Research PaperNo Access

Physical Interpretation of Principal Component Analysis for Structural Dynamics Through String Vibration

College of Mechanics & Construction Engineering, Jinan University, Guangzhou, Guangdong, P. R. China

Dongguan University of Technology, Dongguan 523000, P. R. China

College of Mechanics & Construction Engineering, Jinan University, Guangzhou, Guangdong, P. R. China

The Key Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of China, Guangzhou, Guangdong, P. R. China

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Zhen-Hua Nie

College of Mechanics & Construction Engineering, Jinan University, Guangzhou, Guangdong, P. R. China

The Key Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of China, Guangzhou, Guangdong, P. R. China

E-mail Address: niezh@jnu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0219455419501098Cited by:18 (Source: Crossref)

Abstract

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.

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