{"id":"https://openalex.org/W2954419084","doi":"https://doi.org/10.3390/e21070649","title":"An Effective Approach for Reliability-Based Sensitivity Analysis with the Principle of Maximum Entropy and Fractional Moments","display_name":"An Effective Approach for Reliability-Based Sensitivity Analysis with the Principle of Maximum Entropy and Fractional Moments","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2954419084","doi":"https://doi.org/10.3390/e21070649","mag":"2954419084","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267363"},"language":"en","primary_location":{"id":"doi:10.3390/e21070649","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070649","pdf_url":"https://www.mdpi.com/1099-4300/21/7/649/pdf?version=1561971917","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/7/649/pdf?version=1561971917","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021004981","display_name":"Xufang Zhang","orcid":"https://orcid.org/0000-0003-2860-5979"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xufang Zhang","raw_affiliation_strings":["School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China"],"raw_orcid":"https://orcid.org/0000-0003-2860-5979","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066855201","display_name":"Jiankai Liu","orcid":"https://orcid.org/0000-0003-0117-5817"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiankai Liu","raw_affiliation_strings":["School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101638873","display_name":"Ying Yan","orcid":"https://orcid.org/0000-0002-3609-0496"},"institutions":[{"id":"https://openalex.org/I4210110794","display_name":"Taiyuan Heavy Industry (China)","ror":"https://ror.org/022vzex26","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210110794"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Yan","raw_affiliation_strings":["The Technology Center, Taiyuan Heavy Industry Co. Ltd., Taiyuan 030024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Technology Center, Taiyuan Heavy Industry Co. Ltd., Taiyuan 030024, China","institution_ids":["https://openalex.org/I4210110794"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049245462","display_name":"Mahesh D. Pandey","orcid":"https://orcid.org/0000-0002-5083-2599"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mahesh Pandey","raw_affiliation_strings":["Department of Civil & Environmental Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil & Environmental Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021004981"],"corresponding_institution_ids":["https://openalex.org/I9224756"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1296,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.82977629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"21","issue":"7","first_page":"649","last_page":"649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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"}},{"id":"https://openalex.org/T10396","display_name":"Fatigue and fracture mechanics","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11850","display_name":"Concrete Corrosion and Durability","score":0.9812999963760376,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.7220675349235535},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6725837588310242},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6176464557647705},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5729554295539856},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5597723722457886},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5531757473945618},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.5300642848014832},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5125646591186523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4937048852443695},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4365697503089905},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37935054302215576},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35395294427871704},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32306861877441406},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23745831847190857},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10722032189369202},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08580198884010315}],"concepts":[{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.7220675349235535},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6725837588310242},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6176464557647705},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5729554295539856},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5597723722457886},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5531757473945618},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.5300642848014832},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5125646591186523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4937048852443695},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4365697503089905},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37935054302215576},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35395294427871704},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32306861877441406},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23745831847190857},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10722032189369202},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08580198884010315},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e21070649","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070649","pdf_url":"https://www.mdpi.com/1099-4300/21/7/649/pdf?version=1561971917","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33267363","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267363","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:e936019a35774ef0921f62dbf2c4ebac","is_oa":true,"landing_page_url":"https://doaj.org/article/e936019a35774ef0921f62dbf2c4ebac","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":"Entropy, Vol 21, Iss 7, p 649 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/7/649/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21070649","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7515142","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515142","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21070649","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070649","pdf_url":"https://www.mdpi.com/1099-4300/21/7/649/pdf?version=1561971917","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1367120077","display_name":null,"funder_award_id":"51775095","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2954419084.pdf","grobid_xml":"https://content.openalex.org/works/W2954419084.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W100464641","https://openalex.org/W232805744","https://openalex.org/W1495898891","https://openalex.org/W1572480955","https://openalex.org/W1967316147","https://openalex.org/W1978289729","https://openalex.org/W1983445134","https://openalex.org/W1985551345","https://openalex.org/W1986706483","https://openalex.org/W1987756829","https://openalex.org/W1991548802","https://openalex.org/W1999683741","https://openalex.org/W2002223076","https://openalex.org/W2006772343","https://openalex.org/W2008034786","https://openalex.org/W2014715727","https://openalex.org/W2015882984","https://openalex.org/W2026749015","https://openalex.org/W2029827834","https://openalex.org/W2030104589","https://openalex.org/W2032583510","https://openalex.org/W2034600651","https://openalex.org/W2060228835","https://openalex.org/W2060235242","https://openalex.org/W2070748799","https://openalex.org/W2072620869","https://openalex.org/W2073407183","https://openalex.org/W2073732659","https://openalex.org/W2089779846","https://openalex.org/W2119360871","https://openalex.org/W2123562397","https://openalex.org/W2131733133","https://openalex.org/W2156716810","https://openalex.org/W2370905191","https://openalex.org/W2482939998","https://openalex.org/W2534854550","https://openalex.org/W2737319167","https://openalex.org/W2896671255","https://openalex.org/W2908794637","https://openalex.org/W6755629542"],"related_works":["https://openalex.org/W2034921015","https://openalex.org/W3021846434","https://openalex.org/W2064875109","https://openalex.org/W59993211","https://openalex.org/W2889261288","https://openalex.org/W4385752617","https://openalex.org/W2068679119","https://openalex.org/W2351977092","https://openalex.org/W2048700611","https://openalex.org/W2970690932"],"abstract_inverted_index":{"The":[0],"reliability-based":[1,60,120],"sensitivity":[2,61,121],"analysis":[3,122],"requires":[4],"to":[5,26,30,83,113],"recursively":[6],"evaluate":[7],"a":[8,21,124],"multivariate":[9,125],"structural":[10,33,126],"model":[11],"for":[12,58,118],"many":[13],"failure":[14,34],"probability":[15],"levels.":[16],"This":[17],"is":[18,42,63,108],"in":[19,52,78],"general":[20],"computationally":[22],"intensive":[23],"task":[24],"due":[25],"irregular":[27],"integrations":[28],"used":[29],"define":[31],"the":[32,39,47,59,67,73,79,85,92,101,119],"probability.":[35],"In":[36],"this":[37,53,88],"regard,":[38],"performance":[40,86],"function":[41],"first":[43],"approximated":[44],"by":[45],"using":[46],"multiplicative":[48,102],"dimensional":[49,103],"reduction":[50,104],"method":[51],"paper,":[54],"and":[55,72,111],"an":[56],"approximation":[57],"index":[62],"derived":[64],"based":[65,105],"on":[66],"principle":[68],"of":[69,87,123],"maximum":[70],"entropy":[71,106],"fractional":[74],"moment.":[75],"Three":[76],"examples":[77],"literature":[80],"are":[81],"presented":[82],"examine":[84],"entropy-based":[89],"approach":[90,107],"against":[91],"brute-force":[93],"Monte-Carlo":[94],"simulation":[95],"method.":[96],"Results":[97],"have":[98],"shown":[99],"that":[100],"rather":[109],"efficient":[110],"able":[112],"provide":[114],"reliability":[115],"estimation":[116],"results":[117],"model.":[127]},"counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}