Cumulative spectral moment distribution for robust damage detection in structural health monitoring under uncertain excitation

Traditional frequency-domain methods in structural health monitoring (SHM), such as power spectral density (PSD) analysis, often have limited sensitivity to subtle or distributed damage under nonstationary excitation and noisy operating conditions. This study proposes a cumulative spectral moment distribution (CMSD) framework that combines spectral moment theory with temporal and spatial energy accumulation. The proposed framework captures global spectral characteristics, including energy distribution, spectral spread, and tail behavior, thereby providing a more interpretable and noise-resilient alternative to conventional PSD-based indicators. The method is theoretically supported by spectral moment statistics and Parseval’s theorem and is implemented using efficient FFT-based signal processing. Experimental validation on steel beam specimens with incremental damage shows that CMSD outperforms traditional indicators in sensitivity index, damage progression correlation, and signal-to-noise ratio. In addition, CMSD supports spatial damage localization and early-stage damage detection without requiring explicit modal identification. These findings demonstrate that CMSD is a scalable and practical diagnostic framework for real-time SHM under uncertain dynamic conditions.