{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T20:56:15Z","timestamp":1775595375584,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,24]],"date-time":"2019-12-24T00:00:00Z","timestamp":1577145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The self-organizing fuzzy (SOF) logic classifier is an efficient and non-parametric classifier. Its classification process is divided into an offline training stage, an online training stage, and a testing stage. Representative samples of different categories are obtained through the first two stages, and these representative samples are called prototypes. However, in the testing stage, the classification of testing samples is completely dependent on the prototype with the maximum similarity, without considering the influence of other prototypes on the classification decision of testing samples. Aiming at the testing stage, this paper proposed a new SOF classifier based on the harmonic mean difference (HMDSOF). In the testing stage of HMDSOF, firstly, each prototype was sorted in descending order according to the similarity between each prototype in the same category and the testing sample. Secondly, multiple local mean vectors of the prototypes after sorting were calculated. Finally, the testing sample was classified into the category with the smallest harmonic mean difference. Based on the above new method, in this paper, the multiscale permutation entropy (MPE) was used to extract fault features, linear discriminant analysis (LDA) was used to reduce the dimension of fault features, and the proposed HMDSOF was further used to classify the features. At the end of this paper, the proposed fault diagnosis method was applied to the diagnosis examples of two groups of different rolling bearings. The results verify the superiority and generalization of the proposed fault diagnosis method.<\/jats:p>","DOI":"10.3390\/e22010027","type":"journal-article","created":{"date-parts":[[2019,12,24]],"date-time":"2019-12-24T10:28:43Z","timestamp":1577183323000},"page":"27","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["A New Fuzzy Logic Classifier Based on Multiscale Permutation Entropy and Its Application in Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1713-2830","authenticated-orcid":false,"given":"Wenhua","family":"Du","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoming","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijian","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingrang","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanjiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanjun","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Marine Resource Utilization in South China Sea, Hainan University, Haikou 570228, China"},{"name":"Collage of Information and Communication Engineering, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longjuan","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Marine Resource Utilization in South China Sea, Hainan University, Haikou 570228, China"},{"name":"Collage of Information and Communication Engineering, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaichao","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinjie","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanjun","family":"Shao","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huiling","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingyan","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing 400067, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jsv.2018.07.039","article-title":"Initial center frequency-guided VMD for fault diagnosis of rotating machines","volume":"435","author":"Jiang","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.neucom.2019.03.084","article-title":"A novel fault diagnosis algorithm for rotating machinery based on a sparsity and neighborhood preserving deep extreme learning machine","volume":"350","author":"Li","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"29520","DOI":"10.1109\/ACCESS.2019.2900503","article-title":"A novel Fault Diagnosis Method of Gearbox Based on Maximum Kurtosis Spectral Entropy Deconvolution","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, X.L., Zhou, F.C., He, Y.L., and Wu, Y.J. (2019). Weak fault diagnosis of rolling bearing under variable speed condition using IEWT-based enhanced envelope order spectrum. Meas. Sci. Technol., 30.","DOI":"10.1088\/1361-6501\/aafd7f"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.measurement.2019.03.033","article-title":"Research and application of improved adaptive MOMEDA fault diagnosis method","volume":"140","author":"Wang","year":"2019","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, X.L., Yan, X.L., and He, Y.L. (2019). Weak Fault Feature Extraction and Enhancement of Wind Turbine Bearing Based on OCYCBD and SVDD. Appl. Sci., 9.","DOI":"10.3390\/app9183706"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Gao, Y.D., Villecco, F., and Li, M. (2017). Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis. Entropy, 19.","DOI":"10.3390\/e19040176"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Song, W.Q., Cattani, C., and Chi, C.H. (2019). Fractional Brownian Motion and Quantum-Behaved Particle Swarm Optimization for Short Term Power Load Forecasting: An Integrated Approach. Energy, in press.","DOI":"10.1016\/j.energy.2019.116847"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"125106","DOI":"10.1088\/1361-6501\/aae2d1","article-title":"A narrowband envelope spectra fusion method for fault diagnosis of rolling element bearings","volume":"29","author":"Duan","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","unstructured":"Song, W.Q., Cheng, X.X., and Cattani, C. (2019). Multi-Fractional Brownian Motion and Quantum-Behaved Partial Swarm Optimization for Bearing Degradation Forecasting. Complexity, in press."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.engfailanal.2018.04.053","article-title":"Simulation and experimental analysis of rolling element bearing fault in rotor-bearing-casing system","volume":"92","author":"Yang","year":"2018","journal-title":"Eng. Fail. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6743","DOI":"10.1109\/JSEN.2018.2851100","article-title":"A Novel Intelligent Method for Bearing Fault Diagnosis Based on Hermitian Scale-Energy Spectrum","volume":"18","author":"Zhang","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wang, Z.J., Wang, J.Y., Cai, W.N., Zhou, J., and Du, W.H. (2019). Application of an Improved Ensemble Local Mean Decomposition Method for Gearbox Composite Fault diagnosis. Complexity, 2019.","DOI":"10.1155\/2019\/1564243"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3249","DOI":"10.1177\/1077546317739117","article-title":"An alternative demodulation method using envelope-derivative operator for bearing fault diagnosis of the vibrating screen","volume":"24","author":"Cai","year":"2018","journal-title":"J. Vib. Control."