{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T20:43:03Z","timestamp":1768077783394,"version":"3.49.0"},"reference-count":57,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T00:00:00Z","timestamp":1636848000000},"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>Bearing vibration signals typically have nonlinear components due to their interaction and coupling effects, friction, damping, and nonlinear stiffness. Bearing faults affect the signal complexity at various scales. Hence, measuring signal complexity at different scales is helpful to diagnosis of bearing faults. Numerous studies have investigated multiscale algorithms; nevertheless, multiscale algorithms using the first moment lose important complexity data. Accordingly, generalized multiscale algorithms have been recently introduced. The present research examined the use of refined composite generalized multiscale dispersion entropy (RCGMDispEn) based on the second moment (variance) and third moment (skewness) along with refined composite multiscale dispersion entropy (RCMDispEn) in bearing fault diagnosis. Moreover, multiclass FCM-ANFIS, which is a combination of adaptive network-based fuzzy inference systems (ANFIS), was developed to improve the efficiency of rotating machinery fault classification. According to the results, it is recommended that generalized multiscale algorithms based on variance and skewness be examined for diagnosis, along with multiscale algorithms, and be used to achieve an improvement in the results. The simultaneous usage of the multiscale algorithm and generalized multiscale algorithms improved the results in all three real datasets used in this study.<\/jats:p>","DOI":"10.3390\/e23111510","type":"journal-article","created":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T20:48:36Z","timestamp":1636922916000},"page":"1510","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Bearing Fault Diagnosis Using Refined Composite Generalized Multiscale Dispersion Entropy-Based Skewness and Variance and Multiclass FCM-ANFIS"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0653-2326","authenticated-orcid":false,"given":"Mostafa","family":"Rostaghi","sequence":"first","affiliation":[{"name":"Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9664-7890","authenticated-orcid":false,"given":"Mohammad Mahdi","family":"Khatibi","sequence":"additional","affiliation":[{"name":"Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Reza","family":"Ashory","sequence":"additional","affiliation":[{"name":"Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7612-0840","authenticated-orcid":false,"given":"Hamed","family":"Azami","sequence":"additional","affiliation":[{"name":"Department of Neurology and Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,14]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1109\/TEC.2005.847955","article-title":"Condition Monitoring and Fault Diagnosis of Electrical Motors\u2014A Review","volume":"20","author":"Nandi","year":"2005","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.bspc.2015.08.004","article-title":"Improved multiscale permutation entropy for biomedical signal analysis: Interpretation and application to electroencephalogram recordings","volume":"23","author":"Azami","year":"2016","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","article-title":"Dispersion Entropy: A Measure for Time-Series Analysis","volume":"23","author":"Rostaghi","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Azami, H., and Escudero, J. (2018). Amplitude- and Fluctuation-Based Dispersion Entropy. Entropy, 3.","DOI":"10.3390\/e20030210"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, W., Shen, J., and Yang, X. (2020). Rolling bearing fault detection approach based on improved dispersion entropy and AFSA optimized SVM. Int. J. Electr. Eng. Educ.","DOI":"10.1177\/0020720920940584"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, R., Ran, C., Luo, J., and Feng, S. (2019, January 15\u201317). Rolling bearing fault diagnosis method based on dispersion entropy and SVM. Proceedings of the 2019 International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), Beijing, China.","DOI":"10.1109\/SDPC.2019.00112"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"12170","DOI":"10.1088\/1742-6596\/1820\/1\/012170","article-title":"Research on Fault Diagnosis Method of Train Rolling Bearing Based on Variational Modal Decomposition and Bat Algorithm-Support Vector Machine","volume":"1820","author":"Jin","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_10","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."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.pnpbp.2012.09.015","article-title":"Progress in Neuro-Psychopharmacology & Biological Psychiatry Is mental illness complex? From behavior to brain","volume":"45","author":"Yang","year":"2013","journal-title":"Prog. Neuropsychopharmacol. Biol. Psychiatry"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1103\/PhysRevLett.89.068102","article-title":"Multiscale Entropy Analysis of Complex Physiologic Time Series","volume":"89","author":"Costa","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Aziz, W., and Arif, M. (2005, January 24\u201325). Multiscale permutation entropy of physiological time series. Proceedings of the 2005 Pakistan Section Multitopic Conference INMIC, Karachi, Pakistan.","DOI":"10.1109\/INMIC.2005.334494"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1016\/j.physleta.2014.03.034","article-title":"Analysis of complex time series using refined composite multiscale entropy","volume":"378","author":"Wu","year":"2014","journal-title":"Phys. Lett. