Prediction of stochastic responses of vehicle running through the multi-spans bridge based on an optimized method

Abstract

The dynamic response of a vehicle-bridge system (VBS) has been a key problem in assessments of train-running safety on bridges, ultimately requiring reliability analyses owing to uncertain parameters and random rail irregularities. To improve the computational efficiency and promote the development of a reliability analysis for VBS, this paper proposes a novel approach incorporating a stochastic pseudo-excitation method (SPEM) to optimize a deep learning approach. This approach can more efficiently calculate the dynamic responses of a VBS than the traditional methods. In this study, the dynamic responses of the uncertain system produced by the SPEM were utilized as the training datasets for the deep learning approach. Based on the training datasets, a neural network was established to construct a numerical model consisting of two functional modules: a full convolutional network (FCN) training for the input rail irregularities and gated recurrent unit (GRU) layer for the VBS response prediction, i.e., a SPEM–FCN–GRU (SFG). The GRU cell was simulated by introducing the randomness of the excitation and uncertain parameters of the system into a portion of the cell, thereby enabling the numerical model to convey the randomness of the VBS and to obtain its stochastic response. Addition, long-time-domain samples of the VBS responses were predicted based on the short-time-domain samples. To verify the accuracy and applicability of the proposed method, a train running through a multi-span simply supported railway bridge was investigated. The dynamic responses of the train were analyzed using the training set data and Monte Carlo method (MCM) and the results showed good agreement with each other. Next, by introducing an algorithm combining a convolutional neural network (CNN) with the MCM and GRU (an MCM–CNN–GRU) and comparing it with the method proposed herein, it was verified that the proposed method has better predictions and higher efficiency than those of a traditional neural network. The prediction efficiency of the SFG was analyzed. Based on the shortcomings of the SFG, we proposed an optimized SFG algorithm. The short-time-domain results predicted by the proposed method were input into the training datasets for the deep learning architecture to enhance the number of training data for the prediction of long-time-domain responses. The efficiency and accuracy of the proposed method were verified by comparing them with those of traditional neural networks. As an example, the dynamic responses of a train running through a three-span bridge were computed by the SPEM; these could be adopted to predict those of a train running through a 10-span bridge. Finally, based on the simulated and predicted results, the reliability of the VBS was studied using a first-order reliability method.