VideoCFENet: A Boundary Condition Uncertainty-Driven Neural Network for Cable Force Estimation From Bridge Videos

Accurate measurement of bridge cable forces is essential for ensuring the safety and stability of bridge structures. Existing methods, which primarily rely on a vibration frequency-based approach, face challenges such as unclear boundary conditions and the inaccurate nonlinear relationship between cable frequency and cable force. To address the problem, a video phase vibration-based cable force estimation neural network, VideoCFENet, is proposed, which takes cable length, linear density, bending stiffness, and the first two-order frequencies as inputs, with cable force being the output. The finite element modeling data for training the network is generated using standard stay cable parameters. Furthermore, an innovative boundary condition loss term is introduced into the traditional loss function to reduce the impact of boundary conditions, thereby enhancing prediction accuracy. In addition, a combined optimization method using particle swarm optimization (PSO) and adaptive moment (Adam) estimation is applied in the network training process, effectively accelerating the convergence. VideoCFENet has been evaluated through extensive indoor steel cable experiments and outdoor stay cable tests. The results show that, compared to existing methods, VideoCFENet demonstrates a significant improvement in cable force measurement, with a maximum MAPE of 4.805% and a minimum MAPE of 1.343%, offering promising prospects for engineering applications.