Physics and data hybrid-driven interpretable deep learning for moving force identification

The traffic load information is essential to assess the operational safety of the bridge structures, whereas, it is difficult to measure directly. Moving force identification (MFI) methods are therefore developed to estimate the vehicular loads from bridge responses. However, abundant high-quality prior information about the load is needed in current MFI methods, such as the real-time loading position or moving speed, which is unavailable in practice. To address this issue, a physics-informed neural network (PINN) is developed in this study to directly identify the moving force from the measured structural responses without prior knowledge of the load. The PINN is composed of the trainable data-driven and untrainable model-driven layers. The data-driven part is a convolutional autoencoder. It is fed with the monitored response data, and its output is the identified force time history that is converted to a sparse load map guided by the real loading process of a vehicle. Consecutively in the model-driven layer, the load map is transformed to the structural responses at the sensor positions via an impulse response matrix calculated via dynamic analysis. The difference between the predicted and measured responses is formularized as the loss function to train the PINN in a self-supervised manner, where the real moving force time history is not needed. The numerical and laboratory simply-supported beam models are used to verify the approach, considering different velocities, magnitude, and time-varying frequency components of the moving force. The results demonstrate that the proposed PINN can accurately identify the moving force at an unknown speed with high stability.