Reliability analysis of the vehicle-bridge system with uncertain parameters by SPEM integrating deep leaning method

Abstract

The dynamic response of the vehicle-bridge (VB) system was the key problem in the assessment of railway vehicle running safety on bridges, which performed random vibration analysis due to the necessary uncertain parameter arising from either vehicle or bridge structure. Traditional random analysis methods usually required complete time-history calculated data and modal information to obtain the time-dominate statistics for evaluating the reliability of the vehicle running safety, whose computing was difficult and costs too much. This paper proposed a hybrid approach, which integrated the stochastic pseudo excitation method (SPEM) to optimized deep learning method (OLDM), to study the random vibration of uncertain VB system. The dynamic formulas of the uncertain system were produced by the SPEM, depending on which a neural network was established to construct the numerical model consisting of two functional modules, i.e., convolutional neural network (CNN) training with input rail irregularities and Bi-directional long short-term memory (BiLSTM) layer for the VB system response time-history prediction, i.e., CNN-BiLSTM. Due to the characteristics of calculated responses by SPEM, the BiLSTM cell was simulated by introducing the randomness of excitation and uncertain characteristics of parameters of the system into a portion of the cell, enabling the numerical model to convey the uncertainties of the VB system and obtained its stochastic response. For the proposed method, a vehicle running through a simply-supported railway bridge was applied to verify its accuracy and efficiency. According to the computed dynamic responses of VB system by the SPEM, a deep neural network was optimized for the investigated VB dynamic system. The dynamic statistics and reliability of vehicle were conducted through the optimized deep learning model and compared with the results from the conventional VB model by the Monte Carlo Method (MCM). The influence of training epoch, learn rate drop factor and vehicle running speed were investigated to examine the robustness of the deep learning approach.