Moment-based spectral modeling for progressive damage assessment in structures: a 3D spiral visualization approach

We present the first application of a moment-based spectral damage indicator (SDI) to real bridge data under ambient excitation, enabling physics-grounded, edge-deployable structural health monitoring (SHM). Using vibration measurements from 20 controlled degradation scenarios on the Saigon Bridge—including bearing-pad displacement test 5 (T5), girder-joint loosening (T10), and concrete/anchorage loss (T15–20)—the second spectral moment ( m 2 ) captures energy-dispersion growth due to stiffness reduction and damping increase, from SDI = 0% (baseline) to 13.8% (T5), 42.0% (T10), and 68.4% (T20). Operating with baseline-percentile thresholds (P90 minor, P95–97.5 severe), SDI shows monotonic sensitivity while remaining stable under environmental and operational variability (±3 dB scaling; white/1/ f noise; traffic-intensity stratification). Compared with frequency tracking, SDI avoids mode-pairing/temperature confounds by integrating spectral shape; compared with data-hungry machine learning, it delivers explainable detection with fast Fourier transform-level complexity suitable for edge SHM. We also introduce a three-dimensional spiral visualization that encodes SDI trajectories for interpretable thresholding. The results establish SDI as a computationally efficient, scalable, and physics-interpretable tool for progressive damage assessment in large bridges.