Prediction of the Extreme Dynamic Amplification Factor Based on Bayesian Peaks-over-Threshold–Generalized Pareto Distribution Method and Random Traffic–Bridge Interaction

The accurate prediction of extreme dynamic amplification factor (DAF) values is significantly important to ensure a long-term safety assessment of bridges under stochastic vehicular loading. However, predicting extreme DAFs is challenging due to traffic randomness, road roughness variability, and nonlinear vehicle–bridge interaction (VBI) effects. This study presents an integrated framework for extreme DAF prediction for simply supported bridges by combining stochastic traffic–bridge interaction simulations with Bayesian updating and a Peaks-Over-Threshold–Generalized Pareto Distribution (POT–GPD) model. A coupled VBI model is developed, incorporating cellular automaton-based traffic flow, multi-axle nonlinear vehicle dynamics, finite-element bridge modeling, and stochastic road roughness profiles. A new DAF definition based on dynamic displacement difference is proposed to better represent dynamic effects. DAF samples obtained from VBI simulations under different road roughness levels are analyzed using the POT method, with GPD parameters estimated through maximum likelihood and Bayesian inference. Extreme DAFs corresponding to different return periods are then determined. The results indicate that extreme DAF values increase with worsening road roughness and longer return periods and that the Bayesian POT–GPD approach effectively captures tail behavior while providing reliable uncertainty quantification for extreme DAF prediction.