A physics-guided multi-sensor modal decomposition network for bridge frequency tracking

Bridge structures exhibit time-varying dynamic behaviour during operation. Instantaneous frequencies (IFs) are important indicators for bridge structural health monitoring, but their tracking from measured vibration responses remains challenging because modal components are often mixed, weakly excited, and affected by environmental and operational disturbances. This paper proposes a physics-guided multi-sensor modal decomposition network (MMDN) for bridge IF tracking. The framework contains two methodologically distinct components. First, a physics-guided spatial modal decomposition filter learns sensor-channel projections under reconstruction consistency, modal orthogonality, and band-limited energy concentration constraints, thereby transforming mixed multi-sensor responses into modal-dominated components. Second, an adaptive neural network IF tracker (ANIF-Tracker) estimates the IF of each decomposed component using waveform and local-energy channels together with a peak-weighted loss that emphasizes rapid frequency variations. The MMDN is validated using a numerical simulation model, laboratory-scale experiments, and long-term monitoring data from an in-service cable-stayed bridge. In the numerical case, the learned spatial projection vectors achieve diagonal spatial correlation coefficients of 0.90–0.94 with the prescribed mode shapes, supporting mode-specific decomposition. The MMDN achieves mean RMSEs of 13.74 mHz over the full test set and 47.44 mHz during active moving-load periods. Compared with traditional signal-processing methods and three deep-learning baselines (PatchTST-lite, MSGNet, and PatchMixer), these errors are 53.8% and 50.5% lower than the best competing results for the respective metrics. The laboratory-scale experimental results capture the expected first-order frequency decrease–recovery pattern during vehicle passage, while field monitoring reveals a seasonal frequency trend opposite to temperature changes. These results indicate that embedding structural dynamics knowledge into data-driven learning provides an effective and interpretable tool for time-varying IF tracking in bridge monitoring.