A novel hybrid approach combining PDEM and bayesian optimization deep learning for stochastic vibration analysis in train-track-bridge coupled system

Train-track-bridge (TTB) system is a highly stochastic dynamical system. Deep learning has been applied to stochastic vibration analysis of TTB systems in recent years. However, most machine learning models consider only a single numerical relationship between input data and output responses. This often results in a strong dependence on training data, leading to a lack of robustness and reliability. In this paper, a novel hybrid method combining the probability density evolution method (PDEM) with an improved Bayesian optimization (BO) deep learning model (IDLM) is proposed for the efficient stochastic vibration analysis of uncertain TTB systems. This approach facilitates information exchange between the train-bridge model and the deep learning model. In this approach, PDEM is integrated into the deep learning framework to achieve a cohesive integration of physical and numerical models. The applicability of the PDEM-IDLM method is verified by comparing the predicted stochastic responses with the results of a validated train-bridge model. Furthermore, a case study investigates the effects of training dataset size, vehicle speed, and noise level, providing additional validation of the robustness of the proposed method.