Intelligent Diagnosis of Structural Cracks with Active Sensing Networks Shudong Liua , Chunling Dua,∗, J. Moua , L. Martuaa , J. Zhanga , F. L. Lewisb a A*STAR
Data Storage Institute, DSI Building, 5 Engineering Drive 1, Singapore 117608 and Robotics Research Institute, University of Texas, Arlington, TX76019, USA
b Automation
Abstract This paper considers intelligent diagnosis of structural cracks emanating from rows of rivet holes in thin metallic plates using active sensing networks. Lamb waves are generated using actuators and propagate across the plates and are received by sensors. We extract a robust and effective feature called energy ratio change from time domain signals using wavelet transform. Then we develop neural networks using this feature to diagnose health condition. The sensing network is optimized by developing a mixed integer programming model. The results show that our method can effectively detect cracks and determine their locations, and the number of actuators and sensors of the original sensing network can be significantly reduced while keeping high diagnostic accuracy. Important insights are also obtained such as in which area the sensing network has the weakest diagnostic capability. Keywords: neural networks, crack detection, optimization, lamb wave, structural health monitoring, wavelet transform
1. Introduction Diagnosing and monitoring structural cracks is very important in industries such as aerospace. One main reason is that it is critical in preventing catastrophic disasters before the cracks develop into a failure. Crack is a very popular problem in components in almost all products, especial in old products. A significant number of civil and military aircraft have exceeded their design lifetimes: in 2000, 75% of US Air Force aircraft were more than 25 years old [1]. A recent example of crack problem is that in 2012 the superjumbo A380 has been found minor cracks on its wings and all A380s were ordered to examine cracks. The repair bill is €105 million. In addition, by structural health monitoring (e.g. monitoring cracks), people can transfer the schedule-based maintenance practice to condition-based maintenance, which can significantly improve maintenance agility and reduce the cost over the life time [2]. Diagnosing and monitoring small cracks is not easy, as some cracks may be covered by somethings and people has no access to them. When the products such as aircraft are large, hence finding out small cracks in big products is time-consuming. Moreover, many diagnostic methods also require the operator of the diagnostic systems highly experienced. Hence it is highly desirable to have effective intelligent diagnostic methods to diagnose cracks. ∗ Corresponding
author. Fax: +65 67766527. Email address:
[email protected] (Chunling Du )
Preprint submitted to NDT & E International
April 26, 2012
2 The various dynamic diagnostic methods can be categorized as vibration based methods and wave propagation methods. Many vibration-based methods are insensitive to defects such as cracks which are one of most typical defects in aircrafts. Traditional ultrasonic diagnostics such at Ascan (belong to wave propagation methods) is widely used in practices. However, some these methods have drawbacks such as time-consuming, needing dissembling of the product or stopping its operations, and needing high skills of the operators of the diagnostic instruments. Lamb waves have been used to diagnose defects in the last a few decades, as lamb waves can propagate a long distance (a few meters) with low attenuation so that it can inspect large structures fast. It has been shown that lamb wave based methods are effective or promising in detecting cracks in metallic structures or detecting cracks/delamination in composites. The interaction between lamb waves and defects have been studied by simulation and/or experiments [3-6]. Alleyne and Cawley [7] and Ghosh et al. [8] investigate the efficient use and selection of lamb wave modes and frequencies for different cases. Ihn and Chang [9, 10] propose a method of detecting and monitoring cracks using a piezoelectric active sensing network. A signal processing method based on Short Time Fourier Transform (STFT) is developed and damage indices are used to detect cracks. Park et al. [11] consider diagnosing cracks in a welded zone of a truss member and show that the damage index can be used to detect cracks effectively. Grondel et al. [12] consider detecting cracks at riveted strap joints using both lamb wave method and acoustic emission method. In many diagnostic methods, the diagnostic signals need human to interpret in this way or another. Intelligent diagnostic systems are highly demanded and have a wide application prospect. Artificial intelligence technologies such as neural networks (NN) have been used by some researchers to classify defects. McNad and Dunlop [13] have provided a review of using neural network in defect evaluation. Zgonc and Achenbach [14] develop a neural network for detecting the crack emanating from a hole by scanning the specimen. Liu et al. [15] develop neural networks to detect cracks in a thin plate by simulating the A-scan ultrasonic testing. One key issue in developing the effective diagnostic systems