A Scanning Spatial-Wavenumber Filter based On-Line Damage Imaging Method of Composite Structure

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1 8 th International Symposium on NDT in Aerospace, November 3-5, 26 A Scanning Spatial-Wavenumber Filter based On-Line Damage Imaging Method of Composite Structure More info about this article: Lei QIU, Shenfang YUAN, Yuanqiang Ren Research Center of Structural Health Monitoring and Prognosis, State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics; Nanjing, China lei.qiu@nuaa.edu.cn, ysf@nuaa.edu.cn, renyuanqiang@nuaa.edu.cn Abstract Lamb wave Spatial-Wavenumber Filter (SWF) is gradually applied to Nondestructive Testing (NDT) of composite structures in recent years because it is an effective approach to distinguish wave propagating direction and mode. Nevertheless, to realize on-line damage imaging of composite structures by using SWF, the problem is on how to realize on-line spatial-wavenumber filtering of Lamb waves when the wavenumber response cannot be measured or modelled. This paper proposes an on-line damage imaging method based on a new Scanning Spatial-Wavenumber Filter (SSWF) and PieZoelectric Transducer (PZT) 2-D cruciform array for composite structures. With this method, a 2-D cruciform array constructed by two linear PZT arrays is placed on the composite structure permanently for on-line continuously spatial sampling of the Lamb wave damage scattering signal. For each linear PZT array, a SSWF is designed, which does not rely on any modelled or measured wavenumber response but scans and filters the wavenumber of the damage scattering signal at a designed wavenumber bandwidth to obtain a wavenumber-time image. A 2-D cruciform array based damage localization method is proposed to get the final angle-distance image of the damage which can be localized without blind angle. The method is validated on an aircraft composite fuel tank of variable panel thicess. The validation results show that the damage direction estimation error is less than 2 and the damage distance estimation error is around 2mm in the monitoring area of nearly 6 mm 3 mm. It indicates an acceptable performance of the on-line damage imaging method based on the SSWF for a complex composite structure Keywords: Structural health monitoring, composite structure, damage imaging, Lamb wave, scanning spatialwavenumber filter, 2-D cruciform array. Introduction In recent decades, the damage imaging methodology has been widely studied [-2] such as delay-and-sum imaging method, time reversal focusing method, ultrasonic phased array It utilized a large number of actuator-sensor channels from a network of PieZoelectric Transducer (PZT) to map the structure that was interrogated based on the measurement of damage reflections and induced features differences, producing a visual indication of damage location and size. It has advantages of high signal-to-noise ratio, high damage sensitivity and large scale structure monitoring. This paper studied a damage imaging method of composite structures based on a cruciform array and Spatial Wavenumber-Filtering (SWF) technique. SWF for damage estimation has been gradually studied in recent years. Compared with the time domain and frequency domain analysis of Lamb wave signals, the wavenumber domain analysis is an effective approach to distinguish wave propagating direction and various wave modes. Michaels et al.[3] used a frequency-wavenumber filtering method to analyze the direction and wave modes of damage-scattering signal on an aluminium plate. Sohn et al. [4] created a standing wave filter which was a signal processing technique in frequency-wavenumber domain to isolate only the standing wave components on a composite plate for delamination or disbond evaluation. Rogge and Leckey [5] built the relationship between wavenumber and wave spatial location using SWF and local wavenumber domain analysis to estimate the delamination size and depth of a composite laminate. Yu et al.[6] presented short time-spatial-frequency-wavenumber analysis for obtaining a wavenumber spectrum at a selected frequency and time to decompose Lamb wave modes by SWF. Purekar

