{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T02:50:10Z","timestamp":1778640610690,"version":"3.51.4"},"reference-count":74,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:00:00Z","timestamp":1698537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE\u2013FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE\u2019s performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods.<\/jats:p>","DOI":"10.3390\/e25111494","type":"journal-article","created":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T12:07:45Z","timestamp":1698667665000},"page":"1494","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0653-2326","authenticated-orcid":false,"given":"Mostafa","family":"Rostaghi","sequence":"first","affiliation":[{"name":"Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9664-7890","authenticated-orcid":false,"given":"Mohammad Mahdi","family":"Khatibi","sequence":"additional","affiliation":[{"name":"Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Reza","family":"Ashory","sequence":"additional","affiliation":[{"name":"Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7612-0840","authenticated-orcid":false,"given":"Hamed","family":"Azami","sequence":"additional","affiliation":[{"name":"Centre for Addiction and Mental Health, University of Toronto, Toronto, ON M6J 1H1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.knosys.2018.09.004","article-title":"Intelligent Fault Diagnosis of Rotating Machinery Using Improved Multiscale Dispersion Entropy and MRMR Feature Selection","volume":"163","author":"Yan","year":"2019","journal-title":"Knowl. 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