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Wavelet Network Approach for Structural Damage Identification Using Guided Ultrasonic Waves Hossein Zamani Hosseinabadi, Behzad Nazari, Rassoul Amirfattahi, Hamid Reza Mirdamadi, and Amir Reza Sadri
Abstract— An appropriate wavelet network (WN) approach is introduced for detecting damage location and severity of structures based on measured guided ultrasonic wave (GUW) signals. An algorithm for establishing a multiple-input multiple-output fixed grid wavelet network (FGWN) is proposed. This algorithm consists of three main stages: 1) formation of wavelet latticel; 2) formation of wavelet matrix; and 3) optimizing the wavelet structure by means of orthogonal least square algorithm. Three damage-sensitive features are extracted from the GUW signals: 1) time of flight; 2) normalized damage wave amplitude; and 3) normalized damage wave area. These features are considered as the FGWN inputs and the damage location and severity are estimated. The established FGWN is used for identifying damage location and severity in a structural beam. The beam is investigated and simulated in different damaged conditions. Computed finite element method (FEM) simulation signals are used for training the FGWN. Some other FEM simulation signals, as well as measured experimental ones are used for testing. The proposed damage identification method is compared with three artificial neural network (ANN)-based algorithms. In addition to some other benefits of the proposed WN-based algorithm over ANN-based methods discussed in this paper, the results show that our approach performs better in both damage location and severity detections than other methods. Index Terms— Artificial neural network (ANN), damage identification, guided ultrasonic wave (GUW), structural health monitoring (SHM), wavelet network (WN).
I. I NTRODUCTION
D
UE to increasing awareness of the importance of damage diagnosis systems, guided ultrasonic wave (GUW) technique are widely used for detecting different damage types in aerospace, mechanical, and civil engineering structures in recent years. This technique is used to detect, or indirectly measure the existence, location, severity of damage, and the remaining life of structure under consideration in real applications [1]. The UWs are very sensitive to the discontinuities of structures. Hence, they can be employed for damage identification purposes, especially, for online inspection of in-service
Manuscript received July 29, 2013; revised November 6, 2013; accepted November 13, 2013. The Associate Editor coordinating the review process was Dr. Ruqiang Yan. H. Z. Hosseinabadi, B. Nazari, R. Amirfattahi, and A. R. Sadri are with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156, Iran. H. R. Mirdamadi is with the Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2014.2299528
structures, i.e., structural health monitoring (SHM). Several signal processing approaches are developed to extract damage features from measured GUW signals. A great number of these approaches are based on wavelet transform (WT). Wavelet analysis gives a picture of time-frequency spectrum of a signal; thus, it is well suited for analyzing nonstationary signals, such as GUWs [2]. Taha et al. [3] performed a survey of WT applications in the SHM and GUW-based damage detection methods. In a general SHM signal processing method, after extracting damage-sensitive features, a pattern recognition technique is required to estimate damage severity and location automatically [2]. A great number of studies are carried out to recognize damage patterns in different damage detection and fault diagnosis applications. Statistical pattern recognition using time series modeling is employed for the SHM applications in [4]. The matching pursuit approach is used in [5] by employing the dispersion-based chirp functions for damage detection. Frequency domain analysis based on the segmented chirp Z transform is introduced in [6] to detect the crack growth in structural materials. Warped basis pursuit analysis for damage detection is studied in [7]. Fractal dimension tomography algorithm is employed in [8] for damage detection in composites. The signal spectra of current and vibration are correlated for online half-broken-bar detection on induction motors in [9]. A new dominant-feature identification algorithm is introduced in [10] for condition monitoring applications. Wavelet decomposition-based decision-level fusion technique is used in [11] to recognize fault patterns in induction motors. Acoustic emission feature quantification based on empirical mode decomposition is used in [12] for health monitoring of rotational machine. Hilbert–Huang transform-based vibration signal analysis is performed in [13] for machine health monitoring. Artificial intelligence field approaches gain special popularity in recent studies. Genetic algorithm [14]–[16], artificial neural network (ANN) [17]–[25], support vector machine [26]–[30], and fuzzy logic [31]–[35] are some branches of artificial intelligence that are used for structural damage detection and fault diagnosis applications. One of the most effective computational intelligence methods for pattern recognition that has been widely used for various applications in different areas is wavelet network (WN). The WN takes advantage of the characteristics of the WT in signal processing and the ANN capacity of universal approximation [36]–[38]; hence, it has a great potential to be
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used in a vast amount of applications. Some disadvantages of other computational intelligence methods are overcome by means of the WN. Due to time-frequency localization of the WT, the WNs are more robust than neural networks against contaminated data [39]. Another advantage of the WNs over similar neural network architectures is the possibility of optimizing the WN structure by means of efficient deterministic construction algorithms [40]. Similar to some other fields, the WNs are employed in some studies in the measurement field. Such studies are using the WNs for time-of-flight measurement of ultrasonic pulse echoes [41] and using adaptive WNs for fast harmonic estimation of stationary and time-varying signals [42]. In this paper, due to beneficial characteristics of WNs in signal processing and pattern recognition, we would propose a WN-based algorithm to be used for GUW-based structural damage identification applications for the first time. At first, a specific multiple-input multiple-output fixed grid wavelet network (FGWN) with one hidden layer is proposed. Our proposed FGWN consists of nine steps: 1) normalizing; 2) selecting the mother wavelet; 3) choosing the scale and shift parameters; 4) forming a wavelet lattice; 5) screening; 6) forming a wavelet matrix; 7) performing orthogonal least squares (OLS) algorithm; 8) selecting the number of neurons; and 9) calculating the weight coefficients of neurons. Our proposed wavelet network is an advanced version of the FGWN used in [46], a multiple-input single-output FGWN proposed for segmentation of dermoscopy images. Afterward, based on the proposed FGWN, a novel automatic damage identification algorithm is proposed to be used in GUW-based damage identification applications. In our proposed algorithm, three features, including time of flight (ToF), normalized damage wave amplitude, and normalized damage wave area are extracted from the GUW signals measured from the structure under test. Then, these features are applied to the FGWN, and the location and severity of the structure damage are estimated by the FGWN automatically. To demonstrate the practical utility of the proposed algorithm, the algorithm is employed to quantitatively characterize damage created in a thick steel beam. As mentioned in [43], most of the GUW-based damage identification studies are subject to thin structures. However, Sun et al. [44] used the GUWs for detecting structural damage in a thick steel beam. In this paper, a thick beam similar to the structure used in [44] is considered. The structural beam is investigated and simulated for different conditions of damage. Furthermore, experimental GUW signals and signals resulting from finite element method (FEM) simulations are measured. Seventy FEM simulation signals are used to train the FGWN. Another seven FEM simulation signals, in addition to seven experimental GUW signals are used to test the FGWN. The practicality of the proposed method in damage identification applications can be appropriately illustrated by the results obtained from applying the method on the established experimental set up test signals and simulation ones. The organization of this paper is as follows. In Section II, the proposed damage identification algorithm is introduced. In Section I, basic concepts of the WN are discussed, a suitable
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TABLE I WN T YPES [46]
FGWN algorithm is proposed, and the proposed damage identification method is introduced. In Section III, FEM simulations and experimental setup are explained. The case study is damage location and severity detection in a thick steel beam. In Section IV, the results of damage identification are represented and the simulation results of the proposed algorithm are compared with other methods. Finally, in Section V, some concluding remarks are drawn. II. P ROPOSED DAMAGE I DENTIFICATION A LGORITHM At first, three damage-sensitive features are extracted from GUW signals for estimating the damage location and severity. Afterward, these features are applied to an established FGWN. The structures of the WNs, the proposed FGWN, and the proposed algorithm for damage identification are described in the following sections. A. Wavelet Network The WN takes advantage of the characteristics of the WT, for example, denoising, finding function singularities and the recovery of the characteristic information, and ANN capacity of universal approximation. There are two types of wavelet networks: 1) adaptive wavelet networks (AWNs) and 2) FGWNs [45]. The characteristics of these two networks are shown in Table I. Because of some shortcomings of the AWNs (complex calculations, sensitivity to initial values, and the problem of measuring initial values), their application is limited [45]. In the AWNs, in the same way as neural networks, initial values of network parameters (including weights of neurons, shifts, and scales of wavelets) are selected either randomly or using other methods. These parameters are then updated in the training stage by means of such techniques as the steepest descent gradient or back propagation. Unlike the AWNs, in the FGWNs, the outer parameters of the network, i.e., the number of neurons, the values of scale, and shift parameters, are determined beforehand and only the inner parameters of the network, i.e., weights of neurons, are calculated through such methods as least squares [40]. Thus, in the FGWNs, there are no need to select random initial values for parameters or to use gradient descent, back propagation, or other iterative methods. Because of the FGWN benefits, the FGWN is employed in this paper. Consider a multiple-input multiple-output FGWN with c outputs, d inputs, x = (x 1 , x 2 , . . . , x d )T , and q neurons in the hidden layer. Each output signal of this FGWN can be
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Fig. 1.
Three layered multiple-input multiple-output fixed grid wavelet.
Fig. 2.
calculated as yp =
q
wi, p ψm i ,ni (x) =
i=1
3
Wavelet lattice for 2-D inputs (d = 2).
data to the range [a, b] : q
wi, p 2−m i d/2 ψ 2m i x − ni
(1)
i=1
where wi, p , i = 1, 2, . . . , q and p = 1, 2, . . . , c are weight coefficients, ψm q ,nq are dilated and translated versions of the mother wavelet function ψ : d → , and m i , ni are scale and shift vector parameters, respectively. This network structure is illustrated in Fig. 1. According to the above definitions, any function f ∈ L 2 d could be approximated using a FGWN [40].
