# Entropy Wavelet-Based Method to Increase Efficiency in Highway Bridge Damage Identification
## 4 Numerical Results and Analysis
On the other hand, for the damaged case curve, the high values of CWT coefficients in the regions where there is no damage are eliminated, and the sudden increase in the CWT coefficients is further concentrated in the damage area. In fact, the maximum value of CWT coefficients is further adjusted with the exact damage position, since the damage was located with 99.44% accuracy with edge effects, while, without edge effects, the localization precision was 99.68%. Figure 10:0 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), corresponding to the scenarios of the healthy bridge and the bridge with damage at 25% of L.  
Taking into account that these results are obtained numerically, in order to apply the EWM using signals more similar to those acquired from real-life bridges, 15% of Gaussian noise was added to the numerical signals obtained from the FEM simulations. In order to closely simulate reality, the percentage of added noise is a very high value according to what is usually considered in the literature [64]. Figure 19 shows the equivalent diagram to the one presented in Figure 18, now adding Gaussian noise to the signals before being processed. As it can be observed, despite the noise effect, damage detection is still clearly possible, and is located with 98.12% accuracy, which is an excellent percentage, especially considering the large amount of noise that was added to the signals and the extensive length of the bridge considered. Finally, as it would occur in the practice of signal processing acquired in real-life bridges, the noisy signals are filtered to try to eliminate as much noise as possible and ensure that they are as similar as possible to the signals obtained directly from the FEM  
Figure 10:1 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 noisy signals (15% Gaussian noise), extended to remove edge effects. Scenarios shown: healthy bridge and bridge with damage at 25% L.  
Figure 10:2 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 previously extended to eliminate edge effects. Scenarios shown: healthy bridge and bridge with damage at 25% L.  
simulations before adding noise. To do this, a Savitzky-Golay filter of order 2 and window length 19 is used, in the same way that it was used for the case presented in [1] when applying the WEAM. The corresponding CWT coefficients diagram from filtered signals is shown in Figure 20, and it is possible to see that the curves are smoothed and the damage identification becomes clearer and more precise with respect to the noisy case, locating the damage with an accuracy of 98.76%, thus improving the accuracy in damage identification with signal filtering, and maintaining similarity to the original case before adding Gaussian noise (Figure 18 localizing the damage with 99.68% accuracy). Additionally, to demonstrate the usefulness of the entropy-CWT diagram, particularly in SEI zone 3, instead of graphing the average of the CWT coefficients for the selected useful scale range (181 to 1000), the CWT coefficients for the damaged case analyzed are obtained for a single scale value that is within SEI zone 3, where the chaos increment caused by the damage is already evident. Thus, the scale value of 300 is chosen, and the CWT coefficients are plotted for this damaged case (measuring only at 25% of L) both with and without edge effects; see Figures 21 and 22, respectively. Figure 10:3 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 without being removed. Figure 10:4 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.