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An improved method of detecting chaotic motion for rotor-bearing systems

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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.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Ming-lin Shi  (师名林), De-zhong Wang  (王德忠) & Ji-ge Zhang  (张继革)

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  1. Ming-lin Shi  (师名林)
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  2. De-zhong Wang  (王德忠)
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  3. Ji-ge Zhang  (张继革)
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Correspondence to Ming-lin Shi  (师名林).

Additional information

Foundation item: the National Basic Research Program (973) of China (No. 2009CB724302)

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Shi, Ml., Wang, Dz. & Zhang, Jg. An improved method of detecting chaotic motion for rotor-bearing systems. J. Shanghai Jiaotong Univ. (Sci.) 18, 229–236 (2013). https://doi.org/10.1007/s12204-013-1387-0

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  • DOI: https://doi.org/10.1007/s12204-013-1387-0

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