B. Building FGWN One of the major advantages of the WNs over other neural architectures is the availability of efficient constructive algorithms for defining the network structure [40]. In a FGWN, after determining the structure, the weights wi, p in (1) could be obtained through linear estimation techniques. In this paper, a constructive algorithm is proposed to build a multiple-input multiple-output FGWN. Then, the FGWN is used for damage identification applications for the first time. This algorithm could be described as follows. Notation: In this paper, we use upper case bold letters for showing matrices, lower case bold letters for vectors, and lower case italic letters for scalars. Algorithm: Suppose we have M input–output data. The input matrix is in the form X = [x(1), . . . , x(k) , . . . , x(m) ] (k) (k) T where x(k) = x 1 , . . . , x d is the d−dimensional input vector. The FGWN structure is determined with a nine-stage algorithm. 1) Normalization: Varying the input data within a wide range could reduce the efficiency of FGWN. Thus, the first stage normalizes the vector inputs to a limited range in order to avoid data scattering [47]. If for kth input Tk = max{xr(k) }, tk = min{xr(k) }, r = (1, . . . , d) then the following equation is used for mapping the input
(k) xr,new = (k)
b − a (k) aTk − btk x + Tk − tk r,old Tk − tk
(2) (k)
where xr,old is the r th input of kth sample, and xr,new is its value after the normalization all (k)process. Similarly, (k) (k) T of the vector values xnew = x 1,new , . . . , x d,new fall within the range of [a, b] . From now on, we show the (k) as x. xnew 2) Selecting the Mother Wavelet: Due to the ease of frame generation in (1), a multidimensional single scaling wavelet frame is employed [48]. In addition, Mexican hat wavelet is usually used in signal processing algorithms due to some of its desirable characteristics, such as convenient calculations, ease of implementation, and leading good results, as implied in [49]. Therefore, in this paper, the d−dimensional Mexican hat wavelet is used to implement FGWN. This wavelet is expressed as (3) ψ(x) = d − x2 exp − x2 /2 . 3) Choose the Scale and Shift Parameters: In this stage, the minimum and the maximum scale levels are employed in the form [m min , m max ] and shift parameter are T employed in the [n 1 , . . . , n t , . . . , n d ] , form n j = where n t ∈ n t,min , n t,max , t = 1, . . . , d and d j = 1, . . . , n t,max − n t,min + 1 . t =1
4) Formation of Wavelet Lattice: In this step, the wavelet function is calculated for all of the input vectors according to the following equation: ψm i ,n j (x) = 2−m i d/2 ψ 2m i x − n j (4) where, i = 1, . . . , m max − m min + 1. In (4), ψm i ,n j (x) is calculated by (3). This spatial structure is called wavelet lattice. In Fig. 2, a wavelet lattice is shown for d = 2, where d is the input dimension. In fact, for forming a wavelet lattice, we should calculate ψm i ,n j (x) for all inputs and for all green small circles in the figure.
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As could be revealed from Fig. 2, there are too many nodes in a wavelet lattice to manipulate easily. Therefore, lowering the number of lattice nodes, and selecting the shift and scale parameters of effective wavelets are required. It is done through screening process as follows. 5) Screening: In this stage, for every scale level selected in the stage 4, the set I is formed for each input vector according to
I = (m i , n j ) : ψm i ,n j (x) ≥ ε max ψm i ,n j (x) (5) i
where ε is a chosen small number (typically ε = 0.5). In fact, the screening process selects the effective support of wavelets [48]. The selected wavelets in this stage (members of the set, I ) are shown as nodes with blue large circles in Fig. 2, schematically. 6) Formation of Wavelet Matrix: Suppose the number of selected wavelets in the last stage to be, L. Furthermore, to make the notation simpler, the couple index of m i , n j is replaced by a single index of l = 1, . . . , L. In this stage, W M×L = ψ1 , . . . , ψl , . . . , ψ L matrix is calculated for all input vectors and all of the selected shift and scale parameters, which are in the set I. In this matrix, ψl vectors are considered as regressors [48]. This matrix, which is called wavelet matrix, is calculated as follows: ⎤ ⎡ ψ1 x(1) ... ψ L x(1) ⎢ ψ1 x(2) ... ψ L x(2) ⎥ ⎥ ⎢ (6) W=⎢ ⎥. .. .. .. ⎦ ⎣ . . . ψ1 x(m) ... ψ L x(m) Each output vector is then constructed as yp =
L
wi, p ψi = Wθ p
(7)
i=1
where 1 ≤ p ≤ c and y p is the M−dimensional vector of pth output. The weight vector θ p = [w1, p , . . . , w L , p ]T is constituted from the weights assigned to the neurons of hidden layer and the output y p . Using (7), the output matrix Y could be determined as follows:
wavelet in W is selected, at first. Next, all other wavelets, which are not selected, are made orthogonal to the selected one. In the second step, the most significant of the remaining wavelets is again selected and; then, all not selected wavelets are made orthogonal to the selected one, and the algorithm goes on for the rest of wavelets. The procedure is described in [48]. After selecting a reduced subset of wavelets, the wi, p weight coefficients are set to updated values and each output y p is constructed as yp =
s
wi, p ψi
(9)
i=1
where s is the number of neurons in the hidden layer and wi, p are the updated weights of neurons. After performing OLS algorithm, the W is decomposed an orthonormal matrix (Q) and an upper triangular matrix (A). Thus, the output matrix Y could be expressed as Y = Q M×s As×s s×c .
(10)
8) Selecting the Number of Neurons: Neurons are the nodes creating the hidden layer of the FGWN. By choosing a preliminary number for neurons, the mean squared error (MSE), which is an index for evaluating the performance of the system, could be calculated by (11). Then, the number of neurons would change until the desired error measure is achieved M 2 1 (k) (11) yˆ p − y (k) MSE p = p M k=1
where yˆ p is a function approximation for the pth output. 9) Calculating the Weight Coefficients of Neurons: The weight coefficients of neurons are measured by the least squares method. This calculation is done by the following equation: QT Y = A.
(12)
C. Damage Identification Algorithm
In our damage identification algorithm, three damagesensitive features are extracted from GUW signals to detect Y = [y1 , . . . , y p , . . . , yc ] = [Wθ 1 , . . . , Wθ p , . . . , Wθ c ] damage characteristics. These three features are ToF, normalized amplitude, and normalized area of the damage wave. = W[θ1 , . . . , θ p , . . . , θc ] ⇒ Y M×c These features are applied to the FGWN, as established in the = W M×L × L×c (8) previous section; and then, the damage location and degree of where L×c is the matrix of weight coefficients. severity are estimated. Extracting the features from the GUW 7) Performing OLS Algorithm: Some of the wavelet matrix signals is described in this section. members that might be picked up in the screening In a pulse-echo configuration accompanying the stage could still be redundant. Moreover, in order to GUW-based damage detection application, the GUWs avoid the over-fitting problems that might result from an propagate along the structure toward the damage after being over-parameterization of the model, selecting a reduced generated by an actuator. When they reach the damage area, and effective subset of wavelets is required [40]. In one part of the wave is reflected back by the damage, and this stage, an efficient approach for model structure another part continues to propagate beyond the damage until determination is implemented using the OLS algorithm. it reaches the end of the structure and is then reflected back According to OLS algorithm, to select the best subset by the structure boundary [1]. Thus, the received signal is of W, the following steps should be proceeded (assum- indeed the superposition of three waves: 1) incident wave ing that the size of this subset is s). The most significant (the original wave generated by actuator); 2) the wave
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reflected from the damage; and 3) the wave reflected from the boundary. The most important part for us is the damage reflected wave, which contains information about the damage. Therefore, by extracting the useful features from this portion of the measured GUW signal, the damage characteristics could be estimated. The ToF, i.e., the time lag between the two wave components (incident wave and damage reflected wave) in a signal, is one of the most straightforward features of a GUW signal. This feature describes the relative distance between the sensor and the damage and could be used to estimate the damage location [1]. In fact, wave propagation is the transportation of energy embedded in a wave packet. Therefore, the actual ToF should be considered as the time difference between the moment at which the wave energy reaches its peak amplitude and the initial time of propagation [1]. Therefore, the envelope of scale-averaged wavelet power (SAP) signal is used in this paper to determine exactly the energy peak of the wave packet in the GUW signal. If denotes continuous wavelet transform (CWT) of a signal, is denoted as CWT(ai , n) , i = 1, . . . , M, where ai , n denote scale and time parameters, respectively, and M is the largest scale during CWT, then SAP is defined as follows [50]: S A P (n) =
M 1 |C W T (ai , n)|2 . M
(13)
i=1
After calculating the SAP signal, ToF could be determined. Besides ToF, the normalized peak amplitude and normalized area of damage reflected wave (with respect to the peak amplitude and the area of excitation wave) are considered as the damage features. The degree of damage severity is somewhat reflected back in these two features; if the damage goes more serious, we would expect to have an increase in the peak amplitude and the area of damage reflected wave. In fact, the amplitude of the reflected wave is a little decreased and this wave is gotten smooth somehow during traveling through the specimen body. Therefore, the normalized area of the damage wave, which demonstrates the amount of energy the reflected damage wave has, is also considered in addition to normalized peak amplitude to detect damage severity. Overall, three features, which are appropriately containing the damage location and severity information, are extracted from each signal, as shown in Fig. 3(d). Extracting the features from an acquired GUW signal is illustrated in Fig. 3. The three extracted features can be used to detect damage location and severity roughly. To make the damage identification process automatic and more accurate, a pattern recognition tool is needed. In this paper, according to their beneficial characteristics explained in Sections II-A and II-B, the WNs are employed as pattern recognition tool for damage identification in SHM applications for the first time. The proposed FGWN in Section II-B is used as pattern recognition tool with three inputs, x 1 , x 2 , x 3 , and two outputs, y1 , y2 . The three features that are extracted from the SAP signals are considered as the inputs of the FGWN. The ToF is considered as x 1 , the normalized damage wave amplitude is considered as x 2 , and the normalized damage wave area is considered as x 3 .
