{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:00Z","timestamp":1760241600187,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,11]],"date-time":"2018-06-11T00:00:00Z","timestamp":1528675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61603345"],"award-info":[{"award-number":["61603345"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2015M582202."],"award-info":[{"award-number":["2015M582202."]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>According to the dynamic characteristics of the rolling bearing vibration signal and the distribution characteristics of its noise, a fault identification method based on the adaptive filtering empirical wavelet transform (AFEWT) and kernel density estimation mutual information (KDEMI) classifier is proposed. First, we use AFEWT to extract the feature of the rolling bearing vibration signal. The hypothesis test of the Gaussian distribution is carried out for the sub-modes that are obtained by the twice decomposition of EWT, and Gaussian noise is filtered out according to the test results. In this way, we can overcome the noise interference and avoid the mode selection problem when we extract the feature of the signal. Then we combine the advantages of kernel density estimation (KDE) and mutual information (MI) and put forward a KDEMI classifier. The mutual information of the probability density combining the unknown signal feature vector and the probability density of the known type signal is calculated. The type of the unknown signal is determined via the value of the mutual information, so as to achieve the purpose of fault identification of the rolling bearing. In order to verify the effectiveness of AFEWT in feature extraction, we extract signal features using three methods, AFEWT, EWT, and EMD, and then use the same classifier to identify fault signals. Experimental results show that the fault signal has the highest recognition rate by using AFEWT for feature extraction. At the same time, in order to verify the performance of the AFEWT-KDEMI method, we compare two classical fault signal identification methods, SVM and BP neural network, with the AFEWT-KDEMI method. Through experimental analysis, we found that the AFEWT-KDEMI method is more stable and effective.<\/jats:p>","DOI":"10.3390\/e20060455","type":"journal-article","created":{"date-parts":[[2018,6,11]],"date-time":"2018-06-11T11:01:01Z","timestamp":1528714861000},"page":"455","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Novel Fault Diagnosis Method of Rolling Bearings Based on AFEWT-KDEMI"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-1926","authenticated-orcid":false,"given":"Mingtao","family":"Ge","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 50001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 50001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangfang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 50001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 50001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangyang","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 50001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2017.08.036","article-title":"Early fault diagnosis of bearing and stator faults of the single-phase induction motor using acoustic signals","volume":"113","author":"Glowacz","year":"2018","journal-title":"Measurement"},{"key":"ref_2","first-page":"1","article-title":"Shannon Entropy and K -Means Method for Automatic Diagnosis of Broken Rotor Bars in Induction Motors Using Vibration Signals","volume":"2","year":"2016","journal-title":"Shock Vib."},{"key":"ref_3","first-page":"123","article-title":"Dynamic characteristics for the part fault of outer race in a ball hearing and computer simulation","volume":"4","author":"Cao","year":"2005","journal-title":"J. East. China Jiaotong Univ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.measurement.2016.04.036","article-title":"Recent progress on decoupling diagnosis of hybrid failures in gear transmission systems using vibration sensor signal: A review","volume":"90","author":"Li","year":"2016","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.apacoust.2018.03.010","article-title":"Acoustic based fault diagnosis of three-phase induction motor","volume":"137","author":"Glowacz","year":"2018","journal-title":"Appl. Acoust."},{"key":"ref_6","unstructured":"He, Z.J., Zi, Y.Y., and Meng, Q.F. (2001). Fault Diagnosis Principles of Non-Stationary Signal and Applications to Mechanical Equipment, Higher Education Press."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.ymssp.2018.03.014","article-title":"A denoising scheme for DSPI phase based on improved variational mode decomposition","volume":"110","author":"Xiao","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","first-page":"32","article-title":"Fault diagnosis of rolling bearing based on bispectrum fuzzy clustering","volume":"13","author":"Li","year":"2014","journal-title":"J. Nantong Univ."},{"key":"ref_9","first-page":"298","article-title":"Based on higher-order statistics, rolling bearing fault diagnosis method","volume":"33","author":"Cai","year":"2013","journal-title":"J. Vib. Meas. Diagn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.acha.2004.10.001","article-title":"Nonlinear wavelet thresholding: A recursive method to determine the optimal denoising threshold","volume":"18","author":"Azzalini","year":"2005","journal-title":"Appl. Comput. Harmon. