The Transient POD Method Based on Minimum Error of Bifurcation Parameter

Kuan Lu, Haopeng Zhang, Kangyu Zhang, Yulin Jin, Shibo Zhao, Chao Fu and Yushu Chen
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Kuan Lu: Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Haopeng Zhang: Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Kangyu Zhang: Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Yulin Jin: School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
Shibo Zhao: Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Chao Fu: Centre for Efficiency and Performance Engineering, University of Huddersfield, Queensgate HD1 3DH, UK
Yushu Chen: School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2021, vol. 9, issue 4, 1-21

Abstract: An invariable order reduction model cannot be obtained by the adaptive proper orthogonal decomposition (POD) method in parametric domain, there exists uniqueness of the model with different conditions. In this paper, the transient POD method based on the minimum error of bifurcation parameter is proposed and the order reduction conditions in the parametric domain are provided. The order reduction model equivalence of optimal sampling length is discussed. The POD method was applied for order reduction of a high-dimensional rotor system supported by sliding bearings in a certain speed range. The effects of speed, initial conditions, sampling length, and mode number on parametric domain order reduction are discussed. The existence of sampling length was verified, and two- and three-degrees-of-freedom (DOF) invariable order reduction models were obtained by proper orthogonal modes (POM) on the basis of optimal sampling length.

Keywords: POD method; order reduction; parametric domain; nonlinear dynamics; rotor-bearing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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