is the configuration of the active sensing network. The number of actuators and sensors and their locations dominantly determine the effectiveness of the system. However, the literature about optimization of active sensing network is not rich. In the area of active vibration control, there are some research for optimal placement of actuators and sensors. Bruant et al. [16] deals with the optimization of actuators and sensors locations for active vibration control using genetic algorithm which is a popular method in this area. Liu et al. [17] consider the optimal sensor placement on a spatial lattice structure aiming to maximizing the data information so that the structural dynamic behavior can be characterized. They also use the genetic algorithms. Mehrabian and Yousefi-Koma [18] consider the optimal placement of actuators on an aircraft fin using an innovative optimization method called Invasive Weed Optimization. For more detailed review, please refer to [19]. In this research, we consider detect and localize fatigue cracks at rows of rivet holes in thin metallic plates which simulate aircraft wings, fuselage and other thin structures. We extract a robust feature and develop NNs to diagnose health condition. We also have developed optimization models to optimize locations of actuators and sensor for a given number of actuators and sensors, and use the optimization models to reduce the number of actuators and sensors. The experimental setup is described in section 2. Section 3 presents the diagnostic methodology including feature extraction and the development of NNs. Section 4 describes the optimization of the sensing network. In section 5 results are shown. Finally, section 7 summarizes the conclusions and concludes the paper.
3 2. Experimental setup Thin aluminum plates shown in figure 1 are used to develop and validate diagnostic technologies. The metallic plate is of 500 × 500 × 1.6mm3 with a row of 7 rivet holes. Through-thickness 0.5 mm wide cuts starting from the holes are made using an electrical discharge machining (EDM) machine to simulate the cracks at the holes. The crack orientation is in the direction of linking centers of holes, which is very typical in practical components. We may call this direction as standard direction or reference direction. We also assume the cracks are symmetric to simplify the experiments. In the figure, the crack length is denoted as a mm. The actuators and sensors are put on either side of the row of holes. In this experiment study, we assume there are 7 potential positions for actuators and 7 potential positions for sensors as shown in the figure. The rows of actuators, holes and sensors are parallel to each other. Note that our optimization method for configuring the sensing network is general, allowing any position in the plane to put actuators or sensors. The actuators and sensors are piezoelectric transducers which are thickness-poled and operate in a radial extension mode. The experimental specimens include the healthy plate and the damaged plates with a crack at hole 3 or 4 with 4 different crack lengths (2mm, 6mm 10mm and 16mm). So there are experimental data of 9 patterns. In the earliest setup shown in the figure, 3 actuators and 7 sensors are put by intuitiveness to develop the diagnostic technology. The actuators 1 and 7 are put there corresponding to the end of the row of holes in order to make sure there is enough detection capability for the cracks at the end holes. After we can effectively diagnose cracks based on this original sensing network, we optimize the sensing network to reduce the number of sensors and actuators and find out their locations. 3. Diagnostic methodology When actuators generate lamb waves, the waves will propagate across the plates and received by sensors. The theory of diagnosis is that if there exist cracks on the plate, then the received signals will be different from those from the healthy plates. The variation of received signals at sensors contains information of the characteristics of cracks. So, how to extract features and how to use the extracted features to diagnose health condition are very important components of the diagnostic systems. 3.1. Feature extraction The diagnostic signal generated by an actuator is a five-cycle windowed sinewave burst, which is widely used in the field of non-destructural testing. As there are multiple rivet holes, the received signal at a certain sensor is the result of interference of multiple propagation paths. Hence extracting robust and effective features is very important. We develop a method using continuous wavelet transform (CWT) to extract a robust feature that we call energy ratio change (ERC). Wavelet transform has already been used in damage detection by some researchers [20,21]. One of its notable advantages compared with methods such as Fourier transform is its ability for multiscale analysis. A wavelet is a function of zero average which is defined as t−b 1 ), a, b ∈ R, a 6= 0 ψa,b (t) = p ψ( a |a|
3.1
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Feature extraction
Holes s1
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…
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Figure 1: Experimental setup
