 Elsevier B.V. All rights reserved.

Keywords: Ultrasonic guided wave Time–frequency analysis Wigner–Ville distribution Damage localization Damage imaging

1. Introduction The ultrasonic guided wave has been widely acknowledged as an effective approach for structure damage identification and health monitoring in recent years. Conventional guided wave techniques always need bulky and complicated instruments as well as much human interference. For example, ultrasonic probes could generate or collect guided wave with excellent precision and controllability. However, they always need couplant between the probes and the structure surface to be detected, which would bring great interference into the system. Electro-magnetic acoustic transducers (EMATs) could generate shear horizontal mode guided wave effectively and realize non-contact detection, but their applications are normally limited to magnetic materials. Laserbased ultrasonic instruments have high resolution and great

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precision, but the high cost of the equipment limits its application in engineering [1,2]. As the technology of piezoelectric materials develops, the combination of ultrasonic guided wave and spare piezoelectric actuators or transducers becomes more applicable to this area with the merits of low cost, full range, easy integration, wide frequency response, etc. [2,3]. Several aspects have been taken into study by recent researchers, such as the damage degree assessment against the amplitude changes of the guided wave, excitation of the effective wave mode, localization of the damage, and optimal distribution of the piezoceramics patch array. Both numerical and experimental studies have been conducted in the past decade [4–11]. This paper focuses on the structure damage localization with ultrasonic guided wave provided by the piezoelectric actuators. The basic principle of the method for structure damage localization could be described as below [8,9]: the guided wave pulse is put into the structure with the piezoceramics patch bonded on it and collected by another piezoceramics patch. If there is damage in the structure, the

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propagating guided wave in the structure would be reflected or scattered by the damage. In order to distinguish damage, the difference signal is acquired by the subtraction of the damaged guided wave signal with the damage-free signal, and it is the feature signal that carries the damage information. Based on the difference signal, the structure defect could be detected by geometry localization or imaging demonstration through different paths of the piezoceramic array. For the structure damage localization, no matter the geometrical or imaging method, the key point in the process is to define the arrival time of the signals and acquire the time of the flight (TOF) of the signals. They directly determine the precision of the localization. The approach based on acquisition of the difference signal is reliant on defects causing a measurable change in the scattering. Its success depends on how to analyze the residual signal after the subtraction. The difference signal is always rather weak because the propagation of the ultrasonic guided wave in the structure is rather complicated with the property of multiple modes, frequency dispersion and the reflection interruption from the borders. Low signalto-noise ratio (SNR) of the difference signal always causes a great error for the calculation of the TOF of the signal. And it would further influence the damage localization in the structure. The traditional methods to calculate the TOF of the propagating signals mainly include the thresholding value method, correlation coefficient method, Hilbert envelope method and wavelet transform method. Ref. [10] realizes the guided wave-based pipeline defect characterization with the correlation coefficient to calculate the TOF of the feature signal. Refs. [9,12] utilize Hilbert envelope to define the arrival time of guided wave signal and explore the damage imaging of plate structure based on a PZT array. Damage detection in plate structure based on the Gabor wavelet transform method is explored in Ref. [11]. These methods may not locate the damage precisely and stably for rough time estimation due to the interruption of noise or approximate energy distribution (e.g., wavelet transform). Moreover, time–frequency analysis has been widely used for structure health monitoring based on its excellent ability to analyze non-stationary signal [13–15], and as well it is verified to be quite effective to deal with guided wave signal [16–18]. Researchers have applied time–frequency analysis to various aspects on the guided wave technique, e.g., analyzing the frequency diversion property of guided wave [16], estimating the arrival time of certain wave modes [17,18] and evaluating the degree of structure damage [18]. On the structure damage localization, current studies mainly use the damage information distributed in the time–frequency domain as the diagnostic evidence. However, there is still further work to be discussed on how to improve the accuracy by using the property of time–frequency analysis. In addition, currently there are little works addressing on the structure damage imaging based on time–frequency analysis. This paper considers employment of true time–frequency energy distribution for improving the localization accuracy of structure damage by combining the ultrasonic guided wave approach with the Wigner–Ville Distribution (WVD) method. The proposed scheme is based on the excellent merit of the WVD in exhibiting true time–frequency energy