2 et al. [7] studied a model-dependent SWF based linear PZTs phased array imaging method. They also studied the method further on a composite plate based on finite element modelling [8]. In the above research, the wavenumber of Lamb wave signal was measured by a scanning laser Doppler vibrometer of high spatial resolution or obtained by modelling. Thus, these method are difficult to be applied to on-line damage monitoring. Considering on-line damage imaging by taking the advantage of SWF, a new damage imaging method of composite structure based on a Scanning Spatial-Wavenumber Filter (SSWF) and PZT 2-D cruciform array is proposed in this paper. The scanning spatialwavenumber filter which does not rely on only modelled or measured wavenumber response is proposed first. And then, a damage imaging method based on the filter is proposed, and the corresponding damage localization method of no blind angle is given as well. Finally, the damage monitoring performance of the method for complex composite structure is validated on an aircraft composite fuel tank of variable thicess. 2. The Scanning Spatial-Wavenumber Filter 2. Lamb Wave Time Domain Sampling and Spatial Sampling There is a linear PZT array placed on a structure as shown in Figure. It consists of M PZTs and the distance between the centres of each two adjacent PZTs is Δx. The PZTs are numbered as m=,2,,m. A Cartesian coordinate is built on the array. The centre point of the array is set to be the original point. There is a damage located at (x a, y a ). The direction (angle) and distance of the damage relative to the linear PZT array are supposed to be θ a and l a respectively. To obtain the damage scattering signal, a frequency narrowband excitation signal of central frequency ω is input to the PZT at the original point to excite Lamb wave of frequency narrowband. When the Lamb wave propagates to the damage, the damage scattering signal is generated and it can be acquired by the array. According to some previous studies [9-], the amplitude of Lamb wave A mode is dominant at low excitation frequency. Thus, the damage scattering signal can be approximated to be single-mode signal when the excitation frequency is low. The wavenumber of the damage scattering signal is denoted as k a. It is wavenumber narrowband and it can be considered to be constructed by two components. The first component is the wavenumber projecting at the array direction (X-axis projection wavenumber) k x =k a cosθ a and the second component is the Y-axis projection wavenumber k y =k a sinθ a. Figure 2 gives an example of the damage scattering signal acquired by the linear PZT array. It is shown as a waterfall plot. The horizontal coordinate of the waterfall plot is sampling time and the longitudinal coordinate is sampling distance which is corresponding to the location of the PZTs. Ordinarily speaking, the linear PZT array is seen to be a time domain sampling device. Each PZT can output a time domain sampling signal as shown in Figure 2 when looking the waterfall plot from the time direction (blue line). The sampling dots (length) and the sampling rate are denoted as L and f s respectively. The linear PZT array can be also regarded as a spatial sampling device to acquire spatial response of the damage scattering signal at the area covered by the array when looking the waterfall plot from the distance direction (red line). The spatial sampling rate is 2π/Δx. The spatial response acquired by the linear PZT array at time t r can be represented as equation (), in which, f(x m, t r ) is the damage scattering signal acquired by the PZT located at (x m, ) at time t r, x m =((2m-)-M)Δx/2. t r =r/f s and r=,,l. f(x, t r ) is defined as one spatial sampling of the damage scattering signal at time t r. Thus, the waterfall plot of figure 2 can be regarded to be L times of spatial sampling of the damage scattering signal. Based on this point, the theoretic fundamental of SSWF is given in the next section. 2

3 , =,,,,...,,,...,, f x tr f x tr f x2 tr f xm tr f xm tr () Linear PZTs array 2 3 θ a Δx M Y o Acousitc source (x a, y a ) Wavenumber Fig.. Illustration of Lamb wave wavenumber. X Normalized amplitude Normalized amplitude Time (ms).5 Time domain sampling f(x m, t) X (mm) Waterfall plot of damage scattering signal 9 f(x M, t) Spatial sampling -.5 f(x, t r ) x (mm) Time (ms) Time t r f(x m, t) f(x, t) Fig.2. Lamb wave time domain sampling and spatial sampling. 2.2 The Design of Scanning Spatial-Wavenumber Filter For one time spatial sampling of the damage scattering signal of wavenumber narrowband at low excitation frequency, f(x m, t r ) can be represented as equation (2), in which u(t r ) is the normalized amplitude of the damage scattering signal. L a and X m represent the distance vector of l a and x m respectively. Based on Fraunhofer approximation [2], equation (2) can be approximated to be equation (3), in which, L ˆa denotes the unit direction vector of the L a. In far-field situation, the damage scattering signal can be regarded to be a planar wave acquired by the linear PZT array [2]. Thus, Eq. (3) can be approximated to be equation (4), in which, A(t r ) denotes the amplitude term. By using Fourier Transform, the