# Damage Detection Method Based on Continuous Wavelet Transformation of Lamb Wave Signals
## 7 Discussion of Results  
Two different excitation configurations, pitch-catch and pulse-echo, and damage index based on two different image fusion schemes, compromised fusion \(DI_{a}(x_{i},y_{i})\) and conjunctive fusion \(DI_{m}(x_{i},y_{i})\), were tested in the proposed method. The results presented in Figures 10 and 11 verified that the pulse-echo configuration with the conjunctive fusion scheme was most suitable for the proposed method. The pulse-echo configuration was also computationally inexpensive as it provided better accuracy with only 8 excitations compared to the pitch-catch configuration with 28 excitations. The comparison of signals presented for pulse-echo configuration in Figures 8, 13, 17 and 20 with pitch-catch configuration signals presented in Figure 7 showed that the damage scatterings were much stronger than the edge scatterings in case of pulse-echo configuration, whereas the edge scatterings were stronger in case of pitch-catch configuration, for the same size of damage in both cases. This made the high-possibilities region appear at the edge location instead of the damage location during pitch-catch estimation, as shown in Figure 9a. This is one of the reasons why inaccuracies appeared in damage estimation based on the pitch-catch configuration. The damage possibilities envelopes defined by the coefficient of CWT were normalized in order to range the possibility values from minimum 0 to maximum 1. The damage index \(DI_{m}(x_{i},y_{i})\) produced better estimation of the damage region because it is based on the multiplication of the possibility values at grid points from each sensing path. When the damage possibilities for an individual path were too high at a non-damaged location, it still reduced to zero in the aggregate image when multiplied  
Figure 29: Aggregate damage image in pulse–echo configuration through experiments. with the values from other sensing paths at the same region. The non-zero values of possibility in the aggregate image appeared only at the damage location because the values from all sensing paths were non-zero at that location. For the same reason, \(DI_{m}(x_{i},y_{i})\) worked well even when the damage-scattered fluctuations were too small compared to the excitation fluctuation \(\mathsf{S}_{0}\) for baseline-free signals in Figure 20. Although, the damage-scattered peaks and damage possibilities were too small for an individual sensing path, all the higher-value regions disappeared in the aggregate image because values from other paths at those locations were 0, leaving behind only the damage region having a non-zero contribution from all sensing paths, as evident from Figure 23b. The results presented in Figures 19b and 23b indicated that multiple damage could be accurately estimated with and without the baseline signals. The method could not only accurately locate the damage but also provided the severity of each damage with respect to the other. In these imaging results, the damage D2 of 12 mm diameter appeared to have a higher possibility values than the smaller damage D1 of 10 mm diameter. It made the damage image for D2 more severe in intensity and extent than that of D1. The damage index was based on CWT signals, which have a better signal-to-noise ratio and can extract the time-frequency characteristics exactly from the noisy real-world signals. That is why CWT could process the Lamb signals directly from the damaged plate without a baseline signal from an undamaged plate. In the proposed pulse-echo configuration, the damage-scattered peaks in CWT envelopes were much more dominant than other peaks, therefore any additional noise in real-world problems would still ensure that the damage-scattered peaks have the maximum value of 1 in the CWT envelopes for accurate damage estimation. Generally, the Lamb waves are dispersive in nature, which causes an error in determining its characteristics. The time compensation equal to the half period of the excitation signal is valid when the Lamb waves are not dispersive.