{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T23:12:39Z","timestamp":1768691559156,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,18]],"date-time":"2017-03-18T00:00:00Z","timestamp":1489795200000},"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":["51575202"],"award-info":[{"award-number":["51575202"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Jiangsu Province","award":["BK20160183"],"award-info":[{"award-number":["BK20160183"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a supervised feature extraction method called weighted kernel entropy component analysis (WKECA) for fault diagnosis of rolling bearings. The method is developed based on kernel entropy component analysis (KECA) which attempts to preserve the Renyi entropy of the data set after dimension reduction. It makes full use of the labeled information and introduces a weight strategy in the feature extraction. The class-related weights are introduced to denote differences among the samples from different patterns, and genetic algorithm (GA) is implemented to seek out appropriate weights for optimizing the classification results. The features based on wavelet packet decomposition are derived from the original signals. Then the intrinsic geometric features extracted by WKECA are fed into the support vector machine (SVM) classifier to recognize different operating conditions of bearings, and we obtain the overall accuracy (97%) for the experimental samples. The experimental results demonstrated the feasibility and effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s17030625","type":"journal-article","created":{"date-parts":[[2017,3,20]],"date-time":"2017-03-20T11:39:09Z","timestamp":1490009949000},"page":"625","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Weighted Kernel Entropy Component Analysis for Fault Diagnosis of Rolling Bearings"],"prefix":"10.3390","volume":"17","author":[{"given":"Hongdi","family":"Zhou","sequence":"first","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tielin","family":"Shi","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanglan","family":"Liao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianping","family":"Xuan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Duan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Su","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Jiangnan University, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenzhi","family":"He","sequence":"additional","affiliation":[{"name":"School of Mechanical &amp; Electrical Engineering, Jiangsu Normal University, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wuxing","family":"Lai","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.triboint.2015.12.037","article-title":"A review on signal processing techniques utilized in the fault diagnosis of rolling element bearings","volume":"96","author":"Rai","year":"2016","journal-title":"Tribol. Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.ymssp.2015.04.021","article-title":"Rolling element bearing diagnostics using the Case Western Reserve University data: A benchmark study","volume":"64","author":"Smith","year":"2015","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cong, F., Zhong, W., Tong, S., Tang, N., and Chen, J. (2017). State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics. Sensors, 17.","DOI":"10.3390\/s17020369"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/MIE.2013.2287651","article-title":"Trends in fault diagnosis for electrical machines: a review of diagnostic techniques","volume":"8","author":"Henao","year":"2014","journal-title":"IEEE Ind. Electron. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1846","DOI":"10.1109\/TIE.2014.2361115","article-title":"Induction machine bearing fault detection by means of statistical processing of the stray flux measurement","volume":"62","author":"Frosini","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.jsv.2015.09.016","article-title":"A fault diagnosis scheme for rolling bearing based on local mean decomposition and improved multiscale fuzzy entropy","volume":"360","author":"Li","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.jsv.2014.09.025","article-title":"Vibration signal analysis using parameterized time\u2013frequency method for features extraction of varying-speed rotary machinery","volume":"335","author":"Yang","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1109\/TIA.2010.2049623","article-title":"Diagnosis of bearing faults in induction machines by vibration or current signals: a critical comparison","volume":"46","author":"Immovilli","year":"2008","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.renene.2013.06.025","article-title":"Fault diagnosis for a wind turbine transmission system based on manifold learning and Shannon wavelet support vector machine","volume":"62","author":"Tang","year":"2014","journal-title":"Renew. Energ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1016\/j.ymssp.2006.11.003","article-title":"Fault diagnosis of rotating machinery based on multiple ANFIS combination with GAs","volume":"21","author":"Lei","year":"2007","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.jsv.2016.06.046","article-title":"Machinery fault diagnosis using joint global and local\/nonlocal discriminant analysis with selective ensemble learning","volume":"382","author":"Yu","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3125","DOI":"10.1016\/j.ymssp.2011.05.001","article-title":"Supervised locally linear embedding projection (SLLEP) for machinery fault diagnosis","volume":"25","author":"Li","year":"2011","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1243\/095440604322786992","article-title":"Gearbox condition monitoring using self-organizing feature maps","volume":"218","author":"Liao","year":"2004","journal-title":"Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.ymssp.2016.09.030","article-title":"Nondestructive diagnosis of flip chips based on vibration analysis using PCA-RBF","volume":"85","author":"Su","year":"2017","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.measurement.2014.04.016","article-title":"The fault feature extraction and classification of gear using principal component analysis and kernel principal component analysis based on the wavelet packet transform","volume":"54","author":"Shao","year":"2014","journal-title":"Measurement"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.jsv.2016.09.005","article-title":"Fault diagnosis of gearbox using empirical mode decomposition and multi-fractal detrended cross-correlation analysis","volume":"385","author":"Liu","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.jsv.2007.12.008","article-title":"Vibration-based damage detection in an aircraft wing scaled model using principal component analysis and pattern recognition","volume":"313","author":"Trendafilova","year":"2008","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976698300017467","article-title":"Nonlinear component analysis as a kernel eigenvalue problem","volume":"10","author":"Smola","year":"1998","journal-title":"Neural Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1016\/j.asoc.2011.08.030","article-title":"Weighted principal component extraction with genetic algorithms","volume":"12","author":"Liu","year":"2012","journal-title":"Appl. Soft. