Identification of bridge influence line and multiple-vehicle loads based on physics-informed neural networks

Influence lines (ILs) and vehicle loads identification are critical in the design, health monitoring, and damage detection of bridges. Traditionally, the approach used in most existing literature has been to solve the system of equations directly. However, these approaches require complex calculations such as matrix decomposition and regularization coefficient optimization, making them difficult to implement. In addition, there are difficulties in obtaining accurate axle information and effectively separating the bridge response due to each vehicle. Thus, the improvement of identification algorithms for ILs and multi-vehicle loads remains of significant importance. To address these issues, this paper presents a novel approach that integrates prior physical equations and neural networks. This is achieved by integrating the equation that reflects the relationship between axle loads and bridge response into the neural network, utilizing existing methods for acquiring axle information of vehicles. To validate the effectiveness of the proposed method, it was first applied to theoretical and simulation data. The study then investigated the impact of noise and dynamic effects on the accuracy of the results, as well as the range of the neural network layers and sampling intervals. Finally, the method was implemented for identifying multiple-vehicle loads. The findings of the study confirm the feasibility and numerical stability of the proposed approach. The proposed method eliminates the need for complex computational processes, including matrix decomposition, diagonalization, regularization coefficient optimization, and solution vector smoothing fitting. As a result, the implementation of the algorithm is significantly less challenging, and identification accuracy is improved. It is important to note, however, that the proposed method is relatively more time-consuming due to the iterative learning and training required by the neural network.