where a is the scaling parameter, b is the translation parameter, and ψ(t) is called a mother wavelet. The continuous wavelet transform for the time domain signal f (t) is defined as
1 t−b )dt f (t) p ψ ∗ ( a |a|
W (a, b) =
where the symbol * represents the operator of complex conjugate. Morlet wavelet is used to conduct CWT, as Morlet wavelet is very similar to our diagnostic signals. In the diagnostic method, we use multiple actuators and multiple sensors. For each detection path from a certain actuator to a certain sensor, we define a time window to cut out the interesting part of the time domain signal at the sensor. This time window mainly includes the S0 wave packet of the lamb waves. The time windows are different for different detection paths as the traveling times of the S0 wave packet are different. The windowed time domain signals are then processed using CWT. Let fij (t) denote the windowed segment of the signal received by sensor j from actuator i, and the corresponding CWT coefficients are Wij (a, b). Let scale a∗ denote the scale under which there is the maximal absolute value of Wij (a, b). At the scale a∗ , there is the maximal signal-to-noise ratio. Let
tf
[Wij (a∗ , b)]2 db
Eij = ti
where ti and tf are the initial and end time of the time window, respectively. Eij represents the
3.2
5
Diagnosis with neural networks
transmitted energy in the time window on the path from actuator i to sensor j. Based on the same method, we can calculate the energy of the actuator signals. Let Eii denote the energy of the signal of actuator i and define Eij Rij = Eii i.e., Rij denotes the ratio of the transmitted energy to the actuator’s original energy on the path from actuator i to sensor j. When there is a crack at a certain hole, the energy ratio Rij will change, compared with that of the healthy plate. Let Roij denote the energy ratio of the healthy plate. Define the energy ratio change (ERC) as FijERC =
Rij − Roij Roij
ERCs in different paths work together to reflect the structural characteristics. We use ERC as the feature to diagnose plate’s health. The idea under ERC is similar to the transmission coefficient in the literature [5]. However, as ERC is based on a windowed time region instead of a single time or frequency point, it is more robust to the wave interference during wave propagation. The above procedure of extracting feature is illustrated using Figure 2. Part (a) shows an example of time-domain signals of an actuator and a sensor. The sampling frequency is 20 MHz, i.e. the time length between two sequential time points is 0.05µs. Part (b) shows the result of CWT for the windowed signal of the sensor. As the maximal absolute value of the CWT coefficients is at scale 40, we extract CWT coefficients at this fixed scale and the results are shown in part (c). Figure 3 shows a comparison of the signals at a sensor for a healthy plate and a damaged plate with a 6mm crack at a hole. From this figure we can see that the extracted features in two cases are notable different. The ERC of the plate with a 6mm crack is -39% . Hence ERC can effectively reflect the characteristics of cracks. 3.2. Diagnosis with neural networks In the diagnosis we want to detect cracks and find out their locations. As an example, Figure 4 shows how the extracted feature varies with the crack length of a crack at hole 3. It contains the feature for detection paths A4-S3 and A4-S4 for both finite element simulation and experimental data. From the figure, we can see that the extracted feature for each detection path has no linear relationship with the crack characteristics, which is because of strong wave interference among multiple wave propagation paths. In stead of developing a single damage index using information from different detection paths to diagnose health, we use NNs for health diagnosis by explicitly employing information from different paths, as the single parameter of damage index may lose much information of different detection paths. The multiple layer perceptron neural network (MLP) is one of most popular types of neural networks. It consists of multiple layers of perceptrons which are linked forwardly. Each perceptron has its input and output. At each perceptron, the inputs from its previous perceptrons are summed together and then activated using a certain function. One of most popular activation functions is the sigmoid, a real function f (x) : R → (0, 1) defined as f (x) =
1 1 + e−cx
where c is a constant and x is the sum of input from previous perceptrons. At the last layer of perceptrons, the system outputs the results. The links between perceptrons have weights which
3.2
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Diagnosis with neural networks
(a)
(b)
(c)
Figure 2: Feature extraction from the time domain signals. (a) The time domain signals of a sensor and an actuator.(b) CWT coefficients of the windowed signal. (c) CWT coefficients at the fixed scale 40.
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Diagnosis with neural networks
1.5
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Figure 3: Comparison of signals of a sensor for the healthy plate and the plate with a 6mm crack at a hole. (a) The time domain signals and the time window. (b) The CWT coefficients at the fixed scale 40.
