A Bayesian deep learning approach for random vibration analysis of bridges subjected to vehicle dynamic interaction

Vehicle actions represent the main operational loading for various types of bridges. It is essential to conduct random vibration analysis due to the unavoidable uncertainties arising from both the vehicle and bridge structure. This paper proposes a novel approach for the vehicle-induced random vibration analysis of bridges integrating Bayesian deep learning. The dynamic equation of the stochastic vehicle-bridge interaction system in state space form is deduced, based on which an ensemble of deep neural network is proposed to construct the surrogate model consisting of two designed functional modules, i.e., convolutional layers for excitation input feature extraction and long short-term memory (LSTM) layers for bridge response time series prediction. According to the deduced state space equation, the conventional LSTM cell is modified by introducing randomness to a portion of cell parameters. Probability distributions of the selected network parameters are then estimated by Bayesian inference, enabling the surrogate model to convey the uncertainties of the vehicle-bridge interaction system and rapidly estimate random vibration responses of the bridge. The proposed approach is applied on a railway bridge under high-speed train loading to demonstrate its efficacy. A deep Bayesian neural network is tailored and developed using the present methodology for the studied train-bridge coupling dynamic system. Time domain statistics and frequency-domain responses of the bridge are acquired through the Bayesian deep learning model and compared with the results from a validated vehicle-bridge interaction model. Robustness of the Bayesian deep learning approach is further examined by investigating the influence of training dataset size, vehicle speed, and model input noise.