# Entropy Wavelet-Based Method to Increase Efficiency in Highway Bridge Damage Identification
## 1 Introduction  
Due to the accelerated population growth in recent decades, the construction of cities, towns, and related infrastructures is essential for the adequate interaction of social, well-being, political, and economic activities in every nation around the world [1; 2; 3]. One of the most critical and expensive infrastructures that allows communication between different regions are bridges, which tend to deteriorate and accumulate diverse types of damage, produced by different environmental and human factors [4; 5; 6]. Therefore, damage to bridges, as in any civil structure, is inherent; however, those constructions can provide many years of surface with adequate maintenance programs and appropriate damage identification processes [7; 8; 9]. Thus, a periodical monitoring of civil structures called structural health monitoring (SHM) is fundamental for preserving the service life of bridges, and avoiding tragic accidents resulting from damage not being detected in time [10; 11]. The global monitoring of bridges offers vital information regarding the serviceability and general integrity of the bridges; however, ensuring safety and continuous service depends on the methodology applied to identify damage in all of the critical elements in a timely, accurate, and efficient manner, as well as on the capacity to monitor the damage propagation and the decisions made to correct the structural defects without significantly affecting the operation of these structures. Bridge diagnosis comprises two levels being included in a damage identification process: the detection and localization of damage. As its name indicates, the damage detection alerts us about the existence of damage in the inspected structure, while the damage localization determines the position of the defects on the structure [12]. Failure to detect damage to bridges in a timely manner can cause collapses with tragic consequences. In this regard, an example of this kind of accident happening in the current century is the Entre-os-Rios tragedy, which was a disaster that occurred on 4 March 2001 in Porto Portugal, where the fourth pillar of the Hintze Ribeiro Bridge, which connected the towns of Castelo de Paiva and Eja over the Duero River, had suffered damage that was not detected in time, causing the collapse of two sections of the road and the death of 59 people in vehicles [13]. Similar to the bridge collapse described above, many catastrophic accidents have occurred due to failures, deteriorations, or the accumulation of damage in different elements of bridges, causing the collapse of entire structures and therefore devastating human deaths and substantial economic losses [14; 15; 16; 17]. Historically, the damage identification process has been performed to visually monitor the condition of bridges. However, some important limitations of this process are a lack of regular monitoring, inspection-dependent monitoring, a delay in defect detection, and an inability to determine damage growth stages [18]. As an alternative to visual monitoring, systems based on SHM are used. In a typical SHM of bridges, sensors are dispersed throughout the structure, and the collected data are used to analyze the condition of the bridge [19; 20; 21]. Different parameters can be used to evaluate structures using SHM systems, such as corrosion, cracking, displacement, fatigue, settlement, deformation, temperature, inclination, vibration, water level, etc. [22]. Therefore, it is of vital importance to develop and implement reliable and low-cost methods for the detection and location of non-visible damage in bridges. In recent years, to address the need to safeguard the structural integrity of bridges, SHM systems have been developed worldwide, and different analysis methods for the detection, location, and evaluation of damage in bridges are being investigated.