8
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Figure 4: Extracted feature vs. crack length at hole 3 for both simulation and experimental data
determine the effect of a previous perceptron on its latter perceptron. It is believed that three layers of perceptrons are enough for most problems. We develop two NNs of three-layer MLP type to diagnose health condition. The first NN is used to detect cracks and the second is for determining crack locations. The first NN has 13 input nodes, 8 hidden nodes and 1 output node. An input node is fed with the feature of a certain detection path. We use 13 detection paths in the original sensing network: for A1, there are 4 sensors to recorder signals: S1-S4; for A4, sensors S2-S6; for A7, sensors S4-S7. When the value of the output node is or close to 1, it means the plate has cracks. If it is close to 0, it means the plate is healthy. The second NN has 13 input nodes, 11 hidden nodes and 7 output nodes. Each output node corresponds to a certain hole. When the output is or close to 1, it means there is a crack at the corresponding hole. The 0 output means no crack at this hole. From this NN, we can determine the crack locations. The NNs are trained by an extension of the error backpropagation algorithm. We use simulation data to train the NNs. From figure 4 the simulation data is close to the experimental data. The trained NNs are then used to diagnose real specimens.
4. Optimization of sensing networks The effectiveness of the above diagnostic method is largely determined by the configuration of sensing network, i.e., how many actuators and sensors and where they are. In this section, we consider the optimization of the sensing network. We first develop an optimization model for optimizing the locations of actuators and sensors for given numbers of actuators and sensors, then run this optimization model for a serial of values for the number of actuators and sensors to find out the minimal number of actuators and sensors while keeping high diagnostic accuracy.
9 Now consider optimizing the locations of sensors and actuators for a given number NA of actuators and a given number NS of sensors. From the characteristic curves such as shown in figure 4, we extract an index which represents the diagnostic capability of a certain path for the crack at a certain hole. Let I = {1, 2, ..., 7}, be the set of index. Path ij means the detection path from k (l) denote the ERC of path ij when there is a crack of length l mm at actuator i to sensor j. Let Eij hole k, which has been obtained by extracting feature from simulation data. Define the diagnostic k capability Cij of path ij for the crack at hole k as X k k Cij = |Eij (l)| · W (l) (1) l
where W (l) is the weight which is a decreasing function in crack length l, as we emphasize the capability of detecting small cracks. Let xi be the binary variable associated with actuator i such that xi = 1 if actuator i is used in the detection scheme, otherwise xi = 0. Let yi be the binary variable associated with sensor i such that yi = 1 if sensor i is used in the detection scheme. Let zij be the binary variable associated with path pij such that zij = 1 if the pathPis used. Define the diagnostic capability C k of the sensing k network for the crack at hole k as C k = ij Cij · zij . As the effectiveness of the sensing network is determined by the weakest diagnostic capability for cracks among all holes, the objective of the optimization is to maximize the minimal diagnostic capability among all holes. So the optimization problem is max
C
s.t.
Ck =
X
k Cij · zij , ∀k ∈ I
(2)
C ≤ Ck,
∀k ∈ I
(3)
zij ≤ xi ,
∀i, j ∈ I
(4)
zij ≤ yj , X x i = NA
∀i, j ∈ I
(5)
ij
(6)
i
X
y i = NS
(7)
i
zij , xi , yi ∈ {0, 1}, ∀i, j ∈ I
(8)
The constraint (2) is to obtain the total diagnostic capability of the network for cracks at hole k. Constraint (3) is used to obtain the minimal diagnostic capability among all holes. Constraints (4) and (5) is to make sure that there is no detection path from actuator i to sensor j if either the actuator or the sensor is not used in the detection scheme. Constraints (6) and (7) are used to set the total numbers of actuators and sensors, respectively. This optimization model is a mixed integer linear programming model which is gauranteed to obtain global optimal solutions. We solved it using a toolbox in Matlab. From this optimization model, we obtain the optimal locations of actuators and sensors and the detection paths. Then we can change the values of NA and NS and rerun the optimization model to obtain a serial of optimal network settings. For each optimal setting of the sensing network, we use NNs to diagnose health condition and obtain the diagnostic accuracy. From these results
10 Num_sensors 7s 6s 5s 4s 3s 2s 1s
S1 1 1 1 1 1 1 0
S2 1 1 1 1 0 0 0
S3 1 0 0 0 0 0 0
S4 1 1 1 0 1 0 1
S5 1 1 0 0 0 0 0
S6 1 1 1 1 0 0 0
S7 1 1 1 1 1 1 0
