# Drive-by Bridge Damage Detection Using Continuous Wavelet Transform
## 1 Introduction
Inspired by this approach [51], [PERSON] et al. [52] employed characteristic wavelet coefficients (CWC) extracted from the contact point acceleration of a quarter car to identify bridge damage. While these studies have made significant strides in bridge damage identification using indirect measurements, there remains a critical gap in the literature. Approaches relying on modal-related parameters necessitate prior knowledge of modal parameters such as frequencies, mode shapes in normal/healthy conditions, posing a significant drawback for efficient first-time damage inspection where damage already exists [20; 37; 38; 39; 40; 41]. On the other hand, the studies utilizing non-modal-related parameters [1; 42; 43; 44; 45; 46] and incorporating machine learning demonstrate the capability to identify the presence of damage through continuous monitoring as it propagates throughout the lifespan of the structures. However, they fall short in providing information about the specific location of the damage. Moreover, machine-learning-based indirect inspection methods require extensive training data, presenting additional challenges for damage identification and are prone to overfitting. On the other hand, studies utilizing contact point accelerations show better promise in detecting and localizing damage when the car configurations are known or when the same car is used for both baseline and damaged cases. However, this requirement may pose challenges in real-world applications where a standardized test car configuration is not feasible. Certain studies [50; 51; 52] also showcase significant potential for both detecting and localizing damage, even in cases with no prior information about the damage presence in the bridge. Nevertheless, their effectiveness diminishes in the presence of road roughness, as the high-frequency content of roughness contaminates the extracted components (wavelet coefficients), leading to a hindrance in damage detection. In order to address these gaps and enhance the robustness of bridge damage identification using drive-by monitoring methods, we propose a framework that is based on the continuous wavelet analysis of accelerations recorded on two sensors mounted on a vehicle that crosses the bridge. The proposed framework improves the state-of-the-art in damage detection using drive-by monitoring methods by combining the following aspects, which lead to a more reliable, accurate, and applicable approach. * The proposed method aims to utilize the changes in the static response of the bridge, which was shown to be much more sensitive to damage than its dynamic counterpart. As such, it eliminates the dependence on modal parameters, which are known to be significantly affected by factors other than damage such as environmental factors. * Unlike the methods that depend on contact point acceleration, the proposed method does not require _a priori_ knowledge about the mechanical properties of the instrumented vehicle such as its suspension stiffness and damping. The only vehicle param eter that is required to apply the proposed framework is the vehicle frequency, which can be easily measured. * The proposed framework attenuates the negative impacts of road roughness by using the residual accelerations computed as the difference between front-axle and rear-axle accelerations. * The proposed framework can detect and locate damage in the absence of corresponding data from the undamaged bridge. As such, the article contributes significantly to our common understanding of use of drive-by monitoring methods for damage detection paving the way to more accurate, reliable, and economical structural health monitoring practices.