{"id":"https://openalex.org/W3163894359","doi":"https://doi.org/10.1109/tii.2021.3081418","title":"Online Koopman Operator Learning to Identify Cross-Coupling Effect of Piezoelectric Tube Scanners in Atomic Force Microscopes","display_name":"Online Koopman Operator Learning to Identify Cross-Coupling Effect of Piezoelectric Tube Scanners in Atomic Force Microscopes","publication_year":2021,"publication_date":"2021-05-18","ids":{"openalex":"https://openalex.org/W3163894359","doi":"https://doi.org/10.1109/tii.2021.3081418","mag":"3163894359"},"language":"en","primary_location":{"id":"doi:10.1109/tii.2021.3081418","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tii.2021.3081418","pdf_url":null,"source":{"id":"https://openalex.org/S184777250","display_name":"IEEE Transactions on Industrial Informatics","issn_l":"1551-3203","issn":["1551-3203","1941-0050"],"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 Industrial Informatics","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/A5087621393","display_name":"Xiang Huang","orcid":"https://orcid.org/0000-0001-6028-3864"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Huang","raw_affiliation_strings":["School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, and State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0001-6028-3864","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, and State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075613088","display_name":"Wei Zhou","orcid":"https://orcid.org/0000-0001-5773-8012"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhou","raw_affiliation_strings":["School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, and State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0001-5773-8012","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, and State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100685834","display_name":"Xiuting Li","orcid":"https://orcid.org/0000-0002-3876-583X"},"institutions":[{"id":"https://openalex.org/I204823248","display_name":"Huazhong Agricultural University","ror":"https://ror.org/023b72294","country_code":"CN","type":"education","lineage":["https://openalex.org/I204823248"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuting Li","raw_affiliation_strings":["College of Science, Huazhong Agricultural University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-3876-583X","affiliations":[{"raw_affiliation_string":"College of Science, Huazhong Agricultural University, Wuhan, China","institution_ids":["https://openalex.org/I204823248"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103205239","display_name":"Limin Zhu","orcid":"https://orcid.org/0000-0003-3194-6731"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LiMin Zhu","raw_affiliation_strings":["Shanghai Key Lab of Networked Manufacturing and Enterprise Information, Shanghai, China","State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-3194-6731","affiliations":[{"raw_affiliation_string":"Shanghai Key Lab of Networked Manufacturing and Enterprise Information, Shanghai, China","institution_ids":[]},{"raw_affiliation_string":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hai-Tao Zhang","orcid":"https://orcid.org/0000-0002-8819-8829"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hai-Tao Zhang","raw_affiliation_strings":["School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, and State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-8819-8829","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, and State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6267,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.83487601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"18","issue":"2","first_page":"1111","last_page":"1120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9937000274658203,"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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.9929999709129333,"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/coupling","display_name":"Coupling (piping)","score":0.6704970598220825},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6561951637268066},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6549742221832275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5682972073554993},{"id":"https://openalex.org/keywords/piezoelectricity","display_name":"Piezoelectricity","score":0.49327248334884644},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37818634510040283},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.34562623500823975},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.2774066925048828},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22911182045936584},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.22782230377197266},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.22348874807357788}],"concepts":[{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.6704970598220825},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6561951637268066},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6549742221832275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5682972073554993},{"id":"https://openalex.org/C100082104","wikidata":"https://www.wikidata.org/wiki/Q183759","display_name":"Piezoelectricity","level":2,"score":0.49327248334884644},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37818634510040283},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.34562623500823975},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.2774066925048828},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22911182045936584},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.22782230377197266},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.22348874807357788},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tii.2021.3081418","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tii.2021.3081418","pdf_url":null,"source":{"id":"https://openalex.org/S184777250","display_name":"IEEE