{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:45:34Z","timestamp":1760233534978,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T00:00:00Z","timestamp":1611187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["No. E2018202282"],"award-info":[{"award-number":["No. E2018202282"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the development of reliability theory, people realized that \u201cabsolutely reliable\u201d machines could not be made. With its incomparable advantages, the high-speed permanent-magnet brushless DC motor is usually used in the symmetrical structure of high-speed operation working systems, which at present are widely used in aerospace and other fields. The structure of the manufacturing process involves a strict processing, but in the process of work failure could still occur. No matter what field the high-speed permanent magnet brushless DC motor is applied to, it is very important to identify states and run fault diagnosis, which is of great significance to maintain the reliability of the motor and its working system. In this study, the fault diagnosis method of a high-speed permanent-magnet brushless DC motor is studied, and a combination model of modified gray wolf optimization algorithm (MGWO) and support vector machine (SVM) have been proposed for the motor fault diagnosis research. Based on the traditional gray wolf optimization (GWO) algorithm, the optimization performance of the algorithm is improved by initializing the population through a tent map and introducing a sine wave dynamic adaptive factor. Then the modified algorithm is used to optimize the internal parameters of SVM to improve the diagnostic accuracy of the model. Through the signal acquisition test, the current signals under different fault states and faultless states were collected, and the current signal data set required for the experiment is obtained. The experimental result showed that, compared with GWO or sailfish optimization (SFO) optimized SVM models, Extreme learning machine and Back Propagation neural network classical classification models, the fault diagnosis accuracy of the proposed model is the highest, proving the excellent classification performance and good robustness of the MGWO-SVM model.<\/jats:p>","DOI":"10.3390\/sym13020163","type":"journal-article","created":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T09:49:21Z","timestamp":1611222561000},"page":"163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fault Diagnosis of High-Speed Brushless Permanent-Magnet DC Motor Based on Support Vector Machine Optimized by Modified Grey Wolf Optimization Algorithm"],"prefix":"10.3390","volume":"13","author":[{"given":"Ling-Ling","family":"Li","sequence":"first","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China"},{"name":"Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia-Qi","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China"},{"name":"Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei-Bing","family":"Zhao","sequence":"additional","affiliation":[{"name":"Tianjin Navigation Instrument Research Institute, Tianjin 300131, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,21]]},"reference":[{"key":"ref_1","first-page":"646","article-title":"Gyro motor fault classification model based on a coupled hidden Markov model with a minimum intra-class distance algorithm","volume":"234","author":"Dong","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113658","DOI":"10.1016\/j.eswa.2020.113658","article-title":"Repair equipment allocation problem for a support-and-repair ship on a deep sea: A hybrid multi-criteria decision making and optimization approach","volume":"160","author":"Zhao","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.aei.2014.10.001","article-title":"A research on intelligent fault diagnosis of wind turbines based on ontology and FMECA","volume":"29","author":"Zhou","year":"2015","journal-title":"Adv. Eng. Inform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.sigpro.2016.07.028","article-title":"Fault diagnosis of rotary machinery components using a stacked denoising autoencoder-based health state identification","volume":"130","author":"Lu","year":"2017","journal-title":"Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.isatra.2018.04.005","article-title":"Fault diagnosis of rolling bearings with recurrent neural network-based autoencoders","volume":"77","author":"Liu","year":"2018","journal-title":"ISA Trans."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.neucom.2018.09.050","article-title":"A convolutional neural network based on a capsule network with strong generalization for bearing fault diagnosis","volume":"323","author":"Zhu","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/j.measurement.2018.12.011","article-title":"A support vector machine based fault diagnostics of Induction motors for practical situation of multi-sensor limited data case","volume":"135","author":"Gangsar","year":"2019","journal-title":"Measurement"},{"key":"ref_8","first-page":"5467643","article-title":"Multiple-Fault Detection Methodology Based on Vibration and Current Analysis Applied to Bearings in Induction Motors and Gearboxes on the Kinematic Chain","volume":"2016","author":"Prieto","year":"2016","journal-title":"Shock. Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"136358","DOI":"10.1109\/ACCESS.2019.2919321","article-title":"Whale Vocalization Classification Using Feature Extraction With Resonance Sparse Signal Decomposition and Ridge Extraction","volume":"7","author":"Chen","year":"2019","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.apacoust.2017.10.025","article-title":"A new method to classify railway vehicle axle fatigue crack AE signal","volume":"131","author":"Zhou","year":"2018","journal-title":"Appl. Acoust."