# Entropy Wavelet-Based Method to Increase Efficiency in Highway Bridge Damage Identification
## 6 Conclusions  
This article presents, in detail, the development of the EWM, which is an improved version of the WEAM presented in [1], and whose main objective is to detect and locate damage in highway bridges more efficiently. In particular, the EWM eliminates a large number of steps from the WEAM, providing a simpler, faster, and more accurate method of damage identification.  
To give way to this new method, an algorithm based on the Shannon entropy was implemented, which allows us to know, from the vibration signals acquired on a bridge, the level of chaos produced by the respective CWT coefficients of the signals, and what CWT scale they correspond to. In a similar way to the entropy-CWT diagram, three zones are established for different CWT scale ranges according to the level of chaos of the CWT coefficients and the causes that generate those levels of chaos (effects of natural frequencies, edge effects, and effects of structural damage).  
In this way, the entropy-CWT diagram allows for the defining of the useful CWT scale range in order to identify damage by averaging the CWT coefficients, and is obtained in a few seconds (less than 7 s for each measurement point analyzed in this article). This is dissimilar to the WEAM, which, for the same purpose of establishing the useful CWT scale range, requires the generation of colored 3D CWT diagrams that require a high computational load.  
For validation, the EWM was applied in a finite element model of the RPB, considering the healthy case and different damage scenarios. The results indicate that the EWM is capable of identifying the diverse damage conditions successfully, detecting damage clearly, with localization precision between 98.76% and 99.97% and with results obtained quickly (around 51 s).  
Therefore, the numerical results of the application of the EWM are promising, since, when compared to the WEAM, the precision in locating the damage is further increased, which was already very good with the WEAM (increase of approximately 0.11%). Above all, the disadvantages of the WEAM related to the number of stages required to apply the method are eliminated (going from 11 to 7 stages), thus reducing the computing time by 5.67 times.  
Furthermore, the experimental validation shows that the EWM was able to identify damage in the real-life RPB (removed cable), even when using random transit, thus reinforcing the advantages of this method. In future works, this method will be applied considering diverse severities of damage in different cables of the numerical model, as well as in the real real-life RPB with removed cables in different positions.  
Conceptualization J.M.M.-L.; investigation, resources, and visualization, J.M.M.-L., J.J.Y.-B., M.V.-R. and J.P.A.-S.; formal analysis, J.M.M.-L., M.V.-R. and J.P.A.-S. writing--original draft, review, and editing, all authors. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Council of Humanities, Sciences and Technologies (Consejo Nacional de Humanidades, Ciencias y Tecnologias, CONAHCYT-Mexico) through project 34/2018 of the Program \"Investigadoras e Investigadoras por Mexico\" del CONAHCYT (Catedras CONAHCYT) and the scholarships 161138, 296574, and 253652 given to [PERSON], [PERSON], and [PERSON], respectively, through the \"Sistema Nacional de Investigadoras e Investigadoras (SNII)-CONAHCYT-Mexico. The authors thank to the Instituto Mexicano del Transporte for all the support provided to perform this research.  
Not applicable.  
The data presented in this study are not publicly available due to privacy issues.  
The authors declare no conflicts of interest.