{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T07:10:11Z","timestamp":1778310611180,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:00:00Z","timestamp":1622419200000},"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":["51577008"],"award-info":[{"award-number":["51577008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A misalignment fault is a kind of potential fault in double-fed wind turbines. The reasonable and effective fault prediction models are used to predict its development trend before serious faults occur, which can take measures to repair in advance and reduce human and material losses. In this paper, the Least Squares Support Vector Machine optimized by the Improved Artificial Fish Swarm Algorithm is used to predict the misalignment index of the experiment platform. The mixed features of time domain, frequency domain, and time-frequency domain indexes of vibration or stator current signals are the inputs of the Least Squares Support Vector Machine. The kurtosis of the same signals is the output of the model, and the 3\u03c3 principle of the normal distribution is adopted to set the warning line of misalignment fault. Compared with other optimization algorithms, the experimental results show that the proposed prediction model can predict the development trend of the misalignment index with the least prediction error.<\/jats:p>","DOI":"10.3390\/e23060692","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T21:42:06Z","timestamp":1622497326000},"page":"692","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Misalignment Fault Prediction of Wind Turbines Based on Improved Artificial Fish Swarm Algorithm"],"prefix":"10.3390","volume":"23","author":[{"given":"Zhe","family":"Hua","sequence":"first","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yancai","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiadong","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,31]]},"reference":[{"key":"ref_1","unstructured":"Pek, A. (2020, November 05). GWEC: Wind Power Industry to Install 71.3 GW in 2020, Showing Resilience during COVID-19 Crisis [EB\/OL]. Available online: https:\/\/gwec.net\/gwec-wind-power-industry-to-install-71-3-gw-in-2020-showing-resilience-during-covid-19-crisis."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Wang, Y., Mu, H., and Kang, N. (2017). Research on Misalignment Fault Isolation of Wind Turbines Based on the Mixed-Domain Features. Algorithms, 10.","DOI":"10.3390\/a10020067"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Beretta, M., Julian, A., Sepulveda, J., Cusid\u00f3, J., and Porro, O. (2021). An Ensemble Learning Solution for Predictive Maintenance of Wind Turbines Main Bearing. Sensors, 21.","DOI":"10.3390\/s21041512"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Elasha, F., Shanbr, S., Li, X., and Mba, D. (2019). Prognosis of a Wind Turbine Gearbox Bearing Using Supervised Machine Learning. Sensors, 19.","DOI":"10.3390\/s19143092"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tang, M., Chen, W., Zhao, Q., Wu, H., Long, W., Huang, B., Liao, L., and Zhang, K. (2019). Development of an SVR Model for the Fault Diagnosis of Large-Scale Doubly-Fed Wind Turbines Using SCADA Data. Energies, 12.","DOI":"10.3390\/en12173396"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1080\/15325008.2016.1139015","article-title":"Misalignment faults detection in an induction motor based on multi-scale entropy and artificial neural network","volume":"44","author":"Verma","year":"2016","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5627","DOI":"10.3390\/s150305627","article-title":"An SVM-based solution for fault detection in wind turbines","volume":"15","author":"Santos","year":"2015","journal-title":"Sensors"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1155\/2005\/607319","article-title":"Diagnosis and model based identification of a coupling misalignment","volume":"12","author":"Pennacchi","year":"2005","journal-title":"Shock Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1080\/10916466.2018.1476531","article-title":"On the prediction of solubility of alkane in carbon dioxide using the LSSVM algorithm","volume":"37","author":"Baghban","year":"2019","journal-title":"Pet. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"114543","DOI":"10.1016\/j.applthermaleng.2019.114543","article-title":"Application of support vector regression cooperated with modified artificial fish swarm algorithm for wind tunnel performance prediction of automotive radiators","volume":"164","author":"Yan","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, C., Zhang, F., Li, F., and Wu, H.-S. (2014, January 9\u201311). Improved artificial fish swarm algorithm. Proceedings of the 2014 9th IEEE Conference on Industrial Electronics and Applications, Hangzhou, China.","DOI":"10.1109\/ICIEA.2014.6931262"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ma, H., and Wang, Y. (2009, January 14\u201316). An artificial fish swarm algorithm based on chaos search. Proceedings of the 2009 Fifth International Conference on Natural Computation, Tianjian, China.","DOI":"10.1109\/ICNC.2009.148"},{"key":"ref_13","first-page":"107","article-title":"A review of Artificial Fish Swarm Optimization methods and applications","volume":"5","author":"Neshat","year":"2012","journal-title":"Int. J. Smart Sens. Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1142\/S021800141956010X","article-title":"Support Vector Machine Optimized Using the Improved Fish Swarm Optimization Algorithm and Its Application to Face Recognition","volume":"33","author":"Zhu","year":"2019","journal-title":"Int. J. Pattern Recogn. Artif. