An Integrated Time-frequency Framework for Cable Force Identification in Long Cables of Long-span Bridges

Abstract

Accurate identification of cable forces is crucial for the Structural Health Monitoring (SHM) of long-span cable-stayed bridges. However, vibration-based methods face significant challenges when analyzing closely spaced high-order frequencies in long cables, including the difficulty of identifying low-order frequencies and the propensity for modal aliasing. This paper proposes a novel integrated time-frequency analysis framework to automatically identify cable frequencies from vibration data without prior information. The framework employs a hierarchical approach where the Secondary Fourier Transform (SFT) first automatically estimates the fundamental frequency difference, thereby enabling two advanced techniques: the modified short-time Fourier transform (MSTFT) for sparse modal identification and the modified Hilbert transform (MHT) for high-precision instantaneous frequency (IF) tracking. Several long cables in a certain long-span bridge were employed, and the results demonstrated that the framework successfully identifies cable frequencies from higher-order modes (10^th to 15^th order), effectively compensating for weak low-order signals. SFT provided a rapid and robust estimation of the average frequency difference. Building on this, MSTFT enabled the sparse frequency identification of designated modal orders, while MHT precisely captured IF fluctuations, revealing dynamic force changes that correlated with peak traffic periods. The proposed integrated framework offers a powerful and adaptable solution for cable force identification. The proposed framework automates the analysis, mitigates modal aliasing, and accommodates multi-precision requirements. This enhances traditional vibration-based monitoring, delivering a robust solution for SHM systems to better assess operational safety and optimize the maintenance of long-span bridges.