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1109\/TIP.2008.919370","article-title":"SURE-LET multichannel image denoising: Interscale orthonormal wavelet thresholding","volume":"17","author":"Luisier","year":"2008","journal-title":"IEEE Trans. Image Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1515\/aoa-2015-0035","article-title":"DC Motor Fault Analysis with the Use of Acoustic Signals, Coiflet Wavelet Transform, and K-Nearest Neighbor Classifier","volume":"40","author":"Glowacz","year":"2015","journal-title":"Arch. Acoust."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1016\/j.jmaa.2012.01.010","article-title":"The near shift-invariance of the dual-tree complex wavelet transform revisited","volume":"389","author":"Barri","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1016\/j.neucom.2016.06.072","article-title":"Full frequency de-noising method based on wavelet decomposition and noise-type detection","volume":"214","author":"Dong","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bustos, A., Rubio, H., Castej\u00f3n, C., and Garc\u00eda-Prada, J.C. (2018). EMD-Based Methodology for the Identification of a High-Speed Train Running in a Gear Operating State. Sensors, 18.","DOI":"10.3390\/s18030793"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Niu, D., Liang, Y., and Hong, W.C. (2017). Wind Speed Forecasting Based on EMD and GRNN Optimized by FOA. Energies, 10.","DOI":"10.3390\/en10122001"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1080\/10236198.2016.1254206","article-title":"Difference equation based empirical mode decomposition with application to separation enhancement of multi-fault vibration signals","volume":"23","author":"Li","year":"2016","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10923","DOI":"10.3390\/s150510923","article-title":"Multi-Scale Pixel-Based Image Fusion Using Multivariate Empirical Mode Decomposition","volume":"15","author":"Rehman","year":"2015","journal-title":"Sensors"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Huang, Y., Di, H., Malekian, R., Qi, X., and Li, Z. (2017). Noncontact Measurement and Detection of Instantaneous Seismic Attributes Based on Complementary Ensemble Empirical Mode Decomposition. Energies, 10.","DOI":"10.3390\/en10101655"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3999","DOI":"10.1109\/TSP.2013.2265222","article-title":"Empirical wavelet transforms","volume":"61","author":"Gilles","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Gao, Z., Lin, J., Wang, X., and Xu, X. (2017). Bearing Fault Detection Based on Empirical Wavelet Transform and Correlated Kurtosis by Acoustic Emission. Materials, 10.","DOI":"10.3390\/ma10060571"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ge, M., Wang, J., and Ren, X. (2017). Fault Diagnosis of Rolling Bearings Based on EWT and KDEC. Entropy, 19.","DOI":"10.3390\/e19120633"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5261","DOI":"10.1128\/AEM.00062-07","article-title":"Naive Bayesian classifier for rapid assignment of rRNA sequences into the new bacterial taxonomy","volume":"73","author":"Wang","year":"2007","journal-title":"Appl. Environ. Microbiol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1515\/aoa-2015-0022","article-title":"Recognition of Acoustic Signals of Loaded Synchronous Motor Using FFT, MSAF-5 and LSVM","volume":"40","author":"Glowacz","year":"2015","journal-title":"Arch. Acoust."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.apacoust.2016.07.026","article-title":"A comparative study of the effectiveness of vibration and acoustic emission in diagnosing a defective bearing in a planetry gearbox","volume":"115","author":"Elasha","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0893-6080(03)00169-2","article-title":"Practical selection of SVM parameters and noise estimation for SVM regression","volume":"17","author":"Cherkassky","year":"2004","journal-title":"Neural Netw."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.asoc.2015.10.005","article-title":"Particle swarm optimization for bandwidth determination and feature selection of kernel density estimation based classifiers in diagnosis of breast cancer","volume":"40","author":"Sheikhpour","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4891","DOI":"10.1002\/sim.7032","article-title":"Analyzing infant head flatness and asymmetry using kernel density estimation of directional surface data from a craniofacial 3D model","volume":"35","author":"Vuollo","year":"2016","journal-title":"Stat. Med."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/S0022-247X(02)00630-3","article-title":"Ambiguity functions, Wigner distributions and Cohen\u2019s class for LCA groups","volume":"277","author":"Kutyniok","year":"2003","journal-title":"J. Math. Anal. Appl."},{"key":"ref_32","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\u201365","author":"Smith","year":"2015","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/455\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:08:08Z","timestamp":1760195288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,11]]},"references-count":32,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["e20060455"],"URL":"https:\/\/doi.org\/10.3390\/e20060455","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,6,11]]}}}