Moving load induced dynamic response analysis of bridge based on physics-informed neural network

Abstract

It is crucial to calculate the dynamic response of bridge induced by moving load which is the main live load during operation. Physics-informed neural network (PINN) is powerful in calculating structural response induced by static load as it can provide the prior knowledge for neural network. This paper extends the PINN for dynamic response analysis of bridge subjected to moving load. Firstly, nondimensional partial differential equations of uniform and non-uniform bridges subjected to moving loads are derived. Then, the Dirac function is approximated by Gaussian function, and the corresponding sampling strategy is proposed. Thirdly, the Fourier embedding layer and causal weight are added in the deep neural network and loss function of PINN, respectively. Fourthly, the implementation procedures of the PINN based moving load induced dynamic response analysis method are provided accordingly. Finally, numerical experiments are conducted to verify the effectiveness and superiority proposed method. The results indicate that the moving load induced dynamic response can be obtained by PINN driven by physics (PINN-DP) when the bridge parameters are known, and the response of bridge with unknown parameters can be obtained by PINN driven by both physics and data (PINN-DPD) with small amount of monitored response. Besides, the sampling strategy and causal weights added in the PINN can improve the accuracy of the analyzed results.