Robust Identification of Bridge Vibration Fusing Multi-frequency Phase Unwrapping Technology

Bridges are critical transportation infrastructure whose structural safety directly impacts public safety. Recently, noncontact measurement technologies have gained prominent attention in bridge Structural Health Monitoring (SHM) due to their high efficiency and automation. This paper presents a Multi-frequency Phase Unwrapping-based Bridge Vibration Monitoring method (MB-PM) to address phase distortion and weak signal extraction challenges inherent in traditional phase-based methods under complex environments. The core Multi-frequency Phase Unwrapping (MPU) technique couples an adaptive reliability-weighted sub-band fusion strategy with a temporal phase unwrapping approach to resolve phase wrapping and noise interference. Mechanistically, the framework extracts local phase temporal information by applying an enhanced Phase-based Motion Estimation (PME) approach via Complex Steerable Pyramid (CSP) decomposition across multiple Regions of Interest (ROIs). The MPU technique then fuses multi-scale and multi-directional phase information, while an adaptive frequency-domain filtering algorithm enhances system robustness. Subsequently, a dynamic reference benchmark unifies phase responses across multiple monitoring points, complemented by Phase-based Motion Magnification (PMM) to amplify weak vibration signals for subsequent spectral analysis. Under intense illumination interference, MB-PM limits the displacement-monitoring NRMSE to 0.61%, compared with 2.96% for traditional PME; in the ablation test, enabling MPU further reduces the NRMSE from 1.03% to 0.49%, confirming the effectiveness of the multi-frequency fusion strategy. Field application confirms that synchronous multi-point monitoring successfully captures load-induced transient vibration responses, validating the practical engineering applicability of the proposed method.