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2364","DOI":"10.1109\/LSP.2015.2482603","article-title":"Refined Composite Multiscale Permutation Entropy to Overcome Multiscale Permutation Entropy Length Dependence","volume":"22","author":"Wu","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2872","DOI":"10.1109\/TBME.2017.2679136","article-title":"Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals","volume":"64","author":"Azami","year":"2017","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4031795","DOI":"10.1155\/2019\/4031795","article-title":"Research on novel bearing fault diagnosis method based on improved krill herd algorithm and kernel extreme learning machine","volume":"2019","author":"Wang","year":"2019","journal-title":"Complexity"},{"key":"ref_18","first-page":"1713","article-title":"Fault diagnosis method of rolling bearings based on refined composite multiscale dispersion entropy and support vector machine","volume":"30","author":"LI","year":"2019","journal-title":"China Mech. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.21595\/jve.2019.20815","article-title":"A novel faults detection method for rolling bearing based on RCMDE and ISVM","volume":"21","author":"Zhang","year":"2019","journal-title":"J. Vibroen."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"42013","DOI":"10.1109\/ACCESS.2021.3064962","article-title":"Rolling Bearing Sub-Health Recognition via Extreme Learning Machine Based on Deep Belief Network Optimized by Improved Fireworks","volume":"9","author":"Luo","year":"2021","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhang, W., and Zhou, J. (2019). A Comprehensive Fault Diagnosis Method for Rolling Bearings Based on Refined Composite Multiscale Dispersion Entropy and Fast Ensemble Empirical Mode Decomposition. Entropy, 21.","DOI":"10.3390\/e21070680"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Luo, S., Yang, W., and Luo, Y. (2020). Fault diagnosis of a rolling bearing based on adaptive sparest narrow-band decomposition and refined composite multiscale dispersion entropy. Entropy, 22.","DOI":"10.3390\/e22040375"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"168732","DOI":"10.1109\/ACCESS.2019.2940627","article-title":"An improved empirical wavelet transform and refined composite multiscale dispersion entropy-based fault diagnosis method for rolling bearing","volume":"8","author":"Zheng","year":"2020","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1687814021991264","DOI":"10.1177\/1687814021991264","article-title":"Integrated approach for ball mill load forecasting based on improved EWT, refined composite multi-scale dispersion entropy and fireworks algorithm optimized SVM","volume":"13","author":"Cai","year":"2021","journal-title":"Adv. Mech. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lv, J., Sun, W., Wang, H., and Zhang, F. (2021). Coordinated Approach Fusing RCMDE and Sparrow Search Algorithm-Based SVM for Fault Diagnosis of Rolling Bearings. Sensors, 21.","DOI":"10.3390\/s21165297"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Tong, S., Cong, F., and Xu, J. (2018). Research of feature extraction method based on sparse reconstruction and multiscale dispersion entropy. Appl. Sci., 8.","DOI":"10.3390\/app8060888"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.3390\/e17031197","article-title":"Generalized multiscale entropy analysis: Application to quantifying the complex volatility of human heartbeat time series","volume":"17","author":"Costa","year":"2015","journal-title":"Entropy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"38983","DOI":"10.1109\/ACCESS.2018.2876759","article-title":"Intelligent fault diagnosis of rotating machinery using ICD and generalized composite multi-scale fuzzy entropy","volume":"7","author":"Wei","year":"2018","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.ymssp.2017.06.011","article-title":"Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis","volume":"99","author":"Zheng","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","first-page":"8851310","article-title":"An Integrated Fault Identification Approach for Rolling Bearings Based on Dual-Tree Complex Wavelet Packet Transform and Generalized Composite Multiscale Amplitude-Aware Permutation Entropy","volume":"2020","author":"Liu","year":"2020","journal-title":"Shock Vib."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1109\/TPAMI.2005.109","article-title":"A theoretical and experimental analysis of linear combiners for multiple classifier systems","volume":"27","author":"Fumera","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_32","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 Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1109\/ICPR.1996.547205","article-title":"Combining classifiers","volume":"2","author":"Kittler","year":"1996","journal-title":"Proc. Int. Conf. Pattern Recognit."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2195","DOI":"10.1016\/j.patrec.2005.03.029","article-title":"Feature combination using boosting","volume":"26","author":"Yin","year":"2005","journal-title":"Pattern Recognit. