{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T19:13:24Z","timestamp":1773774804650,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2012,7,27]],"date-time":"2012-07-27T00:00:00Z","timestamp":1343347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, multiscale permutation entropy (MPE) was introduced for feature extraction from faulty bearing vibration signals. After extracting feature vectors by MPE, the support vector machine (SVM) was applied to automate the fault diagnosis procedure. Simulation results demonstrated that the proposed method is a very powerful algorithm for bearing fault diagnosis and has much better performance than the methods based on single scale permutation entropy (PE) and multiscale entropy (MSE).<\/jats:p>","DOI":"10.3390\/e14081343","type":"journal-article","created":{"date-parts":[[2012,7,28]],"date-time":"2012-07-28T03:13:59Z","timestamp":1343445239000},"page":"1343-1356","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":250,"title":["Bearing Fault Diagnosis Based on Multiscale Permutation Entropy and Support Vector Machine"],"prefix":"10.3390","volume":"14","author":[{"given":"Shuen-De","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mechatronic Technology, National Taiwan Normal University, Taipei 10610, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Po-Hung","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chiu-Wen","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mechatronic Technology, National Taiwan Normal University, Taipei 10610, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian-Jiun","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun-Chieh","family":"Wang","sequence":"additional","affiliation":[{"name":"Mechanical and Systems Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11801","DOI":"10.1016\/j.eswa.2009.04.021","article-title":"A novel fault diagnosis method of bearing based on improved fuzzy ARTMAP and modified distance discriminant technique","volume":"36","author":"Xu","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.isatra.2011.06.003","article-title":"A weighted multi-scale morphological gradient filter for rolling element bearing fault detection","volume":"50","author":"Li","year":"2011","journal-title":"ISA Transactions"},{"key":"ref_3","unstructured":"Mehala, N., and Dahiya, R. (2008, January 29\u201331). A comparative study of FFT, STFT and wavelet techniques for induction machine fault diagnostic analysis. Proceedings of the 7th WSEAS International Conference on Computational Intelligence, Man-Machine Systems and Cybernetics, Cairo, Egypt."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1006\/mssp.1997.0102","article-title":"Time-frequency analysis in gear box fault detection using the wigner-ville distribution","volume":"11","author":"Staszewski","year":"1997","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0888-3270(03)00075-X","article-title":"Application of the wavelet transform in machine condition monitoring and fault diagnostics: A review with bibliography","volume":"18","author":"Peng","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.jsv.2008.07.011","article-title":"Fault severity assessment for rolling element bearings using the Lempel-Ziv complexity and continuous wavelet transform","volume":"320","author":"Hong","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.ymssp.2006.02.009","article-title":"Approximate entropy as a diagnostic tool for machine health monitoring","volume":"21","author":"Yan","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6077","DOI":"10.1016\/j.eswa.2010.02.118","article-title":"Bearing fault diagnosis using multi-scale entropy and adaptive neuro-fuzzy inference","volume":"37","author":"Zhang","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.ymssp.2011.11.022","article-title":"Permutation entropy: A nonlinear statistical measure for status characterization of rotary machines","volume":"29","author":"Yan","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"174102\u20131","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. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10072-008-0851-3","article-title":"Permutation entropy to detect vigilance changes and preictal states from scalp EEG in epileptic patients: A priminary study","volume":"29","author":"Bruzzo","year":"2008","journal-title":"Neurol. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.eplepsyres.2007.08.002","article-title":"Predictability analysis of absence seizures with permutation entropy","volume":"77","author":"Li","year":"2007","journal-title":"Epilepsy Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2854","DOI":"10.1016\/j.physa.2009.03.042","article-title":"Forbidden patterns, permutation entropy and stock market inefficiency","volume":"388","author":"Zunino","year":"2009","journal-title":"Physica A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.ijmachtools.2007.09.008","article-title":"Complexity measure of motor current signals for tool flute breakage detection in end milling","volume":"48","author":"Li","year":"2008","journal-title":"Int. J. Mach. Tool. Manufact."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00170-009-2075-y","article-title":"Permutation entropy based real-time chatter detection using audio signal in turning process","volume":"46","author":"Nair","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"068102-1","DOI":"10.1103\/PhysRevLett.89.068102","article-title":"Multiscale entropy analysis of complex physiological time series","volume":"89","author":"Costa","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Aziz, W., and Arif, M. (2005, January 24\u201325). Multiscale permutation entropy of physiological time series. Proceedings of 9th IEEE International Multitopic Conference, Karachi, Pakistan.","DOI":"10.1109\/INMIC.2005.334494"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"046010","DOI":"10.1088\/1741-2560\/7\/4\/046010","article-title":"Multiscale permutation entropy analysis of EEG recordings during sevoflurane anesthesia","volume":"7","author":"Li","year":"2010","journal-title":"J. Neural Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"27:1","DOI":"10.1145\/1961189.1961199","article-title":"LIBSVM: A library for support vector machines","volume":"2","author":"Chang","year":"2011","journal-title":"ACM Transactions on Intelligent Systems and Technology"},{"key":"ref_20","unstructured":"Case Western Reserve University Bearing Data Center Website. Available online: http:\/\/csegroups.case.edu\/bearingdatacenter\/pages\/download-data-file."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol. Circ. Physiol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/8\/1343\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:51:30Z","timestamp":1760219490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/8\/1343"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,27]]},"references-count":21,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2012,8]]}},"alternative-id":["e14081343"],"URL":"https:\/\/doi.org\/10.3390\/e14081343","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7,27]]}}}