spatial response as equation () can be transformed to wavenumber response as equation (5). δ is the Dirac function. i t k f x, t u( t ) e L m r r r a a Xm 2 ˆ 2 xm ( LX a m) ik ˆ a ikala ika a m 2la itr LX f x, t u( t ) e e e e (3) m r r ik ˆ a a m f x, t = A( t ) e LX (4) m r r F k, t 2π A( t ) ( k k cos ) (5) r r a a Thus, a SWF can be designed to be equation (6) based on the wavenumber k a [24-25]. In equation (6), θ is a searching direction which can be changed from to 8. The wavenumber response of the spatial wavenumber filter can be also obtained by using Fourier Transform, as shown in equation (7). It indicates that the SWF has the purpose of selectively passing through the signal of wavenumber k=k a cosθ, while rejecting the signal of the other wavenumbers k k a cosθ. By applying the SWF to the spatial sampling damage scattering signal, the filtered wavenumber response can be expressed as equation (8). The symbol denotes the convolution operation. It can be noted that if θ=θ a, which means that the searching direction of the SWF is equal to the damage direction, the amplitude of the filtered response will reach to the maximum value. The damage direction can be estimated correspondingly. This is the original SWF [7-8]. a a 2 a m a x e, e,..., e,..., e ik cos x ik cos x ik cos x ik cos xm (2) (6) 3

4 x a (7) xx M ika cos x ikx e e 2π cos Φ k k k 2 H k, t f x, t x 4π A( t ) ( k k cos ) ( k k cos ) r r r a a a However, the wavenumber k a must be obtained by modelling or measuring beforehand when using the original SWF. It is difficult to be applied to composite structure at current stage. Therefore to promote the SWF technique to be applied to composite structure, a new SSWF is proposed. It can be seen from equation (6) and (7) that the original SWF is designed to search the damage direction directly based on a linear PZT array. Hence, the wavenumber k a of the damage scattering signal is needed to design the wavenumber of the SWF, but as mentioned above, the wavenumber k a can be considered to be two components including the X-axis projection component and the Y-axis projection component. If the two axis projection wavenumbers can be both obtained, the damage direction can still be estimated. Thus, a SSWF can be designed based on a linear PZT array to search the axis projection wavenumber of the damage scattering not to search the damage direction directly. By using a PZT 2-D cruciform array, damage direction estimation can be achieved. Based on this idea, the SSWF is designed to be equation (9), in which, k n is the wavenumber of the SSWF. The wavenumber response of SSWF is expressed as equation (). 2 i x i x i xm i xm k x e, e,..., e,..., e n x n () xx M ix ikx e e 2π Φ k k k Considering the damage scattering signal is wavenumber narrowband, k n is set to be scanned in a wavenumber narrowband from k to k N, where n=,,n. The wavenumber scanning range is set to be wider than that of the damage scattering signal but it is also limited by the spatial sampling rate. In this paper, k n =-k max +(n-)δk. It is scanned from -k max to +k max. k max is the maximum cut off wavenumber and it is π/δx. Δx is the distance between the centers of each two adjacent PZTs. The wavenumber scanning interval is denoted as Δk. n is also denoted as the scanning step. The maximum scanning step is N=(2k max /Δk)+. For a given k n, the amplitude of the filtered response can be calculated by equation (). If k n =k a cosθ a, which means that the wavenumber of the SSWF is equal to the X-axis projection wavenumber of the damage scattering signal, the amplitude of the filtered response will reach to the maximum value. Thus, a scanning filtered response vector can be obtained shown in equation (2). Figure 3 shows an example. The spatial sampling signal shown in Figure 3(a) comes from the waterfall plot shown in Figure 2 at the time.5ms. The corresponding scanning filtered response is shown in Figure 3(b) which consists of the filtered response from k to k N. The wavenumber corresponding to the maximum value can be considered to be the X-axis projection wavenumber of the damage scattering signal. 2 n H k, t f x, t x 4π A( t ) ( k k cos ) ( k k ) r r k r a a n (8) (9) () H t [ H,..., H,..., H ] (2) r k kn It should be noted that the SSWF is realized numerically as shown in equation (9) and (). There is no need to model or measure the wavenumber response of the damage scattering signal. Thus, it can be on-line applied to composite structure easily. 4

