{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:57:06Z","timestamp":1771660626772,"version":"3.50.1"},"reference-count":58,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61503282"],"award-info":[{"award-number":["61503282"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61976099"],"award-info":[{"award-number":["61976099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2020IB003"],"award-info":[{"award-number":["2020IB003"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> Assessing the complexity of signals or dynamical systems is important in disease diagnosis, mechanical system defect, astronomy analysis, and many other fields. Although entropy measures as complexity estimators have greatly improved, the majority of these measures are quite sensitive to specified parameters and are impacted by short data lengths. This paper proposes a novel entropy algorithm to enhance the existing complexity assessment methods based on classical dispersion entropy (DE) and R\u00e9nyi entropy (RE) by introducing refined composite multiscale coarse-grained treatment and phase transformation. The proposed refined composite multiscale phase R\u00e9nyi dispersion entropy (PRRCMDE) addresses the flaws of various existing entropy approaches while still incorporating their merits. Several simulated signals from logistic mapping, AR model, MIX process, and additive WGN periodic signals are adopted to examine the performance of PRRCMDE from multiple perspectives. It demonstrates that the efficacy of the suggested algorithm can be increased by modifying the DE and RE parameters to a reasonable range. As a real-world application, the bearings\u2019 varied fault types and levels can also be recognized clearly. <\/jats:p>","DOI":"10.1142\/s0218127423500542","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T09:06:31Z","timestamp":1682672791000},"source":"Crossref","is-referenced-by-count":9,"title":["Refined Composite Multiscale Phase R\u00e9nyi Dispersion Entropy for Complexity Measure"],"prefix":"10.1142","volume":"33","author":[{"given":"Yu-Han","family":"Tong","sequence":"first","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7075-1323","authenticated-orcid":false,"given":"Guang","family":"Ling","sequence":"additional","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Hong","family":"Guan","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingju","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"S0218127423500542BIB001","doi-asserted-by":"crossref","first-page":"061918","DOI":"10.1103\/PhysRevE.84.061918","volume":"84","author":"Ahmed M. U.","year":"2011","journal-title":"Phys. Rev. E"},{"key":"S0218127423500542BIB002","doi-asserted-by":"crossref","first-page":"105744","DOI":"10.1016\/j.rinp.2022.105744","volume":"39","author":"Amadi P. O.","year":"2022","journal-title":"Results Phys."},{"key":"S0218127423500542BIB003","doi-asserted-by":"crossref","first-page":"2872","DOI":"10.1109\/TBME.2017.2679136","volume":"64","author":"Azami H.","year":"2017","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"S0218127423500542BIB004","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","volume":"88","author":"Bandt C.","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"S0218127423500542BIB005","doi-asserted-by":"crossref","first-page":"238701","DOI":"10.1103\/PhysRevLett.103.238701","volume":"103","author":"Barnett L.","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"S0218127423500542BIB006","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.3390\/e23121620","volume":"23","author":"Borin A. M. S.","year":"2021","journal-title":"Entropy"},{"key":"S0218127423500542BIB008","first-page":"110939","volume":"146","author":"Chakraborty M.","year":"2022","journal-title":"Chaos Solit. Fract."},{"key":"S0218127423500542BIB009","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.physa.2019.01.031","volume":"523","author":"Chao L.","year":"2019","journal-title":"Physica A"},{"key":"S0218127423500542BIB010","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/TNSRE.2007.897025","volume":"15","author":"Chen W.","year":"2007","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"S0218127423500542BIB011","doi-asserted-by":"crossref","first-page":"068102","DOI":"10.1103\/PhysRevLett.89.068102","volume":"89","author":"Costa M.","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"S0218127423500542BIB012","doi-asserted-by":"crossref","first-page":"112101","DOI":"10.1016\/j.chaos.2022.112101","volume":"158","author":"Deka B.","year":"2022","journal-title":"Chaos Solit. Fract."