{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:53:42Z","timestamp":1760241222169,"version":"build-2065373602"},"reference-count":83,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,31]],"date-time":"2019-12-31T00:00:00Z","timestamp":1577750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51705130","51706058"],"award-info":[{"award-number":["51705130","51706058"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hebei University Science and Technology Research Youth Fund Project","award":["QN2018168"],"award-info":[{"award-number":["QN2018168"]}]},{"name":"China National Key Laboratory of vehicle transmission fund project","award":["9140C340101101"],"award-info":[{"award-number":["9140C340101101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In previous studies, information dynamics methods such as Von Neumann entropy and R\u00e9nyi 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 R\u00e9nyi 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 R\u00e9nyi 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.<\/jats:p>","DOI":"10.3390\/e22010056","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T03:28:53Z","timestamp":1578022133000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Information Dynamic Correlation of Vibration in Nonlinear Systems"],"prefix":"10.3390","volume":"22","author":[{"given":"Zhe","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Vehicle Engineering, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Key Laboratory of Vehicle Transmission, China North Vehicle Research Institute, Beijing 100072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengyue","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyong","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5524","DOI":"10.1103\/PhysRevLett.80.5524","article-title":"Quantum dynamical manifestation of chaotic behavior in the process of entanglement","volume":"80","author":"Furuya","year":"1998","journal-title":"Phys. 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