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.patcog.2005.08.004","article-title":"Combining classifier decisions for robust speaker identification","volume":"39","author":"Mashao","year":"2006","journal-title":"Pattern Recognit."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/j.renene.2018.05.008","article-title":"Multiclass adaptive neuro-fuzzy classifier and feature selection techniques for photovoltaic array fault detection and classification","volume":"127","author":"Belaout","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"123814","DOI":"10.1016\/j.physa.2019.123814","article-title":"Generalized multivariate multiscale sample entropy for detecting the complexity in complex systems","volume":"545","author":"Yin","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1016\/j.physa.2017.08.136","article-title":"Analysis of financial time series using multiscale entropy based on skewness and kurtosis","volume":"490","author":"Xu","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/TFUZZ.2018.2878200","article-title":"A systematic review of fuzzy formalisms for bearing fault diagnosis","volume":"27","author":"Li","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/34.75517","article-title":"Neurocomputations in relational systems","volume":"13","author":"Pedrycz","year":"1991","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"106275","DOI":"10.1016\/j.asoc.2020.106275","article-title":"Fuzzy neural networks and neuro-fuzzy networks : A review the main techniques and applications used in the literature","volume":"92","author":"Vitor","year":"2020","journal-title":"Appl. Soft Comput. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1016\/j.dsp.2009.10.021","article-title":"An intelligent diagnosis system for diabetes on Linear Discriminant Analysis and Adaptive Network Based Fuzzy Inference System: LDA-ANFIS","volume":"20","author":"Dogantekin","year":"2010","journal-title":"Digit. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1080\/01969727308546046","article-title":"A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters","volume":"3","author":"Dunn","year":"1973","journal-title":"J. Cybern."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press.","DOI":"10.1007\/978-1-4757-0450-1"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0098-3004(84)90020-7","article-title":"FCM: The fuzzy c-means clustering algorithm","volume":"10","author":"Bezdek","year":"1984","journal-title":"Comput. Geosci."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Pham, T.D. (2020). Fuzzy Recurrence Plots and Networks with Applications in Biomedicine, Springer.","DOI":"10.1007\/978-3-030-37530-0"},{"key":"ref_47","unstructured":"The MathWorks Inc. (2021, May 04). FCM. Available online: https:\/\/www.mathworks.com\/help\/fuzzy\/fcm.html."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.jsv.2019.01.042","article-title":"A weighted multi-scale dictionary learning model and its applications on bearing fault diagnosis","volume":"446","author":"Zhao","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.ymssp.2017.07.037","article-title":"A robust detector for rolling element bearing condition monitoring based on the modulation signal bispectrum and its performance evaluation against the Kurtogram","volume":"100","author":"Tian","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Kim, S., An, D., and Choi, J.-H. (2020). Diagnostics 101: A Tutorial for Fault Diagnostics of Rolling Element Bearing Using Envelope Analysis in MATLAB. Appl. Sci., 10.","DOI":"10.3390\/app10207302"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.measurement.2016.04.069","article-title":"A new approach based on OMA-empirical wavelet transforms for bearing fault diagnosis","volume":"90","author":"Kedadouche","year":"2016","journal-title":"Measurement"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"(2004). A complex filter for vibration signal demodulation in bearing defect diagnosis. J. Sound Vib., 276, 105\u2013119.","DOI":"10.1016\/j.jsv.2003.08.007"},{"key":"ref_53","unstructured":"Cooper, H., and Hedges, L.V. (1994). Parametric measures of effect size. The Handbook of Research Synthesis, Sage."},{"key":"ref_54","unstructured":"(2020, June 23). Case Western Reserve University Bearing Data Center Website. Available online: https:\/\/engineering.case.edu\/bearingdatacenter\/."},{"key":"ref_55","unstructured":"(2021, June 18). Data Challenge at PHMAP 2021. Available online: http:\/\/phmap.org\/data-challenge\/."},{"key":"ref_56","unstructured":"Lessmeier, C., Kimotho, J.K., Zimmer, D., and Sextro, W. (2019). KAt-Data Center, Chair of Design and Drive Technology, Paderborn University."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Lessmeier, C., Kimotho, J.K., Zimmer, D., and Sextro, W. (2016, January 5\u20138). Condition monitoring of bearing damage in electromechanical drive systems by using motor current signals of electric motors: A benchmark data set for data-driven classification. Proceedings of the PHM Society European Conference, Bilbao, Spain.","DOI":"10.36001\/phme.2016.v3i1.1577"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/11\/1510\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:30:00Z","timestamp":1760167800000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/11\/1510"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,14]]},"references-count":57,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["e23111510"],"URL":"https:\/\/doi.org\/10.3390\/e23111510","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,14]]}}}