{"id":"https://openalex.org/W3115253541","doi":"https://doi.org/10.1109/tie.2020.3044785","title":"Exact Modeling and Multiobjective Optimization of Vernier Machines","display_name":"Exact Modeling and Multiobjective Optimization of Vernier Machines","publication_year":2020,"publication_date":"2020-12-21","ids":{"openalex":"https://openalex.org/W3115253541","doi":"https://doi.org/10.1109/tie.2020.3044785","mag":"3115253541"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2020.3044785","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2020.3044785","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Electronics","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/A5085043204","display_name":"Hang Zhao","orcid":"https://orcid.org/0000-0003-2451-3719"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210105229","display_name":"City University of Hong Kong, Shenzhen Research Institute","ror":"https://ror.org/00xc0ma20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105229"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Hang Zhao","raw_affiliation_strings":["School of Energy and Environment, City University of Hong Kong, Hong Kong","Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0003-2451-3719","affiliations":[{"raw_affiliation_string":"School of Energy and Environment, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100605292","display_name":"Chunhua Liu","orcid":"https://orcid.org/0000-0002-3105-5448"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210105229","display_name":"City University of Hong Kong, Shenzhen Research Institute","ror":"https://ror.org/00xc0ma20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105229"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Chunhua Liu","raw_affiliation_strings":["School of Energy and Environment, City University of Hong Kong, Hong Kong","Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-3105-5448","affiliations":[{"raw_affiliation_string":"School of Energy and Environment, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050892996","display_name":"Zaixin Song","orcid":"https://orcid.org/0000-0002-0599-3350"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210105229","display_name":"City University of Hong Kong, Shenzhen Research Institute","ror":"https://ror.org/00xc0ma20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105229"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Zaixin Song","raw_affiliation_strings":["School of Energy and Environment, City University of Hong Kong, Hong Kong","Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-0599-3350","affiliations":[{"raw_affiliation_string":"School of Energy and Environment, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057858873","display_name":"Wusen Wang","orcid":"https://orcid.org/0000-0001-7892-0067"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210105229","display_name":"City University of Hong Kong, Shenzhen Research Institute","ror":"https://ror.org/00xc0ma20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105229"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Wusen Wang","raw_affiliation_strings":["School of Energy and Environment, City University of Hong Kong, Hong Kong","Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0001-7892-0067","affiliations":[{"raw_affiliation_string":"School of Energy and Environment, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085043204"],"corresponding_institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"],"apc_list":null,"apc_paid":null,"fwci":1.7683,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.85425065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"68","issue":"12","first_page":"11740","last_page":"11751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10278","display_name":"Electric Motor Design and Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10278","display_name":"Electric Motor Design and Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11222","display_name":"Magnetic Properties and Applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12898","display_name":"Induction Heating and Inverter Technology","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/vernier-scale","display_name":"Vernier scale","score":0.9066643714904785},{"id":"https://openalex.org/keywords/torque-ripple","display_name":"Torque ripple","score":0.5964416265487671},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.594167947769165},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5889756679534912},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5873323082923889},{"id":"https://openalex.org/keywords/torque","display_name":"Torque","score":0.5593715906143188},{"id":"https://openalex.org/keywords/stator","display_name":"Stator","score":0.5416340231895447},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.513412594795227},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.49506059288978577},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.464994341135025},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"Harmonic analysis","score":0.45925137400627136},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.4359840750694275},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3180779218673706},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.31282392144203186},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2917204201221466},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.23877650499343872},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2035694122314453},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.1372450292110443},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.09785580635070801},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09031733870506287},{"id":"https://openalex.org/keywords/direct-torque-control","display_name":"Direct torque