{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T13:19:18Z","timestamp":1771679958965,"version":"3.50.1"},"reference-count":29,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,10,23]],"date-time":"2021-10-23T00:00:00Z","timestamp":1634947200000},"content-version":"vor","delay-in-days":295,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51805264"],"award-info":[{"award-number":["51805264"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this study, a fuzzy wavelet neural network with the improved Levenberg\u2013Marquardt algorithm (FWNN\u2010LM) is proposed to conquer nonlinearity and uncertain disturbance problems in the AC servo system. First of all, use the particle swarm optimization algorithm based on Levenberg\u2013Marquardt (LM) to optimize parameters in the FWNN controller. Second, the potentiality of fuzzy rules (PFR) method is developed to optimize the structure of the FWNN by error reduction ratio (ERR). Furthermore, stability of FWNN\u2010LM is proved by the Lyapunov method. Finally, simulation and prototype test results show that this method can improve the accuracy and robustness of the system in presence of load disturbances and parameter perturbations.<\/jats:p>","DOI":"10.1155\/2021\/8086088","type":"journal-article","created":{"date-parts":[[2021,10,23]],"date-time":"2021-10-23T18:35:08Z","timestamp":1635014108000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fuzzy Wavelet Neural Network with the Improved Levenberg\u2013Marquardt Algorithm for the AC Servo System"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9806-1367","authenticated-orcid":false,"given":"Run-Min","family":"Hou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1795-0857","authenticated-orcid":false,"given":"Di-Fen","family":"Shi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4372-9021","authenticated-orcid":false,"given":"Qiang","family":"Gao","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4182-1609","authenticated-orcid":false,"given":"Yuan-Long","family":"Hou","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,10,23]]},"reference":[{"key":"e_1_2_11_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2015.2495300"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109595"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2009.2024655"},{"key":"e_1_2_11_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2009.2020709"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2013.01.004"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2020.104675"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.3233\/ifs-2012-0589"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2012.11.027"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.05.065"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsmcb.2009.2039642"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.12.027"},{"key":"e_1_2_11_12_2","unstructured":"WangJ.andXiaoJ. Constructing fuzzy wavelet network modeling Proceedings of the 2005 International Conference on Intelligent Computing 2005 Hefei China 169\u2013172."},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.11.034"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2013.05.020"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.11.019"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2013.01.004"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2014.07.067"},{"key":"e_1_2_11_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.12.011"},{"key":"e_1_2_11_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2011.2175932"},{"key":"e_1_2_11_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/ijcnn.2013.6706997"},{"key":"e_1_2_11_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2017.04.010"},{"key":"e_1_2_11_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2014.06.007"},{"key":"e_1_2_11_23_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218126618500986"},{"key":"e_1_2_11_24_2","doi-asserted-by":"publisher","DOI":"10.1109\/tnnls.2014.2361267"},{"key":"e_1_2_11_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2014.12.003"},{"key":"e_1_2_11_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-019-2714-7"},{"key":"e_1_2_11_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2018.04.085"},{"key":"e_1_2_11_28_2","article-title":"Nonlinear system modeling using a self-organizing recurrent radial basis function neural network","author":"Han H. G.","year":"2017","journal-title":"Applied Soft Computing"},{"key":"e_1_2_11_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.10.030"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/8086088.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/8086088.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/8086088","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:57:36Z","timestamp":1723244256000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/8086088"}},"subtitle":[],"editor":[{"given":"Long","family":"Wang","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/8086088"],"URL":"https:\/\/doi.org\/10.1155\/2021\/8086088","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-08-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-10-11","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-10-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8086088"}}