# Drive-by Bridge Damage Detection Using Continuous Wavelet Transform
## 1 Introduction
[20; 39] proposed a damage detection method using mode shape squares derived from the amplitude history of Short Time Fourier Transform applied to the recorded acceleration of the vehicle after crossing the bridge. [PERSON] et al. [40] also utilized mode shape squares extracted from the response of a moving vehicle via the Hilbert Transform (HT) for detecting damage in bridges. In a different approach, [PERSON] et al. [41] employed bridge frequencies to identify damage in bridges. They utilized acceleration signals from a quarter car model, processed them using Continuous Wavelet Transform, and analyzed them to quantify the modal frequencies of the bridge under various vehicle speeds and damage scenarios. The reduction in natural frequency served as a damage index, enabling the identification of the presence and severity of the damage. Alternative methods frequently leverage other damage-related parameters, such as instantaneous mode functions and instantaneous amplitude squared (IAS) of the driving component, extracted through data-driven algorithms, incorporating signal processing techniques and machine learning. The benefit of machine learning algorithms lies in their ability to effectively utilize the extensive data amassed by the drive-by monitoring. [PERSON] et al. [42] introduced an innovative method for the indirect health monitoring of bridge populations using acceleration data collected from a mobile sensor network. Distinguishing itself from the majority of literature, the study involved obtaining acceleration responses from a variety of vehicles under both baseline and damaged conditions. In both scenarios, the acceleration data from each vehicle crossing the bridge were collected and processed using Mel-frequency cepstrum (MFC). For damage identification, the extracted MFC coefficients were utilized in combination with Principal Component Analysis [42], Kullback-Leibler (KL) divergence [43], and the root mean square deviation [44]. [PERSON] and [PERSON] [45] proposed a damage assessment method using a deep autoencoder (DAE) with multiple convolutional layers and an LSTM layer. The DAE, trained for healthy bridge conditions, constructed a feature space sensitive to bridge dynamics. The damage index, based on KL divergence, was found to be effective for damage detection and severity quantification, as in [43]. [PERSON] and [PERSON] [1] introduced an innovative deep learning framework for bridge damage detection, employing an artificial neural network (ANN), taking into account environmental factors such as temperature and operational effects such as road roughness, similar to [46]. Some studies studied proposed detection methodologies that do not rely on modal parameters, eliminating the need for acceleration data collected from a mobile sensor network. [PERSON] et al. [47] utilized Instantaneous Mode Functions (IMFs) derived through Empirical Mode Decomposition (EMD) applied to the response of a moving vehicle passing over a bridge. They proposed a damage indicator based on the difference between the IMFs of the vehicle response during passage over a healthy bridge and a damaged bridge to characterize damage. [PERSON] et al. [48] developed a method using the instantaneous amplitude squared (IAS) of the contact point acceleration via Hilbert transform, leveraging its narrowband nature for damage detection and localization. Numerical simulations demonstrated the successful detection and localization of damage using the IAS at the driving frequency. [PERSON] and [PERSON] [49] introduced a novel damage detection method that establishes a physical link between contact point accelerations and the instantaneous curvature of a bridge. This approach facilitates effective and precise damage detection and localization in bridges through drive-by monitoring methods. [PERSON] and [PERSON] [50; 51] proposed a wavelet-based drive-by algorithm for damage detection in bridges, using wavelet coefficients obtained from the acceleration responses of the vehicle within specific frequency bands sensitive to damage.