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2594","DOI":"10.4028\/www.scientific.net\/AMR.538-541.2594","article-title":"A Novel Global Artificial Fish Swarm Algorithm with Improved Chaotic Search","volume":"1897","author":"Xu","year":"2012","journal-title":"Adv. Mater. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1080\/10798587.2017.1293881","article-title":"Particle Swarm Optimization with Chaos-based Initialization for Numerical Optimization","volume":"24","author":"Tian","year":"2018","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_17","first-page":"195","article-title":"A Novel Network Intrusion Detection Based on Support Vector Machine and Tent Chaos Artificial Bee Colony Algorithm","volume":"2","author":"Kuang","year":"2017","journal-title":"J. Netw. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"043104","DOI":"10.1063\/1.3645185","article-title":"Lyapunov exponents for multi-parameter tent and logistic maps","volume":"21","author":"Mark","year":"2011","journal-title":"Chaos"},{"key":"ref_19","first-page":"179","article-title":"Chaotic optimization algorithm based on Tent map","volume":"20","author":"Shan","year":"2005","journal-title":"Control Decis."},{"key":"ref_20","first-page":"129483","article-title":"A multistrategy optimization improved artificial bee colony algorithm","volume":"2014","author":"Liu","year":"2014","journal-title":"Sci. World J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.micpro.2016.05.009","article-title":"Hybrid swarm intelligent parallel algorithm research based on multi-core clusters","volume":"47","author":"Li","year":"2016","journal-title":"Microprocess. Microsyst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.cma.2018.04.037","article-title":"An adaptive multiscale approach for identifying multiple flaws based on XFEM and a discrete artificial fish swarm algorithm","volume":"339","author":"Du","year":"2018","journal-title":"Comput. Method. Appl. Methods"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1080\/03610918.2018.1484481","article-title":"Efficient algorithms for robust estimation in autoregressive regression models using Student\u2019s t distribution","volume":"49","author":"Nduka","year":"2020","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.ins.2019.04.022","article-title":"Enhanced Moth-flame optimizer with mutation strategy for global optimization","volume":"492","author":"Xu","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1007\/s00500-017-2885-z","article-title":"Differential evolution with Gaussian mutation and dynamic parameter adjustment","volume":"23","author":"Sun","year":"2019","journal-title":"Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1109\/TIA.2008.2006322","article-title":"Doubly Fed Induction Machines Diagnosis Based on Signature Analysis of Rotor Modulating Signals","volume":"44","author":"Stefani","year":"2008","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Xue, J., Zhang, L., Wang, Y., and Li, M. (2021). Misalignment Fault Diagnosis for Wind Turbines Based on Information Fusion. Entropy., 23.","DOI":"10.3390\/e23020243"},{"key":"ref_28","unstructured":"William, T., and Mark, F. (2003, January 1\u20134). Case Histories of Current Signature Analysis to Detect Faults in Induction Motor Drives. Proceedings of the IEEE International Electric Machines and Drives Conference (IEMDC\u201903), Madison, WI, USA."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Hong, Y., and Chen, X. (2017). The Application of Dual-Tree Complex Wavelet Transform (DTCWT) Energy Entropy in Misalignment Fault Diagnosis of Doubly-Fed Wind Turbine (DFWT). Entropy, 19.","DOI":"10.3390\/e19110587"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Xiao, Y., and Hua, Z. (2020). Misalignment Fault Prediction of Wind Turbines Based on Combined Forecasting Model. Algorithms, 13.","DOI":"10.3390\/a13030056"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.jsv.2016.12.041","article-title":"Compound faults detection in gearbox via meshing resonance and spectral kurtosis methods","volume":"392","author":"Wang","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yuan, Y., Shao, C., Cao, Z., Chen, W., Yin, A., Yue, H., and Xie, B. (2019). Urban Rail Transit Passenger Flow Forecasting Method Based on the Coupling of Artificial Fish Swarm and Improved Particle Swarm Optimization Algorithms. Sustainability, 11.","DOI":"10.3390\/su11247230"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"950","DOI":"10.4028\/www.scientific.net\/AMM.543-547.950","article-title":"The Fault Diagnosis of Wind Turbine Gearbox Based on QGA-LSSVM","volume":"3082","author":"Jiao","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1177\/0142331219869701","article-title":"Research on early fault warning system of coal mills based on the combination of thermodynamics and data mining","volume":"42","author":"Zhu","year":"2020","journal-title":"Trans. Inst. Meas. Control (Lond.)"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1080\/03610926.2018.1563166","article-title":"New approximations for standard normal distribution function","volume":"49","author":"Omar","year":"2020","journal-title":"Commun. Stat. Theor. Methods"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/6\/692\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:09:23Z","timestamp":1760162963000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/6\/692"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,31]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["e23060692"],"URL":"https:\/\/doi.org\/10.3390\/e23060692","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,31]]}}}