Table 1: Optimal locations of sensors
we can obtain information about how the numbers of actuators and sensors affect the diagnostic accuracies. 5. Results For a given network configuration, we use NNs to diagnose health condition for many specimens to obtain the diagnostic accuracies which are used to represent the effectiveness of the sensing network. For a given sensing network, we train NNs using simulation data. By adding some noise into the simulation data we obtain a large dataset. The dataset is divided into three subsets: training set (60%), validation set (20%) and testing set (20%). During training, we calculate the Euclidean distance (training error) between the output and the target for each pattern. If the Mean Absolute Error (MAE) of all training patterns reaches a certain value (0.001 in our cases) or the number of training epochs reaches a maximal value (30000 epochs in our cases), the training will stop. In most cases, the training procedure is stop after a few hundreds of training epochs. The trained NNs are then used to diagnose real specimens. In the numerical study, we fix 3 actuators and their locations, i.e., using A1, A4 and A7, while changing the number of sensors. Figure 5 shows the diagnostic capability C k at each hole for different number of sensors. From the figure, we can see that for a given number of sensors, the sensing network has strongest diagnostic capability at the middle areas and weakest capability at the boundary areas. This information is important, because from it we can know which sensors are critical and need some redundancy and in which area we can reduce the density of sensors. The optimization results show there are always sensors at S1 and S7 when the number of sensors is greater than 1. From the figure, we can also see that when the number of sensors decreases, the diagnostic capability at each hole decreases. Figure 6 shows the relation between the diagnostic capability of the network and the number of sensors, assuming the capability of 7 sensors is 100%. We can see that when the number of sensors decreases from 7, the trend is that the diagnostic capability decreases first slowly, then faster and faster. It also shows that there may exist some redundant sensors in the sensing network of 7 sensors, as we reduce the number of sensors by 1 from 7, the diagnostic capability has only small decrease. The optimal locations of sensors for the cases of different number of sensors are shown in table 1. The value 1 means there is a sensor at the corresponding location, and 0 means no sensor there. From the table, we can see that in most cases there are sensors at the boundary positions of S1 and S7. This is because the diagnostic capability of the sensing networks is weak at these areas.
11
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Figure 7: Diagnostic accuracy vs. number of sensors
Figure 7 show the diagnostic accuracy varies with the number of sensors, based on the optimized sensing network. Results for diagnosing both simulated and real specimens are shown. The upper plot is for detecting cracks and the lower plot is for determining crack locations. From the figure, we can see that the accuracies decrease when reducing number of sensors. The accuracies in diagnosing real specimens are lower than those for simulated plates. It is because of the difference of simulated data and the experimental data and the NNs are trained only by simulation data. When the number of sensors decreases from 7 to 4 or 5, the NNs can still accurately diagnose real specimens. For an optimized sensing network with 3 actuators and 4 sensors, the number of actuators and sensors is reduced by 50%, compared the settings in the literature of one actuator and one sensor for one hole. When compared with the initial setting of 3 actuators and 7 sensors, the number of sensors and actuators is reduced by 30%. Reducing the number of sensors has many advantages such as reducing signal processing time and data storage space and reducing the complexity of the system and increasing the reliability. Of course, the number of sensors can not be reduced to the degree without any redundancy in practice. 6. Conclusions We have considered intelligent diagnosis of structural cracks emanating from rows of rivet holes in thin metallic plates using active sensing networks. We extract a robust effective feature called ERC from time domain signals using wavelet transform, and then use this feature to develop NNs to diagnose health condition. As the configuration of the sensing network is very important, largely determining the effectiveness of the sensing network, we have developed an innovative method to
