Dynamic displacement reconstruction of bridge based on physics-informed recurrent neural network

Abstract It is extremely challenging to directly measure the dynamic displacement which is essential in bridge state evaluation. The indirect physical-driven displacement reconstruction methods are restricted by the deviation existing between mechanism model and actual bridge, while indirect data-driven methods are restricted by requirement for a large amount of data. This paper proposes a physics-informed recurrent neural network (PI-RNN) based dynamic displacement reconstruction method. Firstly, the recurrent neural network is established, and the physical equation between data of measured points and target points are derived. Then, the derived physical equation is represented as physical information and added in the loss function of the network. Thus, the loss function contains a physical-based regularization term, which can guide the training direction of the network model, alleviate the over-fitting problem, and improve the generalization ability of the network. Subsequently, the displacement response reconstruction procedure based on PI-RNN is provided in detail. Finally, the effectiveness and superiority of the proposed method are verified by numerical and experimental examples. The results indicate that the PI-RNN is superior to RNN in terms of accuracy and efficiency in reconstruction bridge displacement.