{"id":"https://openalex.org/W4412945439","doi":"https://doi.org/10.3390/sym17081222","title":"Variable Step-Size FxLMS Algorithm Based on Cooperative Coupling of Double Nonlinear Functions","display_name":"Variable Step-Size FxLMS Algorithm Based on Cooperative Coupling of Double Nonlinear Functions","publication_year":2025,"publication_date":"2025-08-02","ids":{"openalex":"https://openalex.org/W4412945439","doi":"https://doi.org/10.3390/sym17081222"},"language":"en","primary_location":{"id":"doi:10.3390/sym17081222","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17081222","pdf_url":"https://www.mdpi.com/2073-8994/17/8/1222/pdf?version=1754123988","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/8/1222/pdf?version=1754123988","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067364617","display_name":"Jialong Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I2800710378","display_name":"Naval University of Engineering","ror":"https://ror.org/056vyez31","country_code":"CN","type":"education","lineage":["https://openalex.org/I2800710378"]},{"id":"https://openalex.org/I4210129465","display_name":"Wuhan Ship Development & Design Institute","ror":"https://ror.org/02mcdae06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210129465"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jialong Wang","raw_affiliation_strings":["Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","institution_ids":["https://openalex.org/I2800710378"]},{"raw_affiliation_string":"Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China","institution_ids":["https://openalex.org/I4210129465"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060050730","display_name":"Jian Liao","orcid":"https://orcid.org/0000-0002-6525-4664"},"institutions":[{"id":"https://openalex.org/I2800710378","display_name":"Naval University of Engineering","ror":"https://ror.org/056vyez31","country_code":"CN","type":"education","lineage":["https://openalex.org/I2800710378"]},{"id":"https://openalex.org/I4210129465","display_name":"Wuhan Ship Development & Design Institute","ror":"https://ror.org/02mcdae06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210129465"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Liao","raw_affiliation_strings":["Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","institution_ids":["https://openalex.org/I2800710378"]},{"raw_affiliation_string":"Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China","institution_ids":["https://openalex.org/I4210129465"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100685258","display_name":"Lin He","orcid":"https://orcid.org/0000-0002-1676-254X"},"institutions":[{"id":"https://openalex.org/I2800710378","display_name":"Naval University of Engineering","ror":"https://ror.org/056vyez31","country_code":"CN","type":"education","lineage":["https://openalex.org/I2800710378"]},{"id":"https://openalex.org/I4210129465","display_name":"Wuhan Ship Development & Design Institute","ror":"https://ror.org/02mcdae06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210129465"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin He","raw_affiliation_strings":["Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","institution_ids":["https://openalex.org/I2800710378"]},{"raw_affiliation_string":"Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China","institution_ids":["https://openalex.org/I4210129465"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004532326","display_name":"Xiaopeng Tan","orcid":null},"institutions":[{"id":"https://openalex.org/I2800710378","display_name":"Naval University of Engineering","ror":"https://ror.org/056vyez31","country_code":"CN","type":"education","lineage":["https://openalex.org/I2800710378"]},{"id":"https://openalex.org/I4210129465","display_name":"Wuhan Ship Development & Design Institute","ror":"https://ror.org/02mcdae06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210129465"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaopeng Tan","raw_affiliation_strings":["Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","institution_ids":["https://openalex.org/I2800710378"]},{"raw_affiliation_string":"Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China","institution_ids":["https://openalex.org/I4210129465"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059807506","display_name":"Zongbin Chen","orcid":"https://orcid.org/0000-0003-4617-3807"},"institutions":[{"id":"https://openalex.org/I2800710378","display_name":"Naval University of Engineering","ror":"https://ror.org/056vyez31","country_code":"CN","type":"education","lineage":["https://openalex.org/I2800710378"]},{"id":"https://openalex.org/I4210129465","display_name":"Wuhan Ship Development & Design Institute","ror":"https://ror.org/02mcdae06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210129465"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zongbin Chen","raw_affiliation_strings":["Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, China","institution_ids":["https://openalex.org/I2800710378"]},{"raw_affiliation_string":"Nation Key Laboratory on Ship Vibration & Noise, Wuhan 430033, China","institution_ids":["https://openalex.org/I4210129465"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060050730"],"corresponding_institution_ids":["https://openalex.org/I2800710378","https://openalex.org/I4210129465"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.4628,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.88069282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"17","issue":"8","first_page":"1222","last_page":"1222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10860","display_name":"Speech