13 optimize the sensing network, including determining the optimal number of actuators and sensors and their locations. The optimization problem is formulated as mixed integer linear programming models which can be solved to obtain the global optimal solutions. The results show that our diagnostic method can effectively detect cracks and determine their locations. Using the optimization models the number of actuators and sensors can be significantly reduced. Many important insights are also obtained such as in which area the sensing network has weakest diagnostic capability, which sensors are critical and need some redundancy and which sensors can be removed from the system. The optimization method for sensing network configuration is general, though in the experimental study we fixed the number of actuators and their locations. This general method can be applied to deploy active sensing networks in practice. For large components, there are a large number of potential positions for the actuators and sensors. Hence we need a large amount of simulation data. As a future research, we need to develop a method to reduce the simulation data needed, which is an optimization problem itself. References [1] W. Staszewski, C. Boller, and G. Tomlinson, Health monitoring of aerospace structures: smart sensor technologies and signal processing. J. Wiley, 2004. [2] C. Boller, “Ways and options for aircraft structural health management,” Smart Materials and Structures, vol. 10, no. 3, p. 432, 2001. [3] D. Alleyne and P. Cawley, “The interaction of lamb waves with defects,” Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 39, pp. 381 –397, May 1992. [4] Z. S. Chang and A. Mal, “Scattering of lamb waves from a rivet hole with edge cracks,” Mechanics of Materials, vol. 31, pp. 197–204, Mar. 1999. [5] Y. Lu, L. Ye, Z. Su, and C. Yang, “Quantitative assessment of through-thickness crack size based on lamb wave scattering in aluminium plates,” NDT & E International, vol. 41, pp. 59– 68, Jan. 2008. [6] P. Fromme and M. B. Sayir, “Detection of cracks at rivet holes using guided waves,” Ultrasonics, vol. 40, pp. 199–203, May 2002. [7] D. N. Alleyne and P. Cawley, “Optimization of lamb wave inspection techniques,” NDT & E International, vol. 25, no. 1, pp. 11–22, 1992. [8] T. Ghosh, T. Kundu, and P. Karpur, “Efficient use of lamb modes for detecting defects in large plates,” Ultrasonics, vol. 36, pp. 791–801, May 1998. [9] J. B. Ihn and F. K. Chang, “Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: I. diagnostics,” Smart Materials & Structures, vol. 13, pp. 609–620, June 2004. [10] J. B. Ihn and F. K. Chang, “Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: II. validation using riveted joints and repair patches,” Smart Materials & Structures, vol. 13, pp. 621–630, June 2004.
14 [11] S. Park, C.-B. Yun, and Y. Roh, “Damage diagnostics on a welded zone of a steel truss member using an active sensing network system,” NDT & E International, vol. 40, pp. 71–76, Jan. 2007. [12] S. Grondel, C. Delebarre, J. Assaad, J. P. Dupuis, and L. Reithler, “Fatigue crack monitoring of riveted aluminium strap joints by lamb wave analysis and acoustic emission measurement techniques,” NDT & E International, vol. 35, pp. 137–146, Apr. 2002. [13] A. McNab and I. Dunlop, “A review of artificial intelligence applied to ultrasonic defect evaluation,” Insight, vol. 37, no. 1, pp. 11–16, 1995. Anglais. [14] K. Zgonc and J. D. Achenbach, “A neural network for crack sizing trained by finite element calculations,” NDT & E International, vol. 29, pp. 147–155, June 1996. [15] S. W. Liu, J. H. Huang, J. C. Sung, and C. C. Lee, “Detection of cracks using neural networks and computational mechanics,” Computer Methods In Applied Mechanics and Engineering, vol. 191, no. 25-26, pp. 2831–2845, 2002. [16] I. Bruant, L. Gallimard, and S. Nikoukar, “Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm,” Journal of Sound and Vibration, vol. 329, no. 10, pp. 1615 – 1635, 2010. [17] W. Liu, W. cheng Gao, Y. Sun, and M. jian Xu, “Optimal sensor placement for spatial lattice structure based on genetic algorithms,” Journal of Sound and Vibration, vol. 317, pp. 175 – 189, 2008. [18] A. R. Mehrabian and A. Yousefi-Koma, “A novel technique for optimal placement of piezoelectric actuators on smart structures,” Journal of the Franklin Institute, vol. 348, no. 1, pp. 12 – 23, 2011. [19] M. I. Frecker, “Recent advances in optimization of smart structures and actuators,” Journal of Intelligent Material Systems and Structures, vol. 14, pp. 207–216, Apr. 2003. [20] S. Legendre, D. Massicotte, J. Goyette, and T. K. Bose, “Wavelet-transform-based method of analysis for lamb-wave ultrasonic NDE signals,” IEEE Transactions On Instrumentation and Measurement, vol. 49, pp. 524–530, June 2000. [21] A. Abbate, J. Koay, J. Frankel, S. C. Schroeder, and P. Das, “Signal detection and noise suppression using a wavelet transform signal processor: Application to ultrasonic flaw detection,” IEEE Transactions On Ultrasonics Ferroelectrics and Frequency Control, vol. 44, pp. 14–26, Jan. 1997.