control","score":0.08028927445411682},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07596921920776367},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.07468149065971375}],"concepts":[{"id":"https://openalex.org/C69710193","wikidata":"https://www.wikidata.org/wiki/Q14946576","display_name":"Vernier scale","level":2,"score":0.9066643714904785},{"id":"https://openalex.org/C2779675184","wikidata":"https://www.wikidata.org/wiki/Q7826797","display_name":"Torque ripple","level":5,"score":0.5964416265487671},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.594167947769165},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5889756679534912},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5873323082923889},{"id":"https://openalex.org/C144171764","wikidata":"https://www.wikidata.org/wiki/Q48103","display_name":"Torque","level":2,"score":0.5593715906143188},{"id":"https://openalex.org/C2776529397","wikidata":"https://www.wikidata.org/wiki/Q190312","display_name":"Stator","level":2,"score":0.5416340231895447},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.513412594795227},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.49506059288978577},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.464994341135025},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.45925137400627136},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.4359840750694275},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3180779218673706},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.31282392144203186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2917204201221466},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.23877650499343872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2035694122314453},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.1372450292110443},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.09785580635070801},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09031733870506287},{"id":"https://openalex.org/C109871850","wikidata":"https://www.wikidata.org/wiki/Q1227571","display_name":"Direct torque control","level":4,"score":0.08028927445411682},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07596921920776367},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.07468149065971375},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C80962145","wikidata":"https://www.wikidata.org/wiki/Q207450","display_name":"Induction motor","level":3,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tie.2020.3044785","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2020.3044785","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.44999998807907104,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1225439561","display_name":null,"funder_award_id":"51677159","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3663872014","display_name":null,"funder_award_id":"52077186","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":30,"referenced_works":["https://openalex.org/W1553373771","https://openalex.org/W1992960460","https://openalex.org/W2009525440","https://openalex.org/W2018890340","https://openalex.org/W2056329563","https://openalex.org/W2059915427","https://openalex.org/W2060612859","https://openalex.org/W2067254251","https://openalex.org/W2126105956","https://openalex.org/W2165048816","https://openalex.org/W2246089238","https://openalex.org/W2247358853","https://openalex.org/W2326024518","https://openalex.org/W2327641358","https://openalex.org/W2343997752","https://openalex.org/W2528172956","https://openalex.org/W2552728747","https://openalex.org/W2762646264","https://openalex.org/W2789253593","https://openalex.org/W2799425108","https://openalex.org/W2900486992","https://openalex.org/W2900798153","https://openalex.org/W2910049100","https://openalex.org/W2964433003","https://openalex.org/W2983680425","https://openalex.org/W2999650510","https://openalex.org/W3014598445","https://openalex.org/W3036388601","https://openalex.org/W3037220408","https://openalex.org/W6648548384"],"related_works":["https://openalex.org/W2054844037","https://openalex.org/W2069827955","https://openalex.org/W3158414702","https://openalex.org/W3015531115","https://openalex.org/W2799787427","https://openalex.org/W4389722951","https://openalex.org/W4389723662","https://openalex.org/W2139269360","https://openalex.org/W4290973875","https://openalex.org/W3212543277"],"abstract_inverted_index":{"This":[0,102],"article":[1],"presents":[2],"a":[3,8,17,93],"high-fidelity":[4],"analytical":[5,74],"solution":[6],"and":[7,67,121,139],"fast":[9],"integrated":[10,103],"optimization":[11,104,123],"method":[12,20,105],"for":[13,97],"vernier":[14,31,38,100],"machines.":[15,32],"First,":[16],"harmonic":[18,79],"modeling":[19],"(HMM)":[21],"is":[22,81,125],"adopted":[23],"to":[24,45,91],"obtain":[25],"the":[26,34,49,57,62,73,77,84,98,111,116,122,128,131,142],"magnetic":[27,51],"field":[28],"distribution":[29],"of":[30,37,48,53,130],"Particularly,":[33],"stator":[35],"teeth":[36],"machines":[39],"are":[40,134],"divided":[41],"into":[42],"several":[43],"blocks":[44],"take":[46],"account":[47],"local":[50],"saturation":[52],"soft-magnetic":[54],"material.":[55],"Then,":[56],"electromagnetic":[58],"parameters,":[59],"such":[60],"as":[61],"average":[63],"torque,":[64],"torque":[65],"ripple,":[66],"efficiency,":[68],"can":[69,106],"be":[70],"calculated":[71],"via":[72],"model.":[75],"Next,":[76],"proposed":[78],"model":[80],"combined":[82],"with":[83,141],"nondominated":[85],"sorting":[86],"genetic":[87],"algorithm":[88],"II":[89],"(NSGA-II)":[90],"determine":[92],"multiobjective":[94],"optimal":[95,132],"design":[96],"studied":[99],"machine.":[101],"save":[107],"computation":[108],"time,":[109],"because":[110],"data":[112],"interaction":[113],"process":[114],"between":[115],"finite-element":[117],"analysis":[118],"(FEA)":[119],"software":[120,124],"eliminated.":[126],"Finally,":[127],"performances":[129],"case":[133],"verified":[135],"by":[136],"both":[137],"FEA":[138],"experiments":[140],"prototype.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5}],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2025-10-10T00:00:00"}