5 Normalized amplitude x (mm) (a) Spatial sampling signal Normalized amplitude Wavenumber (rad/s) (b) Scanning filtered wavenumber response Fig.3. Example of the scanning spatial-wavenumber filtering result. 3. The Damage imaging and localization method 3. Damage imaging method based on the scanning spatial-wavenumber filter As discussed in Section 2.2, a SSWF can be designed to filter the damage scattering signal of one time spatial sampling at time t r. Thus, it can be also designed to filter the damage scattering signal of L times spatial sampling. This process can be regarded to be a time scanning process performed from t to t L, as shown in Figure 4(a). Based on the time scanning process, a matrix of the scanning spatial-wavenumber filtering result can be obtained as represented in equation (3). Each row of the matrix represents the scanning spatialwavenumber filtering result at different wavenumber k n at one time spatial sampling and each column of the matrix represents the filtering result at different times..8.6 Absolute arrival time, t R.8 Time (ms) (a) Demonstration of damage imaging process -2 2 Wavenumber (rad/m) Projection Wavenumber, k n (b) Example of damage imaging result Fig.4. Damage imaging process and an example of wave-number time image. H LN 5 t H... H tr... H tl Finally, a wavenumber-time image can be generated by imaging the matrix H, as shown in Figure 4(b). In the wavenumber-time image, the wavenumber and the time corresponding to the point of the highest pixel value can be estimated to be the X-axis projection wavenumber k n =k a cosθ a and the absolute arrival time t R of the damage scattering signal respectively. It should be noted that the absolute arrival time is not the actual time-offlight of the damage scattering signal. If a 2-D cruciform array constructed by two linear PZT (3)

6 arrays is adopted, the X-axis and Y-axis projection wavenumbers can be obtained. Combining with the two axis projection wavenumbers and the absolute arrival time, the damage localization of no blind angle can be achieved as given in the next section. 3.2 Damage Localization based on PZT 2-D Cruciform Array The PZT 2-D cruciform array is constructed by two linear PZT arrays which are numbered as No. and No.2 respectively. They are shown in Figure 5. The centre point of the PZT 2-D cruciform array is set to be the origin point. X-axis and Y-axis are set to be along with No. PZT array and No.2 PZT array respectively. The Lamb wave is excited at the origin point at time t e. When the damage scattering signal is acquired by the PZT 2-D cruciform array, the axis projection wavenumber and the absolute arrival time (k n, t R ) of No. PZT array and the (k n2, t R2 ) of No.2 PZT array can be obtained by using the damage imaging method. Then, the damage can be localized based on the following method. k n2 Y o No. PZT array θ a k a k n X No.2 PZT array (a) Damage direction estimation Damage (x a, y a ) t R2 t e +t a Y o Excitation t R t e +t a l a =C g t a /2 No. PZT array No.2 PZT array (b) Damage distance estimation Damage (x a, y a ) Damage scattering X Fig.5. Schematic diagram of damage localization based on PZT 2-D cruciform array. k 9, (, 2 ) 2 a 8 arctan( ), ( ) 27, (, 2 ) k n2 arctan( ), (, 2 ) n2 36 +arctan( ), (, 2 ) (4) t t tr 2 ta tr te ct g a la 2 R R2 For damage direction estimation as shown in Figure 5(a), the wavenumber k n can be regarded to be the X-axis projection wavenumber of k a and the wavenumber k n2 can be regarded to be the Y-axis projection wavenumber. They are expressed as k n =k a cosθ a and k n2 =k a sinθ a Based on it, the direction θ a of the damage direction relative to the centre point of the PZT 2-D cruciform array can be calculated by equation (4). It shows that θ a can be calculated from to 36 without any blind angle. For damage distance estimation as shown in Figure 5(b), the absolute arrival time t R obtained from the wavenumber-time image 6 (5)

7 contains two parts. The first part is the excitation time t e which can be determined by the excitation signal. The second part is the actual time-of-flight t a including the time of Lamb wave signal propagating from the excitation position to the damage position and the time of the damage scattering signal propagating back to the PZT 2-D cruciform array. The damage distance l a relative to the centre point of the PZT 2-D cruciform array can be calculated by equation (5) combing with Lamb wave group velocity c g. The final damage position can be expressed as x a =l a cosθ a and y a =l a sinθ a. 4. Validation on an aircraft composite fuel tank 4. Validation Setup To validate the performance of the damage imaging method on complex composite structure, an aircraft composite fuel tank is adopted as shown in Figure 6(a). The dimension of the fuel tank is 6mm 3mm 24mm (length width height). The composite panel of the fuel tank is made of T3/QY89 