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Principal component analysis (PCA) has been successfully applied in structural dynamics in recent years. However, it is usually used as a black-box, resulting in a gap between the application aspect and the physics essence of the problem. Thus a physical interpretation of PCA is necessary, along with further investigation, especially on the mechanism involved. This paper provides a physical meaning of the PCA by the theoretical analysis and numerical experiment on the vibration of a 1D string. Conditions that make the interpretation feasible were identified. The theoretical derivation and numerical simulation results indicate that the PCA gives a good estimation of the modal participation ratio in terms of energy, and the principal component coefficient (PCC) can be used to estimate the structural modes. The physical interpretation gives a new perspective on how the current methods work while providing the possibility of further application of the PCA related methods to structural dynamic problems.

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.