Robust linear and nonlinear structural damage detection using recursive canonical correlation analysis

A novel approach for robust damage detection of linear and nonlinear systems using recursive canonical correlation analysis (RCCA) is proposed in this paper. The method generates proper orthogonal modes (POMs) at each time stamp that are recursively tracked to provide iterative eigenspace updates, using first order eigen perturbation (FOEP) method. The transformed responses obtained are subsequently fit using time varying auto regressive (TVAR) models, in order to aid as damage sensitive features (DSFs) for identifying temporal and spatial patterns of damage. As most of the past work utilize offline algorithms that gather data in windows and operate in batch mode, recursive algorithms that provide iterative eigenspace updates at each instant of time, are missing in the context of structural health monitoring (SHM). This greatly motivates the development of the present work, where the both uni and multi directional structural responses are considered to be available in real time. The transformed responses are obtained by using the proposed algorithm that utilizes FOEP for multi-directional block covariance structure to solve the recursive generalized eigenvalue problem. The TVAR coefficients modeled on the transformed responses obtained in real time using FOEP, and residual error examined in a recursive framework, act as efficient real time DSFs for detecting damage online. Numerical simulations carried out on nonlinear systems and backed by experimental setups devised in controlled laboratory conditions, demonstrate the efficacy of the RCCA algorithm. Application of the proposed algorithm on the combined ambient and earthquake responses obtained from the UCLA Factor Building, demonstrates the robustness of the proposed methodology as an ideal candidate for real time SHM.