{"id":"https://openalex.org/W2579665834","doi":"https://doi.org/10.1109/tnnls.2016.2641475","title":"A Regularized SNPOM for Stable Parameter Estimation of RBF-AR(X) Model","display_name":"A Regularized SNPOM for Stable Parameter Estimation of RBF-AR(X) Model","publication_year":2017,"publication_date":"2017-01-20","ids":{"openalex":"https://openalex.org/W2579665834","doi":"https://doi.org/10.1109/tnnls.2016.2641475","mag":"2579665834","pmid":"https://pubmed.ncbi.nlm.nih.gov/28113350"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2016.2641475","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2016.2641475","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067160162","display_name":"Xiaoyong Zeng","orcid":null},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoyong Zeng","raw_affiliation_strings":["Collaborative Innovation Center of Resource-Conserving and Environment-Friendly Society and Ecological Civilization, Changsha, China","School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, China","School of Information Science and Engineering, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center of Resource-Conserving and Environment-Friendly Society and Ecological Civilization, Changsha, China","institution_ids":[]},{"raw_affiliation_string":"School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]},{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101463302","display_name":"Hui Peng","orcid":"https://orcid.org/0000-0002-9794-9225"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Peng","raw_affiliation_strings":["Collaborative Innovation Center of Resource-Conserving and Environment-Friendly Society and Ecological Civilization, Changsha, China","School of Information Science and Engineering, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center of Resource-Conserving and Environment-Friendly Society and Ecological Civilization, Changsha, China","institution_ids":[]},{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003477501","display_name":"Feng Zhou","orcid":"https://orcid.org/0000-0002-5513-743X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Zhou","raw_affiliation_strings":["Collaborative Innovation Center of Resource-Conserving and Environment-Friendly Society and Ecological Civilization, Changsha, China","School of Information Science and Engineering, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center of Resource-Conserving and Environment-Friendly Society and Ecological Civilization, Changsha, China","institution_ids":[]},{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067160162"],"corresponding_institution_ids":["https://openalex.org/I139660479","https://openalex.org/I56934997"],"apc_list":null,"apc_paid":null,"fwci":2.8508,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.90704152,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"29","issue":"4","first_page":"779","last_page":"791"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.658740222454071},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.6359061002731323},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6316184997558594},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.5947831869125366},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.525864839553833},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5257970690727234},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.5236846208572388},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4800209105014801},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.4700668752193451},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4332963824272156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43080925941467285},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4296455383300781},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4103177785873413},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3571551442146301},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2531589865684509},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11664199829101562}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.658740222454071},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.6359061002731323},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6316184997558594},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.5947831869125366},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.525864839553833},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5257970690727234},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.5236846208572388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4800209105014801},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.4700668752193451},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4332963824272156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43080925941467285},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4296455383300781},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4103177785873413},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3571551442146301},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2531589865684509},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11664199829101562},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2016.2641475","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2016.2641475","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:28113350","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28113350","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2557440349","display_name":null,"funder_award_id":"71271215","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4202076506","display_name":null,"funder_award_id":"71221061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5999908261","display_name":null,"funder_award_id":"61540037","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7456065007","display_name":null,"funder_award_id":"61403045","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7975564520","display_name":null,"funder_award_id":"51507015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W843782545","https://openalex.org/W1199505928","https://openalex.org/W1862263964","https://openalex.org/W1972948535","https://openalex.org/W1980770037","https://openalex.org/W1999933124","https://openalex.org/W2005256561","https://openalex.org/W2018617609","https://openalex.org/W2021607192","https://openalex.org/W2026131661","https://openalex.org/W2028725248","https://openalex.org/W2029955511","https://openalex.org/W2031852278","https://openalex.org/W2033532682","https://openalex.org/W2037624308","https://openalex.org/W2045943086","https://openalex.org/W2046138726","https://openalex.org/W2056201402","https://openalex.org/W2058979137","https://openalex.org/W2066043610","https://openalex.org/W2074221952","https://openalex.org/W2086901931","https://openalex.org/W2092766760","https://openalex.org/W2097531754","https://openalex.org/W2101791369","https://openalex.org/W2118237987","https://openalex.org/W2125181236","https://openalex.org/W2127510298","https://openalex.org/W2132157489","https://openalex.org/W2152689354","https://openalex.org/W2161083632","https://openalex.org/W2162538606","https://openalex.org/W2163204284","https://openalex.org/W2169457105","https://openalex.org/W2321140187","https://openalex.org/W4251846825","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2026673180","https://openalex.org/W1959514624","https://openalex.org/W200101083","https://openalex.org/W2939592218","https://openalex.org/W2359835307","https://openalex.org/W327962130","https://openalex.org/W4380487384","https://openalex.org/W1997338499","https://openalex.org/W4378552425","https://openalex.org/W2589353378"],"abstract_inverted_index":{"Recently,":[0],"the":[1,16,43,46,51,72,81,90,116,120,127,134,142,147,165],"radial":[2],"basis":[3],"function":[4],"(RBF)":[5],"network-style":[6],"coefficients":[7],"AutoRegressive":[8],"(with":[9],"exogenous":[10],"inputs)":[11],"[RBF-AR(X)]":[12],"model":[13,95],"identified":[14],"by":[15,61],"structured":[17],"nonlinear":[18,33,103,111,117],"parameter":[19,74],"optimization":[20,52,112],"method":[21,124],"(SNPOM)":[22],"has":[23],"attracted":[24],"considerable":[25],"interest":[26],"because":[27],"of":[28,83,92],"its":[29],"significant":[30],"performance":[31],"in":[32,50,146],"system":[34],"modeling.":[35],"However,":[36],"this":[37,65],"promising":[38],"technique":[39],"may":[40,55,152],"occasionally":[41],"confront":[42],"problem":[44,145],"that":[45,133],"parameters":[47,82,91,99,104,118,148],"are":[48],"divergent":[49],"process,":[53,150],"which":[54],"be":[56],"a":[57,67,97,102,109],"potential":[58,143],"issue":[59],"ignored":[60],"most":[62],"researchers.":[63],"In":[64],"paper,":[66],"regularized":[68,121],"SNPOM,":[69],"together":[70],"with":[71,141],"regularization":[73],"detection":[75],"technique,":[76],"is":[77,137],"presented":[78],"to":[79,139],"estimate":[80],"RBF-AR(X)":[84,94],"models.":[85],"This":[86],"approach":[87,136],"first":[88],"separates":[89],"an":[93],"into":[96],"linear":[98,128],"set":[100],"and":[101,106,119,151,161],"set,":[105],"then":[107],"combines":[108],"gradient-based":[110],"algorithm":[113],"for":[114,125],"estimating":[115,126],"least":[122],"squares":[123],"parameters.":[129],"Several":[130],"examples":[131],"demonstrate":[132],"proposed":[135],"effective":[138],"cope":[140],"unstable":[144],"search":[149],"also":[153],"yield":[154],"better":[155,162],"or":[156],"similar":[157],"multistep":[158],"forecasting":[159],"accuracy":[160],"robustness":[163],"than":[164],"previous":[166],"method.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}
