{"id":"https://openalex.org/W7208829757","doi":"https://doi.org/10.1038/s41598-026-70227-9","title":"An extended interval structure automated belief rule-based bearing fault diagnosis method for complex engineering systems","display_name":"An extended interval structure automated belief rule-based bearing fault diagnosis method for complex engineering systems","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7208829757","doi":"https://doi.org/10.1038/s41598-026-70227-9"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-026-70227-9","doi":"https://doi.org/10.1038/s41598-026-70227-9","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-70227-9","pdf_url":"https://www.nature.com/articles/s41598-026-70227-9_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-026-70227-9_reference.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135772250","display_name":"Xingchi Yan","orcid":"https://orcid.org/0009-0000-7302-313X","observed_orcids":["https://orcid.org/0009-0000-7302-313X"]},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XingChi Yan","raw_affiliation_strings":["School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China","institution_ids":["https://openalex.org/I134052481"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100602634","display_name":"Yuxi Liu","orcid":"https://orcid.org/0000-0002-0182-084X","observed_orcids":["https://orcid.org/0000-0002-0182-084X"]},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"YuXi Liu","raw_affiliation_strings":["School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China","institution_ids":["https://openalex.org/I134052481"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081265309","display_name":"Ning Li","orcid":"https://orcid.org/0000-0002-4534-9009","observed_orcids":["https://orcid.org/0000-0002-4534-9009","https://orcid.org/0009-0005-1124-1672"]},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ning Li","raw_affiliation_strings":["School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China","institution_ids":["https://openalex.org/I134052481"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013289800","display_name":"Dongping Wang","orcid":"https://orcid.org/0000-0002-4705-8774","observed_orcids":["https://orcid.org/0000-0002-4705-8774"]},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"DongPing Wang","raw_affiliation_strings":["School of Literature, Harbin Normal University, Harbin, 150025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Literature, Harbin Normal University, Harbin, 150025, China","institution_ids":["https://openalex.org/I134052481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147710352","display_name":"Yan Yu","orcid":"https://orcid.org/0009-0009-6265-6252","observed_orcids":["https://orcid.org/0009-0009-6265-6252"]},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Yu","raw_affiliation_strings":["School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Harbin Normal University, Harbin, 150025, China","institution_ids":["https://openalex.org/I134052481"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100602634"],"corresponding_institution_ids":["https://openalex.org/I134052481"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.9965999722480774,"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/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.9965999722480774,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.0012000000569969416,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bearing-fault-diagnosis","display_name":"bearing fault diagnosis","score":0.9980000257492065},{"id":"https://openalex.org/keywords/belief-rule-base","display_name":"belief rule base","score":0.9449999928474426},{"id":"https://openalex.org/keywords/interval-structure","display_name":"interval structure","score":0.3880000114440918},{"id":"https://openalex.org/keywords/evidential-reasoning","display_name":"evidential reasoning","score":0.7900000214576721},{"id":"https://openalex.org/keywords/vibration-characteristics","display_name":"vibration characteristics","score":0.5440000295639038},{"id":"https://openalex.org/keywords/xgboost-feature-selection","display_name":"XGBoost feature selection","score":0.9169999957084656},{"id":"https://openalex.org/keywords/rule-interpretability","display_name":"rule interpretability","score":0.5740000009536743},{"id":"https://openalex.org/keywords/hybrid-inference","display_name":"hybrid inference","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7396000027656555},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6322000026702881},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5856000185012817},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.5356000065803528},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5198000073432922},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.515999972820282},{"id":"https://openalex.org/C175551986","wikidata":"https://www.wikidata.org/wiki/Q47089","display_name":"Fault (geology)","level":2,"score":0.5055000185966492},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C149271511","wikidata":"https://www.wikidata.org/wiki/Q1417149","display_name":"Rule-based system","level":2,"score":0.44839999079704285},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C199978012","wikidata":"https://www.wikidata.org/wiki/Q1273815","display_name":"Bearing (navigation)","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3643999993801117},{"id":"https://openalex.org/C152745839","wikidata":"https://www.wikidata.org/wiki/Q5438153","display_name":"Fault detection and isolation","level":3,"score":0.34549999237060547},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33180001378059387},{"id":"https://openalex.org/C20162079","wikidata":"https://www.wikidata.org/wiki/Q1151406","display_name":"Case-based