Fig. 3. Extracting features from a GUW signal. (a) GUW signal. (b) CWT of the signal. (c) SAP and its envelope. (d) Extracting ToF, normalized damage wave amplitude, and normalized damage wave area, as the damage features.
By accepting these features as inputs, the FGWN could estimate the locations and severities of the corresponding damage embedded in the GUW signals. The outputs y1 , y2 of the FGWN are considered as damage location and damage severity, respectively. Our damage identification algorithm is illustrated in Fig. 4 schematically.
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Fig. 4.
Proposed damage identification algorithm.
Fig. 5.
Configuration of specimen with a sample saw-cut crack.
III. C ASE S TUDY: DAMAGE I DENTIFICATION IN T HICK S TEEL B EAM A. FEM Simulations for Database Development In this paper, a steel beam with a rectangular cross section (h × b = 34 × 25 mm2 ) and a length of 300 mm is considered, which is similar to the specimen used in [44]. The beam is simulated for different damaged conditions and the corresponding signals are obtained using FEM simulations generated by any FEM software. It is assumed that the specimen is free from any prestress conditions; therefore, any changes in the propagation characteristics of the GUWs could be consequently correlated with the existence of damage only. The damage is a saw-cut slot with 1-mm width and having several severities (S = 2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm) located in several distances (D = 140, 150, 160, 170, 175, 180, 190, 200, 210, 220, 230, and 240 mm) in the beam. Overall, 84 3-D dynamic simulations are performed. In the simulations, the boundary conditions of the specimen are considered as free-free and the time history outputs are recorded at a sampling frequency of 4 MHz. This frequency is consistent with the experimental instrumentation specifications. The actuator and sensor are placed according to a pulse-echo configuration, as shown in Fig. 5. B. Experiment Setup For evaluating the proposed damage identification algorithm, an experimental study is carried out. Lead zirconate titanate (PZT) transducers with dimensions of 25 × 10 × 1 mm3 , density of 7.8 g/cm3 , and capacitance of 7500 pF are used for both generating and sensing the GUWs. A steel beam (ST52 alloy) with the size mentioned in section 3.1 is investigated. The transducers are bonded to the surface
Fig. 6. Experiment setup and the test specimen (with a 2.5-mm notch) for guided wave propagation [43].
of the beam. Notches of different depths (2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm) are machined in the specimen. The distance between the notch and the beam edge is 175 mm. A SHM system is developed to extract the required signals. The PZT transducers are actuated by a function generator with amplitude of 5 V. A two channel digital oscilloscope is used to acquire sensor signals with sampling frequency of 4 Mhz. Fig. 6 illustrates the experimental setup and the inspected specimen. C. Diagnostic Wave Since the results are very sensitive to the excitation wave, in a GUW-based damage identification system, the excitation frequency and the number of cycles need a careful selection. The excitation frequency should be selected such that it could minimize the dispersion phenomenon. On the other hand, the number of cycles should be selected in such a way as to avoid overlapping between the generated wave and the reflected waves. The dispersion curve of Lamb waves could be used to pick an appropriate frequency. According to the dispersion curves, for minimizing the dispersion phenomenon, the excitation frequency should be between 28 and 42 kHz for the structure under examination [43]. Therefore,
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Fig. 7.
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Excitation waveform. A 3.5-Hz Hanning modulated sinusoidal signal at 35 kHz in (a) time domain and (b) frequency domain [43].
Fig. 8. Two of simulation signals and equivalent experimental ones. (a) and (b) Simulation and experimental signals computed from undamaged beam. (c) and (d) Simulation and experimental signals relevant to damaged beam (D = 175 mm, S = 10 mm).
a 3.5-Hz Hanning modulated sinusoidal signal at 35 kHz is used as excitation signal. Fig. 7 shows the excitation waveform. More details about Lamb wave dispersion curves and the way of determining the diagnostic wave are explained in [43]. Using the excitation signal in order to stimulate the structural beam, the structure responses can be measured by the sensor placed near the actuator, both in computer simulations and experimental tests. Fig. 8 shows the responses of undamaged structure and also one example of damaged beam, to the
excitation signal. These responses are measured from both FEM simulations and experimental tests. IV. R ESULTS AND D ISCUSSION Our damage identification algorithm is used to detect the location and severity of the damage in the experimental signals. For this intent, the FGWN in the proposed algorithm should be trained at first. Seventy seven damage scenarios from FEM simulations are used to train the FGWN. These scenarios
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Fig. 9.
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Experimental signal (a) before and (b) after the preprocessing stage.
Fig. 10. Outputs of the FGWN for estimating locations of the damages. (a) Training process output as well as the corresponding mean square error. (b) Output as well as the corresponding mean square error of testing FEM simulation signals. (c) Output as well as the corresponding mean square error of testing experimental signals.
would pertain to seven different damage severities (S = 2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm), and eleven different damage locations (D = 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, and 240 mm). Seven damage scenarios (pertaining to the location D = 175 mm, and different severities S = 2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm) from FEM simulations are used for testing the network. In addition to seven FEM signals, seven captured experimental signals are used as test signals. Thus, there are 77 signals, i.e., FEM simulation signals, for training the FGWN as well as two groups of seven signals, i.e., FEM simulation and experimental signals, for testing. Before applying to the algorithm, all signals should be normalized with respect to their peak amplitude to make FEM simulation and experimental signals in a same range. Furthermore, since the experimental GUW signals are noisy and have
dc offsets, they should be preprocessed. The preprocessing stage includes removing dc offset, denoising, and normalizing the signal. The WT is employed in the denoising step. For wavelet decomposition, the 10th-order Daubechies basis function, which is one of the most preferable mother wavelets, is applied. Fig. 9 shows a sample experimental signal before and after the preprocessing stage. Fig. 10 shows the outputs of the FGWN as well as the mean square errors for estimating locations of the corresponding damage cases. This figure illustrates the outputs of the FGWN in the steps of both training and testing (testing both FEM simulations and experimental signals). Fig. 11 shows the outputs of the FGWN as well as the mean square errors for estimating the severities of the corresponding damage cases. In the figures, both targets and outputs are normalized to a range [−1 1].
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Fig. 11. Outputs of the FGWN for estimating severities of the damages. (a) Training process output as well as the corresponding mean square error. (b) Output as well as the corresponding mean square error of testing FEM simulation signals. (c) Output as well as the corresponding mean square error of testing experimental signals. TABLE II E STIMATING THE D AMAGE L OCATIONS OF FEM S IMULATION AND E XPERIMENTAL S IGNALS BY M EANS OF D IFFERENT A LGORITHMS
As illustrated in Figs. 10 and 11, the FGWN training and testing errors are reasonably small. The efficiency of the damage identification algorithm would depend on two major factors: 1) usefulness of the extracted features from the signals and 2) the performance of the FGWN. In the proposed damage identification algorithm, errors are small and also the proposed FGWN outputs could follow the actual outputs for both severity and location detections appropriately according
to the figures. Therefore, it can be concluded from the results shown in both Figs. 10 and 11 that the selected features have proper efficiency; in another word, the features would be selected and be extracted properly. Moreover, the performance of the FGWN would be satisfactory. The FGWN efficiency could depend on FGWN parameters, such as the number of neurons as well as of scale and shift parameters. There could be a tradeoff between the number of these parameters
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TABLE III E STIMATING THE D AMAGE S EVERITIES OF FEM S IMULATION AND E XPERIMENTAL S IGNALS BY M EANS OF D IFFERENT A LGORITHMS
TABLE IV AVERAGE VALUES OF R ELATIVE E RRORS FOR D IFFERENT D AMAGE I DENTIFICATION A LGORITHMS IN E STIMATING D AMAGE L OCATIONS AND S EVERITIES F ROM FEM S IMULATION AND E XPERIMENTAL S IGNALS
and the FGWN convergence rate. By selecting these numbers properly, other than acquiring the best results, the FGWN training and testing steps could take place only in a few seconds. In order to compare the accuracy and reliability of the proposed damage identification algorithm, the proposed FGWN is replaced by a three layered feed-forward backpropagation ANN and the outputs of the ANN are acquired. The ANN is established with a hidden layer of 10 neurons, which is the same as the number of neurons in the hidden layer of the FGWN. Unlike the FGWN, the results of estimating damage characteristics with ANN are not the same for different experiments; i.e., estimating the damage characteristics by means of ANN for several times with the same data would not lead to the same results. Thus, in this paper, estimating the
damage locations and severities with ANN is repeated several times and the best results are considered. Furthermore, the results of the proposed damage identification algorithm are compared with two other effective existing ANN-based damage detection methods, called: 1) damage characteristic point (DCP) and 2) digital damage fingerprint (DDF) metrics. These metrics are proposed in [43] and [17], respectively. Tables II and III illustrate damage identification results obtained from the proposed FGWN-based algorithm, ANN-based algorithm, and two other procedures: 1) the DCP and 2) DDF algorithms. These results would pertain to both experimental and FEM simulation signals. Table II illustrates the results from estimating damage locations, whereas Table III illustrates the results from estimating damage severities by the different algorithms.
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Fig. 12. Relative errors of estimating damage location of FEM simulation signals for different algorithms.
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Fig. 15. Relative errors of estimating damage severity of experimental signals for different algorithms.
identification algorithm is lower than those of other ANN based methods. Furthermore, the average values of estimating relative errors for damage location and severity detections of FEM simulation and experimental signals are illustrated in Table IV for different algorithms. As illustrated in Table IV, for most cases, using the proposed FGWN-based method, the average values of relative errors would be lower than those by other methods. It could be concluded from the results that, the WN could estimate damage characteristics better than ANN could. Another advantage of WN is that its results are the same during different experiments, i.e., unlike ANNs, estimating the damage characteristics by means of WN for several times with the same data would lead to the same results. Fig. 13. Relative errors of estimating damage location of experimental signals for different algorithms.
