Damage assessment with state–space embedding strategy and singular value decomposition under stochastic excitation

Abstract

A multivariate time-series analysis employing a state–space embedding strategy and singular value decomposition is presented in this article to detect infrastructure damage. After summarizing the current state–space reconstruction method, the univariate state–space reconstruction is extended to multivariate (or global) reconstruction for observed time series at multiple locations. Under the hypothesis that reconstructed phase state geometry will change with damage, a reduced feature based on Mahalanobis distance of the most significant singular value vector, which is calculated from the reconstructed trajectory, is proposed. Both the area under receiver operating characteristic curve and deflection coefficient are used as comparison metrics to illustrate the presence and severity of damage. The advantage of this proposed approach is computational efficiency and easy implementation using state–space methodology since it does not require high-dimensional neighbor searches, as previous methods have proposed. Validation of the approach is demonstrated using a 6-degree-of-freedom linear spring–mass system and the IASC-ASCE 4-story benchmark experimental structure. Results from both test beds show that damage occurrence and severity can be successfully identified.