reasoning","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C4554734","wikidata":"https://www.wikidata.org/wiki/Q593744","display_name":"Knowledge base","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C37335422","wikidata":"https://www.wikidata.org/wiki/Q6888134","display_name":"Model-based reasoning","level":3,"score":0.29120001196861267},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C16910744","wikidata":"https://www.wikidata.org/wiki/Q7705759","display_name":"Test data","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C115925183","wikidata":"https://www.wikidata.org/wiki/Q1412694","display_name":"Knowledge-based systems","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1038/s41598-026-70227-9","doi":"https://doi.org/10.1038/s41598-026-70227-9","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-70227-9","pdf_url":"https://www.nature.com/articles/s41598-026-70227-9_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1038/s41598-026-70227-9","doi":"https://doi.org/10.1038/s41598-026-70227-9","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-70227-9","pdf_url":"https://www.nature.com/articles/s41598-026-70227-9_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5007096894","display_name":null,"funder_award_id":"PL2025F015","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"}],"funders":[{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208829757.pdf","grobid_xml":"https://content.openalex.org/works/W7208829757.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W2055122450","https://openalex.org/W2905166565","https://openalex.org/W3034192853","https://openalex.org/W3178126331","https://openalex.org/W4206353554","https://openalex.org/W4210340868","https://openalex.org/W4226343678","https://openalex.org/W4296126073","https://openalex.org/W4303182758","https://openalex.org/W4308766051","https://openalex.org/W4362653123","https://openalex.org/W4366692523","https://openalex.org/W4390187605","https://openalex.org/W4391687111","https://openalex.org/W4392710854","https://openalex.org/W4394986749","https://openalex.org/W4396664978","https://openalex.org/W4400872149","https://openalex.org/W4400966535","https://openalex.org/W4401246585","https://openalex.org/W4401283218","https://openalex.org/W4409327194","https://openalex.org/W4415700554","https://openalex.org/W7140185263","https://openalex.org/W7154998914","https://openalex.org/W7155188993","https://openalex.org/W7160698789","https://openalex.org/W7165160741","https://openalex.org/W7167597445","https://openalex.org/W7169827314","https://openalex.org/W7170277043"],"related_works":["https://openalex.org/W7203910646","https://openalex.org/W7083448487","https://openalex.org/W7126049807","https://openalex.org/W4409327143","https://openalex.org/W7221563442","https://openalex.org/W4401069866","https://openalex.org/W4399328718","https://openalex.org/W4404448367","https://openalex.org/W7135230530","https://openalex.org/W7210269247"],"abstract_inverted_index":{"Abstract":[0],"Reliable":[1],"bearing":[2,137,199],"fault":[3],"diagnosis":[4],"requires":[5],"models":[6],"that":[7,216],"remain":[8],"accurate":[9],"under":[10,81],"changing":[11],"operating":[12],"conditions":[13],"while":[14],"providing":[15],"transparent":[16],"diagnostic":[17,185,223],"reasoning.":[18],"Conventional":[19],"belief":[20,49,127],"rule":[21,35,50,68,99,123],"base":[22,51],"(BRB)":[23],"methods":[24],"are":[25,59,108,114,129],"interpretable":[26,95],"but":[27],"suffer":[28],"from":[29,78],"rule-combination":[30],"explosion,":[31],"reliance":[32],"on":[33,206],"expert-defined":[34],"bases,":[36],"and":[37,84,125,145,157,178,194,201,227],"inflexible":[38],"inference":[39,174],"procedures.":[40],"This":[41,87],"study":[42],"proposes":[43],"an":[44,153,219],"extended":[45],"interval":[46,66],"structure":[47],"automated":[48],"model":[52],"(EIBRB-Auto).":[53],"Eight":[54],"physically":[55],"meaningful":[56],"vibration":[57],"features":[58],"first":[60],"selected":[61],"using":[62,116,132,139],"XGBoost.":[63],"An":[64],"adaptive":[65],"merging-based":[67],"extraction":[69],"algorithm":[70],"(AIM-RE)":[71],"then":[72],"constructs":[73],"eight-dimensional":[74],"hyperrectangular":[75],"rules":[76,96,107],"directly":[77,158],"training":[79,91,144],"data":[80,142,148],"four":[82,209],"purity":[83],"separability":[85],"constraints.":[86],"process":[88],"compresses":[89],"1,376":[90],"samples":[92,103,113],"into":[93],"156":[94],"without":[97,183],"Cartesian":[98],"combinations.":[100],"During":[101],"diagnosis,":[102],"matching":[104],"the":[105,162,169,190,198,203],"extracted":[106],"classified":[109,159],"directly,":[110],"whereas":[111],"unmatched":[112],"processed":[115],"evidential":[117],"reasoning":[118,225],"(ER).":[119],"The":[120],"attribute":[121],"weights,":[122,124],"consequent":[126],"degrees":[128],"subsequently":[130],"optimized":[131],"P-CMA-ES.":[133],"In":[134],"a":[135,180],"cross-load":[136],"experiment":[138,200],"20":[140],"N":[141,147],"for":[143,149],"40":[146],"testing,":[150],"EIBRB-Auto":[151,187,217],"achieved":[152,179,202],"accuracy":[154,205],"of":[155,161,208],"97.82%":[156],"72.02%":[160],"test":[163],"samples.":[164],"Compared":[165],"with":[166],"ER-only":[167],"inference,":[168],"hybrid":[170],"mechanism":[171],"reduced":[172],"total":[173],"time":[175],"by":[176],"54.50%":[177],"2.20-fold":[181],"speedup":[182],"reducing":[184],"accuracy.":[186],"also":[188],"outperformed":[189],"compared":[191],"BRB":[192],"variants":[193],"conventional":[195],"classifiers":[196],"in":[197],"highest":[204],"three":[207],"public":[210],"benchmark":[211],"datasets.":[212],"These":[213],"results":[214],"demonstrate":[215],"provides":[218],"effective":[220],"balance":[221],"among":[222],"performance,":[224],"efficiency,":[226],"rule-level":[228],"interpretability.":[229]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2026-09-06T00:00:00"}