{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T16:01:12Z","timestamp":1762444872491,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T00:00:00Z","timestamp":1549929600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Start-up Research fund of NWPU","award":["31020180QD001"],"award-info":[{"award-number":["31020180QD001"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51805434 and 61833002"],"award-info":[{"award-number":["51805434 and 61833002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Postdoctoral Innovative Talent Plan","award":["BX20180257"],"award-info":[{"award-number":["BX20180257"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multi-scale permutation entropy (MPE) is a statistic indicator to detect nonlinear dynamic changes in time series, which has merits of high calculation efficiency, good robust ability, and independence from prior knowledge, etc. However, the performance of MPE is dependent on the parameter selection of embedding dimension and time delay. To complete the automatic parameter selection of MPE, a novel parameter optimization strategy of MPE is proposed, namely optimized multi-scale permutation entropy (OMPE). In the OMPE method, an improved Cao method is proposed to adaptively select the embedding dimension. Meanwhile, the time delay is determined based on mutual information. To verify the effectiveness of OMPE method, a simulated signal and two experimental signals are used for validation. Results demonstrate that the proposed OMPE method has a better feature extraction ability comparing with existing MPE methods.<\/jats:p>","DOI":"10.3390\/e21020170","type":"journal-article","created":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T02:49:44Z","timestamp":1550026184000},"page":"170","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7997-8348","authenticated-orcid":false,"given":"Xianzhi","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Shubin","family":"Si","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Yu","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Astronautical Science and Mechanics, Harbin Institute of Technology (HIT), Harbin 150001, China"}]},{"given":"Yongbo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation Entropy: A Natural Complexity Measure for Time Series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. 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