{"id":"https://openalex.org/W1989542623","doi":"https://doi.org/10.1109/tim.2011.2138370","title":"Parametric Identification of Parallel Hammerstein Systems","display_name":"Parametric Identification of Parallel Hammerstein Systems","publication_year":2011,"publication_date":"2011-04-26","ids":{"openalex":"https://openalex.org/W1989542623","doi":"https://doi.org/10.1109/tim.2011.2138370","mag":"1989542623"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2011.2138370","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2011.2138370","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","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/A5056957450","display_name":"Maarten Schoukens","orcid":"https://orcid.org/0000-0002-4904-1255"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]},{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["BE","NL"],"is_corresponding":false,"raw_author_name":"Maarten Schoukens","raw_affiliation_strings":["Department of Fundamental Electricity and Instrumentation (ELEC), Vrije Universiteit Brussel, Brussels, Belgium","Dept. of Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Fundamental Electricity and Instrumentation (ELEC), Vrije Universiteit Brussel, Brussels, Belgium","institution_ids":["https://openalex.org/I13469542"]},{"raw_affiliation_string":"Dept. of Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussels, Belgium","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034235885","display_name":"Rik Pintelon","orcid":"https://orcid.org/0000-0003-2389-2075"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]},{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["BE","NL"],"is_corresponding":false,"raw_author_name":"Rik Pintelon","raw_affiliation_strings":["Department of Fundamental Electricity and Instrumentation (ELEC), Vrije Universiteit Brussel, Brussels, Belgium","Dept. of Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Fundamental Electricity and Instrumentation (ELEC), Vrije Universiteit Brussel, Brussels, Belgium","institution_ids":["https://openalex.org/I13469542"]},{"raw_affiliation_string":"Dept. of Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussels, Belgium","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074429391","display_name":"Yves Rolain","orcid":"https://orcid.org/0000-0003-2738-7914"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]},{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["BE","NL"],"is_corresponding":false,"raw_author_name":"Yves Rolain","raw_affiliation_strings":["Department of Fundamental Electricity and Instrumentation (ELEC), Vrije Universiteit Brussel, Brussels, Belgium","Dept. of Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Fundamental Electricity and Instrumentation (ELEC), Vrije Universiteit Brussel, Brussels, Belgium","institution_ids":["https://openalex.org/I13469542"]},{"raw_affiliation_string":"Dept. of Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussels, Belgium","institution_ids":["https://openalex.org/I865915315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.0568,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.98347432,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"12","first_page":"3931","last_page":"3938"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9998000264167786,"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":0.9998000264167786,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T12810","display_name":"Real-time simulation and control systems","score":0.9934999942779541,"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/parametric-statistics","display_name":"Parametric statistics","score":0.6730350852012634},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.5485658049583435},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5395923852920532},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5267935395240784},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.5231512784957886},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.522860050201416},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5045419931411743},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4914745092391968},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47469133138656616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40593504905700684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38642263412475586},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37733542919158936},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36376363039016724},{"id":"https://openalex.org/keywords/data-modeling","display_name":"Data modeling","score":0.17498323321342468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10278430581092834},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09399846196174622},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0887109637260437}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6730350852012634},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.5485658049583435},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5395923852920532},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5267935395240784},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.5231512784957886},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.522860050201416},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5045419931411743},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4914745092391968},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47469133138656616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40593504905700684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38642263412475586},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37733542919158936},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36376363039016724},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.17498323321342468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10278430581092834},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09399846196174622},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0887109637260437},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tim.2011.2138370","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2011.2138370","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","raw_type":"journal-article"},{"id":"pmh:oai:vubissmart:VUBISSMART:2000:71224","is_oa":false,"landing_page_url":"https://biblio.vub.ac.be/vubir/parametric-identification-of-parallel-hammerstein-systems(bcea2987-038a-4d35-b64d-7f92b04f56ea).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402573","display_name":"VUBIR (Vrije Universiteit Brussel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13469542","host_organization_name":"Vrije Universiteit Brussel","host_organization_lineage":["https://openalex.org/I13469542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W616910851","https://openalex.org/W1494908267","https://openalex.org/W1515361063","https://openalex.org/W1521591241","https://openalex.org/W1598493736","https://openalex.org/W1968757006","https://openalex.org/W1972945233","https://openalex.org/W1983569967","https://openalex.org/W1988086333","https://openalex.org/W2027694259","https://openalex.org/W2067729466","https://openalex.org/W2086248552","https://openalex.org/W2094655564","https://openalex.org/W2106578181","https://openalex.org/W2125351848","https://openalex.org/W2134572560","https://openalex.org/W2137720674","https://openalex.org/W2271358270","https://openalex.org/W2484009170","https://openalex.org/W2547960410","https://openalex.org/W2984447667","https://openalex.org/W2989346022","https://openalex.org/W2994876357","https://openalex.org/W4249762338"],"related_works":["https://openalex.org/W2396122647","https://openalex.org/W2138831083","https://openalex.org/W2770381769","https://openalex.org/W3184983074","https://openalex.org/W2021940933","https://openalex.org/W1909999440","https://openalex.org/W1576040274","https://openalex.org/W2094241856","https://openalex.org/W2101377286","https://openalex.org/W50782446"],"abstract_inverted_index":{"This":[0,115],"paper":[1],"proposes":[2],"a":[3,21,35,46,83,99,137,140],"parametric":[4,22],"identification":[5,43,107],"method":[6,44,133],"for":[7,68,122,128],"parallel":[8,86],"Hammerstein":[9],"systems.":[10],"The":[11,42,132],"linear":[12,36,64,100,124],"dynamic":[13,125],"parts":[14],"of":[15,38,61,85],"the":[16,29,54,57,62,74,77,90,93,113,123,129],"system":[17],"are":[18,32,80,96],"modeled":[19],"by":[20,34],"rational":[23],"function":[24,60],"in":[25],"thez-":[26],"ors-domain,":[27],"while":[28],"static":[30,94,130],"nonlinearities":[31,95],"represented":[33],"combination":[37],"nonlinear":[39],"basis":[40],"functions.":[41],"uses":[45],"three-step":[47],"procedure":[48],"to":[49,111],"obtain":[50],"initial":[51],"estimates.":[52,114],"In":[53,73,89],"first":[55],"step,":[56,76,92],"frequency":[58],"response":[59],"best":[63],"approximation":[65],"is":[66,109,134],"estimated":[67,97],"different":[69],"input":[70],"excitation":[71],"levels.":[72],"second":[75],"power-dependent":[78],"dynamics":[79],"decomposed":[81],"over":[82],"number":[84],"orthogonal":[87],"branches.":[88],"last":[91],"using":[98],"least":[101],"squares":[102],"estimation.":[103],"Furthermore,":[104],"an":[105],"iterative":[106,116],"scheme":[108,117],"introduced":[110],"refine":[112],"alternately":[118],"estimates":[119],"updated":[120],"parameters":[121],"systems":[126],"and":[127,139],"nonlinearities.":[131],"illustrated":[135],"on":[136],"simulation":[138],"validation":[141],"measurement":[142],"example.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}