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.renene.2018.10.047","article-title":"Machine learning methods for wind turbine condition monitoring: A review","volume":"133","author":"Stetco","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2378","DOI":"10.1109\/TIA.2019.2895797","article-title":"Machine Learning-Based Fault Diagnosis for Single- and Multi-Faults in Induction Motors Using Measured Stator Currents and Vibration Signals","volume":"55","author":"Ali","year":"2019","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108067","DOI":"10.1016\/j.measurement.2020.108067","article-title":"A GOA-MSVM based strategy to achieve high fault identification accuracy for rotating machinery under different load conditions","volume":"163","author":"Zhang","year":"2020","journal-title":"Measurement"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1007\/s40565-018-0402-8","article-title":"Fault diagnosis of wind turbine bearing based on stochastic subspace identification and multi-kernel support vector machine","volume":"7","author":"Zhao","year":"2019","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1109\/TII.2015.2462315","article-title":"Recursive Undecimated Wavelet Packet Transform and DAG SVM for Induction Motor Diagnosis","volume":"11","author":"Keskes","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1687814019878041","DOI":"10.1177\/1687814019878041","article-title":"Experimental investigation and multi-conditions identification method of centrifugal pump using Fisher discriminant ratio and support vector machine","volume":"11","author":"Qiu","year":"2019","journal-title":"Adv. Mech. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zeng, B., Guo, J., Zhu, W., Xiao, Z., Yuan, F., and Huang, S. (2019). A Transformer Fault Diagnosis Model Based On Hybrid Grey Wolf Optimizer and LS-SVM. Energies, 12.","DOI":"10.3390\/en12214170"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1002\/tee.23069","article-title":"Fault diagnosis of transformer based on modified grey wolf optimization algorithm and support vector machine","volume":"15","author":"Huang","year":"2020","journal-title":"IEEJ Trans. Electr. Electron. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yu, J., Zhang, C., and Wang, S. (2020). Multichannel one-dimensional convolutional neural network-based feature learning for fault diagnosis of industrial processes. Neural Comput. Appl.","DOI":"10.1007\/s00521-020-05171-4"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.rser.2019.04.021","article-title":"Artificial intelligence-based fault detection and diagnosis methods for building energy systems: Advantages, challenges and the future","volume":"109","author":"Zhao","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4867","DOI":"10.1109\/TPEL.2013.2242093","article-title":"Fault Detection for Modular Multilevel Converters Based on Sliding Mode Observer","volume":"28","author":"Shao","year":"2013","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.aei.2018.06.006","article-title":"Fault diagnosis of rolling bearing based on optimized soft competitive learning Fuzzy ART and similarity evaluation technique","volume":"38","author":"Wan","year":"2018","journal-title":"Adv. Eng. Inform."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4109","DOI":"10.1109\/TIE.2008.2007527","article-title":"Advances in Diagnostic Techniques for Induction Machines","volume":"55","author":"Bellini","year":"2008","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4328","DOI":"10.1109\/TPEL.2017.2711598","article-title":"A Nonintrusive Diagnostic Method for Open-Circuit Faults of Locomotive Inverters Based on Output Current Trajectory","volume":"33","author":"Wu","year":"2017","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5842","DOI":"10.1109\/TPEL.2013.2257862","article-title":"State Observer-Based Sensor Fault Detection and Isolation, and Fault Tolerant Control of a Single-Phase PWM Rectifier for Electric Railway Traction","volume":"28","year":"2013","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1109\/TPEL.2020.3004531","article-title":"Multiswitch Open-Circuit Fault Diagnosis of Microgrid Inverter Based on Slidable Triangu-larization Processing","volume":"36","author":"Huang","year":"2021","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.jocs.2017.06.006","article-title":"A big data driven sustainable manufacturing framework for condition-based maintenance prediction","volume":"27","author":"Kumar","year":"2018","journal-title":"J. Comput. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jpowsour.2016.04.080","article-title":"Fault diagnosis and prognostic of solid oxide fuel cells","volume":"321","author":"Wu","year":"2016","journal-title":"J. Power Sources"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1504\/IJSNET.2020.104927","article-title":"Hidden Markov model based rotate vector reducer fault detection using acoustic emissions","volume":"32","author":"An","year":"2020","journal-title":"Int. J. Sens. Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1049\/hve.2019.0067","article-title":"Method of inter-turn fault detection for next-generation smart transformers based on deep learning algorithm","volume":"4","author":"Duan","year":"2019","journal-title":"High Volt."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, X., Zhang, B., and Gao, D. (2020). Bearing fault diagnosis base on multi-scale CNN and LSTM model. J. Intell. Manuf.","DOI":"10.1007\/s10845-020-01600-2"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1007\/s42835-020-00430-9","article-title":"Failure Diagnosis Method of Photovoltaic Generator Using Support Vector Machine","volume":"15","author":"Cho","year":"2020","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.epsr.2016.06.016","article-title":"Evaluation of electrical insulation in three-phase induction motors and classification of failures using neural networks","volume":"140","author":"Guedes","year":"2016","journal-title":"Electr. Power Syst. