Prediction of Cable Forces under Complex Boundary and Material Conditions Using a Physics-Informed Neural Network

Accurate estimation of cable forces is essential for assessing the dynamic behavior and structural integrity of cable-supported bridges. Conventional string and beam theories often yield unreliable results for short cables or those equipped with dampers, while high-fidelity physical models require parameters that are typically unavailable for aging bridges. This study proposes a hybrid framework combining a finite-difference-based physical model with a two-stage neural network approach: One Model for One Cable (OMOC) and One Model for All Cables (OMAC). The OMOC approach employs a feedforward neural network trained on natural frequencies to estimate cable forces for individual cables with high accuracy. The OMAC approach extends this concept using a physics-informed neural network that incorporates the eigenvalue matrix from the physical model as a physics-based loss term, enabling generalized prediction across multiple cables with similar properties. The proposed framework achieves reliable and efficient cable force estimation from limited dynamic data, significantly improving computational efficiency while maintaining physical interpretability. This approach provides a practical tool for dynamic monitoring and maintenance of cable-supported bridges.