An Improved Method of Detecting Chaotic Motion for Rotor-Bearing Systems

doi:10.1007/s12204-013-1387-0

Abstract

Abstract: Based on reconstructing the phase space and calculating the largest Lyapunov exponent, an improved method of detecting chaotic motion is presented for rotor-bearing systems. The method is an improvement to the Wolf method and the Rosenstein algorithm. The improved method introduces the correlation integral function method to estimate the embedding dimension and the reconstruction delay simultaneously, and it makes tracks for the evolutions of every pair of the nearest neighbors to improve the utilization of the reconstructed phase space. Numerical calculation and experimental verification show that the improved method can estimate the proper reconstruction parameters and detect chaotic motion of rotor-bearing systems accurately. In addition, the analytical results show that the current approach is robust to variations of the embedding dimension and the reconstruction delay, and it is applicable to small data sets.

Key words: rotor-bearing| phase space reconstruction| Lyapunov exponent| chaotic motion

摘要： Based on reconstructing the phase space and calculating the largest Lyapunov exponent, an improved method of detecting chaotic motion is presented for rotor-bearing systems. The method is an improvement to the Wolf method and the Rosenstein algorithm. The improved method introduces the correlation integral function method to estimate the embedding dimension and the reconstruction delay simultaneously, and it makes tracks for the evolutions of every pair of the nearest neighbors to improve the utilization of the reconstructed phase space. Numerical calculation and experimental verification show that the improved method can estimate the proper reconstruction parameters and detect chaotic motion of rotor-bearing systems accurately. In addition, the analytical results show that the current approach is robust to variations of the embedding dimension and the reconstruction delay, and it is applicable to small data sets.

关键词: rotor-bearing| phase space reconstruction| Lyapunov exponent| chaotic motion

CLC Number:

TL 353

SHI Ming-lin* (师名林), WANG De-zhong (王德忠), ZHANG Ji-ge (张继革). An Improved Method of Detecting Chaotic Motion for Rotor-Bearing Systems[J]. Journal of shanghai Jiaotong University (Science), 2013, 18(2): 229-236.

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