distribution. It has the anti-noise property and can reveal true energy distribution of the damage, so it is supposed to outperform current Hilbert envelope and wavelet transform methods in estimating the TOF of the guided wave signal. This paper first presents the WVD-based principle of damage localization in one-dimensional structure. Furthermore, a feature function, which is extracted from the time–frequency distribution, is applied as the fundamental of the damage imaging algorithm for two-dimensional plate structure. The rest of this paper is organized as follows. The theoretical background of the proposed study is introduced in Section 2. In Section 3, the experimental studies are set up to verify the proposed scheme on a one-dimensional structure for damage localization and a plate structure for damage imaging. Finally, conclusions have been remarked in Section 4. 2. Theoretical background 2.1. Principle of the WVD-based method As introduced before, the TOF plays an important role in localization of the structure damage. Furthermore, choosing a proper baseline to distinguish the arrival time of the guided wave pulse is the pivotal step of calculating the TOF. This paper applies the method of time–frequency distribution (TFD) to define the arrival time of signal. Since the TFD can exhibit the signal energy in the time– frequency domain, so we can achieve a better knowledge on how the energy is changed along the time. To get the TFD for a signal, various time–frequency analysis methods are available. The short-time Fourier transform (STFT) and the wavelet transform are two of many common methods. However, they can only express the approximate energy distribution in the time–frequency domain [19]. In this paper, the Wigner–Ville distribution (WVD) is employed based on the theory that WVD can well describe true time–frequency energy distribution of a signal [19]. The WVD is motivated by the time–frequency energy density which describes the signal's energy distribution in terms of both time and frequency. Mathematically, the WVD is computed by correlating the signal with a time and frequency translation of itself as expressed below [19]: Z  τ  τ WV x ðt; ωÞ ¼ x t þ xn t− e−jωτ dτ ð1Þ 2 2 The WVD is a TFD of bilinearity, which is more suitable to analyze nonlinear and non-stationary signals. Let XðωÞ denote the Fourier transform of the signal x(t), then from the time/frequency marginal property of WVD, we can have 1 2π

Z

þ∞

−∞

Z WV x ðt; ωÞ dω ¼

Z

¼ Z

þ∞ −∞

−∞

Z

þ∞ −∞

Z þ∞  τ  τ 1 x t þ xn t− e−jωτ dω dτ 2 2 2π −∞

  τ  τ x t þ xn t− δðτÞ dτ ¼ xðtÞj2 2 2

WV x ðt; ωÞdt ¼ Z

¼

þ∞

þ∞ −∞

e−jωτ

Z

þ∞ −∞

þ∞ −∞

Z

þ∞ −∞

ð2Þ

 τ  τ x t þ xn t− e−jωτ dt dτ 2 2

xðtÞxn ðt−τÞdt dτ ¼ jXðωÞj2

ð3Þ

D. Dai, Q. He / Signal Processing 96 (2014) 21–28

Based on Eqs. (2) and (3), we can readily obtain the following relationship: Z þ∞ Z þ∞  1 τ  τ x t þ xn t− e−jωτ dt dω 2π −∞ −∞ 2 2 Z þ∞ Z þ∞ 1 jXðωÞj2 dω ¼ jxðtÞj2 dt ð4Þ ¼ 2π −∞ −∞ Eq. (4) illustrates that the energy contained in WVx(t, ω) is equal to the energy in the original signal x(t). Theoretically, the WVD method is the most energy-concentrated distribution in Cohen's class, and there is no energy smearing on the frequency plane of WVD [19]. It should be also noted that on the time–frequency domain of WVD, there are cross-terms which need to be eliminated to avoid misleading information about the signals [19]. To reduce the adverse effect of the crossterms of WVD, the Smoothed Pseudo-Wigner–Ville Distribution (SPWVD) [19] is employed in this study to smooth WVD in time and frequency independently as shown as  τ  τ SPWV x ðt; ω; g; hÞ ¼ ∬ gðuÞhðτÞx t−u þ xn t−u− e−jωτ du dτ 2 2