and Audio Processing","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6276987195014954},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6033463478088379},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.6003146767616272},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5171305537223816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.501549243927002},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37640395760536194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3603270351886749},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19251921772956848},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.17565873265266418},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15540924668312073},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1470264494419098},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08985185623168945},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.08118465542793274}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6276987195014954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6033463478088379},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.6003146767616272},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5171305537223816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.501549243927002},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37640395760536194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3603270351886749},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19251921772956848},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.17565873265266418},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15540924668312073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1470264494419098},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08985185623168945},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.08118465542793274},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17081222","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17081222","pdf_url":"https://www.mdpi.com/2073-8994/17/8/1222/pdf?version=1754123988","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17081222","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17081222","pdf_url":"https://www.mdpi.com/2073-8994/17/8/1222/pdf?version=1754123988","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412945439.pdf","grobid_xml":"https://content.openalex.org/works/W4412945439.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W2010917058","https://openalex.org/W2012280426","https://openalex.org/W2066571294","https://openalex.org/W2080773601","https://openalex.org/W2089515469","https://openalex.org/W2115947173","https://openalex.org/W2116899572","https://openalex.org/W2160498832","https://openalex.org/W2178028293","https://openalex.org/W2330072965","https://openalex.org/W2366285415","https://openalex.org/W2510067816","https://openalex.org/W2948935853","https://openalex.org/W2997875915","https://openalex.org/W2999564272","https://openalex.org/W3013192954","https://openalex.org/W3025966395","https://openalex.org/W3027282195","https://openalex.org/W3124542158","https://openalex.org/W3128862690","https://openalex.org/W3217340562","https://openalex.org/W4211181686","https://openalex.org/W4319872907","https://openalex.org/W4386540308","https://openalex.org/W4394018481","https://openalex.org/W4399466323","https://openalex.org/W6702447301","https://openalex.org/W6804466809","https://openalex.org/W6807844337","https://openalex.org/W6991778154"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4409439182","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W1982160337","https://openalex.org/W1971380437","https://openalex.org/W2052122378"],"abstract_inverted_index":{"Based":[0],"on":[1],"the":[2,23,32,75,90,96],"principle":[3],"of":[4,38,47,80,147],"symmetry,":[5],"we":[6],"propose":[7],"a":[8,54,61,81,137],"variable":[9,109],"step-size":[10],"FxLMS":[11],"algorithm":[12,42,98,123],"with":[13],"double":[14],"nonlinear":[15,48],"functions":[16],"cooperative":[17],"coupling":[18],"(DNVSS-FxLMS),":[19],"aiming":[20],"to":[21,59],"optimize":[22],"contradiction":[24],"between":[25,63],"convergence":[26,65,128],"rate":[27],"and":[28,51,66,107,133,140],"steady-state":[29,68,115,130],"error":[30,116,131],"in":[31,127],"active":[33,145],"pressure":[34,150],"pulsation":[35,151],"control":[36,146],"system":[37,91,149],"hydraulic":[39,83,148],"systems.":[40],"The":[41,85,120],"innovatively":[43],"couples":[44],"two":[45],"types":[46],"mechanisms":[49],"(rational-fractional":[50],"exponential-function-based),":[52],"constructing":[53],"refined":[55],"error-step":[56],"mapping":[57],"relationship":[58],"achieve":[60],"balance":[62],"rapid":[64],"low":[67],"error.":[69],"Simulation":[70],"experiments":[71],"were":[72],"conducted":[73],"considering":[74],"complex":[76,153],"time-varying":[77],"operating":[78,154],"environment":[79],"simulation-based":[82],"system.":[84],"results":[86],"demonstrate":[87],"that,":[88],"when":[89],"undergoes":[92],"unstable":[93],"random":[94],"changes,":[95],"DNVSS-FxLMS":[97,122],"converges":[99],"at":[100],"least":[101],"twice":[102],"as":[103,105],"fast":[104],"traditional":[106],"existing":[108],"step":[110],"size":[111],"algorithms,":[112],"while":[113],"reducing":[114],"by":[117],"2\u20135":[118],"dB.":[119],"proposed":[121],"exhibits":[124],"significant":[125],"advantages":[126],"rate,":[129],"reduction,":[132],"tracking":[134],"capability,":[135],"providing":[136],"highly":[138],"efficient":[139],"robust":[141],"solution":[142],"for":[143],"real-time":[144],"under":[152],"conditions.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}