carbon fibre and the thicess is variable. The central part of the composite panel is the thickest part and it consists of 58 stacked layers. The thicess of each layer is.25 mm and the total thicess is 7.25 mm. The thinnest parts are at the two ends and the thicesses are both 4.5 mm. (a) Validation system (b) The PZT 2-D cruciform array 5mm B Damage (-8, ) E I (-4, 5) - O Ref C F Ref 2 (-4, 3) Y (, ) (, 5) G H Ref 3 A D (4, 2) (4, 25) (8, ) X (8, ) No.2 PZT array No. PZT array 6mm 44mm 5mm 5mm mm mm 5mm (c) The damage positions and the placement of the PZT 2-D cruciform array Fig.6. Illustration of the validation system performed on the aircraft composite fuel tank. A PZT 2-D cruciform array is placed on the composite panel as shown in Figure 6(b). The distance between the centres of each two adjacent PZTs is Δx=9. mm. Thus, the maximum cut off wavenumber of the linear PZT array is k max =349 rad/m. Another 3 reference PZTs are used to measure the Lamb wave group velocity. Their positions are labelled as Ref, Ref 2 and Ref 3 as shown in Figure 6(c). The 9 damages labelled as A to I are simulated on the structure and their positions are shown in Figure 6(c). The damage direction is defined according to counter clockwise direction relative to the positive direction of X-axis. The Lamb 7

8 wave based SHM system [3] shown in Figure 6(a) is used to excite and receive Lamb wave signals. The excitation signal is a five-cycle sine burst modulated by Hanning window [4]. The center frequency of the excitation signal is 55 khz and the excitation amplitude is ±7 volts. The sampling rate is MS/s and the sampling length is 8 samples including pre-samples. PZT 2-5 is used to be the Lamb wave actuator for No. PZT, and PZT -5 is used to be the actuator for No.2 PZT. The method based on the continuous complex Shannon wavelet transform is used to measure the group velocity [4]. PZT-4 is used to excite Lamb wave. The measuring results by using the 3 reference PZTs are c g-ref =695.5m/s, c g- Ref2=83.8m/s and c g-ref3 =928.2m/s respectively. Finally, the average group velocity c g =82.5m/s is obtained and it is applied to the following damage localization. 4.2 Damage imaging validation The damage E is selected to be an example to show the damage imaging and localization process. The damage imaging method is applied to the damage scattering signal. The wavenumber scanning interval is set to be Δk= rad/m and the wavenumber scanning range is from -k max =-349 rad/m to k max =349 rad/m. Figure 7 shows the two wavenumber-time images of the damage E. For damage direction estimation, the axis projection wavenumbers k n =-87 rad/m and k n2 =299 rad/m are obtained from the two wavenumber-time images. The damage direction is θ a =6.3. For damage distance estimation, the Lamb wave excitation time must be obtained first. The excitation signal is also acquired by the SHM system. By using the continuous complex Shannon wavelet transform [4], the envelope of the excitation signal can be obtained. The time which is corresponding to the maximum value of the envelope is judged to be the excitation time t e =.3ms. The absolute arrival time t R =.2964ms and t R2 =.297ms are obtained based on the damage imaging results shown in Figure 7. According to equation (5) and the average group velocity c g =82.5 m/s, the damage distance is l a =73. mm. Finally, the damage position is obtained to be (-48.5 mm, 66. mm), and the damage localization error is Δl=8.2 mm..8.6 k n =-87 rad/m, t R =.2964 ms k n2 =299 rad/m, t R2 =.297 ms.8 Time (ms) Time (ms) Wavenumber (rad/m) (a) No. linear PZT array Wavenumber (rad/m) (b) No.2 linear PZT array Fig7. Damage imaging results of the damage E. According to the damage imaging and location process discussed above, the damage localization results of the 9 damages are listed in Table. It indicates that the damage localization results are in accordance with the actual damage. For the damage A, it is in the blind angle area of No. PZT array. For the damage C and F, they are in the blind angle area of No.2 PZT array but all of them can be localized correctly. For the damage I, the Lamb wave excited at the array must pass through the thicess variable area of the composite panel and the corresponding damage scattering signal also must pass through the thicess variable area. After that, it can be acquired by the PZT 2-D cruciform array. Thus, the distance estimation error of the damage I is relative larger than the other damages. Totally speaking, 8