ð5Þ

where g and h are two real even windows. According to the excellent time–frequency energy distribution property of the WVD method, we define a function for a specific signal u(t) as Q u ðtÞ ¼ SPWV u ðt; ωc Þ

ð6Þ

where ωc is referred to the frequency index value of the peak point on the SPWVD of the analyzed signal. The Qu(t) exhibits the useful time-domain energy distribution referred to the damage information of the designated signal u(t). The definition of Qu(t) has two important properties: one is the anti-noise property as it can be seen as the filtered energy in frequency with an extremely narrow passband at the center frequency ωc (corresponding to the exact damage information) and so the interference from background noise and other modes of the guided wave can be eliminated; the other is that it reveals the true energy distribution along time so the damage with elevated energy can be well identified inside. Based on these two properties, the Qu(t) can be used to accurately estimate the TOF information of the analyzed signal. Furthermore, Qu(t) is also adopted as the feature function for damage imaging of the two-dimensional structure and it would be introduced later in detail. 2.2. Principle of damage localization for one-dimensional structure The basic principle of the damage localization based on the ultrasonic guided wave can be illustrated in Fig. 1 on a beam structure with the dimension L  W  D. The excitation guided wave is put into the structure by the piezoceramics (PZT A) bonded on the beam, and the output signal is received by PZT B. If there is damage in the structure, the wave pulse propagating inside would be reflected or scattered by the damage. Both the input excitation signal xA(t) and the output signal at PZT B, xB (t), are collected by the data acquisition system before and after the damage is set. Then the damage-scattered signal xD ðtÞ is acquired by the subtraction of damage output

23

Fig. 1. Illustrative diagram of the damage localization for a one-dimensional structure.

signal and the healthy output signal: xD ðtÞ ¼ xdamage ðtÞ−xhealth ðtÞ B B

ð7Þ

ðtÞ and xdamage ðtÞ represent the output signal where xhealth B B of PZT B before and after the structure is damaged respectively. In Fig. 1, the distance between the PZT A and PZT B is l0 and T0 represents the arrival time for signal propagation from PZT A to PZT B. x denotes the distance between PZT B and the damage location and T1 denotes the interval from the time when PZT B receives the input excited signal from PZT A to the time when PZT B receives the signal reflected by the damage. Suppose that the spread velocity of the ultrasonic guided wave pulse stays constant after being scattered by the damage [9,20,21], we can get the relationship as below: l0 2x ¼ T1 T0

ð8Þ

The value of l0 is fixed and the TOF T0, T1 would be defined by the signal processing. Then we can calculate the value of x and the damage location is hence determined in a one-dimensional structure. Defining the TOF of the signals plays an extremely important role to locate the damage position precisely. In this paper, we choose the SPWVD introduced in Section 2.1 as the signal processing method to calculate the arrival time of the signal. As exhibited in Fig. 1, let tA, tB and tD denote the arrival time of the excitation signal xA(t), output signal xB(t) and the difference signal xD(t), respectively, the arrival time could be defined as follows: 8 t ¼ t c jmaxðQ xA ðtÞÞ; > > t > A < t B ¼ t c jmaxðQ xB ðtÞÞ; t > > > t ¼ t jmaxðQ ðtÞÞ: : D

c

t

ð9Þ

xD

In the equation, maxð⋅Þ denotes the peak point tc of the t function Q(t). And then the propagating time of the guided wave pulse in the structure could be calculated as (

T 0 ¼ t B −t A ; T 1 ¼ t D −t B :

ð10Þ

With the definition of the TOF T0 and T1, the damage location in one-dimension structure could be calculated by Eq. (8). Due to the excellent energy distribution property, the WVD-based method is hoped to be rather effective as verified in the following experimental study.

