{"id":"https://openalex.org/W4416264534","doi":"https://doi.org/10.1631/fitee.2400730","title":"Swarm intelligent computing of electric eel foraging heuristics for fractional Hammerstein autoregressive exogenous noise model identification","display_name":"Swarm intelligent computing of electric eel foraging heuristics for fractional Hammerstein autoregressive exogenous noise model identification","publication_year":2025,"publication_date":"2025-10-01","ids":{"openalex":"https://openalex.org/W4416264534","doi":"https://doi.org/10.1631/fitee.2400730"},"language":"en","primary_location":{"id":"doi:10.1631/fitee.2400730","is_oa":false,"landing_page_url":"https://doi.org/10.1631/fitee.2400730","pdf_url":null,"source":{"id":"https://openalex.org/S4210189857","display_name":"Frontiers of Information Technology & Electronic Engineering","issn_l":"2095-9184","issn":["2095-9184","2095-9230"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers of Information Technology &amp; Electronic Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5041013020","display_name":"Faisal Altaf","orcid":"https://orcid.org/0000-0003-0325-2409"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Faisal Altaf","raw_affiliation_strings":["Graduate School of Engineering Science and Technology, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":"https://orcid.org/0009-0007-7621-5875","affiliations":[{"raw_affiliation_string":"Graduate School of Engineering Science and Technology, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067886687","display_name":"Ching-Lung Chang","orcid":"https://orcid.org/0000-0002-0094-4250"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Ching-Lung Chang","raw_affiliation_strings":["Department of Computer Science and Information Engineering, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078449856","display_name":"Naveed Ishtiaq Chaudhary","orcid":"https://orcid.org/0000-0002-9568-3216"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Naveed Ishtiaq Chaudhary","raw_affiliation_strings":["Future Technology Research Center, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":"https://orcid.org/0000-0002-9568-3216","affiliations":[{"raw_affiliation_string":"Future Technology Research Center, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086839255","display_name":"Taimoor Ali Khan","orcid":"https://orcid.org/0009-0004-0975-2564"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Taimoor Ali Khan","raw_affiliation_strings":["International Graduate School of Artificial Intelligence, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Graduate School of Artificial Intelligence, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038314889","display_name":"Zeshan Aslam Khan","orcid":"https://orcid.org/0000-0003-3902-5814"},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]},{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["PK","TW"],"is_corresponding":false,"raw_author_name":"Zeshan Aslam Khan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, International Islamic University, Islamabad, 44000, Pakistan","International Graduate School of Artificial Intelligence, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, International Islamic University, Islamabad, 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]},{"raw_affiliation_string":"International Graduate School of Artificial Intelligence, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065890412","display_name":"Chi\u2010Min Shu","orcid":"https://orcid.org/0000-0001-9455-6162"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chi-Min Shu","raw_affiliation_strings":["Department of Safety, Health and Environmental Engineering, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Safety, Health and Environmental Engineering, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100740838","display_name":"Muhammad Asif Zahoor Raja","orcid":"https://orcid.org/0000-0001-9953-822X"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Muhammad Asif Zahoor Raja","raw_affiliation_strings":["Future Technology Research Center, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Future Technology Research Center, Yunlin University of Science and Technology, Yunlin, 64002, Taiwan, China","institution_ids":["https://openalex.org/I75357094"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5041013020"],"corresponding_institution_ids":["https://openalex.org/I75357094"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.40501028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"10","first_page":"1954","last_page":"1968"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.2687999904155731,"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/T11081","display_name":"Advanced Control Systems Design","score":0.2687999904155731,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.12729999423027039,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.11680000275373459,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.574999988079071},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5692999958992004},{"id":"https://openalex.org/keywords/swarm-behaviour","display_name":"Swarm behaviour","score":0.5516999959945679},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.5303000211715698},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.49959999322891235},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.48840001225471497},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.43130001425743103},{"id":"https://openalex.org/keywords/metaheuristic","display_name":"Metaheuristic","score":0.4228000044822693},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.37540000677108765}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5849999785423279},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5692999958992004},{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.5516999959945679},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.5303000211715698},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.49959999322891235},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.48840001225471497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45010000467300415},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.43130001425743103},{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40549999475479126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39079999923706055},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.37540000677108765},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C79610928","wikidata":"https://www.wikidata.org/wiki/Q1656743","display_name":"Parameter