{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:53:38Z","timestamp":1772268818088,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T00:00:00Z","timestamp":1661299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zhejiang University","award":["ICT2022B06"],"award-info":[{"award-number":["ICT2022B06"]}]},{"name":"Zhejiang University","award":["01000205020503131"],"award-info":[{"award-number":["01000205020503131"]}]},{"name":"Zhejiang University","award":["202101AU070061"],"award-info":[{"award-number":["202101AU070061"]}]},{"name":"Yunnan Normal University","award":["ICT2022B06"],"award-info":[{"award-number":["ICT2022B06"]}]},{"name":"Yunnan Normal University","award":["01000205020503131"],"award-info":[{"award-number":["01000205020503131"]}]},{"name":"Yunnan Normal University","award":["202101AU070061"],"award-info":[{"award-number":["202101AU070061"]}]},{"name":"Educational Commission of Yunnan Province of China","award":["ICT2022B06"],"award-info":[{"award-number":["ICT2022B06"]}]},{"name":"Educational Commission of Yunnan Province of China","award":["01000205020503131"],"award-info":[{"award-number":["01000205020503131"]}]},{"name":"Educational Commission of Yunnan Province of China","award":["202101AU070061"],"award-info":[{"award-number":["202101AU070061"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Due to the complicated engineering operation of the check valve in a high\u2212pressure diaphragm pump, its vibration signal tends to show non\u2212stationary and non\u2212linear characteristics. These leads to difficulty extracting fault features and, hence, a low accuracy for fault diagnosis. It is difficult to extract fault features accurately and reliably using the traditional MPE method, and the ELM model has a low accuracy rate in fault classification. Multi\u2212scale weighted permutation entropy (MWPE) is based on extracting multi\u2212scale fault features and arrangement pattern features, and due to the combination of extracting a sequence of amplitude features, fault features are significantly enhanced, which overcomes the deficiency of the single\u2212scale permutation entropy characterizing the complexity of vibration signals. It establishes the check valve fault diagnosis model from the twin extreme learning machine (TELM). The TELM fault diagnosis model established, based on MWPE, aims to find a pair of non\u2212parallel classification hyperplanes in the equipment state space to improve the model\u2019s applicability. Experiments show that the proposed method effectively extracts the characteristics of the vibration signal, and the fault diagnosis model effectively identifies the fault state of the check valve with an accuracy rate of 97.222%.<\/jats:p>","DOI":"10.3390\/e24091181","type":"journal-article","created":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T21:03:51Z","timestamp":1661375031000},"page":"1181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Research on Twin Extreme Learning Fault Diagnosis Method Based on Multi-Scale Weighted Permutation Entropy"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5419-4777","authenticated-orcid":false,"given":"Xuyi","family":"Yuan","sequence":"first","affiliation":[{"name":"Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yugang","family":"Fan","sequence":"additional","affiliation":[{"name":"Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4218-105X","authenticated-orcid":false,"given":"Chengjiang","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaodong","family":"Wang","sequence":"additional","affiliation":[{"name":"Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17149","DOI":"10.1007\/s00521-020-05169-y","article-title":"A novel validation framework to enhance deep learning models in time\u2212series forecasting","volume":"32","author":"Livieris","year":"2020","journal-title":"Neural Comput. 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