Fig. 14. Relative errors of estimating damage severity of FEM simulation signals for different algorithms.
According to the results shown in the tables, an excellent quantitative prediction for the locations and severities of damage could be achieved by means of the proposed FGWN-based damage identification method. Relative errors for damage location and severity estimations of both FEM simulation and experimental GUW signals are shown in Figs. 12–15, for different algorithms. As shown in the figures, in most cases the estimation error of the proposed FGWN-based damage
V. C ONCLUSION In this paper, a proposed version of the WNs was employed for structural damage identification and the SHM applications using the GUWs, for the first time. A multiple-input multipleoutput FGWN was established and based on this FGWN, an algorithm for feature extraction and pattern recognition was proposed to quantitatively characterize damage in a thick steel beam. The FEM simulation signals were used for training the FGWN, whereas both FEM simulation and experimental signals were used for testing the proposed damage identification algorithm. Excellent quantitative diagnostic results for damage locations and severities were achieved by means of the proposed damage identification algorithm, which demonstrate practical utility and usefulness of the algorithm in the damage identification field. Comparing with an ANN-based and two other existing effective damage detection methods, called DCP and DDF, the efficiency of the proposed algorithm could be verified. According to the damage identification results, the proposed WN-based algorithm would have some advantages over other ANN-based algorithms. 1) For defining the network structure of a WN, an efficient constructive algorithm could be used. 2) By extracting the suitable features with respect to GUWs characteristics, the proposed WN-based algorithm could estimate damage locations and severities more accurate than other ANN-based algorithms.
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3) Unlike ANN, the results from WN-based methods would not change in several experiments, i.e., training and testing a WN several times with the same data would lead to the same results. The proposed damage identification algorithm could be used to detect damage characteristics of different structures based on measuring GUW signals for different SHM applications. R EFERENCES [1] Z. Su and L. Ye, Identification of Damage Using Lamb Waves: From Fundamentals to Applications. Berlin, Germany: Springer-Verlag, 2009, ch. 1. [2] A. Raghavan and C. E. Cesnik, “Review of guided-wave structural health monitoring,” Shock Vibrat. Dig., vol. 39, no. 2, pp. 91–116, 2007. [3] M. M. Taha, A. Noureldin, J. L. Lucero, and T. J. Baca, “Wavelet transform for structural health monitoring: A compendium of uses and features,” Struct. Health Monitor., vol. 5, no. 3, pp. 267–295, Sep. 2006. [4] M. Gul and F. N. Catbas, “Statistical pattern recognition for Structural Health Monitoring using time series modeling: Theory and experimental verifications,” Mech. Syst. Signal Process., vol. 23, no. 7, pp. 2192–2204, Oct. 2009. [5] J. C. Hong, K. H. Sun, and Y. Y. Kim, “Waveguide damage detection by the matching pursuit approach employing the dispersion-based chirp functions,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 53, no. 3, pp. 592–605, Mar. 2006. [6] P. Daponte, F. Maceri, and R. S. Olivito, “Ultrasonic signal-processing techniques for the measurement of damage growth in structural materials,” IEEE Trans. Instrum. Meas., vol. 44, no. 6, pp. 1003–1008, Dec. 1995. [7] L. De Marchi, M. Xu, B. Ruzzene, E. Baravelli, and N. Speciale, “Warped basis pursuit for damage detection using lamb waves,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 57, no. 12, pp. 2734–2741, Dec. 2010. [8] X. Chen, X. Li, S. Wang, Z. Yang, B. Chen, and Z. He, “Composite damage detection based on redundant second-generation wavelet transform and fractal dimension tomography algorithm of lamb wave,” IEEE Trans. Instrum. Meas., vol. 62, no. 5, pp. 1354–1363, May 2013. [9] J. Rangel-Magdaleno, R. Romero-Troncoso, R. A. Osornio-Rios, E. Cabal-Yepez, and L. M. Contreras-Medina, “Novel methodology for online half-broken-bar detection on induction motors,” IEEE Trans. Instrum. Meas., vol. 58, no. 5, pp. 1690–1698, May 2009. [10] J. H. Zhou, C. K. Pang, Z. W. Zhong, and F. L. Lewis, “Tool wear monitoring using acoustic emissions by dominant-feature identification,” IEEE Trans. Instrum. Meas., vol. 60, no. 2, pp. 547–559, Feb. 2011. [11] G. Niu, A. Widodo, J. D. Son, B. S. Yang, D. H. Hwang, and D. S. Kang, “Decision-level fusion based on wavelet decomposition for induction motor fault diagnosis using transient current signal,” Expert Syst. Appl., vol. 35, no. 3, pp. 918–928, Oct. 2008. [12] R. Li and D. He, “Rotational machine health monitoring and fault detection using EMD-based acoustic emission feature quantification,” IEEE Trans. Instrum. Meas., vol. 61, no. 4, pp. 990–1001, Apr. 2012. [13] R. Yan and R. X. Gao, “Hilbert–Huang transform-based vibration signal analysis for machine health monitoring,” IEEE Trans. Instrum. Meas., vol. 55, no. 6, pp. 2320–2329, Dec. 2006. [14] R. S. He and S. F. Hwang, “Damage detection by a hybrid real-parameter genetic algorithm under the assistance of gray relation analysis,” Eng. Appl. Artif. Intell., vol. 20, no. 7, pp. 980–992, Oct. 2007. [15] K. Y. Chen, “Forecasting systems reliability based on support vector regression with genetic algorithms,” Rel. Eng. Syst. Safety, vol. 92, no. 4, pp. 423–432, Apr. 2007. [16] X. Zhang, D. Liang, J. Zeng, and A. Asundi, “Genetic algorithmsupport vector regression for high reliability SHM system based on FBG sensor network,” Opt. Lasers Eng., vol. 50, no. 2, pp. 148–153, Feb. 2012. [17] Z. Su and L. Ye, “A fast damage locating approach using digital damage fingerprints extracted from Lamb wave signals,” Smart Mater. Struct., vol. 14, no. 5, pp. 1047–1054, Oct. 2005. [18] F. Cau, A. Fanni, A. Montisci, P. Testoni, and M. Usai, “A signalprocessing tool for non-destructive testing of inaccessible pipes,” Eng. Appl. Artif. Intell., vol. 19, no. 7, pp. 753–760, Oct. 2006.
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[42] S. K. Jain and S. N. Singh, “Fast harmonic estimation of stationary and time-varying signals using EA-AWNN,” IEEE Trans. Instrum. Meas., vol. 62, no. 2, pp. 335–343, Feb. 2013. [43] S. A. Atashipour, H. R. Mirdamadi, M. H. Hemasian-Etefagh, R. Amirfattahi, and S. Ziaei-Rad, “An effective damage identification approach in thick steel beams based on guided ultrasonic waves for structural health monitoring applications,” J. Intell. Mater. Syst. Struct., vol. 24, no. 5, pp. 584–597, Nov. 2012. [44] K. Sun, G. Meng, F. Li, L. Ye, and Y. Lu, “Damage identification in thick steel beam based on guided ultrasonic waves,” J. Intell. Mater. Syst. Struct., vol. 21, no. 3, pp. 225–232, Feb. 2010. [45] S. A. Billings and H. L. Wei, “A new class of wavelet networks for nonlinear system identification,” IEEE Trans. Neural Netw., vol. 16, no. 4, pp. 862–874, Jul. 2005. [46] A. Sadri, M. Zekri, S. Sadri, N. Gheissari, M. Mokhtari, and F. Kolahdouzan, “Segmentation of dermoscopy images using wavelet networks,” IEEE Trans. Biomed. Eng., vol. 60, no. 4, pp. 1134–1141, Apr. 2013. [47] R. Baron and B. Girau, “Parameterized normalization: Application to wavelet networks,” in Proc. IEEE Int. Conf. Neural Netw., vol. 2. May 1998, pp. 1433–1437. [48] Q. Zhang, “Using wavelet network in nonparametric estimation,” IEEE Trans. Neural Netw., vol. 8, no. 2, pp. 227–236, Mar. 1997. [49] J. Gonzalez-Nuevo, F. Argueso, M. Lopez-Caniego, L. Toffolatti, J. L. Sanz, P. Vielva, et al., “The Mexican hat wavelet family: Application to point source detection in CMB maps,” Monthly Notices R. Astronom. Soc., vol. 369, no. 4, pp. 1603–1610, 2006. [50] G. Georgiou and F. S. Cohen, “Tissue characterization using the continuous wavelet transform: Part I: Decomposition method,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 48, no. 2, pp. 355–363, Mar. 2001.
Hossein Zamani Hosseinabadi was born in Isfahan, Iran, in 1988. He received the B.Sc. and M.Sc. degrees in electrical engineering from the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, in 2010 and 2013, respectively. His current research interests include analog/mixed signal integrated circuits, implementable and wearable electronics, hardware implementation of signal processing algorithms, and digital signal processing.
Behzad Nazari received the B.Sc., M.Sc., and Ph.D. degrees from the Electrical Engineering Department, Sharif University of Technology, Tehran, Iran, in 1993, 1995, and 2004, respectively. He is currently an Assistant Professor with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran. His current research interests include image and signal processing.
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Rassoul Amirfattahi was born in 1969. He received the B.S. degree in electrical engineering from the Isfahan University of technology, Isfahan, Iran, in 1993, and the M.S. degree in biomedical engineering and the Ph.D. degree in electrical engineering from the Amirkabir University of Technology (The Tehran Polytechnic), Tehran, Iran, in 1996 and 2002, respectively. He joined the Isfahan University of Technology in 2003, where he is currently an Associate Professor and the Director of the Digital Signal Processing Research Laboratory, Department of Electrical and Computer Engineering. He is the author or co-author of more than 150 technical papers, one book, and two book chapters. His current research interests include biomedical signal and image processing, speech and audio analysis, biological system modeling, and DSP algorithms.
