A Hybrid Physics-Based and Data-Driven Approach with Transfer Learning for Dynamic Response Analysis of Vehicle-Bridge System

To efficiently solve the time-domain dynamic responses of vehicle-bridge interaction (VBI) systems,a transfer learning method that integrates physical information with data-driven approaches (TL-PINN) was proposed.The closed-form solution of a simply supported beam under a moving vehicle was derived,and the modal superposition method was employed to decouple the bridge vibration equation in both time and space.A physics-informed neural network (PINN) framework was constructed to train a benchmark model for a single-axle vehicle crossing the bridge.Using this model as the “source domain”, its network parameters were transferred to the target domain of a two-axle vehicle and fine-tuned.A parametric study was conducted by varying the bridge span,vehicle speed,and vehicle weight to verify the generalization capability of the method.The results indicate that,without data-driven components,the PINN can only identify low-frequency vibration components of the VBI system,while high-frequency responses are inadequately captured.After introducing data-driven elements,the TL-PINN accurately captures the full-frequency response of the bridge structure,with identification accuracy superior to traditional numerical methods.This approach maintains stable convergence while reducing the required iteration steps by approximately 60%,and all performance evaluation metrics outperform those of models without transfer learning,with improvements exceeding 50% in some scenarios.The research provides a new pathway for the efficient application of PINN in solving vehicle-bridge coupling problems.