Mechanism of Principal Component Analysis in Structural Dynamics under Ambient Excitation

Abstract

Principal component analysis (PCA) is a classical dimensionally reduction method having been widely applied in structural health monitoring (SHM) systems. However, it usually works as a “black-box” in most applications, i.e. the outputs of PCA only make sense statistically without physical meaning. This problem causes the difficulty to estimate the stability of the current PCA-based SHM methods, due to the unclear physical essence in engineering. This paper aims to propose a physical interpretation of PCA when it is applied to the response data from a multi-freedom system under ambient excitation. Both non-damping and damping cases are analyzed theoretically and verified by both numerical and laboratory experiments. The results indicate there is a close connection between the outputs of PCA and dynamical parameters: PCA can reveal information about the mode shape and modal participation of the structure. This work gives a theoretical foundation of the current PCA-based SHM method under ambient excitation, leading to the possibility of further advancement.