Vehicle stochastic response prediction of sea-crossing railway bridges under correlated wind and wave via machine learning

Offshore railway bridges are exposed to the complex coastal environment, and vehicles could experience significant responses when vehicles cross the sea-crossing bridge. To predict the vehicle response subjected to the stochastic excitations (wind and wave actions), Archimedes copulas are applied to identify the correlation between wind speed and wave height. Based on the Gibbs sampling, an algorithm of Markov Chain Monte Carlo (MCMC), training samples are sampled from the optimal copula model (e.g., Clayton copula) as the input parameters. Taking a representative vehicle-bridge model as the study object, wind tunnel and wave flume scaling tests are performed to obtain the aerodynamic characteristics with the influence of wave surface. The external loads are calculated using the Morison equation and the MacCamy-Fuchs equation. Vehicle indexes as the output parameters are quantified using Support Vector Machine (SVM), Gaussian Process (GP), and Neural Network (NN) Machine Learning (ML) method. Training and testing results indicate that the NN algorithm outperforms other training strategies even though SVM and GP reasonably predict the vehicle dynamic response. Since the wind and wave action is lateral, vertical acceleration performs insensitivity to input parameters and is mainly influenced by track irregularity.