# Damage Detection Method Based on Continuous Wavelet Transformation of Lamb Wave Signals  
[PERSON]  
1 State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China; [EMAIL_ADDRESS] (M.S.H. There are several damage estimation methods based on the sparse array of PZT transducers, which have shown a great potential for the identification of local damage. However, the Lamb wave signals generated by PZT transducers are dispersive and multimodal. An accurate interpretation of transducer data is important for the extraction of damage features such as location and severity from complicated Lamb wave signals. Therefore, sophisticated signal processing techniques such as fast Fourier transform [5], short-time Fourier transform [6], Hilbert transform [7], warped frequency transform [8], and signal-difference-based correlation coefficient [9; 10] have been used to accurately analyze the dynamic response signals scattered by damage. Among these methods, the continuous wavelet transformation (CWT) [11; 12] has recently gained attention and popularity due to its powerful time-frequency feature extraction from complicated signals, its ability to detect the signal singularity for physical damage inspection, and to depress the dispersive characteristics of the Lamb waves [13; 14]. In recent years, Lamb-wave-based imaging methods such as phased array [15; 16] and delay-and-sum [17; 18; 19] algorithms have been widely used for damage localization in plate-like structures. The damage imaging methods have been further empowered by probabilistic approaches such as Probability-Based Diagnostic Imaging (PDI) [20; 21; 22], Reconstruction Algorithm for Probabilistic Inspection of Damage (RAPID) [23; 24], Algebraic Reconstruction Techniques (ART), and Lamb Wave Tomography (LWT) [25; 26]. These methods have used different parameters to define the probability regions for individual sensing paths, which were then used to reconstruct the damage images. For example, the PDI methods have used the weight distribution functions [20; 21; 27; 28; 29; 30] to define the probability region between actuator-sensor pairs. These distribution functions depended on a scale/shape factor, \(\beta\), which controlled the effective size of the elliptical probability area for each sensing path. Similarly, the RAPID and LWT methods used the difference between damaged and undamaged signals to define the signal difference coefficient (SDC) [23; 24; 31; 32; 33; 34]. The SDC also depended on \(\beta\), which controlled the effective size of the probability region. In most of these methods, the probability of finding the damage depended on the intersection of direct paths between actuator-sensors pairs [20; 21; 23; 24; 33; 34; 35; 36; 25]. The probability of accurately locating the damage increases if more direct path intersections fall around the damage region. Consequently, the use of more transducers increases the path intersections and obtains more accurate damage imaging. That is one of the reasons why these methods faced difficulties locating the multiple damage with fewer transducers. Furthermore, these methods were based on the signal difference obtained by the comparison of the damaged signal with the baseline signal, which required additional data to be recorded and processed [27; 29; 30; 31; 33; 34; 35; 36], and the baseline data may not always be available for practical applications. In the current research, instead of using any probability distribution function, the possibilities of damage presence are directly defined by CWT of the normalized damage-scattered signals. No separate parameter is used to define the size of the possibility region, it is directly defined by the damage-scattered peak in the normalized CWT signals. The damage possibilities from individual sensing pairs are fused using conjunctive and compromised fusion schemes to image the damage. The method was tested for pitch-catch and pulse-echo arrangements of transducers.