STUDY ON CHARACTERIZATION METHOD OF PHASE-POINT SATURATION BASED ON THE CAPACITY DIMENSION

Shihui Lang, Hua Zhu, Chunling Wei, Weiwei Zhou and Yutan Li
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Shihui Lang: School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China
Hua Zhu: School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China
Chunling Wei: School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China
Weiwei Zhou: School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China
Yutan Li: School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-15

Abstract: In this study, the characterization method and evolution law of phase-point saturation based on the capacity dimension in fractal theory are studied to investigate the running-in process and state identification of a system. Tests of the running-in process under different working conditions were conducted on a ring-disc tribometer, and the friction signals were collected. The phase trajectories in different stages were then constructed and the fractal dimensions were calculated. The phase-point saturation parameter is proposed to reflect the degree of saturation of a phase space filled with phase points, and its reliability, noise-resistance, correlation with the fractal dimension, and effectiveness of the characterization of the running-in process were thoroughly investigated. The results demonstrate that the proposed phase-point saturation parameter is reliable and resistant to noise and can be used to identify changes in the system state. Furthermore, there is a negative correlation between the phase-point saturation parameter and the fractal dimension, and the phase-point saturation parameter can effectively characterize the state characteristics and describe the running-in process. During the running-in process, the phase-point saturation changes from high to low and tends to be stable when it reaches the running-in state. When entering the stable wear stage, the value of the parameter is maintained near the minimum, it fluctuates little as compared with the correlation dimension, and it exhibits good stability. Therefore, the proposed phase-point saturation parameter has important theoretical significance and application value for the quantitative characterization of the running-in process and state identification.

Keywords: Capacity Dimension; Phase Trajectory; Phase-Point Saturation; Correlation Dimension; State Recognition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500359

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