# Damage Detection Method Based on Continuous Wavelet Transformation of Lamb Wave Signals
## 4 Implementation Using the Damaged Signals  
The baseline signals from the undamaged plate may not always be available to calculate the difference signals in the practical environment. It also increases the computational cost by calculating two additional signals for each sensing path, i.e., undamaged and difference signals. In addition, a tiny incorrect baseline can make the whole estimation wrong. Therefore, the proposed method was implemented using signals directly from the current state of the plate. The baseline-free implementation presented here is for the multiple damage scenario shown in Figure 16. The damaged signal and coefficient of CWT for sensing path A8B8 are shown in Figure 20a,b, respectively. The damage-scattered fluctuations in these signals are too small compared to the excitation fluctuation; therefore, the region of these plots containing the damage-scattered fluctuations is shown separately in Figure 20c,d, respectively. The damage-scattered peaks can be clearly seen in Figure 20d.  
The damage possibilities for sensing path A8B8 using baseline-free estimations are presented in Figure 21 along with actual D1 and D2. Figure 21a contains the possibilities without time compensation and Figure 21b with time compensation. Since, the damage-scattered peaks are too small, the damage possibility values for D1 is hardly visible, whereas for D2 it is so small that it is not even visible. It is because the possibility values for the excitation peak is very high. Similar to Figure 20c,d, the damage-focused regions of Figure 21a,b are shown separately in Figure 22a,b, respectively. The highest damage possibility region near the actuator-sensor locations has been left out of these images, and the distributions around D1 and D2 are more visible now compared to surrounding regions.  
Similarly, the damage possibilities from the other seven sensing paths were plotted and fused for damage imaging. The high-possibility regions for each sensing pair were near the actuator-sensor pairs, just as for the case of A8B8. The aggregate images without and with time compensation are shown in Figure 23a,b, respectively. The time-compensated signals could accurately image both the damage, whereas the localization of damage without compensation did not work for this case either. It should be noticed that the high-possibility regions near each actuator-sensor pair disappeared in the aggregate image. It is because the possibility values from other sensing pairs at these locations were almost 0, which reduced the aggregate value to 0 using multiplication-based \(DI_{m}(x_{i},y_{i})\). The individual damage possibility values from all 8 sensing pairs and the aggregate value at damage locations based on \(DI_{m}(x_{i},y_{i})\) are presented in Table 1 for the pulse-echo configuration. Non-zero damage possibility values from all sensing pairs existed at the damage locations, which made the non-zero aggregate value appear only at the damage locations.  
Figure 20: (**a**) Damaged signal at A8B8; (**b**) coefficient of CWT with and without time compensation at A8B8; (**c**) damage-focused region of signal (**a**); (**d**) damage-focused region of signal (**b**).  
Figure 21: Baseline-free damage possibilities in multiple damage scenario for sensing path A8B8: (**a**) without time compensation; (**b**) with time compensation.  
Figure 22: Damage-focused region of (**a**) Figure 21a; (**b**) Figure 21b.  
Figure 23: Baseline-free aggregate damage image for multiple damage scenario in pulse–echo configuration: (**a**) without time compensation; (**b**) with time compensation.