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1109\/TTE.2020.2982785","article-title":"Detection of Winding Faults Using Image Features and Binary Tree Support Vector Machine for Autotransformer","volume":"6","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1093\/comjnl\/bxz035","article-title":"Enhanced SVM\u2013KPCA Method for Brain MR Image Classification","volume":"63","author":"Neffati","year":"2019","journal-title":"Comput. J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Ge, J., Niu, T., Xu, D., Yin, G., and Wang, Y. (2020). A Rolling Bearing Fault Diagnosis Method Based on EEMD-WSST Signal Reconstruction and Multi-Scale En-tropy. Entropy, 22.","DOI":"10.3390\/e22030290"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"106906","DOI":"10.1016\/j.measurement.2019.106906","article-title":"A new wind turbine health condition monitoring method based on VMD-MPE and feature-based transfer learning","volume":"148","author":"Ren","year":"2019","journal-title":"Measurement"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3640","DOI":"10.1109\/TII.2019.2939678","article-title":"Information Theoretical Measurements From Induction Motors Under Several Load and Voltage Conditions for Bearing Faults Classification","volume":"16","author":"Bazan","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2833","DOI":"10.1007\/s10489-020-01684-6","article-title":"A novel classification method based on ICGOA-KELM for fault diagnosis of rolling bearing","volume":"50","author":"Chen","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zhang, J., Sun, H., Sun, Z., Dong, Y., and Dong, W. (2020). Open-Circuit Fault Diagnosis of Wind Power Converter Using Variational Mode Decomposition, Trend Feature Analysis and Deep Belief Network. Appl. Sci., 10.","DOI":"10.20944\/preprints202002.0392.v1"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1109\/TMECH.2020.3009449","article-title":"Ensemble generalized multiclass support-vector-machine-based health evaluation of complex degradation systems","volume":"25","author":"Wu","year":"2020","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"107123","DOI":"10.1016\/j.ymssp.2020.107123","article-title":"Two-dimensional time series sample entropy algorithm: Applications to rotor axis orbit feature identification","volume":"147","author":"Huachun","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"137945","DOI":"10.1109\/ACCESS.2019.2943071","article-title":"Fault Diagnosis of Analog Circuits Based on IH-PSO Optimized Support Vector Machine","volume":"7","author":"Yuan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"110232","DOI":"10.1016\/j.enbuild.2020.110232","article-title":"A comparison study of basic data-driven fault diagnosis methods for variable refrigerant flow system","volume":"224","author":"Zhou","year":"2020","journal-title":"Energy Build."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1108\/AA-09-2018-0125","article-title":"Application of sensitive dimensionless parameters and PSO\u2013SVM for fault classification in rotating machinery","volume":"40","author":"Qin","year":"2019","journal-title":"Assem. Autom."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1550019","DOI":"10.1142\/S0218001415500196","article-title":"The Application of HIWO\u2013SVM in Analog Circuit Fault Diagnosis","volume":"29","author":"Hu","year":"2015","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"103476","DOI":"10.1109\/ACCESS.2020.2999311","article-title":"An Improved Gray Wolf Optimizer MPPT Algorithm for PV System With BFBIC Converter Under Partial Shading","volume":"8","author":"Guo","year":"2020","journal-title":"IEEE Access"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"105586","DOI":"10.1016\/j.knosys.2020.105586","article-title":"Evolutionary and adaptive inheritance enhanced Grey Wolf Optimization algorithm for binary domains","volume":"194","author":"Ozsoydan","year":"2020","journal-title":"Knowledge-Based Syst."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.asoc.2017.06.044","article-title":"An efficient modified grey wolf optimizer with L\u00e9vy flight for optimization tasks","volume":"60","author":"Heidari","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey wolf optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"54270","DOI":"10.1109\/ACCESS.2018.2869632","article-title":"Application of the Improved Chaotic Self-Adapting Monkey Algorithm into Radar Systems of Internet of Things","volume":"6","author":"Cui","year":"2018","journal-title":"IEEE Access"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.asoc.2018.01.044","article-title":"Non-interactive approach to solve multi-objective thermal power dispatch problem using composite search algorithm","volume":"65","author":"Singh","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.jclepro.2019.04.331","article-title":"Renewable energy prediction: A novel short-term prediction model of photovoltaic output power","volume":"228","author":"Li","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.apenergy.2015.11.060","article-title":"Online implementation of SVM based fault diagnosis strategy for PEMFC systems","volume":"164","author":"Li","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"64","DOI":"10.17531\/ein.2015.1.9","article-title":"Recognition of armature current of DC generator depending on rotor speed using FFT, MSAF-1 and LDA","volume":"17","author":"Glowacz","year":"2015","journal-title":"Ekspolatacja Niezawodn. Maint. Reliab."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2413","DOI":"10.1515\/amm-2017-0355","article-title":"Fault Diagnosis of Three Phase Induction Motor Using Current Signal, MSAF-Ratio15 and Selected Classifiers","volume":"62","author":"Glowacz","year":"2017","journal-title":"Arch. Met. Mater."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/163\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:13:31Z","timestamp":1760159611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,21]]},"references-count":56,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020163"],"URL":"https:\/\/doi.org\/10.3390\/sym13020163","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,21]]}}}