Robust multi-damage localisation using common eigenvector analysis and covariance matrix changes

Damage-induced local singularities in structural characteristic deflection shapes (CDS's) are widely used in non-model-based damage localisation. Despite substantial advances in this kind of methods, several issues must be addressed to boost their efficiency and practical applications. This study deals with two essential problems of CDS-based damage localisation: the noise robustness of CDS estimation and the criterion to properly weight damage information of several CDS's. On the first problem, it is well known that CDS estimation is vulnerably compromised by various uncertainties such as measurement noise and computational errors, which will decrease the accuracy and increase the difficulties in damage localisation. A modified common eigenvector analysis (CEA) is proposed based on a bank of digital filters and a joint approximate diagonalisation technique, which statistically estimates the CDS's as the common eigenvectors of a set of covariance matrices. On the second problem, a new robust damage index (DI) is proposed, which is comprised of damage-caused local shape distortions of several CDS's weighted by their participation factors in the covariance matrix at zero-time delay. The advantage of doing this is to include fair contributions from changes of all CDS's concerned and the proposed DI provides a measure of damage-induced changes in the covariance matrix. Then a numerical study is presented to demonstrate the noise robustness of the modified CEA method over proper orthogonal decomposition and second-order blind identification in CDS estimation. Moreover, a comparison of the proposed DI over some traditional damage localisation methods is conducted based on an experimental study. The results of numerical and experimental studies demonstrate that the proposed CDS estimation method is more robust to noise and the proposed DI is highly accurate for multi-damage localisation.