Physics-constrained liquid neural network for wind-induced vibrations prediction of hanger cables on long-span suspension bridges

Wind-induced vibrations (WIVs) of hanger cables on long-span suspension bridges could accelerate fatigue in suspension bridge suspension cables, damage damping devices, and other serviceability issues. The existing high-fidelity fluid-structure simulations are costly for real-time capable monitoring and purely data-driven approaches often violate basic physical laws and struggle to generalize under changing wind conditions. Prediction of hanger cable WIVs under strong non-stationarity and cross-domain distribution shifts has long faced challenges such as insufficient generalization, extrapolation distortion, and limited real-time performance. In this work, a Physics-Constrained Liquid Neural Network (PC-LNN) is developed for short‑term prediction of hanger cable response under wind loads. The time series data of hanger cable acceleration and wind are directly used as model inputs without manual feature extraction. Liquid time constant (LTC) neurons are used to adapt to non-stationary dynamics, and lightweight aerodynamic residuals ensure consistency with an SDOF balance. By a two-stage training process, the framework achieves seamless integration between measurement sensor data and the dominant structure-fluid dynamics model. Under unified data preprocessing and strict cross-hanger cables and cross-bridge segmentation, transfer learning evaluation is conducted. The results show that PC-LNN maintains high correlation and low bias in amplitude and dominant frequency predictions, preserves spectral structure, and exhibits no inter-group systematic drift across all target cables. Compared with other time series prediction models and baseline models, PC-LNN is at the forefront of accuracy, further indicating that physical residuals significantly reduce extrapolation errors in high-amplitude locked-frequency intervals. This study provides a replicable and engineering-friendly approach for reliable prediction of hanger cable WIVs, with particular emphasis on VIV events observed in field monitoring data.