# Damage Detection Method Based on Continuous Wavelet Transformation of Lamb Wave Signals
## 3 Implementation Using the Difference Signals
### Single Damage Scenario  
For the single damage scenario shown in Figure 4, if the pitch-catch configuration was utilized, the signals from A2 to A8 in undamaged and damaged plates are shown in Figure 7(a,b), respectively. The undamaged signal contained the excitation signal S\({}_{0}\), which travelled a direct path between actuator to sensor represented by distance \(L_{A-s}\) in Figure 1, and another signal scattered by edge of the plate. The damaged signal contained the direct excitation S\({}_{0}\) and a damage-scattered signal, which travelled a longer distance \(L_{A-D}+L_{D-S}\). The undamaged and damaged dynamic response signals were evaluated in the discrete form in the time domain. The subtraction of the undamaged signal from the damaged signal was called the difference signal, which represented the presence of  
Figure 6: Set of path loci in the discretized domain for sensing path: (**a**) A2A8; (**b**) A8B8.  
damage in the plate. The difference of the signals in Figure 7a,b is presented in Figure 7c. The first fluctuation in the difference signal represented the damage-scattered signal whereas, rest of the scatterings in Figure 7b,c were caused by the plate edges. The ToF for damage-scattered signals in Figure 7b,c was represented by Equation (1). The coefficient of CWT for the normalized difference signal was calculated using Equation (7), which provided the possibilities envelope for damage imaging, presented in Figure 7d. Similarly, the damage possibilities curves for all other actuator-sensor pairs in pitch-catch configuration were calculated.  
In the pulse-echo configuration, when A8 excited the Lamb wave signal and B8 received the signal, the undamaged and damaged signals are presented in Figure 8a,b, respectively. The first fluctuation in the difference signal presented in Figure 8c was caused by the scattering from the damage, and the remaining fluctuations were caused by the scattering from plate edges. The coefficient of the normalized CWT signal as the damage possibilities curve for A8S8 is presented in Figure 8d. Similarly, the damage possibility envelopes for all other actuator-sensor pairs were calculated for the pulse-echo configuration. The envelopes based on the peaks of CWT coefficients in Figures 7d and 8d defined the possibilities of damage existence as a field value for the set of path loci shown in Figure 6a,b, respectively, using Equation (9).  
The time compensation in CWT signals was not made at this stage. The resulting damage possibility images for paths A2A8 and A8B8 are shown in Figure 9a,b, respectively. The actual damage D1 is also presented in these figures, which falls on the first fluctuation in the difference signal, as explained earlier. Similar damage possibility images were created for each sensing path in both the configurations. For the pitch-catch configuration, \(DI_{a}(x_{i},y_{i})\) based on the compromised fusion scheme and \(DI_{m}(x_{i},y_{i})\) based on the conjunctive fusion scheme provided the aggregate possibility for damage estimation in Figure 10a,b, respectively. Similarly, for the pulse-echo configuration, the aggregate damage images for \(DI_{a}(x_{i},y_{i})\) and \(DI_{m}(x_{i},y_{i})\) are shown in Figure 11a,b, respectively. The results indicate that the pulse-echo configuration provided a better damage estimation in both the fusion schemes with only eight sensing paths as compared to the pitch-catch configuration with 28 sensing paths. Therefore, the pulse-echo configuration was used for the remaining analyses in this paper.