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D. Dai, Q. He / Signal Processing 96 (2014) 21–28

2.3. Scheme of damage imaging for two-dimensional structure Consider that N piezoelectric patches in a spatially distributed array are bonded on a plate (PZT 1, 2, …, N), as shown in Fig. 2. Taking the reciprocity into account, there would be N(N−1)/2 transmit–receiver paths for the guided wave propagation in the plate. For each path, the principle of damage localization is also based on the signal scattering or reflection on the damage, as introduced in Section 2.2. The synthesis of location information in each path by the transducer array makes up the overall view of the localization of the two-dimensional structure [20,21]. Due to the difference of the transducers and the different propagating distances, the received signal should be normalized and compensated [21]. Taking one of the paths for example, the received signals of actuator/transducer pairs are first normalized scaled according to sffiffiffiffiffi xj ðtÞ dj ð11Þ xj ðtÞ ¼ maxðxj ðtÞÞ d1 where xj(t) is the output guided wave signal being collected at the receiving end of the transmit–receiver pair, and xj ðtÞ is the normalized form of xj(t) after the distance compensation, and maxð⋅Þ denotes the maximum value of the signal. dj represents the distance between the actuator and the transducer of the jth path and d1 is the distance of the transmit–receiver pair which is set as the referenced path. In this way the signal is normalized so that the amplitude of the direct arrival signal is unity for the first transducer pair (the reference pair) and pffiffiffi the others are scaled appropriately to reflect the 1= R attenuation in amplitude with distance [9,21]. To distinguish the damage, the output signals are collected before and after the damage is set, respectively. Then the difference signal, which carries the information of the damage scatter, is acquired by the subtraction of the healthy output signal from the damage output signal: xj dif f ðtÞ ¼ xj damage ðtÞ−xj health ðtÞ

f In the equation, Q dif ðtÞ represents useful time-domain j energy distribution information referred to the damage f information in the difference signal xdif ðtÞ and can be got j as defined in Section 2.1. In addition, the cg is the group velocity of the target guided wave pulse, and dx,y is the distance between a point (x, y) and the transducer pair. Here dx,y could be calculated by the equation as below:

dx;y ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxTj −xÞ2 þ ðyTj −yÞ2 þ ðxRj −xÞ2 þ ðyRj −yÞ2

ð14Þ

where ðxTj ; yTj Þ and ðxRj ; yRj Þ are the coordinates of the transmitter and the receiver, respectively. Taking all the transducer pairs into account, the damage image of the two-dimensional structure could be acquired by f Iðx; yÞ ¼ ∑I dif ðx; yÞ j

ð15Þ

In this way we could distinguish the damage location in a two-dimensional structure by imaging. The scheme is summarized as exhibited in Fig. 3. This kind of image generation method is actually based on the time delay of signal propagating in the structure, just similar to the principle of the damage localization in one-dimensional structure. Here the SPWVD makes a great contribution to

ð12Þ Fig. 3. Scheme of the damage imaging for a two-dimensional structure.

The difference signal can be used to form an image by mapping them into spatial coordinates:   f dif f dx;y ðx; yÞ ¼ Q ð13Þ I dif j j cg

Fig. 2. Illustrative diagram of the damage localization for a two-dimensional structure.

Fig. 4. Experimental setup of damage localization for one-dimensional structure.

D. Dai, Q. He / Signal Processing 96 (2014) 21–28

the imaging by providing a precise energy distribution of the difference signal. 3. Experimental results 3.1. Damage localization of a beam structure As demonstrated in Section 2.2, the experiment of onedimensional damage localization for a beam structure is set up in Fig. 4. The experiments use an aluminum beam with the dimension L¼1000 mm, W¼200 mm, D¼2 mm. In the experimental study, a 20 mm diameter cylinder (with a weight of 137 g) was positioned on the beam to simulate the damage. The mass was bonded to the plate with epoxy adhesive to act as a linear scatterer [9]. The distance between PZT A and PZT B is l0 ¼180 mm, and distance between the damage position and PZT B is set as 60 mm. Since the method is based on the difference signal, we try the best to make the external environment unchangeable in the procedure of the experiment to guarantee that the difference signal is only related to the damage being set on the beam.

