{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T17:54:12Z","timestamp":1777571652549,"version":"3.51.4"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,6]],"date-time":"2018-11-06T00:00:00Z","timestamp":1541462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675409"],"award-info":[{"award-number":["51675409"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["xjj2017163"],"award-info":[{"award-number":["xjj2017163"]}]},{"name":"the Natural Science Foundation of Shanxi Province, China","award":["2014011024-6"],"award-info":[{"award-number":["2014011024-6"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The weak compound fault feature is difficult to extract from a gearbox because the signal components are complex and inter-modulated. An approach (that is abbreviated as MRPE-MOMEDA) for extracting the weak fault features of a transmission based on a multipoint optimal minimum entropy deconvolution adjustment (MOMEDA) and the permutation entropy was proposed to solve this problem in the present paper. The complexity of the periodic impact signal was low and the permutation entropy was relatively small. Moreover, the amplitude of the impact was relatively large. Based on these advantages, the multipoint reciprocal permutation entropy (MRPE) was proposed to track the impact fault source of the weak fault feature in gearbox compound faults. The impact fault period was indicated through MRPE. MOMEDA achieved signal denoising. The optimal filter coefficients were solved using MOMEDA. It exhibits an outstanding performance for noise suppression of gearbox signals with a periodic impact. The results from the transmission show that the proposed method can identify multiple faults simultaneously on a driving gear in the 4th gear of the transmission.<\/jats:p>","DOI":"10.3390\/e20110850","type":"journal-article","created":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T03:45:22Z","timestamp":1541562322000},"page":"850","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy"],"prefix":"10.3390","volume":"20","author":[{"given":"Huer","family":"Sun","sequence":"first","affiliation":[{"name":"The School of Mechanical Engineering, North University of China, Xueyuan Road, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao","family":"Wu","sequence":"additional","affiliation":[{"name":"The School of Mechanical Engineering, North University of China, Xueyuan Road, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohua","family":"Liang","sequence":"additional","affiliation":[{"name":"The School of Mechanical Engineering, North University of China, Xueyuan Road, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qunfeng","family":"Zeng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,6]]},"reference":[{"key":"ref_1","unstructured":"Lin, J., and Chen, Q. (2010, January 27\u201329). In application of the EEMD method to multiple faults diagnosis of gearbox. Proceedings of the 2nd International Conference on Advanced Computer Control, Shenyang, China."},{"key":"ref_2","first-page":"104","article-title":"Wind turbine gearbox multi-fault diagnosis based on CMF-EEMD","volume":"2016","author":"Wang","year":"2016","journal-title":"Electr. Mach. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2589","DOI":"10.1016\/j.ymssp.2011.02.017","article-title":"Virtual prototype and experimental research on gear multi-fault diagnosis using wavelet-autoregressive model and principal component analysis method","volume":"25","author":"Li","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.ymssp.2006.05.002","article-title":"Static-transmission-error vibratory-excitation contributions from plastically deformed gear teeth caused by tooth bending-fatigue damage","volume":"21","author":"Mark","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s11071-005-1398-y","article-title":"Dynamics of a gear system with faults in meshing stiffness","volume":"41","author":"Litak","year":"2005","journal-title":"Nonlinear Dynam."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.neucom.2016.02.028","article-title":"A statistical comparison of neuroclassifiers and feature selection methods for gearbox fault diagnosis under realistic conditions","volume":"194","author":"Pacheco","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_7","first-page":"176","article-title":"Local regularity analysis with wavelet transform in gear tooth failure detection","volume":"25","year":"2017","journal-title":"Manag. Syst. Prod. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0016-7142(78)90005-4","article-title":"Minimum entropy deconvolution","volume":"16","author":"Wiggins","year":"1980","journal-title":"Geoexploration"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.ymssp.2006.02.005","article-title":"Enhancement of autoregressive model based gear tooth fault detection technique by the use of minimum entropy deconvolution filter","volume":"21","author":"Endo","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.ymssp.2016.03.016","article-title":"Identification of multiple faults in rotating machinery based on minimum entropy deconvolution combined with spectral kurtosis","volume":"81","author":"He","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.ymssp.2012.06.010","article-title":"Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection","volume":"33","author":"Mcdonald","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.jsv.2016.11.033","article-title":"Minimum entropy deconvolution optimized sinusoidal synthesis and its application to vibration based fault detection","volume":"390","author":"Li","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.ymssp.2016.05.036","article-title":"Multipoint optimal minimum entropy deconvolution and convolution fix: Application to vibration fault detection","volume":"82","author":"Mcdonald","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.measurement.2015.08.019","article-title":"A fault diagnosis method combined with LMD, sample entropy and energy ratio for roller bearings","volume":"76","author":"Han","year":"2015","journal-title":"Measurement"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1243\/09544062JMES1224","article-title":"Spectral entropy: A complementary index for rolling element bearing performance degradation assessment","volume":"223","author":"Pan","year":"2009","journal-title":"Proc. Inst. Mech. Eng. Pt. C J. Mechan."},{"key":"ref_17","unstructured":"Hao, R., Feng, Z., and Chu, F. (2010, January 12\u201314). Application of support vector machine based on pattern spectrum entropy in fault diagnostics of bearings. Proceedings of the Prognostics and System Health Management Conference, Macao, China."},{"key":"ref_18","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. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2650","DOI":"10.3390\/e14081343","article-title":"Bearing fault diagnosis based on multiscale permutation entropy and support vector machine","volume":"14","author":"Wu","year":"2012","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shi, Z., Song, W., and Taheri, S. (2016). Improved LMD, permutation entropy and optimized K-means to fault diagnosis for roller bearings. Entropy, 18.","DOI":"10.3390\/e18030070"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"022911","DOI":"10.1103\/PhysRevE.87.022911","article-title":"Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information","volume":"87","author":"Fadlallah","year":"2013","journal-title":"Phys. Rev. E Stat. Nonlin. Soft Matter Phys."},{"key":"ref_22","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":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/j.ymssp.2005.02.003","article-title":"Gearbox fault diagnosis using empirical mode decomposition and hilbert spectrum","volume":"20","author":"Liu","year":"2006","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/850\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:28:12Z","timestamp":1760196492000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/850"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,6]]},"references-count":23,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["e20110850"],"URL":"https:\/\/doi.org\/10.3390\/e20110850","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,6]]}}}