identification problem","level":3,"score":0.35120001435279846},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.34360000491142273},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C165287380","wikidata":"https://www.wikidata.org/wiki/Q2916569","display_name":"Foraging","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C119487961","wikidata":"https://www.wikidata.org/wiki/Q863960","display_name":"Swarm intelligence","level":3,"score":0.28040000796318054},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2759999930858612},{"id":"https://openalex.org/C42536954","wikidata":"https://www.wikidata.org/wiki/Q7049462","display_name":"Nonlinear autoregressive exogenous model","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1631/fitee.2400730","is_oa":false,"landing_page_url":"https://doi.org/10.1631/fitee.2400730","pdf_url":null,"source":{"id":"https://openalex.org/S4210189857","display_name":"Frontiers of Information Technology & Electronic Engineering","issn_l":"2095-9184","issn":["2095-9184","2095-9230"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers of Information Technology &amp; Electronic Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W2045293688","https://openalex.org/W2290883490","https://openalex.org/W2566671743","https://openalex.org/W2606385482","https://openalex.org/W2911012399","https://openalex.org/W2919979744","https://openalex.org/W2981953956","https://openalex.org/W3039611570","https://openalex.org/W3046282702","https://openalex.org/W3163903840","https://openalex.org/W3212797097","https://openalex.org/W3216979551","https://openalex.org/W4224221083","https://openalex.org/W4295016000","https://openalex.org/W4295127301","https://openalex.org/W4297231402","https://openalex.org/W4307303302","https://openalex.org/W4309550476","https://openalex.org/W4309819127","https://openalex.org/W4311044977","https://openalex.org/W4313216050","https://openalex.org/W4313399434","https://openalex.org/W4313476913","https://openalex.org/W4313681627","https://openalex.org/W4315498059","https://openalex.org/W4318218525","https://openalex.org/W4323041519","https://openalex.org/W4323661220","https://openalex.org/W4367315995","https://openalex.org/W4367607270","https://openalex.org/W4379931141","https://openalex.org/W4382721878","https://openalex.org/W4386507838","https://openalex.org/W4386708829","https://openalex.org/W4387177654","https://openalex.org/W4387873343","https://openalex.org/W4388247898","https://openalex.org/W4388571731","https://openalex.org/W4389230699","https://openalex.org/W4389410010","https://openalex.org/W4389744173","https://openalex.org/W4390064131","https://openalex.org/W4390409984","https://openalex.org/W4391014866","https://openalex.org/W4391809912","https://openalex.org/W4392930616","https://openalex.org/W4392935067","https://openalex.org/W4392976123","https://openalex.org/W4393355993","https://openalex.org/W4393862877","https://openalex.org/W4398139501","https://openalex.org/W4399224784","https://openalex.org/W4399701668","https://openalex.org/W4400146594","https://openalex.org/W4402343062","https://openalex.org/W4403581999"],"related_works":[],"abstract_inverted_index":{"Fractional":[0],"calculus":[1],"is":[2,59,108,133,140,193],"considered":[3],"a":[4,40,77],"useful":[5],"tool":[6],"for":[7,86,97,187,210],"gaining":[8],"deeper":[9],"insights":[10],"into":[11],"systems":[12,22],"with":[13,158,207],"memory":[14],"effects":[15],"or":[16],"history.":[17],"Fractional-order":[18],"modeling":[19],"of":[20,29,45,76,89,119,138,144,184,190,199],"nonlinear":[21],"may":[23],"increase":[24],"the":[25,30,46,63,67,74,90,112,117,127,136,153,164,168,177,185,188],"stiffness":[26],"and":[27,99,135,150,176,202],"complexity":[28],"system,":[31],"but":[32],"also":[33,109,194],"provides":[34],"better":[35],"insights.":[36],"This":[37,71],"study":[38,72],"introduces":[39],"swarm":[41,78],"intelligence-based":[42,79],"parameter":[43,87,148],"estimation":[44,88,189],"fractional":[47],"Hammerstein":[48],"autoregressive":[49],"exogenous":[50],"noise":[51,95,212],"(fractional-HARX)":[52],"model.":[53,70],"The":[54,104,130,181],"Gr\u00fcnwald\u2013Letnikov":[55],"finite":[56],"difference":[57],"formula":[58],"used":[60],"to":[61,115,123],"develop":[62],"fractional-HARX":[64,91,191],"model":[65,92,114],"from":[66,152],"standard":[68,208],"HARX":[69],"presents":[73],"design":[75],"electric":[80],"eel":[81],"foraging":[82],"optimization":[83,160,166,171],"algorithm":[84],"(EEFOA)":[85],"under":[93],"multiple":[94,211],"scenarios":[96],"second-":[98],"third-order":[100],"polynomial":[101],"type":[102],"nonlinearity.":[103],"key-term":[105],"separation":[106],"principle":[107],"incorporated":[110],"in":[111,126,142,156],"system":[113],"reduce":[116],"occurrence":[118],"redundant":[120],"parameters":[121],"due":[122],"cross-product":[124],"terms":[125,143],"information":[128],"vector.":[129],"designed":[131],"methodology":[132],"examined,":[134],"superiority":[137],"EEFOA":[139,186],"endorsed":[141],"convergence,":[145],"robustness,":[146],"stiff":[147],"estimation,":[149],"deviation":[151,209],"mean":[154],"point":[155],"comparison":[157],"state-of-the-art":[159],"heuristics":[161],"such":[162],"as":[163],"whale":[165],"algorithm,":[167,172],"African":[169],"vulture":[170],"Harris":[173],"hawk\u2019s":[174],"optimizer,":[175],"reptile":[178],"search":[179],"algorithm.":[180],"statistical":[182,197],"significance":[183],"models":[192],"established":[195],"using":[196],"indices":[198],"best,":[200],"mean,":[201],"worst":[203],"fitness":[204],"values":[205],"along":[206],"scenarios.":[213]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-11-17T00:00:00"}
