# Drive-by Bridge Damage Detection Using Continuous Wavelet Transform
## 1 Introduction  
The aging of transport infrastructure presents a challenging dilemma for infrastructure managers tasked with maintaining extensive networks within budget constraints. Bridges play a crucial role in both road and rail transport, and their failure can disrupt transport networks and pose safety risks [1]. Notably, recent years have witnessed significant bridge collapses, such as the Tretten Bridge in 2022 and the Randklev Bridge in 2023 in Norway, illustrating the imperative for continuous inspection and monitoring. This underscores the need to prioritize ongoing safety assessments to ensure the well-being of bridges and implement intelligent maintenance practices. The development of Structural Health Monitoring (SHM) techniques has been underway for decades as a crucial step in achieving these goals. The vibration-based methodology within SHM methods presents innovative solutions to the previously mentioned challenges. Typically, these methods leverage changes in structural modal characteristics before and after damage occurs, making them capable of detecting not only surface faults but also sensitive to interior damage. However, conventional vibration-based methods usually necessitate multiple sensors and specialized data collection systems tailored to specific applications [2; 3; 4; 5; 6; 7; 8; 9]. The custom nature and associated costs of traditional SHM approaches often pose obstacles for large-scale monitoring initiatives. Consequently, there has been a notable shift towards adopting indirect monitoring techniques for bridges, ranging from drone-based visual inspections [10; 11] to capturing bridge vibration signals using measurements collected on a specially equipped passing vehicle, commonly known as \"drive-by monitoring\" or \"vehicle scanning method\" (VSM). In VSM method, initially proposed by [PERSON] et al. [12], the instrumented vehicle serves as both the actuator and receiver while traversing a bridge. Drive-by monitoring systems offer advantages over vision-based damage identification systems, as signals collected from the vehicle can reveal structural changes caused by damage on a bridge, providing valuable insights into the impact of the damage on the overall behavior of the structure [13]. As a result, this approach has gained popularity and undergone further development to extract the dynamic characteristics of bridges including natural frequencies [14; 15; 16; 17; 18; 19], mode shapes [20; 21; 22; 23; 24], and damping ratios [25; 26; 27]. Some studies focused on estimating and characterizing road profiles [28; 29; 30]. Several studies validated theoretical and numerical findings through laboratory and field experiments [31; 32; 33; 34; 35]. However, the literature on damage identification is relatively sparse in comparison to the abundance of articles addressing modal properties using drive-by monitoring methods. Damage detection techniques, being one of the core components of SHM, offer essential means for assessing the condition of bridges [36]. To this end, typically, drive-by monitoring methods establish a bridge damage index using either modal-related parameters or other damage-related parameters extracted from the vibration data using data-driven algorithms. In modal-parameter-based methods, as the name suggests, the initial step involves identifying the frequency, mode shapes, and damping of the bridge using the acceleration data obtained from the vehicles. Subsequently, the bridge damage index is constructed based on these modal characteristics. For example, [PERSON] and [PERSON] [37] introduced an innovative algorithm for bridge damage detection based on mode shapes, using laser vibrometers and accelerometers on an instrumented vehicle. The algorithm demonstrated effectiveness and precision, particularly at speeds below 8 m/s. Similarly, [PERSON] et al. [38] assessed bridge damage, including support immobilization and reduced girder stiffness at mid-span, utilizing mode shapes recovered from passing vehicle responses. [PERSON] et al.