Hamid Reza Mirdamadi received the B.Sc. degree in civil engineering, the M.Sc. (Hons.) degree in structural engineering, and the Ph.D. (Hons.) degree in structural-earthquake engineering from the Sharif University of Technology, Tehran, Iran, in 1986, 1990, and 1999, respectively. He is currently an Associate Professor with the Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran. His current research interests include smart structures (dynamics, vibrations, and controls), smart piezoelectric materials, micro/nano electromechanical systems, fluid-structure interaction, structural health monitoring, and structural system identification.
Amir Reza Sadri was born in Isfahan, Iran. He received the B.Sc. degree in electrical engineering from the Department of Electrical Engineering, University of Kashan, Kashan, Iran, and the M.Sc. degree in electrical engineering from the Isfahan University of Technology, Isfahan, in 2012. His current research interests include medical image processing, system identification, signalprocessing applications in control engineering, intelligent control, and renewable energy.
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Wavelet Network Approach for Structural Damage Identification Using Guided Ultrasonic Waves Hossein Zamani Hosseinabadi, Behzad Nazari, Rassoul Amirfattahi, Hamid Reza Mirdamadi, and Amir Reza Sadri
Abstract— An appropriate wavelet network (WN) approach is introduced for detecting damage location and severity of structures based on measured guided ultrasonic wave (GUW) signals. An algorithm for establishing a multiple-input multiple-output fixed grid wavelet network (FGWN) is proposed. This algorithm consists of three main stages: 1) formation of wavelet latticel; 2) formation of wavelet matrix; and 3) optimizing the wavelet structure by means of orthogonal least square algorithm. Three damage-sensitive features are extracted from the GUW signals: 1) time of flight; 2) normalized damage wave amplitude; and 3) normalized damage wave area. These features are considered as the FGWN inputs and the damage location and severity are estimated. The established FGWN is used for identifying damage location and severity in a structural beam. The beam is investigated and simulated in different damaged conditions. Computed finite element method (FEM) simulation signals are used for training the FGWN. Some other FEM simulation signals, as well as measured experimental ones are used for testing. The proposed damage identification method is compared with three artificial neural network (ANN)-based algorithms. In addition to some other benefits of the proposed WN-based algorithm over ANN-based methods discussed in this paper, the results show that our approach performs better in both damage location and severity detections than other methods. Index Terms— Artificial neural network (ANN), damage identification, guided ultrasonic wave (GUW), structural health monitoring (SHM), wavelet network (WN).
I. I NTRODUCTION
D
UE to increasing awareness of the importance of damage diagnosis systems, guided ultrasonic wave (GUW) technique are widely used for detecting different damage types in aerospace, mechanical, and civil engineering structures in recent years. This technique is used to detect, or indirectly measure the existence, location, severity of damage, and the remaining life of structure under consideration in real applications [1]. The UWs are very sensitive to the discontinuities of structures. Hence, they can be employed for damage identification purposes, especially, for online inspection of in-service
Manuscript received July 29, 2013; revised November 6, 2013; accepted November 13, 2013. The Associate Editor coordinating the review process was Dr. Ruqiang Yan. H. Z. Hosseinabadi, B. Nazari, R. Amirfattahi, and A. R. Sadri are with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156, Iran. H. R. Mirdamadi is with the Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2014.2299528
structures, i.e., structural health monitoring (SHM). Several signal processing approaches are developed to extract damage features from measured GUW signals. A great number of these approaches are based on wavelet transform (WT). Wavelet analysis gives a picture of time-frequency spectrum of a signal; thus, it is well suited for analyzing nonstationary signals, such as GUWs [2]. Taha et al. [3] performed a survey of WT applications in the SHM and GUW-based damage detection methods. In a general SHM signal processing method, after extracting damage-sensitive features, a pattern recognition technique is required to estimate damage severity and location automatically [2]. A great number of studies are carried out to recognize damage patterns in different damage detection and fault diagnosis applications. Statistical pattern recognition using time series modeling is employed for the SHM applications in [4]. The matching pursuit approach is used in [5] by employing the dispersion-based chirp functions for damage detection. Frequency domain analysis based on the segmented chirp Z transform is introduced in [6] to detect the crack growth in structural materials. Warped basis pursuit analysis for damage detection is studied in [7]. Fractal dimension tomography algorithm is employed in [8] for damage detection in composites. The signal spectra of current and vibration are correlated for online half-broken-bar detection on induction motors in [9]. A new dominant-feature identification algorithm is introduced in [10] for condition monitoring applications. Wavelet decomposition-based decision-level fusion technique is used in [11] to recognize fault patterns in induction motors. Acoustic emission feature quantification based on empirical mode decomposition is used in [12] for health monitoring of rotational machine. Hilbert–Huang transform-based vibration signal analysis is performed in [13] for machine health monitoring. Artificial intelligence field approaches gain special popularity in recent studies. Genetic algorithm [14]–[16], artificial neural network (ANN) [17]–[25], support vector machine [26]–[30], and fuzzy logic [31]–[35] are some branches of artificial intelligence that are used for structural damage detection and fault diagnosis applications. One of the most effective computational intelligence methods for pattern recognition that has been widely used for various applications in different areas is wavelet network (WN). The WN takes advantage of the characteristics of the WT in signal processing and the ANN capacity of universal approximation [36]–[38]; hence, it has a great potential to be
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used in a vast amount of applications. Some disadvantages of other computational intelligence methods are overcome by means of the WN. Due to time-frequency localization of the WT, the WNs are more robust than neural networks against contaminated data [39]. Another advantage of the WNs over similar neural network architectures is the possibility of optimizing the WN structure by means of efficient deterministic construction algorithms [40]. Similar to some other fields, the WNs are employed in some studies in the measurement field. Such studies are using the WNs for time-of-flight measurement of ultrasonic pulse echoes [41] and using adaptive WNs for fast harmonic estimation of stationary and time-varying signals [42]. In this paper, due to beneficial characteristics of WNs in signal processing and pattern recognition, we would propose a WN-based algorithm to be used for GUW-based structural damage identification applications for the first time. At first, a specific multiple-input multiple-output fixed grid wavelet network (FGWN) with one hidden layer is proposed. Our proposed FGWN consists of nine steps: 1) normalizing; 2) selecting the mother wavelet; 3) choosing the scale and shift parameters; 4) forming a wavelet lattice; 5) screening; 6) forming a wavelet matrix; 7) performing orthogonal least squares (OLS) algorithm; 8) selecting the number of neurons; and 9) calculating the weight coefficients of neurons. Our proposed wavelet network is an advanced version of the FGWN used in [46], a multiple-input single-output FGWN proposed for segmentation of dermoscopy images. Afterward, based on the proposed FGWN, a novel automatic damage identification algorithm is proposed to be used in GUW-based damage identification applications. In our proposed algorithm, three features, including time of flight (ToF), normalized damage wave amplitude, and normalized damage wave area are extracted from the GUW signals measured from the structure under test. Then, these features are applied to the FGWN, and the location and severity of the structure damage are estimated by the FGWN automatically. To demonstrate the practical utility of the proposed algorithm, the algorithm is employed to quantitatively characterize damage created in a thick steel beam. As mentioned in [43], most of the GUW-based damage identification studies are subject to thin structures. However, Sun et al. [44] used the GUWs for detecting structural damage in a thick steel beam. In this paper, a thick beam similar to the structure used in [44] is considered. The structural beam is investigated and simulated for different conditions of damage. Furthermore, experimental GUW signals and signals resulting from finite element method (FEM) simulations are measured. Seventy FEM simulation signals are used to train the FGWN. Another seven FEM simulation signals, in addition to seven experimental GUW signals are used to test the FGWN. The practicality of the proposed method in damage identification applications can be appropriately illustrated by the results obtained from applying the method on the established experimental set up test signals and simulation ones. The organization of this paper is as follows. In Section II, the proposed damage identification algorithm is introduced. In Section I, basic concepts of the WN are discussed, a suitable
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TABLE I WN T YPES [46]
FGWN algorithm is proposed, and the proposed damage identification method is introduced. In Section III, FEM simulations and experimental setup are explained. The case study is damage location and severity detection in a thick steel beam. In Section IV, the results of damage identification are represented and the simulation results of the proposed algorithm are compared with other methods. Finally, in Section V, some concluding remarks are drawn. II. P ROPOSED DAMAGE I DENTIFICATION A LGORITHM At first, three damage-sensitive features are extracted from GUW signals for estimating the damage location and severity. Afterward, these features are applied to an established FGWN. The structures of the WNs, the proposed FGWN, and the proposed algorithm for damage identification are described in the following sections. A. Wavelet Network The WN takes advantage of the characteristics of the WT, for example, denoising, finding function singularities and the recovery of the characteristic information, and ANN capacity of universal approximation. There are two types of wavelet networks: 1) adaptive wavelet networks (AWNs) and 2) FGWNs [45]. The characteristics of these two networks are shown in Table I. Because of some shortcomings of the AWNs (complex calculations, sensitivity to initial values, and the problem of measuring initial values), their application is limited [45]. In the AWNs, in the same way as neural networks, initial values of network parameters (including weights of neurons, shifts, and scales of wavelets) are selected either randomly or using other methods. These parameters are then updated in the training stage by means of such techniques as the steepest descent gradient or back propagation. Unlike the AWNs, in the FGWNs, the outer parameters of the network, i.e., the number of neurons, the values of scale, and shift parameters, are determined beforehand and only the inner parameters of the network, i.e., weights of neurons, are calculated through such methods as least squares [40]. Thus, in the FGWNs, there are no need to select random initial values for parameters or to use gradient descent, back propagation, or other iterative methods. Because of the FGWN benefits, the FGWN is employed in this paper. Consider a multiple-input multiple-output FGWN with c outputs, d inputs, x = (x 1 , x 2 , . . . , x d )T , and q neurons in the hidden layer. Each output signal of this FGWN can be
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Fig. 1.
