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Information Dynamic Correlation of Vibration in Nonlinear Systems.
Zhe Wu1, Guang Yang1, Qiang Zhang2,3
1School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study introduces a novel application of information dynamics methods, specifically Von Neumann and Rényi entropy, to analyze macroscopic nonlinear mechanical systems. The research demonstrates the effectiveness of these entropy measures in understanding system dynamics and correlations.
Area of Science:
- Mechanical Engineering
- Nonlinear Dynamics
- Information Theory
Background:
- Information dynamics methods like Von Neumann entropy and Rényi entropy are established in various fields but underutilized in macroscopic nonlinear mechanical systems.
- Existing methods for characterizing mechanical system dynamics lack the ability to fully capture nonlinear system correlations.
Purpose of the Study:
- To investigate the applicability of Von Neumann and Rényi entropy for analyzing the dynamic behavior of macroscopic nonlinear mechanical systems.
- To propose a new method for describing nonlinear features and coupling relationships in mechanical systems using information dynamics.
Main Methods:
- Application of Von Neumann entropy and Rényi entropy to theoretical and practical analysis of a typical chaotic system and a real macroscopic nonlinear system.
- Development and implementation of a full-vector multi-scale Rényi entropy for exploring chaos and correlation in multi-body mechanical systems.
Main Results:
- Validation of the proposed entropy-based method for characterizing nonlinear mechanical system dynamics.
- Demonstrated effectiveness of the full-vector multi-scale Rényi entropy in modal identification, system dynamics evolution, and fault diagnosis.
- Successful exploration of chaos and correlation in complex multi-body mechanical systems.
Conclusions:
- Von Neumann and Rényi entropy are effective tools for studying macroscopic nonlinear mechanical systems.
- The proposed full-vector multi-scale Rényi entropy offers a powerful approach for analyzing nonlinear vibration correlations and system dynamics.
- This research significantly extends the application of information dynamics to the field of mechanical nonlinear system dynamics.
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