Online Robust Detection of Structural Anomaly Under Environmental Variability via Orthogonal Projection and Noisy Low-Rank Matrix Completion

A long-standing challenge for the structural health monitoring (SHM) community is the masking effect of environmental variability, typically addressed by orthogonal projection (OP)-based data normalization to isolate the influence of environmental variability and enable structural anomaly detection. However, conventional OP techniques, such as principal component analysis, rely on clean and complete data, and their performance degrades in the presence of outliers or missing entries. To overcome this limitation, this paper proposes an integrated approach that combines OP with noisy low-rank matrix completion (NLRMC). The main advantage of NLRMC is its ability to couple low-rank and sparse decomposition with matrix completion, simultaneously handling data corruption and missingness to recover incomplete datasets and enable robust anomaly detection. By incorporating novelty-indicator extraction, a fully online, unsupervised anomaly-detection procedure is established. Validation on a vibration-based SHM dataset from the KW51 railway bridge confirms that the NLRMC-OP approach achieves reliable detection of operational state changes before and after retrofitting, even under both data corruption and missing scenarios. This study advances the usability of SHM data and facilitates efficient decision-making, while also highlighting the broader significance of leveraging the low-rank data structure in AI-enabled operation and maintenance of civil infra-structure.