# Entropy Wavelet-Based Method to Increase Efficiency in Highway Bridge Damage Identification
## 1 Introduction
In recent decades, SHM techniques, based on the analysis and post-processing of the vibration responses of bridges, have become the most promising alternatives used to efficiently detect, locate, and evaluate the severity of damage in this type of civil structure, guaranteeing its integrity and predicting its useful life [23; 24]. Thus, vibration-based methods for identifying damage in structures subjected to moving loads, such as bridges, can be broadly classified into parametric and non-parametric methods [25]. Parametric methods work with data in the modal domain [26; 27; 28; 29; 30; 31]. On the other hand, non-parametric methods use data in the time or frequency domain; these include wavelet theory [32; 33; 34; 35], empirical mode decomposition [36; 37; 38], time series analysis [39; 40; 41], multiple signal classification [42; 43], entropy [44; 45; 46; 47], neural networks [48; 49; 50], fractals [51; 52], principal component analysis [53; 54; 55; 56], etc. In particular, the wavelet energy accumulation method (WEAM) is a non-parametric method, previously developed in [1], with the objective of detecting and locating damage in vehicular bridges. This method overcomes the limitations of the parametric methods, and provides additional advantages from the previously developed non-parametric methods. Despite the advantages of WEAM, which include its ability to detect and locate diverse types of damage in bridges with high precision, in different locations, and of various severities via the use of a few sensors distributed on the bridge deck, its main disadvantages are that it involves a significant number of stages, as well as the requirement of a high computing time. According to the aforementioned issues, in this article, a new method, called the entropy wavelet-based method (EWM), is presented, which eliminates the drawbacks of the WEAM via the implementation of an algorithm based on the Shannon entropy [57]. This method avoids the need of obtaining three-dimensional colored CWT (continuous wavelet transform) diagrams with very good resolutions, a very wide initial scale range, and the appropriate choice of the color map to begin investigating whether there has been damage caused to the analyzed bridge via the use of monitoring data, as well as in which area of those diagrams the damage identification is easier, which again requires a significant computing time. With the entropy-based algorithm that is developed and implemented in this study, it is possible to know the most convenient specific scale value or scale range in a very timely manner, allowing for the identification of damage without a loss of precision in the damage location, thus saving a significant amount of computational time; this will be of great help for practical systematic applications on the bridges of the Federal Highway Network of a specific country. Thus, in this work, an entropy wavelet analysis is carried out, which gives rise to the new EWM, which improves the WEAM, making it more efficient for damage identification in highway bridges via the use of the vibration data obtained from numerical simulations, based on the finite element model of the Rio Papaloapan Bridge (RPB) in healthy conditions and with diverse damage scenarios (different locations and damage severities), which was calibrated by taking the vibration monitoring data of the real bridge in operation as reference. Moreover, the vibration data acquired from the real-life RPB in its healthy condition and with a removed cable are used to validate this new method in an experimental manner. Therefore, with the implementation of the algorithm based on the Shannon entropy, it is possible to optimize the WEAM in order to have a new, more efficient, and simple method (EWM) for the identification of damage in highway bridges, allowing us to obtain results for damage detection and localization with precision and with very low computing time.