# Entropy Wavelet-Based Method to Increase Efficiency in Highway Bridge Damage Identification
## 4 Numerical Results and Analysis
Scenarios shown: healthy bridge and bridge with intermediate severity damage (30% intensity) at 25% L.  
As it can be seen in both diagrams, the increase in the CWT coefficients in the damage zone is noticeable, even more so for the case without edge effects. Therefore, Figure 22 shows that the damage can be identified clearly and very accurately (99.92% accuracy in locating the damage), even with the CWT coefficients corresponding to a single scale value; however, this scale must be very well chosen based on the entropy-CWT diagram. On the other hand, the EWM is applied again, as shown in Section 3.3 of this article, to demonstrate the capacity of the EWM in order to identify damage of different severities and in different positions, taking as reference the diagram shown in Figure 20, which is the final diagram obtained by applying the EWM to identify damage for the case of a bridge with intermediate level damage (30% reduction in cross-sectional area) at 25% of L. This was completed to obtain the two corresponding diagrams for the case of low severity damage (10% reduction in cross-sectional area) at 50% of L (Figure 23) and high severity damage (50% reduction in cross-sectional area) at 75% of L (Figure 24). Figure 10:5 Average CWT coefficients for the scale range from 181 to 1000 from the respective average of 3 measurement points (25%, 50%, and 75% of L) with signals filtered from noisy signals (15% Gaussian noise), extended to remove edge effects. Scenarios shown: healthy bridge and bridge with low severity damage (10% intensity) at 50% L.  
Figure 10:6 CWT coefficients for the scale value of 300, corresponding to the scenario with damage at 25% of L and measuring at 25% of L. Edge effects eliminated via signal extension. As it can be seen in both Figures 23 and 24, the EWM is capable of clearly identifying damage of different severities in different positions with efficiency, low computing time consumption, and high precision. To obtain each of those diagrams, as well as the diagram in Figure 20, about 51 s were required, while, in terms of the precision of damage location, the damage established at 50% of L was located with 99.04% accuracy (Figure 23), the damage established at 75% of L was identified with 99.97% accuracy (Figure 24), and, previously, the damage defined at 25% of L was located with 98.76% precision (Figure 20). In the same way as was completed for the case shown in Figure 22, the respective CWT coefficients diagram is obtained for a single scale value (300), but now for a case with damage at 75% of L and measuring only at 25% of L. The results are shown in Figure 25, and it is possible to see that the damage was identified with high precision (99.40% accuracy) with a single scale value and with a single measurement point, which is the furthest from the damage position. Finally, for a comparison of identical cases applying the WEAM and the EWM, the scenario presented in the last diagram of Figure 12 obtained from [1] applying the MAEW to the bridge with intermediate intensity damage (30%) at 75% of L using filtered signals  
Figure 10:7 Average CWT coefficients for the scale range from 181 to 1000 from the respective average of 3 measurement points (25%, 50%, and 75% of L) with signals filtered from noisy signals (15% Gaussian noise), extended to remove edge effects. Scenarios shown: healthy bridge and bridge with high severity damage (50% intensity) at 75% L.  
Figure 10:8 CWT coefficients for the scale value of 300, corresponding to the scenario with damage at 75% of L and measuring at 25% of L. Edge effects eliminated by signal extension.