Transactions on Industrial Informatics","issn_l":"1551-3203","issn":["1551-3203","1941-0050"],"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 Industrial Informatics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3114873950","display_name":null,"funder_award_id":"61903148","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3362626677","display_name":null,"funder_award_id":"2019KFYXMBZ032","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4534745162","display_name":null,"funder_award_id":"U2013211","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4721231785","display_name":null,"funder_award_id":"51729501","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6213055193","display_name":null,"funder_award_id":"61803168","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6816196766","display_name":null,"funder_award_id":"U1713203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G960411949","display_name":null,"funder_award_id":"2019CFA005","funder_id":"https://openalex.org/F4320322186","funder_display_name":"Natural Science Foundation of Hubei Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322186","display_name":"Natural Science Foundation of Hubei Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1537372611","https://openalex.org/W1549386224","https://openalex.org/W1591018827","https://openalex.org/W1668383791","https://openalex.org/W2014356541","https://openalex.org/W2067035505","https://openalex.org/W2075540265","https://openalex.org/W2078394884","https://openalex.org/W2078898317","https://openalex.org/W2083759001","https://openalex.org/W2116347266","https://openalex.org/W2131637550","https://openalex.org/W2148009876","https://openalex.org/W2561027863","https://openalex.org/W2606103509","https://openalex.org/W2754813553","https://openalex.org/W2775511193","https://openalex.org/W2789557667","https://openalex.org/W2889208868","https://openalex.org/W2891089306","https://openalex.org/W2892862852","https://openalex.org/W2910679949","https://openalex.org/W2941517668","https://openalex.org/W2953699434","https://openalex.org/W2963006871","https://openalex.org/W2964119648","https://openalex.org/W2973514646","https://openalex.org/W2979087491","https://openalex.org/W2979973533","https://openalex.org/W3009956540","https://openalex.org/W3013153792","https://openalex.org/W3032458511","https://openalex.org/W3099674394","https://openalex.org/W3099803807","https://openalex.org/W3100692477","https://openalex.org/W3102091866","https://openalex.org/W3139852389","https://openalex.org/W6637215321","https://openalex.org/W6774602429"],"related_works":["https://openalex.org/W3002588386","https://openalex.org/W2386767533","https://openalex.org/W2801599544","https://openalex.org/W2185545173","https://openalex.org/W2140208051","https://openalex.org/W2360154135","https://openalex.org/W2136401474","https://openalex.org/W2917748363","https://openalex.org/W2922850166","https://openalex.org/W1720013624"],"abstract_inverted_index":{"As":[0,68],"one":[1],"of":[2,7,13,27,65,99,120,127,141,157,159,170,195],"the":[3,10,24,61,66,75,82,95,117,121,128,134,139,166,171,181,184],"most":[4],"significant":[5],"applications":[6,191],"nanopositioning":[8],"technology,":[9],"tremendous":[11],"development":[12],"atomic":[14],"force":[15],"microscopes":[16],"(AFMs)":[17],"has":[18],"been":[19],"witnessed":[20],"these":[21],"years.":[22],"Essentially,":[23],"scanning":[25],"motions":[26],"AFMs":[28],"are":[29,150],"generally":[30],"driven":[31],"by":[32],"piezoelectric":[33],"tube":[34],"scanners":[35],"(PTSs),":[36],"whose":[37],"cross-coupling":[38,63,97],"effect":[39],"hinders":[40],"their":[41],"high":[42],"speed":[43],"and":[44,168],"high-precision":[45],"positioning.":[46],"Therefore,":[47],"it":[48],"becomes":[49],"an":[50,69,102,106,145,160],"urgent":[51],"yet":[52],"challenging":[53],"mission":[54],"to":[55,93,152,179,189],"establish":[56],"a":[57],"niche":[58],"model":[59,130],"for":[60,116],"nonlinear":[62,96],"dynamics":[64,98,193],"PTS.":[67],"emergent":[70],"pure":[71],"data-driven":[72],"learning":[73,187],"approach,":[74],"Koopman":[76,122,185],"operator":[77,123,186],"sheds":[78],"some":[79],"light":[80],"on":[81],"PTS":[83],"modeling":[84,173,194],"methodology,":[85],"which":[86,164],"is":[87,114,177],"thus":[88],"adopted":[89],"in":[90,101,132,144,192],"this":[91],"article":[92,176],"approximate":[94,153],"PTSs":[100,158],"infinite-dimensional":[103],"space.":[104],"Moreover,":[105],"online":[107],"high-order":[108],"extended":[109],"dynamic":[110],"mode":[111],"decomposition":[112],"algorithm":[113],"proposed":[115,172],"finite-dimensional":[118],"approximation":[119],"online.":[124],"The":[125],"merit":[126],"present":[129],"lies":[131],"updating":[133],"identified":[135],"cross":[136,155],"coupling":[137,156],"upon":[138],"arrival":[140],"new":[142],"data":[143],"incremental":[146],"way.":[147],"Finally,":[148],"experiments":[149],"conducted":[151],"theX\u2013Yaxes":[154],"NTMDT":[161],"Prima":[162],"AFM,":[163],"verifies":[165],"effectiveness":[167],"superiority":[169],"algorithm.":[174],"This":[175],"expected":[178],"pave":[180],"way":[182],"from":[183],"theory":[188],"real":[190],"abundant":[196],"nanoscale":[197],"measurement":[198],"systems.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}