Learning-based video motion magnification for cable force estimation under micro-amplitude vibration

Cable force is a crucial indicator for assessing the mechanical state and in-service performance of cable-supported structures. Conventional vision-based measurement methods often suffer from limited displacement detectability, unstable frequency identification, and susceptibility to noise interference under micro-amplitude vibration conditions. To address these limitations, this paper proposes a non-contact vision-based cable force estimation method assisted by learning-based video motion magnification (LBVMM). Initially, the proposed method first employs LBVMM to amplify micro-amplitude cable vibration responses in video sequences, thereby significantly improving the observability of motion features. Subsequently, a line tracking algorithm (LTA) is utilized to extract the subpixel-level displacement time histories of the cable. Dominant vibration frequencies are then identified through frequency-domain analysis, and the cable force is estimated using the frequency-based vibration method. Systematic validation is conducted through synthetic video experiments, laboratory cable vibration tests, and field tests on a tied-arch bridge. The results indicate that LBVMM enhances micro-amplitude vibration responses while preserving edge sharpness, temporal continuity, and frequency stability. Furthermore, the method demonstrates strong robustness under high magnification factors and noise-contaminated conditions. The results further confirm that the proposed method enables the accurate identification of cable vibration frequencies, with cable force estimation errors below 2%. Ultimately, this study demonstrates that the proposed vision-based cable force estimation framework provides high measurement reliability and robust noise tolerance, offering an efficient, low-cost, and non-contact solution for bridge cable assessment.