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

Bridges are critical transportation infrastructure whose structural safety directly impacts public safety. Recently, non-contact measurement technologies have gained prominent attention in bridge structural health monitoring 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 frequencydomain 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 loadinduced transient vibration responses, validating the practical engineering applicability of the proposed method.