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1260002","DOI":"10.1142\/S0218001412600026","article-title":"Kernel entropy-based unsupervised spectral feature selection","volume":"26","author":"Zhang","year":"2012","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1109\/TPAMI.2009.100","article-title":"Kernel Entropy Component Analysis","volume":"32","author":"Jenssen","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1016\/j.neucom.2015.05.032","article-title":"Sparse kernel entropy component analysis for dimensionality reduction of biomedical data","volume":"168","author":"Shi","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.neucom.2014.06.045","article-title":"Wavelet kernel entropy component analysis with application to industrial process monitoring","volume":"147","author":"Yang","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/LGRS.2011.2167212","article-title":"Kernel entropy component analysis for remote sensing image clustering","volume":"9","author":"Jenssen","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jenssen, R. (2011, January 18\u201321). Kernel Entropy Component Analysis: New Theory and Semi-Supervised Learning. Proceedings of the IEEE International Workshop on Machine Learning for Signal Processing, Beijing, China.","DOI":"10.1109\/MLSP.2011.6064626"},{"key":"ref_26","unstructured":"Rheinboldt, W. (1990). Introduction to Statistical Pattern Recognition, Academic press. [2nd ed.]."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/TEVC.2005.856069","article-title":"Evolutionary discriminant analysis","volume":"10","author":"Sierra","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_28","first-page":"547","article-title":"On measures of entropy and information","volume":"1","author":"Renyi","year":"1961","journal-title":"Fourth Berkeley Symp. Math. Statist. Prob."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Emmert-Streib, F., and Dehmer, M. (2009). Information Theory and Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-84816-7"},{"key":"ref_30","unstructured":"Gao, L., Qi, L., Chen, E., and Guan, L. (2014, January 14\u201318). A fisher discriminant framework based on Kernel Entropy Component Analysis for feature extraction and emotion recognition. Proceedings of the IEEE International Conference on Multimedia and Expo Workshops (ICMEW), Chengdu, China."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Mitchell, M. (1998). An Introduction to Genetic Algorithms, MIT Press.","DOI":"10.7551\/mitpress\/3927.001.0001"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/79.543973","article-title":"Genetic algorithms and their applications","volume":"13","author":"Tang","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1755","DOI":"10.1016\/j.ymssp.2006.07.014","article-title":"Subspace-based gearbox condition monitoring by kernel principal component analysis","volume":"21","author":"He","year":"2007","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"341","DOI":"10.3390\/s150100341","article-title":"Application of wavelet packet entropy flow manifold learning in bearing factory inspection using the ultrasonic technique","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sigpro.2013.04.015","article-title":"Wavelets for fault diagnosis of rotary machines: A review with applications","volume":"96","author":"Yan","year":"2014","journal-title":"Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"9941","DOI":"10.1016\/j.eswa.2009.01.065","article-title":"Application of an intelligent classification method to mechanical fault diagnosis","volume":"36","author":"Lei","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1016\/j.ymssp.2006.01.007","article-title":"Fault diagnosis of rotating machinery based on improved wavelet package transform and SVMs ensemble","volume":"21","author":"Hu","year":"2007","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.finel.2013.11.001","article-title":"Wavelet-based numerical analysis: A review and classification","volume":"81","author":"Li","year":"2014","journal-title":"Finite Elem. Anal. Des."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.ymssp.2008.07.002","article-title":"Normalized wavelet packets quantifiers for condition monitoring","volume":"23","author":"Feng","year":"2009","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s12541-012-0045-z","article-title":"Research on on-line automatic diagnostic technology for scratch defect of rolling element bearings","volume":"13","author":"Chen","year":"2012","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zhou, H., Shi, T., Liao, G., Xuan, J., Su, L., He, Z., and Lai, W. (2015). Using supervised kernel entropy component analysis for fault diagnosis of rolling bearings. J. Vib. Control.","DOI":"10.1177\/1077546315608724"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/S0301-679X(99)00077-8","article-title":"A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings","volume":"32","author":"Tandon","year":"1999","journal-title":"Tribol. Int."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1177\/1077546312463747","article-title":"Fault diagnosis of rolling bearings based on marginal fisher analysis","volume":"20","author":"Jiang","year":"2014","journal-title":"J. Vib. Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/625\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:30:46Z","timestamp":1760207446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/625"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,18]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["s17030625"],"URL":"https:\/\/doi.org\/10.3390\/s17030625","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,18]]}}}