The vibration response data on the bridge deck under the load of moving vehicles contains a wealth of information about the geometric parameters of the bridge, enabling effective identification of structural damage. Machine learning can extract key information from the response data and capture linear relationships within it. Taking the Shaozhou Bridge as the research background, this study established a finite element model for a cable-stayed bridge and applied loads from two-axle trucks with various vehicle parameters to the cable-stayed bridge model under different small damage conditions to simulate the vibration response of the cable-stayed bridge model under moving load. Principal component analysis (PCA) was employed for dimensionality reduction and compression of acceleration data, and Bayesian-optimized least squares support vector machine (BO-LSSVM) was used to analyze both damage localization and quantification of the cable-stayed bridge under different load combinations. Additionally, in response to inaccuracies in predicting damage for multiple cables, a method was proposed to integrate localization labels into the damage data. The results indicate that, through a substantial amount of damage response data, the BO-LSSVM model can identify the optimal hyperparameter combinations, effectively analyzing complex response data and monitoring cable damage levels using moving vehicle loads. Utilizing PCA for dimensionality reduction and compression of acceleration response data maintains predictive accuracy while enhancing the computational efficiency of machine learning, thus conserving computational resources. Furthermore, the method of adding localization labels to multiple damage feature data can improve damage identification accuracy. This study provides a model reference and theoretical basis for real-time monitoring of damage in practical engineering.