},{"key":"S0218127423500542BIB013","doi-asserted-by":"crossref","first-page":"108977","DOI":"10.1016\/j.measurement.2021.108977","volume":"176","author":"Dong W.","year":"2021","journal-title":"Measurement"},{"key":"S0218127423500542BIB014","doi-asserted-by":"crossref","first-page":"121864","DOI":"10.1016\/j.physa.2019.121864","volume":"532","author":"Fan Q.","year":"2019","journal-title":"Physica A"},{"key":"S0218127423500542BIB015","doi-asserted-by":"crossref","first-page":"109974","DOI":"10.1016\/j.measurement.2021.109974","volume":"185","author":"Gao S.","year":"2022","journal-title":"Measurement"},{"key":"S0218127423500542BIB016","first-page":"4213412","volume":"2020","author":"Gong Y.","year":"2020","journal-title":"Complexity"},{"key":"S0218127423500542BIB017","doi-asserted-by":"crossref","first-page":"105835","DOI":"10.1016\/j.cnsns.2021.105835","volume":"99","author":"Gu D.","year":"2021","journal-title":"Commun. Nonlin. Sci. Numer. Simul."},{"key":"S0218127423500542BIB018","first-page":"1850088-1","volume":"28","author":"Hua S.","year":"2018","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127423500542BIB019","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.3390\/e17053110","volume":"17","author":"Humeau-Heurtier A.","year":"2015","journal-title":"Entropy"},{"key":"S0218127423500542BIB020","doi-asserted-by":"crossref","first-page":"110843","DOI":"10.1016\/j.measurement.2022.110843","volume":"191","author":"Jiang W.","year":"2022","journal-title":"Measurement"},{"key":"S0218127423500542BIB021","doi-asserted-by":"crossref","first-page":"125686","DOI":"10.1016\/j.physa.2020.125686","volume":"568","author":"Kang H.","year":"2021","journal-title":"Physica A"},{"key":"S0218127423500542BIB022","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0020-0255(86)90006-X","volume":"40","author":"Kosko B.","year":"1986","journal-title":"Inf. Sci."},{"key":"S0218127423500542BIB023","first-page":"35","volume":"374","author":"Lacasa L.","year":"2017","journal-title":"Physica D"},{"key":"S0218127423500542BIB024","doi-asserted-by":"crossref","first-page":"47663","DOI":"10.1109\/ACCESS.2019.2907997","volume":"7","author":"Li C.","year":"2019","journal-title":"IEEE Access"},{"key":"S0218127423500542BIB025","doi-asserted-by":"crossref","first-page":"126627","DOI":"10.1016\/j.jmaa.2022.126627","volume":"517","author":"Li C. B.","year":"2023","journal-title":"J. Math. Anal. Appl."},{"key":"S0218127423500542BIB026","doi-asserted-by":"crossref","first-page":"1950024-1","DOI":"10.1142\/S021812741950024X","volume":"29","author":"Ling G.","year":"2019","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127423500542BIB027","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1016\/j.neuroimage.2013.08.056","volume":"85","author":"Lobier M.","year":"2014","journal-title":"Neuroimage"},{"key":"S0218127423500542BIB028","first-page":"2050174-1","volume":"30","author":"Ma L.","year":"2020","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127423500542BIB029","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1093\/cercor\/bhs031","volume":"23","author":"Ng B. S. W.","year":"2013","journal-title":"Cereb. Cortex"},{"key":"S0218127423500542BIB030","doi-asserted-by":"crossref","first-page":"6071","DOI":"10.3390\/s21186071","volume":"21","author":"Nieto-del-Amor F.","year":"2021","journal-title":"Sensors"},{"key":"S0218127423500542BIB031","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/PROC.1981.12022","volume":"69","author":"Oppenheim A. V.","year":"1981","journal-title":"P. IEEE"},{"key":"S0218127423500542BIB032","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","volume":"88","author":"Pincus S. M.","year":"1991","journal-title":"Proc. Natl. Acad. Sci."},{"key":"S0218127423500542BIB033","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421501285"},{"key":"S0218127423500542BIB034","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1016\/j.medengphy.2009.06.004","volume":"31","author":"Ramdani S.","year":"2009","journal-title":"Med. Eng. Phys."},{"key":"S0218127423500542BIB035","doi-asserted-by":"crossref","first-page":"052117","DOI":"10.1103\/PhysRevE.101.052117","volume":"101","author":"Restrepo J. F.","year":"2020","journal-title":"Phys. Rev. E"},{"key":"S0218127423500542BIB036","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","volume":"23","author":"Rostaghi M.","year":"2016","journal-title":"IEEE Sign. Proc. Lett."