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Information Dynamic Correlation of Vibration in Nonlinear Systems

1
School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China
2
School of Mechanical and Vehicle Engineering, Beijing Institute of Technology, Beijing 100081, China
3
Key Laboratory of Vehicle Transmission, China North Vehicle Research Institute, Beijing 100072, China
*
Authors to whom correspondence should be addressed.
Entropy 2020, 22(1), 56; https://doi.org/10.3390/e22010056
Received: 26 November 2019 / Revised: 18 December 2019 / Accepted: 22 December 2019 / Published: 31 December 2019
(This article belongs to the Section Signal and Data Analysis)
In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics. View Full-Text
Keywords: information dynamics correlation; Von Neumann entropy; nonlinear system; Rényi entropy; full vector multi-scale Rényi entropy information dynamics correlation; Von Neumann entropy; nonlinear system; Rényi entropy; full vector multi-scale Rényi entropy
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MDPI and ACS Style

Wu, Z.; Yang, G.; Zhang, Q.; Tan, S.; Hou, S. Information Dynamic Correlation of Vibration in Nonlinear Systems. Entropy 2020, 22, 56. https://doi.org/10.3390/e22010056

AMA Style

Wu Z, Yang G, Zhang Q, Tan S, Hou S. Information Dynamic Correlation of Vibration in Nonlinear Systems. Entropy. 2020; 22(1):56. https://doi.org/10.3390/e22010056

Chicago/Turabian Style

Wu, Zhe, Guang Yang, Qiang Zhang, Shengyue Tan, and Shuyong Hou. 2020. "Information Dynamic Correlation of Vibration in Nonlinear Systems" Entropy 22, no. 1: 56. https://doi.org/10.3390/e22010056

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