# EMD-Shannon Entropy-Based Methodology to Detect Incipient Damages in a Truss Structure
## 1 Introduction
WVD provides a time-frequency (TF) representation of transient and non-linear signals; however, cross-term items (frequencies not contained into the time-series signal) appear in the representation, affecting the technique's ability to correctly estimate the instantaneous frequencies related to possible damages in the structure [36]. STSM models such as AR (autoregressive), MA (moving average), or ARMA (autoregressive moving average), among others, are used mainly to model the behavior of time signals with linear or time-invariant properties; however, they present problems when modeling noisy and non-linear (NL) structural responses, which are generally measured in structural responses [37]. In order to lessen the problems encountered when using the aforementioned techniques, other SPS are employed for monitoring structure conditions, such as wavelet transform (WT) [2; 38; 39; 40; 41; 42; 43] and blind source separation (BSS) [44; 45]. In particular, WT is a TF strategy designed to handle non-linear and non-stationary signals. Unfortunately, to ensure the best possible results using WT, an appropriate selection of wavelet mother, as well as the decomposition level, is of vital importance to correctly monitor the structure's condition [46; 47]. The BSS method is a relative new signal processing technique employed for monitoring structure conditions, which is capable of exposing features that are blended together in the measured response; nevertheless, it still presents problems in the analysis of signals with non-stationary properties [48]. In recent years, empirical mode decomposition (EMD)-based methods have been introduced for SHM of simple beams or few structural elements [28; 49; 50; 51; 52] and system identification [53; 54; 55; 56]. EMD-based methods are capable of analyzing NL and NS time series signals according to their frequency information [57], making them suitable tools for detecting damage in a structure, since the measured signals include non-linear and non-stationary properties. It must be noted that the aforementioned works have employed the EMD methods in civil structures to identify modal parameters such as natural frequencies, damping ratios, and modal shapes, among others, and to detect mainly consolidated damages (damage levels from moderate to high), requiring a high quantity of computational resources, because several indices such as energy, kurtosis, skewness, among others, are employed, as well as a high number of sensors; in several cases, sensors are placed next to damage, which is unrealistic in real-life situations. In addition, it should be noted that some of the aforementioned works make modifications to EMD methods in an attempt to overcome limitations, such as the capability of dealing with noisy signals, or improving the decomposition of the signal. While the obtained results from the adapted techniques are good, the resulting algorithms are application-specific, which might lead to sub-optimal results if the algorithms are not used for the specific application for which they were designed. Hence, it is evident that more effort for proposing low-complex and efficient methodologies based on the EMD methods, i.e., Ensemble-EMD (EEMD), and Complete-EEMD (CEEMD), without specific personalization, and few sensors for damage detection into civil structures mainly incipient damages (light damage level), a condition that slightly modifies the features into the measured signal, are still required. Considering the benefits that EMD methods can generate in a vibration-based SHM scheme, in this article, a methodology based on both the EMD method and the Shannon Entropy Index (SEI) for detecting incipient damages in a 3D 9-bay truss-type bridge is presented. The most representative EMD-methods, i.e., EMD, EEMD, and CEEMD, are investigated in order to evaluate their performance for this task. In order to evaluate the effectiveness of the proposal, an exhaustive experimentation by considering four damage-severity levels produced by corrosion is carried out.