{"id":"https://openalex.org/W3120719535","doi":"https://doi.org/10.1109/access.2021.3050134","title":"Research on the Inverse Problem of Reliability Evaluation\u2013Model and Algorithm","display_name":"Research on the Inverse Problem of Reliability Evaluation\u2013Model and Algorithm","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3120719535","doi":"https://doi.org/10.1109/access.2021.3050134","mag":"3120719535"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3050134","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3050134","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09317857.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09317857.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087011161","display_name":"Tao Niu","orcid":"https://orcid.org/0000-0003-4461-9481"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tao Niu","raw_affiliation_strings":["School of Electrical Engineering, Chongqing University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0003-4461-9481","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101935689","display_name":"Fan Li","orcid":"https://orcid.org/0000-0003-3946-5924"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fan Li","raw_affiliation_strings":["School of Electrical Engineering, Chongqing University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0003-3946-5924","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028864691","display_name":"Bo Hu","orcid":"https://orcid.org/0000-0002-0844-3303"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Hu","raw_affiliation_strings":["School of Electrical Engineering, Chongqing University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0002-0844-3303","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007708445","display_name":"Hui L\u00fc","orcid":"https://orcid.org/0000-0001-5105-6280"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Lu","raw_affiliation_strings":["School of Electrical Engineering, Chongqing University, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102510789","display_name":"Lvbin Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lvbin Peng","raw_affiliation_strings":["School of Electrical Engineering, Chongqing University, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017941662","display_name":"Kaigui Xie","orcid":"https://orcid.org/0000-0002-7057-4304"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaigui Xie","raw_affiliation_strings":["School of Electrical Engineering, Chongqing University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0002-7057-4304","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101862805","display_name":"Kan Cao","orcid":"https://orcid.org/0000-0003-1588-8586"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kan Cao","raw_affiliation_strings":["State Grid Hubei Electric Power Research Institute, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Grid Hubei Electric Power Research Institute, Wuhan, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064489503","display_name":"Kunpeng Zhou","orcid":"https://orcid.org/0000-0001-9439-2129"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kunpeng Zhou","raw_affiliation_strings":["State Grid Hubei Electric Power Research Institute, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Grid Hubei Electric Power Research Institute, Wuhan, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5087011161"],"corresponding_institution_ids":["https://openalex.org/I158842170"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.681,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.66997593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"9","issue":null,"first_page":"12648","last_page":"12656"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11941","display_name":"Power System Reliability and Maintenance","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T11941","display_name":"Power System Reliability and Maintenance","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9901999831199646,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.7990682125091553},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.6711201667785645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6376134157180786},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5296725034713745},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5235825777053833},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.5150232315063477},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4542042911052704},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.44464555382728577},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.444095253944397},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43994826078414917},{"id":"https://openalex.org/keywords/reliability-engineering","display_name":"Reliability engineering","score":0.430209755897522},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40836387872695923},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.3483714461326599},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2418106198310852},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13821610808372498},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11716488003730774}],"concepts":[{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.7990682125091553},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.6711201667785645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6376134157180786},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5296725034713745},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5235825777053833},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.5150232315063477},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4542042911052704},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.44464555382728577},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.444095253944397},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43994826078414917},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.430209755897522},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40836387872695923},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3483714461326599},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2418106198310852},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13821610808372498},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11716488003730774},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3050134","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3050134","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09317857.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3b3d622588124d2a82a05a8141b8e6b0","is_oa":true,"landing_page_url":"https://doaj.org/article/3b3d622588124d2a82a05a8141b8e6b0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 9, Pp 12648-12656 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3050134","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3050134","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09317857.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G250161483","display_name":null,"funder_award_id":"5100-202099273A-0-0-00","funder_id":"https://openalex.org/F4320326707","funder_display_name":"State Grid Corporation of China"}],"funders":[{"id":"https://openalex.org/F4320326707","display_name":"State Grid Corporation of China","ror":"https://ror.org/05twwhs70"},{"id":"https://openalex.org/F4320335967","display_name":"Science and Technology Project of State Grid","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3120719535.pdf","grobid_xml":"https://content.openalex.org/works/W3120719535.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1968904586","https://openalex.org/W2011544673","https://openalex.org/W2020791881","https://openalex.org/W2053623324","https://openalex.org/W2072802808","https://openalex.org/W2105381590","https://openalex.org/W2130198414","https://openalex.org/W2136782285","https://openalex.org/W2137055330","https://openalex.org/W2169848883","https://openalex.org/W2317896555","https://openalex.org/W2500834297","https://openalex.org/W2783623659","https://openalex.org/W2795483994","https://openalex.org/W2804256238","https://openalex.org/W2919391570"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4210910892","https://openalex.org/W2206497186","https://openalex.org/W4225691068","https://openalex.org/W2277985843","https://openalex.org/W1542828544"],"abstract_inverted_index":{"Due":[0],"to":[1,47,55,118,144,181,189],"the":[2,13,24,48,68,97,101,112,120,126,146,149,157,165,172,183],"high":[3],"dependence":[4],"of":[5,18,29,42,50,66,89,100,148],"economic":[6],"and":[7,26,95,125,171,193],"social":[8],"development":[9],"on":[10,74,111],"power":[11,19,174],"systems,":[12],"demand":[14],"for":[15,83],"reliable":[16],"operation":[17],"systems":[20],"is":[21,70,116,142],"increasing.":[22],"Considering":[23],"popularity":[25],"widespread":[27],"installation":[28],"smart":[30],"meters,":[31],"accurate":[32],"system/node":[33,52],"reliability":[34,43,53,58,85,91,123,152],"indexes":[35,54,86],"can":[36],"be":[37],"obtained.":[38],"The":[39],"inverse":[40],"problem":[41],"evaluation":[44],"(IPRE)":[45],"refers":[46],"use":[49],"known":[51],"obtain":[56],"component":[57,90,122,151],"parameters.":[59,153],"In":[60],"this":[61,187],"paper,":[62],"a":[63,75,106,139],"novel":[64],"method":[65,141,184],"solving":[67],"IPRE":[69,102],"proposed.":[71],"First,":[72],"based":[73,110],"nonsequential":[76],"Monte":[77],"Carlo":[78],"(NSMC)":[79],"method,":[80],"analytical":[81],"expressions":[82],"system":[84,175],"in":[87,176,186],"terms":[88],"parameters":[92],"are":[93,103,128,179],"derived,":[94],"then,":[96],"nonlinear":[98],"equations":[99],"constructed.":[104],"Second,":[105],"high-order":[107],"polynomial":[108],"approximation":[109],"conjugate":[113],"gradient":[114],"algorithm":[115],"used":[117,143,180],"calculate":[119],"unknown":[121],"parameters,":[124],"results":[127],"compared":[129],"with":[130],"those":[131],"obtained":[132,150],"using":[133],"traditional":[134],"neural":[135],"networks":[136],"method.":[137],"Finally,":[138],"continuation":[140],"correct":[145],"errors":[147],"Three":[154],"cases,":[155],"namely,":[156],"IEEE":[158],"1979":[159],"Reliability":[160],"Test":[161,168],"System":[162,169],"(IEEE":[163],"RTS-79),":[164],"Roy":[166],"Billinton":[167],"(RBTS)":[170],"Chuanyu":[173],"Southwest":[177],"China,":[178],"test":[182],"proposed":[185],"paper":[188],"verify":[190],"its":[191],"feasibility":[192],"accuracy.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
