Recursive principal component analysis with forgetting factor for operational modal analysis of linear time-varying system

To update the model on-line and track the changing instantaneous modal shapes and modal frequencies of slow time-varying systems under unobservable random excitation operating conditions, a novel time-domain on-line operational modal analysis (OMA) algorithm based on recursive principal component analysis (RPCA) with forgetting factor is addressed. The algorithm is to update the covariance matrix with forgetting factor, and eigenvalues and eigenvectors tokened system properties are acquired. Finally, numerical simulations with three-degree-of-freedom system with time-varying mass are used to illustrate this method.