Recursive principal component analysis for model order reduction with application in nonlinear Bayesian filtering

Proper orthogonal decomposition (POD) is a useful technique for feature extraction, model order reduction and data compression and has been widely used in different science and engineering disciplines. Numerous papers have been published on the application of offline POD, i.e., batch POD (BPOD) in civil and mechanical engineering encompassing Karhunen–Loève decomposition (KLD), principal component analysis (PCA), and singular value decomposition (SVD). Nevertheless, online POD which is more suited for online feature extraction and monitoring has been scarcely addressed when dealing with civil and mechanical systems, particularly in structural dynamics. In this paper, a number of recursive POD (RPOD) methods in form of recursive PCA (RPCA) are overviewed with their application to structural dynamics. RPCA with numerical eigenvalue decomposition (EVD), incremental principal component analysis (IPCA), matrix perturbation method, and Kalman filter RPCA (KFRPCA) are presented; their performance is probed in terms of initialization, structural parameter modification, noisy observation, and alteration of loading statistics. The novel KFRPCA algorithm developed in this paper is reformulated to resolve the unobservability issue of higher modes which was present in its previous version in the published literature. Online stochastic output-only system identification is presented by synergizing RPCA with nonlinear Bayesian filter. Augmented extended Kalman filter (AEKF) is employed to perform unknown-input dual estimation.