Structural Damage Localization via RPCA-Based Decomposition of Full-Field Responses with a Differential Damage Index

This study addresses the challenge of separating local damage information from full-field structural responses under complex environmental and noise conditions by proposing a structural damage localization method that integrates piecewise denoising, Robust Principal Component Analysis (RPCA), and a differential damage index. First, full-field responses obtained from vision-based measurement are processed through piecewise denoising and continuous displacement extraction, and then organized into a structural spatiotemporal response matrix. RPCA is subsequently employed to separate low-rank global response components from sparse local anomalies, and a damage index is constructed by differencing sparse-component statistical features between healthy and damaged states. Moving-load tests on a simply supported beam show that the DI peak in the damaged region is approximately 28 times higher than the non-damaged background level, and the identified DI peak accurately falls within the actual damage region. Compared with RMS, kurtosis, curvature index, wavelet energy, PCA residual, and RPCA sparse-energy indicators, the proposed method is the only one that achieves zero regional localization error. Under noise levels of 40–20 dB, all 30 repeated trials achieve a 100% localization success rate, and the success rate remains 93.33% even at 10 dB. Moreover, the localization results remain stable when λ/λ0 varies from 0.50 to 1.50. Even when the number of spatial measurement points is reduced from 3401 to 128, the method maintains zero mean localization error and a 100% localization success rate. These results demonstrate that the synergy among piecewise denoising, RPCA decomposition, and state-difference enhancement effectively highlights damage-induced local anomalies, providing a robust and physically interpretable framework for full-field-response-based structural damage localization.