时间序列关联维数在非线性系统运动性态识别中的应用

ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2003, Vol. 24 ›› Issue (1): 28-31.

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Characteristic Identification of Nonlinear Dynamics System with the Fractal Dimension of Time Series

ZHAO Yu-cheng¹, ZHANG Yu-lian², ZHANG Ya-hong¹, XU Qing-yu¹

1. Department of Engineering Mechanics; Xi'an Jiaotong University; Xi'an 710049; China;2. Department of Mechanics; Zhejiang Ocean University; Zhoushan 316004; China

Received:2002-01-31 Revised:2002-07-09 Online:2003-02-25 Published:2003-02-25

Abstract

Abstract: The present wor k is trying to identify the pr operty of an unknown nonlinear system by nonlinear time series. For analysis, the typical nonlinear equation, Duffing equation, is studied. Using the figur es of fractal dimensionof time series and the par ameter of the nonlinear system, Poincare figures, phase figures, and fr equency spectrumfigures, the following conclusions may be obtained: according to the figures of fractal dimension tr ending, the cr itical paramet ers or regions of the nonlinear model from the stable state to bifurcation or chaotic state can be identifiedeffectively. Finally, the bifurcation cr itical parameters of Jeffcott rotor and run condition of the rotor system are identified by this met hod well.

Key words: fractal dimension, bifurcation, chaos, critical parameters, fluid film bearing rotor system

CLC Number:

O322

ZHAO Yu-cheng;ZHANG Yu-lian;ZHANG Ya-hong;XU Qing-yu. Characteristic Identification of Nonlinear Dynamics System with the Fractal Dimension of Time Series[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2003, 24(1): 28-31.

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Characteristic Identification of Nonlinear Dynamics System with the Fractal Dimension of Time Series

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