},{"key":"S0218127423500542BIB037","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.3390\/e23111510","volume":"23","author":"Rostaghi M.","year":"2021","journal-title":"Entropy"},{"key":"S0218127423500542BIB038","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","volume":"85","author":"Schreiber T.","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"S0218127423500542BIB039","doi-asserted-by":"crossref","first-page":"105271","DOI":"10.1016\/j.cnsns.2020.105271","volume":"89","author":"Shang D.","year":"2020","journal-title":"Commun. Nonlin. Sci."},{"key":"S0218127423500542BIB040","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1002\/sys.21356","volume":"19","author":"Sinha K.","year":"2016","journal-title":"Syst. Eng."},{"key":"S0218127423500542BIB041","doi-asserted-by":"crossref","first-page":"923","DOI":"10.3390\/e21100923","volume":"21","author":"Song E.","year":"2019","journal-title":"Entropy"},{"key":"S0218127423500542BIB042","doi-asserted-by":"crossref","first-page":"109566","DOI":"10.1016\/j.jfa.2022.109566","volume":"283","author":"Suguro T.","year":"2022","journal-title":"J. Funct. Anal."},{"key":"S0218127423500542BIB043","doi-asserted-by":"crossref","first-page":"110180","DOI":"10.1016\/j.measurement.2021.110180","volume":"186","author":"Tan H.","year":"2021","journal-title":"Measurement"},{"key":"S0218127423500542BIB044","doi-asserted-by":"crossref","first-page":"127506","DOI":"10.1016\/j.physa.2022.127506","volume":"600","author":"Wan L.","year":"2022","journal-title":"Physica A"},{"key":"S0218127423500542BIB045","doi-asserted-by":"crossref","first-page":"110473","DOI":"10.1016\/j.chaos.2020.110473","volume":"142","author":"Wang Z.","year":"2021","journal-title":"Chaos Solit. Fract."},{"key":"S0218127423500542BIB046","first-page":"171","volume":"6","author":"Wang Z.","year":"2021","journal-title":"ICSP Proc."},{"key":"S0218127423500542BIB047","doi-asserted-by":"crossref","first-page":"112266","DOI":"10.1016\/j.chaos.2022.112266","volume":"160","author":"Wang Y.","year":"2022","journal-title":"Chaos Solit. Fract."},{"key":"S0218127423500542BIB048","doi-asserted-by":"crossref","first-page":"108964","DOI":"10.1016\/j.ymssp.2022.108964","volume":"172","author":"Wang Z.","year":"2022","journal-title":"Mech. Syst. Sign. Process."},{"key":"S0218127423500542BIB049","first-page":"2250032-1","volume":"32","author":"Wu C.","year":"2022","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127423500542BIB050","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.physa.2014.01.016","volume":"400","author":"Xia J.","year":"2014","journal-title":"Physica A"},{"key":"S0218127423500542BIB051","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/s11071-021-06528-7","volume":"105","author":"Xu M.","year":"2021","journal-title":"Nonlin. Dyn."},{"key":"S0218127423500542BIB052","doi-asserted-by":"crossref","first-page":"0339","DOI":"10.3389\/fphy.2020.00339","volume":"8","author":"Yadav G. S.","year":"2020","journal-title":"Front. Phys."},{"key":"S0218127423500542BIB053","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.3390\/e14081553","volume":"14","author":"Zanin M.","year":"2012","journal-title":"Entropy"},{"key":"S0218127423500542BIB054","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.21595\/jve.2019.20815","volume":"21","author":"Zhang X.","year":"2019","journal-title":"J. Vibroeng."},{"key":"S0218127423500542BIB055","doi-asserted-by":"crossref","first-page":"110023","DOI":"10.1016\/j.measurement.2021.110023","volume":"185","author":"Zhang X.","year":"2021","journal-title":"Measurement"},{"key":"S0218127423500542BIB056","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1016\/j.ymssp.2016.09.010","volume":"85","author":"Zheng J.","year":"2017","journal-title":"Mech. Syst. Sign. Process."},{"key":"S0218127423500542BIB057","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.isatra.2021.05.042","volume":"123","author":"Zheng J.","year":"2022","journal-title":"ISA Trans."},{"key":"S0218127423500542BIB058","doi-asserted-by":"crossref","first-page":"123089","DOI":"10.1016\/j.physa.2019.123089","volume":"540","author":"Zhou Q.","year":"2020","journal-title":"Physica A"},{"key":"S0218127423500542BIB059","doi-asserted-by":"crossref","first-page":"112137","DOI":"10.1016\/j.measurement.2022.112137","volume":"205","author":"Zhou Y.","year":"2022","journal-title":"Measurement"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127423500542","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T09:10:47Z","timestamp":1682673047000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127423500542"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4]]},"references-count":58,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10.1142\/S0218127423500542"],"URL":"https:\/\/doi.org\/10.1142\/s0218127423500542","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4]]},"article-number":"2350054"}}