# A Deep Learning Approach to Detect Failures in Bridges Based on the Coherence of Signals
## 1 Introduction  
To use a metaphor, infrastructural networks can be described as the veins and arteries of a country. Indeed, they allow for the flux of people and goods, which is essential for the flourishing of culture and economics. Among the components of traffic routes, bridges are the most impactful on a system's resilience. Additionally, bridges are potentially subject to a very large spectrum of degradation processes linked to their constructive materials, structural characteristics and exposure to external agents [1, 2, 3]. This is why an efficient approach to the management and maintenance of these structures has always been considered of paramount importance, with the United States leading the way since the 1970s. The latter has become a hot topic in the last decade, made even more evident by serious facts and collapses happening worldwide with worrying frequency [4, 5]. Many factors contribute to this process: in particular, the scientific literature on bridge safety affirms that ageing and damage caused by natural disasters are the most relevant threats to bridges' integrity, with 7 out of 10 structural failures due to a combination of such factors [6, 7]. To make things worse, data from the World Meteorological Organizationreport a concerning five-time increase in the occurrence of natural disasters over the past 50 years, mainly driven by climate change and more extreme weather conditions [8]. According to most countries' policies, after such exceptional events affect a bridge, its structural safety should be assessed through extraordinary visual inspections, which oversee the deployment of testing equipment to check the status of the superstructure, substructure and underwater elements [9]. However, not only is this practice extremely expensive and time-consuming, but also, its results are questionable and surely not able to capture any phenomena of drift of the structural behaviour of the bridge, which are quantitative and evolve slowly over time [10; 11]. Instead, the continuous monitoring of the bridge through sensors is much more informative. To make a comparison of the two techniques, continuous monitoring might be considered, for example, in the form of a video, while a visual inspection is more similar to a picture. On the other hand, a significant analysis effort is required to extract such valuable information from the huge amount of data produced daily by a monitoring system. In this regard, machine learning represents a precious resource. The design and implementation of efficient algorithms based on artificial intelligence allow for analysing data from heterogeneous sensors simultaneously, making it possible to capture the complexity of a bridge's structural behaviour. This approach can lead to more autonomous, accurate and robust processing of the monitoring data [12]. In recent years, researchers in the structural health monitoring (SHM) community have been exploring the potential applications of deep learning-based approaches for detecting structural damage and assessing the overall condition of structures. By leveraging the power of deep learning, these approaches have the potential to improve the reliability and efficiency of SHM systems, thereby enhancing the safety and performance of structures. [PERSON] et al. [13] demonstrated the effectiveness of a one-dimensional convolutional neural network (CNN) for anomaly identification with vibration signals in bridges. [PERSON] et al. [14] proposed a novel data anomaly detection method that uses computer vision and deep learning techniques. This approach involves converting the original time series measurement values into image vectors, which are then input to a deep neural network to detect various anomalies. In their study, [PERSON] and [PERSON] [15] employed an approach to detect damages in structures by training an RNN using the natural frequency and corresponding Johansen countergation residuals, by removing seasonal patterns from the data with variational mode decomposition algorithm. [PERSON] et al.