Three layered multiple-input multiple-output fixed grid wavelet.
Fig. 2.
calculated as yp =
q
wi, p ψm i ,ni (x) =
i=1
3
Wavelet lattice for 2-D inputs (d = 2).
data to the range [a, b] : q
wi, p 2−m i d/2 ψ 2m i x − ni
(1)
i=1
where wi, p , i = 1, 2, . . . , q and p = 1, 2, . . . , c are weight coefficients, ψm q ,nq are dilated and translated versions of the mother wavelet function ψ : d → , and m i , ni are scale and shift vector parameters, respectively. This network structure is illustrated in Fig. 1. According to the above definitions, any function f ∈ L 2 d could be approximated using a FGWN [40].
B. Building FGWN One of the major advantages of the WNs over other neural architectures is the availability of efficient constructive algorithms for defining the network structure [40]. In a FGWN, after determining the structure, the weights wi, p in (1) could be obtained through linear estimation techniques. In this paper, a constructive algorithm is proposed to build a multiple-input multiple-output FGWN. Then, the FGWN is used for damage identification applications for the first time. This algorithm could be described as follows. Notation: In this paper, we use upper case bold letters for showing matrices, lower case bold letters for vectors, and lower case italic letters for scalars. Algorithm: Suppose we have M input–output data. The input matrix is in the form X = [x(1), . . . , x(k) , . . . , x(m) ] (k) (k) T where x(k) = x 1 , . . . , x d is the d−dimensional input vector. The FGWN structure is determined with a nine-stage algorithm. 1) Normalization: Varying the input data within a wide range could reduce the efficiency of FGWN. Thus, the first stage normalizes the vector inputs to a limited range in order to avoid data scattering [47]. If for kth input Tk = max{xr(k) }, tk = min{xr(k) }, r = (1, . . . , d) then the following equation is used for mapping the input
(k) xr,new = (k)
b − a (k) aTk − btk x + Tk − tk r,old Tk − tk
(2) (k)
where xr,old is the r th input of kth sample, and xr,new is its value after the normalization all (k)process. Similarly, (k) (k) T of the vector values xnew = x 1,new , . . . , x d,new fall within the range of [a, b] . From now on, we show the (k) as x. xnew 2) Selecting the Mother Wavelet: Due to the ease of frame generation in (1), a multidimensional single scaling wavelet frame is employed [48]. In addition, Mexican hat wavelet is usually used in signal processing algorithms due to some of its desirable characteristics, such as convenient calculations, ease of implementation, and leading good results, as implied in [49]. Therefore, in this paper, the d−dimensional Mexican hat wavelet is used to implement FGWN. This wavelet is expressed as (3) ψ(x) = d − x2 exp − x2 /2 . 3) Choose the Scale and Shift Parameters: In this stage, the minimum and the maximum scale levels are employed in the form [m min , m max ] and shift parameter are T employed in the [n 1 , . . . , n t , . . . , n d ] , form n j = where n t ∈ n t,min , n t,max , t = 1, . . . , d and d j = 1, . . . , n t,max − n t,min + 1 . t =1
4) Formation of Wavelet Lattice: In this step, the wavelet function is calculated for all of the input vectors according to the following equation: ψm i ,n j (x) = 2−m i d/2 ψ 2m i x − n j (4) where, i = 1, . . . , m max − m min + 1. In (4), ψm i ,n j (x) is calculated by (3). This spatial structure is called wavelet lattice. In Fig. 2, a wavelet lattice is shown for d = 2, where d is the input dimension. In fact, for forming a wavelet lattice, we should calculate ψm i ,n j (x) for all inputs and for all green small circles in the figure.
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As could be revealed from Fig. 2, there are too many nodes in a wavelet lattice to manipulate easily. Therefore, lowering the number of lattice nodes, and selecting the shift and scale parameters of effective wavelets are required. It is done through screening process as follows. 5) Screening: In this stage, for every scale level selected in the stage 4, the set I is formed for each input vector according to
I = (m i , n j ) : ψm i ,n j (x) ≥ ε max ψm i ,n j (x) (5) i
where ε is a chosen small number (typically ε = 0.5). In fact, the screening process selects the effective support of wavelets [48]. The selected wavelets in this stage (members of the set, I ) are shown as nodes with blue large circles in Fig. 2, schematically. 6) Formation of Wavelet Matrix: Suppose the number of selected wavelets in the last stage to be, L. Furthermore, to make the notation simpler, the couple index of m i , n j is replaced by a single index of l = 1, . . . , L. In this stage, W M×L = ψ1 , . . . , ψl , . . . , ψ L matrix is calculated for all input vectors and all of the selected shift and scale parameters, which are in the set I. In this matrix, ψl vectors are considered as regressors [48]. This matrix, which is called wavelet matrix, is calculated as follows: ⎤ ⎡ ψ1 x(1) ... ψ L x(1) ⎢ ψ1 x(2) ... ψ L x(2) ⎥ ⎥ ⎢ (6) W=⎢ ⎥. .. .. .. ⎦ ⎣ . . . ψ1 x(m) ... ψ L x(m) Each output vector is then constructed as yp =
L
wi, p ψi = Wθ p
(7)
i=1
where 1 ≤ p ≤ c and y p is the M−dimensional vector of pth output. The weight vector θ p = [w1, p , . . . , w L , p ]T is constituted from the weights assigned to the neurons of hidden layer and the output y p . Using (7), the output matrix Y could be determined as follows:
wavelet in W is selected, at first. Next, all other wavelets, which are not selected, are made orthogonal to the selected one. In the second step, the most significant of the remaining wavelets is again selected and; then, all not selected wavelets are made orthogonal to the selected one, and the algorithm goes on for the rest of wavelets. The procedure is described in [48]. After selecting a reduced subset of wavelets, the wi, p weight coefficients are set to updated values and each output y p is constructed as yp =
s
wi, p ψi
(9)
i=1
where s is the number of neurons in the hidden layer and wi, p are the updated weights of neurons. After performing OLS algorithm, the W is decomposed an orthonormal matrix (Q) and an upper triangular matrix (A). Thus, the output matrix Y could be expressed as Y = Q M×s As×s s×c .
(10)
8) Selecting the Number of Neurons: Neurons are the nodes creating the hidden layer of the FGWN. By choosing a preliminary number for neurons, the mean squared error (MSE), which is an index for evaluating the performance of the system, could be calculated by (11). Then, the number of neurons would change until the desired error measure is achieved M 2 1 (k) (11) yˆ p − y (k) MSE p = p M k=1
where yˆ p is a function approximation for the pth output. 9) Calculating the Weight Coefficients of Neurons: The weight coefficients of neurons are measured by the least squares method. This calculation is done by the following equation: QT Y = A.
(12)
C. Damage Identification Algorithm
In our damage identification algorithm, three damagesensitive features are extracted from GUW signals to detect Y = [y1 , . . . , y p , . . . , yc ] = [Wθ 1 , . . . , Wθ p , . . . , Wθ c ] damage characteristics. These three features are ToF, normalized amplitude, and normalized area of the damage wave. = W[θ1 , . . . , θ p , . . . , θc ] ⇒ Y M×c These features are applied to the FGWN, as established in the = W M×L × L×c (8) previous section; and then, the damage location and degree of where L×c is the matrix of weight coefficients. severity are estimated. Extracting the features from the GUW 7) Performing OLS Algorithm: Some of the wavelet matrix signals is described in this section. members that might be picked up in the screening In a pulse-echo configuration accompanying the stage could still be redundant. Moreover, in order to GUW-based damage detection application, the GUWs avoid the over-fitting problems that might result from an propagate along the structure toward the damage after being over-parameterization of the model, selecting a reduced generated by an actuator. When they reach the damage area, and effective subset of wavelets is required [40]. In one part of the wave is reflected back by the damage, and this stage, an efficient approach for model structure another part continues to propagate beyond the damage until determination is implemented using the OLS algorithm. it reaches the end of the structure and is then reflected back According to OLS algorithm, to select the best subset by the structure boundary [1]. Thus, the received signal is of W, the following steps should be proceeded (assum- indeed the superposition of three waves: 1) incident wave ing that the size of this subset is s). The most significant (the original wave generated by actuator); 2) the wave
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reflected from the damage; and 3) the wave reflected from the boundary. The most important part for us is the damage reflected wave, which contains information about the damage. Therefore, by extracting the useful features from this portion of the measured GUW signal, the damage characteristics could be estimated. The ToF, i.e., the time lag between the two wave components (incident wave and damage reflected wave) in a signal, is one of the most straightforward features of a GUW signal. This feature describes the relative distance between the sensor and the damage and could be used to estimate the damage location [1]. In fact, wave propagation is the transportation of energy embedded in a wave packet. Therefore, the actual ToF should be considered as the time difference between the moment at which the wave energy reaches its peak amplitude and the initial time of propagation [1]. Therefore, the envelope of scale-averaged wavelet power (SAP) signal is used in this paper to determine exactly the energy peak of the wave packet in the GUW signal. If denotes continuous wavelet transform (CWT) of a signal, is denoted as CWT(ai , n) , i = 1, . . . , M, where ai , n denote scale and time parameters, respectively, and M is the largest scale during CWT, then SAP is defined as follows [50]: S A P (n) =
M 1 |C W T (ai , n)|2 . M
(13)
i=1
After calculating the SAP signal, ToF could be determined. Besides ToF, the normalized peak amplitude and normalized area of damage reflected wave (with respect to the peak amplitude and the area of excitation wave) are considered as the damage features. The degree of damage severity is somewhat reflected back in these two features; if the damage goes more serious, we would expect to have an increase in the peak amplitude and the area of damage reflected wave. In fact, the amplitude of the reflected wave is a little decreased and this wave is gotten smooth somehow during traveling through the specimen body. Therefore, the normalized area of the damage wave, which demonstrates the amount of energy the reflected damage wave has, is also considered in addition to normalized peak amplitude to detect damage severity. Overall, three features, which are appropriately containing the damage location and severity information, are extracted from each signal, as shown in Fig. 3(d). Extracting the features from an acquired GUW signal is illustrated in Fig. 3. The three extracted features can be used to detect damage location and severity roughly. To make the damage identification process automatic and more accurate, a pattern recognition tool is needed. In this paper, according to their beneficial characteristics explained in Sections II-A and II-B, the WNs are employed as pattern recognition tool for damage identification in SHM applications for the first time. The proposed FGWN in Section II-B is used as pattern recognition tool with three inputs, x 1 , x 2 , x 3 , and two outputs, y1 , y2 . The three features that are extracted from the SAP signals are considered as the inputs of the FGWN. The ToF is considered as x 1 , the normalized damage wave amplitude is considered as x 2 , and the normalized damage wave area is considered as x 3 .