25

As demonstrated by the dispersion curve of guided wave in Fig. 5, for the structure with a certain thickness, an excitation signal with a proper frequency could bring less wave modes in the structure, which would make the wave propagation less complicated. Usually, S0 or A0 mode is the first choice for damage detection [16,22]. As indicated in Fig. 5, through selecting the low frequency S0 mode, the phase and group velocities are approximately independent of frequency. In this study, the excitation signal on PZT A is a 5 cycle wave pulse by windowing an 85 kHz sine wave with a Hanning function. Through the experimental study, we find that guided wave pulse with the center frequency of 85 kHz could excite the outstanding S0 mode in the plate. That is why we choose 85 kHz as the excitation frequency and use the S0 mode wave packet as the target signal to locate the damage. The amplitude of the signal is 15Vp-p. The excitation signal is generated by an arbitrary waveform generator (Type RIGOL DG 1022) and then both the excitation signal (at PZT A) and the output signal (at PZT B) are recorded by a digital oscilloscope (Type TEK DPO2012). Fig. 6(a) exhibits the waveforms of the input excitation signal, the output healthy signal, the output damaged

Fig. 5. Dispersion curve of guided wave in an aluminum plate structure: (a) phase velocity and (b) group velocity.

Fig. 6. Signal processing for TOF estimation: (a) original waveforms, (b) Hilbert envelopes, and (c) Gabor wavelet transform for (1) input excitation signal, (2) output healthy signal, (3) output damaged signal, and (4) difference signal, respectively.

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D. Dai, Q. He / Signal Processing 96 (2014) 21–28

signal and the difference signal. The difference signal, acquired by the subtraction of the healthy signal from the damaged signal, carries the information about the damage. As demonstrated in Fig. 6(a), the difference signal is rather week and has a low SNR, which may cause notable errors for damage localization. As aforementioned, TOF plays a key role in localization of the damage position. In the experiment three methods are applied to calculate the arrival time of the signal for a comparison. Fig. 6(b) exhibits the Hilbert envelope of the signals in Fig. 6(a). The arrival time of ultrasonic guided wave pulse is defined as the value of time related to the curve peak. The curve is not smooth enough because of the interruption of the noise, especially for the difference signal, which may cause large errors. The Gabor-wavelet transform only considers the information at a certain scale, so it has a de-noising effect for the analyzed results. As demonstrated in Fig. 6(c), the Gabor-wavelet transform method outperforms the Hilbert envelope method greatly. Fig. 7 demonstrates the SPWVD of the signals in Fig. 6(a). In the TFDs, the peak points correspond to the most concentration of the energy. The time value of these points is taken as the arrival time of the wave pulse. Besides the de-noising effect similar to the Gabor-wavelet transform method, the WVD-based method also has the excellent energy distribution

merit in representing the damage. As Table 1 shows the proposed WVD-based method illustrates a precise localization for the damage position and it works with good repeatable property. Comparing the results of three methods as exhibited in Table 2, the WVD-based method can work much better for the damage localization than the Hilbert envelope and Gabor-wavelet transform methods. Benefited from the excellent time–frequency energy distribution property of the WVD, the proposed WVD-based method makes the Table 1 Multiple measurements of the damage localization for beam structure based on SPWVD analysis. Experiment No.

TOF of excitation TOF of damage signal T0 (ms) scattering signal T1 (ms)

Damage position x (mm)

1 2 3 4 5 6 7 8

0.0424 0.0422 0.0424 0.0424 0.0424 0.0424 0.0424 0.0422

60.28 59.00 59.86 61.13 61.55 59.01 59.43 60.99

0.0284 0.0278 0.0282 0.0288 0.0290 0.0278 0.0280 0.0286

Fig. 7. SPWVDs of signals: (a) the input excitation signal; (b) the output healthy signal; (c) the output damaged signal; and (d) the difference signal.