9 the damage direction estimation error is less than 2 and the damage distance estimation error is around 2mm. Considering that the monitoring area is nearly 6mm 3mm and the structure is of variable thicess, the damage localization error can be accepted. Damage label Table. Damage localization results of the 9 damages on the composite panel of the fuel tank. (k n, t R ) (rad/m, ms) (k n2, t R2 ) (rad/m, ms) Localized position (, mm) Actual position (, mm) Direction and distance error (, mm) A (39,.285) (,.259) (., 94.3) (., 8.) (., 4.3) 4.3 B (-79,.3635) (238,.359) (27., 38.6) (28.7, 28.) (-.6,.5).2 C (-,.3227) (32,.323) (9., 2.4) (9.,.) (., 2.4) 2.4 D (8,.3466) (24,.3428) (53.2, 37.8) (5.3, 28.) (.9, 9.8).7 E (-87,.3474) (299,.347) (6.3, 73.) (4.9, 55.2) (.3, 7.8) 8.2 F (-,.334) (35,.3293) (9., 58.8) (9., 5.) (., 8.8) 8.8 G (5,.3337) (299,.3323) (8.4, 28.8) (78.7, 24.) (.7, 4.4) 7.5 H (38,.334) (299,.3323) (82.7, 237.7) (8.9, 253.2) (.8, -5.5) 7.4 I (-4,.3389) (3,.336) (97.7, 282.4) (97.6, 32.7) (., -2.3) 2.3 Δl (mm) 5. Conclusion To promote spatial-wavenumber filtering technique to be applied to on-line damage monitoring of composite structure, this paper proposes a new on-line damage imaging method based on a SSWF and PZT 2-D cruciform array. The SSWF can be designed only according to the maximum cut off wavenumber of the linear PZT array to scan the actual wavenumber of the damage scattering signal to give out a wavenumber-time image. By using the PZT 2-D cruciform array, the axis projection wavenumbers of the damage scattering signal can be obtained from the two wavenumber-time images and the damage direction can estimated correspondingly without any blind angle. According to the absolute arrival time obtained from the wavenumber-time images and combing with the Lamb wave group velocity, the damage distance can be estimated. The method is validated on the aircraft composite fuel tank of variable thicess and the validation results show that the damage imaging method is feasible to be applied to complex composite structure. 6. Acowledgements This work is supported by National Science Fund for Distinguished Young Scholars of China (Grant No ), key program of Natural Science Foundation of China (Grant No ), National Natural Science Foundation of China (Grant No ), Aviation Foundation of China (Grant No ), Priority Academic Program Development of Jiangsu Higher Education Institutions of China, Qing Lan Project of China and Young Elite Scientist Sponsorship Program by CAST of China. References. C Boller, F K Chang, and Y Fujino, Encyclopedia of structural health monitoring, John Wiley, January Z Su and L Ye, Identification of damage using lamb waves: from fundamentals to applications, Springer, January T E Michaels, J E Michaels and M Ruzzene, Frequency-wavenumber domain analysis of guided wavefields, Ultrasonics, Vol 5, No 4, pp , May 2. 9

10 4. H Sohn, D Dutta, J Y Yang, M DeSimio, S Olson and E Swenson, Automated detection of delamination and disbond from wavefield images obtained using a scanning laser vibrometer, Smart Materials and Structures, Vol 2, No 4, 457, March M D Rogge, C A Leckey, Characterization of impact damage in composite laminates using guided wavefield imaging and local wavenumber domain analysis, Ultrasonics, Vol 53, No 7, pp , March L Yu, C A Leckey and Z Tian, Study on crack scattering in aluminum plates with Lamb wave frequency-wavenumber analysis, Smart Materials and Structures, Vol 22, No 6, 659, May A S Purekar, D J Pines, S Sundararaman and D E Adams, Directional piezoelectric phased array filters for detecting damage in isotropic plates, Smart Materials and Structures, Vol 3, No 4, pp 838, June A S Purekar and D J Pines, Damage detection in thin composite laminates using piezoelectric phased sensor arrays and guided lamb wave interrogation, Journal of Intelligent Material Systems and Structures, Vol 2, No, pp 995-, June B Xu and V Giurgiutiu, Single mode tuning effects on Lamb wave time reversal with piezoelectric wafer active sensors for structural health monitoring, Journal of Nondestructive Evaluation, Vol 26, No 2, pp , November 27.. H W Park, S B Kim and H Sohn, Understanding a time reversal process in Lamb wave propagation, Wave Motion, Vol 46, No 7, pp , November 29.. L Qiu, S Yuan, X Zhang and Y Wang, A time reversal focusing based impact imaging method and its evaluation on complex composite structures, Smart Materials and Structures, Vol 2, No, 54, August C A Balanis, Antenna theory analysis and design, John Wiley, April L Qiu and S Yuan, On development of a multi-channel PZT array scanning system and its evaluating application on UAV wing box, Sensors and Actuators A: physical, Vol 5, No 2, pp 22-23, April L Qiu, M Liu, X Qing, and S Yuan, A quantitative multi-damage monitoring method for large-scale complex composite, Structural Health Monitoring, Vol 2, No 3, pp 83-96, May 23.