Fig. 3. Extracting features from a GUW signal. (a) GUW signal. (b) CWT of the signal. (c) SAP and its envelope. (d) Extracting ToF, normalized damage wave amplitude, and normalized damage wave area, as the damage features.
By accepting these features as inputs, the FGWN could estimate the locations and severities of the corresponding damage embedded in the GUW signals. The outputs y1 , y2 of the FGWN are considered as damage location and damage severity, respectively. Our damage identification algorithm is illustrated in Fig. 4 schematically.
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Fig. 4.
Proposed damage identification algorithm.
Fig. 5.
Configuration of specimen with a sample saw-cut crack.
III. C ASE S TUDY: DAMAGE I DENTIFICATION IN T HICK S TEEL B EAM A. FEM Simulations for Database Development In this paper, a steel beam with a rectangular cross section (h × b = 34 × 25 mm2 ) and a length of 300 mm is considered, which is similar to the specimen used in [44]. The beam is simulated for different damaged conditions and the corresponding signals are obtained using FEM simulations generated by any FEM software. It is assumed that the specimen is free from any prestress conditions; therefore, any changes in the propagation characteristics of the GUWs could be consequently correlated with the existence of damage only. The damage is a saw-cut slot with 1-mm width and having several severities (S = 2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm) located in several distances (D = 140, 150, 160, 170, 175, 180, 190, 200, 210, 220, 230, and 240 mm) in the beam. Overall, 84 3-D dynamic simulations are performed. In the simulations, the boundary conditions of the specimen are considered as free-free and the time history outputs are recorded at a sampling frequency of 4 MHz. This frequency is consistent with the experimental instrumentation specifications. The actuator and sensor are placed according to a pulse-echo configuration, as shown in Fig. 5. B. Experiment Setup For evaluating the proposed damage identification algorithm, an experimental study is carried out. Lead zirconate titanate (PZT) transducers with dimensions of 25 × 10 × 1 mm3 , density of 7.8 g/cm3 , and capacitance of 7500 pF are used for both generating and sensing the GUWs. A steel beam (ST52 alloy) with the size mentioned in section 3.1 is investigated. The transducers are bonded to the surface
Fig. 6. Experiment setup and the test specimen (with a 2.5-mm notch) for guided wave propagation [43].
of the beam. Notches of different depths (2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm) are machined in the specimen. The distance between the notch and the beam edge is 175 mm. A SHM system is developed to extract the required signals. The PZT transducers are actuated by a function generator with amplitude of 5 V. A two channel digital oscilloscope is used to acquire sensor signals with sampling frequency of 4 Mhz. Fig. 6 illustrates the experimental setup and the inspected specimen. C. Diagnostic Wave Since the results are very sensitive to the excitation wave, in a GUW-based damage identification system, the excitation frequency and the number of cycles need a careful selection. The excitation frequency should be selected such that it could minimize the dispersion phenomenon. On the other hand, the number of cycles should be selected in such a way as to avoid overlapping between the generated wave and the reflected waves. The dispersion curve of Lamb waves could be used to pick an appropriate frequency. According to the dispersion curves, for minimizing the dispersion phenomenon, the excitation frequency should be between 28 and 42 kHz for the structure under examination [43]. Therefore,
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Fig. 7.
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Excitation waveform. A 3.5-Hz Hanning modulated sinusoidal signal at 35 kHz in (a) time domain and (b) frequency domain [43].
Fig. 8. Two of simulation signals and equivalent experimental ones. (a) and (b) Simulation and experimental signals computed from undamaged beam. (c) and (d) Simulation and experimental signals relevant to damaged beam (D = 175 mm, S = 10 mm).
a 3.5-Hz Hanning modulated sinusoidal signal at 35 kHz is used as excitation signal. Fig. 7 shows the excitation waveform. More details about Lamb wave dispersion curves and the way of determining the diagnostic wave are explained in [43]. Using the excitation signal in order to stimulate the structural beam, the structure responses can be measured by the sensor placed near the actuator, both in computer simulations and experimental tests. Fig. 8 shows the responses of undamaged structure and also one example of damaged beam, to the
excitation signal. These responses are measured from both FEM simulations and experimental tests. IV. R ESULTS AND D ISCUSSION Our damage identification algorithm is used to detect the location and severity of the damage in the experimental signals. For this intent, the FGWN in the proposed algorithm should be trained at first. Seventy seven damage scenarios from FEM simulations are used to train the FGWN. These scenarios
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Experimental signal (a) before and (b) after the preprocessing stage.
Fig. 10. Outputs of the FGWN for estimating locations of the damages. (a) Training process output as well as the corresponding mean square error. (b) Output as well as the corresponding mean square error of testing FEM simulation signals. (c) Output as well as the corresponding mean square error of testing experimental signals.
would pertain to seven different damage severities (S = 2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm), and eleven different damage locations (D = 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, and 240 mm). Seven damage scenarios (pertaining to the location D = 175 mm, and different severities S = 2.5, 5, 7.5, 10, 12.5, 15, and 17.5 mm) from FEM simulations are used for testing the network. In addition to seven FEM signals, seven captured experimental signals are used as test signals. Thus, there are 77 signals, i.e., FEM simulation signals, for training the FGWN as well as two groups of seven signals, i.e., FEM simulation and experimental signals, for testing. Before applying to the algorithm, all signals should be normalized with respect to their peak amplitude to make FEM simulation and experimental signals in a same range. Furthermore, since the experimental GUW signals are noisy and have
dc offsets, they should be preprocessed. The preprocessing stage includes removing dc offset, denoising, and normalizing the signal. The WT is employed in the denoising step. For wavelet decomposition, the 10th-order Daubechies basis function, which is one of the most preferable mother wavelets, is applied. Fig. 9 shows a sample experimental signal before and after the preprocessing stage. Fig. 10 shows the outputs of the FGWN as well as the mean square errors for estimating locations of the corresponding damage cases. This figure illustrates the outputs of the FGWN in the steps of both training and testing (testing both FEM simulations and experimental signals). Fig. 11 shows the outputs of the FGWN as well as the mean square errors for estimating the severities of the corresponding damage cases. In the figures, both targets and outputs are normalized to a range [−1 1].
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Fig. 11. Outputs of the FGWN for estimating severities of the damages. (a) Training process output as well as the corresponding mean square error. (b) Output as well as the corresponding mean square error of testing FEM simulation signals. (c) Output as well as the corresponding mean square error of testing experimental signals. TABLE II E STIMATING THE D AMAGE L OCATIONS OF FEM S IMULATION AND E XPERIMENTAL S IGNALS BY M EANS OF D IFFERENT A LGORITHMS
As illustrated in Figs. 10 and 11, the FGWN training and testing errors are reasonably small. The efficiency of the damage identification algorithm would depend on two major factors: 1) usefulness of the extracted features from the signals and 2) the performance of the FGWN. In the proposed damage identification algorithm, errors are small and also the proposed FGWN outputs could follow the actual outputs for both severity and location detections appropriately according
to the figures. Therefore, it can be concluded from the results shown in both Figs. 10 and 11 that the selected features have proper efficiency; in another word, the features would be selected and be extracted properly. Moreover, the performance of the FGWN would be satisfactory. The FGWN efficiency could depend on FGWN parameters, such as the number of neurons as well as of scale and shift parameters. There could be a tradeoff between the number of these parameters
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TABLE III E STIMATING THE D AMAGE S EVERITIES OF FEM S IMULATION AND E XPERIMENTAL S IGNALS BY M EANS OF D IFFERENT A LGORITHMS
TABLE IV AVERAGE VALUES OF R ELATIVE E RRORS FOR D IFFERENT D AMAGE I DENTIFICATION A LGORITHMS IN E STIMATING D AMAGE L OCATIONS AND S EVERITIES F ROM FEM S IMULATION AND E XPERIMENTAL S IGNALS
and the FGWN convergence rate. By selecting these numbers properly, other than acquiring the best results, the FGWN training and testing steps could take place only in a few seconds. In order to compare the accuracy and reliability of the proposed damage identification algorithm, the proposed FGWN is replaced by a three layered feed-forward backpropagation ANN and the outputs of the ANN are acquired. The ANN is established with a hidden layer of 10 neurons, which is the same as the number of neurons in the hidden layer of the FGWN. Unlike the FGWN, the results of estimating damage characteristics with ANN are not the same for different experiments; i.e., estimating the damage characteristics by means of ANN for several times with the same data would not lead to the same results. Thus, in this paper, estimating the
damage locations and severities with ANN is repeated several times and the best results are considered. Furthermore, the results of the proposed damage identification algorithm are compared with two other effective existing ANN-based damage detection methods, called: 1) damage characteristic point (DCP) and 2) digital damage fingerprint (DDF) metrics. These metrics are proposed in [43] and [17], respectively. Tables II and III illustrate damage identification results obtained from the proposed FGWN-based algorithm, ANN-based algorithm, and two other procedures: 1) the DCP and 2) DDF algorithms. These results would pertain to both experimental and FEM simulation signals. Table II illustrates the results from estimating damage locations, whereas Table III illustrates the results from estimating damage severities by the different algorithms.
