Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems

Kuan Lu, Yulin Jin, Yushu Chen, Yongfeng Yang, Lei Hou, Zhiyong Zhang, Zhonggang Li, Chao Fu

Research output: Contribution to journalReview article

4 Citations (Scopus)

Abstract

This paper presents a review of proper orthogonal decomposition (POD) methods for order reduction in a variety of research areas. The historical development and basic mathematical formulation of the POD method are introduced. POD for parametric dynamic systems is introduced, and a physical interpretation of the POD approach based on the proper orthogonal modes (POMs) is presented. The equivalence between POD and three other order reduction methods is discussed: the first alternative method is singular value decomposition (SVD), the second is principal component analysis (PCA), and the third is Karhunen-Loeve decomposition (KLD). A classification of POD methods is described based on the parameter adaptation and sampling. Actual applications of POD methods for order reduction in engineering systems are illustrated. Finally, outlooks on the use of POD methods in high-dimensional nonlinear dynamic systems are presented in more detail to provide direct guidance for researchers in various areas of engineering.

LanguageEnglish
Pages264-297
Number of pages34
JournalMechanical Systems and Signal Processing
Volume123
Early online date19 Jan 2019
DOIs
Publication statusPublished - 15 May 2019
Externally publishedYes

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Dynamical systems
Singular value decomposition
Systems engineering
Principal component analysis
Sampling

Cite this

Lu, Kuan ; Jin, Yulin ; Chen, Yushu ; Yang, Yongfeng ; Hou, Lei ; Zhang, Zhiyong ; Li, Zhonggang ; Fu, Chao. / Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. In: Mechanical Systems and Signal Processing. 2019 ; Vol. 123. pp. 264-297.
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abstract = "This paper presents a review of proper orthogonal decomposition (POD) methods for order reduction in a variety of research areas. The historical development and basic mathematical formulation of the POD method are introduced. POD for parametric dynamic systems is introduced, and a physical interpretation of the POD approach based on the proper orthogonal modes (POMs) is presented. The equivalence between POD and three other order reduction methods is discussed: the first alternative method is singular value decomposition (SVD), the second is principal component analysis (PCA), and the third is Karhunen-Loeve decomposition (KLD). A classification of POD methods is described based on the parameter adaptation and sampling. Actual applications of POD methods for order reduction in engineering systems are illustrated. Finally, outlooks on the use of POD methods in high-dimensional nonlinear dynamic systems are presented in more detail to provide direct guidance for researchers in various areas of engineering.",
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Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. / Lu, Kuan; Jin, Yulin; Chen, Yushu; Yang, Yongfeng; Hou, Lei; Zhang, Zhiyong; Li, Zhonggang; Fu, Chao.

In: Mechanical Systems and Signal Processing, Vol. 123, 15.05.2019, p. 264-297.

Research output: Contribution to journalReview article

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AU - Chen, Yushu

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AU - Fu, Chao

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