Main girder dynamic alignment reconstruction of cable-stayed bridge based on physics-informed neural network

The main girder dynamic alignment (MGDA) is important in condition assessment of cable-stayed bridges during operation. However, it is challenging to measure the MGDA of cable-stayed bridge with high-accuracy due to the limited sensor number. This paper proposes an indirect reconstruction method for MGDA of cable-stayed bridge based on physics-informed neural network (PINN) and few sensors. Firstly, the cables of cable-stayed bridge are simplified as continuously elastic supports, and the dimensionless motion equation of the simplified model is derived accordingly. Then, two surrogate models are developed with neural network to simulate MGDA and external excitation, and the Fourier embedding layer is incorporated into the network. Besides, the spatial and temporal causal weights are added in to the physics-informed loss function to improve the model approximation, and different total loss functions are calculated for training the two surrogate models. Thirdly, the procedures for reconstructing the MGDA of cable-stayed bridge based on the developed PINN are provided in detail. Finally, the effectiveness of the proposed method is verified by numerical experiments, and the effects of sensor number, road roughness, damage state and measurement noise are systematically explored. The results indicate that the proposed method takes advantage of the PINN in calculating structural response with sparse data, and can accurately monitor the MGDA of a cable-stayed bridge indirectly with limited sensor number.