Structural damage detection by integrating robust PCA and classical PCA for handling environmental variations and imperfect measurement data

This paper proposes a vibration-based structural damage detection approach considering the effects of uncertainties, including environmental variations and random errors that possibly stem from measurement and automatic modal identification. The existing methods that only employ the classical Principle Component Analysis (PCA) have been demonstrated effective to remove the effects of environmental variations while extremely sensitive to random errors. Therefore, the robust PCA is firstly introduced to remove the random errors, especially outliers, that significantly corrupt the low-rank property of the stacked damage sensitive feature (DSF) matrix. Then, the classical PCA is used to extract the environmental variation-free residues, which are inherently damage-dependent and can be used to detect the existence of damage. The problem of missing data is also considered in this study. It is tackled by adding virtual random errors to the locations of missing entities and thus can be addressed by the introduced robust PCA. The advantages of the proposed approach include: (1) Handling the random error-contaminated DSF data regardless of the error’s amplitude, which is an intractable problem for the existing classical PCA-based methods to consider the environmental effects; (2) Damage detection process can be automatic since the missing data can be automatically predicted and the random errors are not required to be manually distinguished. The effectiveness and performance of the proposed method are demonstrated on a numerical beam structure and an experimentally tested wooden bridge model.