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Fig. 12. Relative errors of estimating damage location of FEM simulation signals for different algorithms.
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Fig. 15. Relative errors of estimating damage severity of experimental signals for different algorithms.
identification algorithm is lower than those of other ANN based methods. Furthermore, the average values of estimating relative errors for damage location and severity detections of FEM simulation and experimental signals are illustrated in Table IV for different algorithms. As illustrated in Table IV, for most cases, using the proposed FGWN-based method, the average values of relative errors would be lower than those by other methods. It could be concluded from the results that, the WN could estimate damage characteristics better than ANN could. Another advantage of WN is that its results are the same during different experiments, i.e., unlike ANNs, estimating the damage characteristics by means of WN for several times with the same data would lead to the same results. Fig. 13. Relative errors of estimating damage location of experimental signals for different algorithms.
Fig. 14. Relative errors of estimating damage severity of FEM simulation signals for different algorithms.
According to the results shown in the tables, an excellent quantitative prediction for the locations and severities of damage could be achieved by means of the proposed FGWN-based damage identification method. Relative errors for damage location and severity estimations of both FEM simulation and experimental GUW signals are shown in Figs. 12–15, for different algorithms. As shown in the figures, in most cases the estimation error of the proposed FGWN-based damage
V. C ONCLUSION In this paper, a proposed version of the WNs was employed for structural damage identification and the SHM applications using the GUWs, for the first time. A multiple-input multipleoutput FGWN was established and based on this FGWN, an algorithm for feature extraction and pattern recognition was proposed to quantitatively characterize damage in a thick steel beam. The FEM simulation signals were used for training the FGWN, whereas both FEM simulation and experimental signals were used for testing the proposed damage identification algorithm. Excellent quantitative diagnostic results for damage locations and severities were achieved by means of the proposed damage identification algorithm, which demonstrate practical utility and usefulness of the algorithm in the damage identification field. Comparing with an ANN-based and two other existing effective damage detection methods, called DCP and DDF, the efficiency of the proposed algorithm could be verified. According to the damage identification results, the proposed WN-based algorithm would have some advantages over other ANN-based algorithms. 1) For defining the network structure of a WN, an efficient constructive algorithm could be used. 2) By extracting the suitable features with respect to GUWs characteristics, the proposed WN-based algorithm could estimate damage locations and severities more accurate than other ANN-based algorithms.
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3) Unlike ANN, the results from WN-based methods would not change in several experiments, i.e., training and testing a WN several times with the same data would lead to the same results. The proposed damage identification algorithm could be used to detect damage characteristics of different structures based on measuring GUW signals for different SHM applications. R EFERENCES [1] Z. Su and L. Ye, Identification of Damage Using Lamb Waves: From Fundamentals to Applications. Berlin, Germany: Springer-Verlag, 2009, ch. 1. [2] A. Raghavan and C. E. Cesnik, “Review of guided-wave structural health monitoring,” Shock Vibrat. Dig., vol. 39, no. 2, pp. 91–116, 2007. [3] M. M. Taha, A. Noureldin, J. L. Lucero, and T. J. Baca, “Wavelet transform for structural health monitoring: A compendium of uses and features,” Struct. Health Monitor., vol. 5, no. 3, pp. 267–295, Sep. 2006. [4] M. Gul and F. N. Catbas, “Statistical pattern recognition for Structural Health Monitoring using time series modeling: Theory and experimental verifications,” Mech. Syst. Signal Process., vol. 23, no. 7, pp. 2192–2204, Oct. 2009. [5] J. C. Hong, K. H. Sun, and Y. Y. Kim, “Waveguide damage detection by the matching pursuit approach employing the dispersion-based chirp functions,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 53, no. 3, pp. 592–605, Mar. 2006. [6] P. Daponte, F. Maceri, and R. S. Olivito, “Ultrasonic signal-processing techniques for the measurement of damage growth in structural materials,” IEEE Trans. Instrum. Meas., vol. 44, no. 6, pp. 1003–1008, Dec. 1995. [7] L. De Marchi, M. Xu, B. Ruzzene, E. Baravelli, and N. Speciale, “Warped basis pursuit for damage detection using lamb waves,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 57, no. 12, pp. 2734–2741, Dec. 2010. [8] X. Chen, X. Li, S. Wang, Z. Yang, B. Chen, and Z. He, “Composite damage detection based on redundant second-generation wavelet transform and fractal dimension tomography algorithm of lamb wave,” IEEE Trans. Instrum. Meas., vol. 62, no. 5, pp. 1354–1363, May 2013. [9] J. Rangel-Magdaleno, R. Romero-Troncoso, R. A. Osornio-Rios, E. Cabal-Yepez, and L. M. Contreras-Medina, “Novel methodology for online half-broken-bar detection on induction motors,” IEEE Trans. Instrum. Meas., vol. 58, no. 5, pp. 1690–1698, May 2009. [10] J. H. Zhou, C. K. Pang, Z. W. Zhong, and F. L. Lewis, “Tool wear monitoring using acoustic emissions by dominant-feature identification,” IEEE Trans. Instrum. Meas., vol. 60, no. 2, pp. 547–559, Feb. 2011. [11] G. Niu, A. Widodo, J. D. Son, B. S. Yang, D. H. Hwang, and D. S. Kang, “Decision-level fusion based on wavelet decomposition for induction motor fault diagnosis using transient current signal,” Expert Syst. Appl., vol. 35, no. 3, pp. 918–928, Oct. 2008. [12] R. Li and D. He, “Rotational machine health monitoring and fault detection using EMD-based acoustic emission feature quantification,” IEEE Trans. Instrum. Meas., vol. 61, no. 4, pp. 990–1001, Apr. 2012. [13] R. Yan and R. X. Gao, “Hilbert–Huang transform-based vibration signal analysis for machine health monitoring,” IEEE Trans. Instrum. Meas., vol. 55, no. 6, pp. 2320–2329, Dec. 2006. [14] R. S. He and S. F. Hwang, “Damage detection by a hybrid real-parameter genetic algorithm under the assistance of gray relation analysis,” Eng. Appl. Artif. Intell., vol. 20, no. 7, pp. 980–992, Oct. 2007. [15] K. Y. Chen, “Forecasting systems reliability based on support vector regression with genetic algorithms,” Rel. Eng. Syst. Safety, vol. 92, no. 4, pp. 423–432, Apr. 2007. [16] X. Zhang, D. Liang, J. Zeng, and A. Asundi, “Genetic algorithmsupport vector regression for high reliability SHM system based on FBG sensor network,” Opt. Lasers Eng., vol. 50, no. 2, pp. 148–153, Feb. 2012. [17] Z. Su and L. Ye, “A fast damage locating approach using digital damage fingerprints extracted from Lamb wave signals,” Smart Mater. Struct., vol. 14, no. 5, pp. 1047–1054, Oct. 2005. [18] F. Cau, A. Fanni, A. Montisci, P. Testoni, and M. Usai, “A signalprocessing tool for non-destructive testing of inaccessible pipes,” Eng. Appl. Artif. Intell., vol. 19, no. 7, pp. 753–760, Oct. 2006.
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Hossein Zamani Hosseinabadi was born in Isfahan, Iran, in 1988. He received the B.Sc. and M.Sc. degrees in electrical engineering from the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, in 2010 and 2013, respectively. His current research interests include analog/mixed signal integrated circuits, implementable and wearable electronics, hardware implementation of signal processing algorithms, and digital signal processing.
Behzad Nazari received the B.Sc., M.Sc., and Ph.D. degrees from the Electrical Engineering Department, Sharif University of Technology, Tehran, Iran, in 1993, 1995, and 2004, respectively. He is currently an Assistant Professor with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran. His current research interests include image and signal processing.
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Rassoul Amirfattahi was born in 1969. He received the B.S. degree in electrical engineering from the Isfahan University of technology, Isfahan, Iran, in 1993, and the M.S. degree in biomedical engineering and the Ph.D. degree in electrical engineering from the Amirkabir University of Technology (The Tehran Polytechnic), Tehran, Iran, in 1996 and 2002, respectively. He joined the Isfahan University of Technology in 2003, where he is currently an Associate Professor and the Director of the Digital Signal Processing Research Laboratory, Department of Electrical and Computer Engineering. He is the author or co-author of more than 150 technical papers, one book, and two book chapters. His current research interests include biomedical signal and image processing, speech and audio analysis, biological system modeling, and DSP algorithms.
Hamid Reza Mirdamadi received the B.Sc. degree in civil engineering, the M.Sc. (Hons.) degree in structural engineering, and the Ph.D. (Hons.) degree in structural-earthquake engineering from the Sharif University of Technology, Tehran, Iran, in 1986, 1990, and 1999, respectively. He is currently an Associate Professor with the Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran. His current research interests include smart structures (dynamics, vibrations, and controls), smart piezoelectric materials, micro/nano electromechanical systems, fluid-structure interaction, structural health monitoring, and structural system identification.
Amir Reza Sadri was born in Isfahan, Iran. He received the B.Sc. degree in electrical engineering from the Department of Electrical Engineering, University of Kashan, Kashan, Iran, and the M.Sc. degree in electrical engineering from the Isfahan University of Technology, Isfahan, in 2012. His current research interests include medical image processing, system identification, signalprocessing applications in control engineering, intelligent control, and renewable energy.
