# EMD-Shannon Entropy-Based Methodology to Detect Incipient Damages in a Truss Structure
## 1 Introduction  
Civil structures represent a pillar in the economy and modern life because they provide protection to people and communication among different countries [1; 2]. Among different kinds of civil structures, truss-type designs are one of the most employed structures in the design of civil structures because they offer great benefits such as ease of assembly and light weight. In this regard, this type of design has been used to construct bridges, towers, cranes, roof supports, and building skeletons, among others [3; 4; 5]. Nevertheless, they suffer continuous degradation or failure during their service life because of excitations produced by human or natural hazards, such as earthquakes, tornadoes, hurricanes, and wind, among others [6; 7; 8]. Hence, a continuous assessment of their structural integrity, known as structural health monitoring (SHM), is of paramount importance, since any deterioration or failure can be attended to early, in order to avoid potential human and economic losses. In the past decade, several SHM schemes that make use of experimental procedures such as visual inspections, acoustic emission, ultrasound, laser scanning, and image processing produced by X-raysand thermography, among others, are employed for assessing structural conditions [9; 10; 11; 12; 13; 14]. However, these procedures require a priori knowledge of the damage location, as well as an easy access to the area to be evaluated, and in certain cases, it is required to temporarily close the structure during its evaluation, which in real-life situations is not always possible [15]. For these reasons, a great deal of research of SHM in recent years has been focused on the development of new procedures based on vibration monitoring, because it has been demonstrated to be capable of detecting damages in hidden areas before they can be identified by visual inspections. Further, a SHM scheme based on vibration monitoring presents the advantages of being low cost and generating a continuous monitoring of structure without interrupting its normal operation [16; 17]. The main idea of using a vibration-based SHM scheme is that damage in the structure affects its structural physical characteristics such as mass, stiffness, and damping, among others, producing a change in the measured response, which depends mainly on the severity level of damage. Particularly, the incipient fault produces slight modifications in the properties of the measured signal when they are compared with the ones measured when the structure was in a healthy condition [2]. Hence, a powerful signal processing technique or method capable of estimating subtle features in the measured signals is of vital relevance to detect damage, mainly in its incipient state, in order to schedule the corresponding maintenance in the civil structure. In recent years, numerous signal processing strategies (SPS) that analyze vibrations to perform damage detection in civil structures have been proposed, among which the Fast Fourier transform (FFT) and its variants known as frequency response function (FRF) [18; 19; 20; 21; 22], multiple signal classification (MUSIC) [3; 23; 24; 25], Wigner-Ville distribution (WVD) [26; 27], and statistical time series models (STSM) [4; 28; 29; 30; 31; 32] are the most employed. Nevertheless, although good results have been reported using the aforementioned techniques, they present significant limitations. For instance, FFT, and its variation FRF, cannot analyze signals that have non-linearity properties and a non-stationary (NS) nature, which are generally encountered in the measured responses of civil structures. In addition, they cannot adequately analyze noisy signals, producing errors in the estimated results [33; 34]. On the other hand, MUSIC method is an efficient tool to analyze noisy signals; however, the number of frequencies that are present in the time signal must be known a-priori, which, in practical terms, is not possible. Moreover, transient signals still cannot be processed correctly [35].