{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T16:48:19Z","timestamp":1772556499244,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T00:00:00Z","timestamp":1534809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China (NSFC)","award":["51741907, 51679095"],"award-info":[{"award-number":["51741907, 51679095"]}]},{"name":"the Fundamental Research Project for Application","award":["A17-302-a12"],"award-info":[{"award-number":["A17-302-a12"]}]},{"name":"Hubei Provincial Major Project for Technical Innovation","award":["2017AAA132"],"award-info":[{"award-number":["2017AAA132"]}]},{"name":"the Open Fund of Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station","award":["2017KJX06"],"award-info":[{"award-number":["2017KJX06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As crucial equipment during industrial manufacture, the health status of rotating machinery affects the production efficiency and device safety. Hence, it is of great significance to diagnose rotating machinery faults, which can contribute to guarantee the running stability and plan for maintenance, thus promoting production efficiency and economic benefits. For this purpose, a hybrid fault diagnosis model with entropy-based feature extraction and SVM optimized by a chaos quantum sine cosine algorithm (CQSCA) is developed in this research. Firstly, the state-of-the-art variational mode decomposition (VMD) is utilized to decompose the vibration signals into sets of components, during which process the preset parameter K is confirmed with the central frequency observation method. Subsequently, the permutation entropy values of all components are computed to constitute the feature vectors corresponding to different kind of signals. Later, the newly developed sine cosine algorithm (SCA) is employed and improved with chaotic initialization by a Duffing system and quantum technique to optimize the support vector machine (SVM) model, with which the fault pattern is recognized. Additionally, the availability of the optimized SVM with CQSCA was revealed in pattern recognition experiments. Finally, the proposed hybrid fault diagnosis approach was employed for engineering applications as well as contrastive analysis. The comparative results show that the proposed method achieved the best training accuracy 99.5% and best testing accuracy 97.89%. Furthermore, it can be concluded from the boxplots of different diagnosis methods that the stability and precision of the proposed method is superior to those of others.<\/jats:p>","DOI":"10.3390\/e20090626","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T11:12:42Z","timestamp":1534849962000},"page":"626","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Hybrid Fault Diagnosis Approach for Rotating Machinery with the Fusion of Entropy-Based Feature Extraction and SVM Optimized by a Chaos Quantum Sine Cosine Algorithm"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4084-1085","authenticated-orcid":false,"given":"Wenlong","family":"Fu","sequence":"first","affiliation":[{"name":"College of Electrical Engineering &amp; New Energy, China Three Gorges University, Yichang 443002, China"},{"name":"Hubei Provincial Key Laboratory for Operation and Control and Cascaded Hydropower Station, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiawen","family":"Tan","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering &amp; New Energy, China Three Gorges University, Yichang 443002, China"},{"name":"Hubei Provincial Key Laboratory for Operation and Control and Cascaded Hydropower Station, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoshun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zubing","family":"Zou","sequence":"additional","affiliation":[{"name":"China Three Gorges Corporation, Chengdu 610041, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiankun","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering &amp; New Energy, China Three Gorges University, Yichang 443002, China"},{"name":"Hubei Provincial Key Laboratory for Operation and Control and Cascaded Hydropower Station, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tie","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering &amp; New Energy, China Three Gorges University, Yichang 443002, China"},{"name":"Hubei Provincial Key Laboratory for Operation and Control and Cascaded Hydropower Station, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ymssp.2018.02.016","article-title":"Artificial intelligence for fault diagnosis of rotating machinery: A review","volume":"108","author":"Liu","year":"2018","journal-title":"Mech. 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