D. Dai, Q. He / Signal Processing 96 (2014) 21–28

localization more precise and more stable. The Gaborwavelet transform method could get a repeatable result; however, the method only represents an approximate energy distribution and thus it causes a greater error than the WVD-based method. Moreover, the Hilbert envelope method is sensitive to the noise and the results are rather unreliable. As a result, the experimental results of damage localization for one-dimensional structure verify that the WVDbased time–frequency method could be applied for structure health monitoring effectively. The true time–frequency energy distribution property of the WVD could make the evaluated results more reliable and more stable. In the next experiment, we will manipulate the WVDbased method for two-dimensional damage localization.

3.2. Damage imaging of a plate structure According to the basic scheme introduced in Section 2.3, the experiment is operated on an 800  600  2 mm aluminum plate. The experimental setup is similar to that of damage localization for the beam structure. The positions of three piezoceramics patches are A (50, 150), B (230, 30), C (230, 270). The damage is simulated in the same way as the experiment above, and the position is O (150,150). Note that a 250  300 mm area in the middle of the plate is chosen as the imaging area and the coordinates of the PZT transducers and the set damage are referred to the borders of this area, as demonstrated in Fig. 8(a). Fig. 8(b) exhibits the experimental setup used for damage imaging of the plate aluminum.

27

The excitation signal is the 5 cycle wave pulse by windowing a sine wave with a Hanning function. The center frequency of the signal is 120 kHz and the amplitude is 20Vp-p. The signals are collected on three paths (AB, AC, BC) respectively. The imaging procedure follows the description in Section 2.3 and the result is demonstrated in Fig. 9. In the figures the symbols “+” represent the positions of PZTs A, B and C, and the “n” marks the correct location of the set damage. Fig. 9(a) demonstrates the imaging of the undamaged plate. After the damage is set, the result of the damage imaging of two-dimensional structure is exhibited in Fig. 9(b). Considering about the complexity of the guided wave pulse propagating in the plate, we only take the triangle area enclosed by PZTs A, B, C as the effective imaging area as illustrated in the shadowed area in Fig. 8. Comparing Fig. 9(a) and (b), it can be concluded that the proposed imaging method could precisely locate the damage in a two-dimensional structure. This verifies that the proposed combination of the ultrasonic guided wave approach and the WVD-based time–frequency method is indeed an effective way for structure damage detection. 4. Conclusion In this paper, the damage localization of one-dimensional structure and the damage imaging of two-dimensional structure are experimentally studied. The main contribution of this paper is the combination of the ultrasonic guided wave approach with the WVD-based time–frequency analysis method for precision damage localization. Through the

Table 2 Comparison results of Hilbert envelope, Gabor-wavelet transform and SPWVD methods for damage localization. Method

Correct position x0 (mm)

Hilbert envelope Gabor-wavelet transform SPWVD

60

Average position (mm) x ¼ 1n ∑ðx1 þ ⋯ þ xn Þ

Standard deviation (mm) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Δx ¼ n−1 ∑ðxi −xÞ2

63.47 67.58 60.15

8.35 2.39 0.99

Fig. 8. Exhibition of the experiment: (a) illustration of imaging area and the distribution of the piezoelectric actuator/transducer pairs and (b) experimental setup.

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D. Dai, Q. He / Signal Processing 96 (2014) 21–28

their help in providing valuable comments and suggestions to improve the paper. References

Fig. 9. Imaging result of the plate structure: (a) undamaged plate and (b) damaged plate.

experimental studies, the combination has been proved to be rather effective for damage localization in one-dimensional and two-dimensional structures. The excellent performance of the proposed WVD-based scheme for damage localization is essentially due to that the WVD can most exactly express the true time–frequency energy distribution of the damage signal. On the merits of precise and stable localization, the proposed scheme is helpful to explore damage detection in real engineering applications, such as defect detection of the pipeline. Moreover, the proposed damage imaging algorithm provides a new approach for two-dimensional structure damage localization, which has a great potential to build a better structure health monitoring system.

Acknowledgments This work is supported by the National Natural Science Foundation of China under Grants 11274300 and 51005221. The anonymous reviewers are sincerely appreciated for

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