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4301","DOI":"10.1109\/TIE.2017.2762623","article-title":"Statistical Spectral Analysis for Fault Diagnosis of Rotating Machines","volume":"65","author":"Ciabattoni","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"44871","DOI":"10.1109\/ACCESS.2019.2909300","article-title":"Application of Parameter Optimized Variational Mode Decomposition Method in Fault Diagnosis of Gearbox","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lv, Y., Yuan, R., and Shi, W. (2018). Fault Diagnosis of Rotating Machinery Based on the Multiscale Local Projection Method and Diagonal Slice Spectrum. Appl. Sci., 8.","DOI":"10.3390\/app8040619"},{"key":"ref_18","unstructured":"Mo, Z.L., Wang, J.Y., Zhang, H., and Miao, Q. (2019). Weighted Cyclic Harmonic-to-Noise Ratio for Rolling Element Bearing Fault Diagnosis. IEEE Trans. Instrum. Meas., 1\u201311."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"125107","DOI":"10.1088\/1361-6501\/ab26a2","article-title":"An intelligent fault diagnosis framework dealing with arbitrary length inputs under different working conditions","volume":"30","author":"An","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"130804","DOI":"10.1109\/ACCESS.2019.2939546","article-title":"Robust Fault Diagnosis of Rolling Bearing Using Multivariate Intrinsic Multiscale Entropy Analysis and Neural Network Under Varying Operating Conditions","volume":"7","author":"Yuan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.knosys.2018.09.004","article-title":"Intelligent fault diagnosis of rotating machinery using improved multiscale dispersion entropy and mRMR feature selection","volume":"163","author":"Yan","year":"2019","journal-title":"Knowl. Based Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.mechmachtheory.2014.01.011","article-title":"A fault diagnosis method based on local mean decomposition and multi-scale entropy for roller bearings","volume":"75","author":"Liu","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, Z.J., Zheng, L.K., and Du, W.H. (2019). A novel method for intelligent fault diagnosis of bearing based on capsule neural network. Complexity, 2019.","DOI":"10.1155\/2019\/6943234"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.ymssp.2016.12.027","article-title":"Using multi-scale entropy and principal component analysis to monitor gears degradation via the motor current signature analysis","volume":"90","author":"Aouabdi","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2198","DOI":"10.1109\/TITS.2018.2865410","article-title":"A Newly Robust Fault Detection and Diagnosis Method for High-Speed Trains","volume":"20","author":"Chen","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.neucom.2015.01.016","article-title":"Multi-fault diagnosis for rotating machinery based on orthogonal supervised linear local tangent space alignment and least square support vector machine","volume":"157","author":"Su","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"68718","DOI":"10.1109\/ACCESS.2019.2918560","article-title":"Multiscale Fluctuation-Based Dispersion Entropy and Its Applications to Neurological Diseases","volume":"7","author":"Azami","year":"2019","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/TMECH.2017.2728371","article-title":"Fault Diagnosis for Rotating Machinery Using Multiple Sensors and Convolutional Neural Networks","volume":"23","author":"Xia","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4222","DOI":"10.1109\/TIM.2018.2890329","article-title":"Application of Spectral Kurtosis and Improved Extreme Learning Machine for Bearing Fault Classification","volume":"68","author":"Udmale","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.eswa.2016.09.031","article-title":"A new k-harmonic nearest neighbor classifier based on the multi-local means","volume":"67","author":"Pan","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wang, Z.J., Zheng, L.K., Wang, J.Y., and Du, W.H. (2019). Research of novel bearing fault diagnosis method based on improved krill herd algorithm and kernel Extreme Learning Machine. Complexity, 2019.","DOI":"10.1155\/2019\/4031795"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.ins.2018.03.004","article-title":"Self-organising fuzzy logic classifier","volume":"447","author":"Gu","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"D\u00e1valos, A., Jabloun, M., Ravier, P., and Buttelli, O. (2019). On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator\u2019s Variance. Entropy, 21.","DOI":"10.3390\/e21050450"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"17050","DOI":"10.1109\/ACCESS.2019.2893497","article-title":"A New Bearing Fault Diagnosis Method based on Fine-to-Coarse Multiscale Permutation Entropy, Laplacian Score and SVM","volume":"7","author":"Huo","year":"2019","journal-title":"IEEE Access"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"89845","DOI":"10.1109\/ACCESS.2019.2926348","article-title":"Research of Bearing Fault Diagnosis Method Based on Multi-Layer Extreme Learning Machine Optimized by Novel Ant Lion Algorithm","volume":"7","author":"Zheng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.1007\/s12206-017-0514-5","article-title":"A rolling bearing fault diagnosis strategy based on improved multiscale permutation entropy and least squares SVM","volume":"31","author":"Li","year":"2017","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Rodriguez, N., Alvarez, P., and Barba, L. (2019). Combining Multi-Scale Wavelet Entropy and Kernelized Classification for Bearing Multi-Fault Diagnosis. Entropy, 21.","DOI":"10.3390\/e21020152"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.ymssp.2018.07.034","article-title":"A novel deep output kernel learning method for bearing fault structural diagnosis","volume":"117","author":"Mao","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jsv.2018.08.025","article-title":"Application of dispersion entropy to status characterization of rotary machines","volume":"438","author":"Rostaghi","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Rodriguez, N., Cabrera, G., and Lagos, C. (2017). Stationary Wavelet Singular Entropy and Kernel Extreme Learning for Bearing Multi-Fault Diagnosis. Entropy, 19.","DOI":"10.3390\/e19100541"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.patrec.2008.08.010","article-title":"An experimental comparison of performance measures for classification","volume":"30","author":"Ferri","year":"2009","journal-title":"Pattern Recognit. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:45:12Z","timestamp":1760190312000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,24]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["e22010027"],"URL":"https:\/\/doi.org\/10.3390\/e22010027","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,24]]}}}