{"id":"https://openalex.org/W2044221688","doi":"https://doi.org/10.1109/tsmc.2014.2310712","title":"Multivariate Probabilistic Collocation Method for Effective Uncertainty Evaluation With Application to Air Traffic Flow Management","display_name":"Multivariate Probabilistic Collocation Method for Effective Uncertainty Evaluation With Application to Air Traffic Flow Management","publication_year":2014,"publication_date":"2014-04-02","ids":{"openalex":"https://openalex.org/W2044221688","doi":"https://doi.org/10.1109/tsmc.2014.2310712","mag":"2044221688"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2014.2310712","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2014.2310712","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","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/A5061300320","display_name":"Yi Zhou","orcid":"https://orcid.org/0000-0003-4638-898X"},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yi Zhou","raw_affiliation_strings":["Department of Electrical Engineering, University of North Texas, Denton, TX, USA","Department of Electrical Engineering , University of North Texas, Denton, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of North Texas, Denton, TX, USA","institution_ids":["https://openalex.org/I123534392"]},{"raw_affiliation_string":"Department of Electrical Engineering , University of North Texas, Denton, TX, USA","institution_ids":["https://openalex.org/I123534392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029213376","display_name":"Yan Wan","orcid":"https://orcid.org/0000-0002-7508-5833"},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yan Wan","raw_affiliation_strings":["Department of Electrical Engineering, University of North Texas, Denton, TX, USA","Department of Electrical Engineering , University of North Texas, Denton, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of North Texas, Denton, TX, USA","institution_ids":["https://openalex.org/I123534392"]},{"raw_affiliation_string":"Department of Electrical Engineering , University of North Texas, Denton, TX, USA","institution_ids":["https://openalex.org/I123534392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103231201","display_name":"Sandip Roy","orcid":"https://orcid.org/0000-0002-5558-9698"},"institutions":[{"id":"https://openalex.org/I72951846","display_name":"Washington State University","ror":"https://ror.org/05dk0ce17","country_code":"US","type":"education","lineage":["https://openalex.org/I72951846"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sandip Roy","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, USA","School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, USA","institution_ids":["https://openalex.org/I72951846"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA USA","institution_ids":["https://openalex.org/I72951846"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109272489","display_name":"Christine Taylor","orcid":null},"institutions":[{"id":"https://openalex.org/I44896327","display_name":"Mitre (United States)","ror":"https://ror.org/03ks2a131","country_code":"US","type":"company","lineage":["https://openalex.org/I44896327"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christine Taylor","raw_affiliation_strings":["MITRE Corporation, McLean, VA, USA","[Mitre Corporation, McLean, VA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MITRE Corporation, McLean, VA, USA","institution_ids":["https://openalex.org/I44896327"]},{"raw_affiliation_string":"[Mitre Corporation, McLean, VA, USA]","institution_ids":["https://openalex.org/I44896327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103806119","display_name":"Craig Wanke","orcid":null},"institutions":[{"id":"https://openalex.org/I44896327","display_name":"Mitre (United States)","ror":"https://ror.org/03ks2a131","country_code":"US","type":"company","lineage":["https://openalex.org/I44896327"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Craig Wanke","raw_affiliation_strings":["MITRE Corporation, McLean, VA, USA","[Mitre Corporation, McLean, VA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MITRE Corporation, McLean, VA, USA","institution_ids":["https://openalex.org/I44896327"]},{"raw_affiliation_string":"[Mitre Corporation, McLean, VA, USA]","institution_ids":["https://openalex.org/I44896327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042806986","display_name":"Dinesh Ramamurthy","orcid":null},"institutions":[{"id":"https://openalex.org/I2802036773","display_name":"Enterprise Holdings","ror":"https://ror.org/0381ha386","country_code":"US","type":"company","lineage":["https://openalex.org/I2802036773"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dinesh Ramamurthy","raw_affiliation_strings":["Enterprise Holdings, St. Louis, MO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Enterprise Holdings, St. Louis, MO, USA","institution_ids":["https://openalex.org/I2802036773"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063416695","display_name":"Junfei Xie","orcid":"https://orcid.org/0000-0001-7406-3221"},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Junfei Xie","raw_affiliation_strings":["Department of Electrical Engineering, University of North Texas, Denton, TX, USA","Department of Electrical Engineering , University of North Texas, Denton, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of North Texas, Denton, TX, USA","institution_ids":["https://openalex.org/I123534392"]},{"raw_affiliation_string":"Department of Electrical Engineering , University of North Texas, Denton, TX, USA","institution_ids":["https://openalex.org/I123534392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":3.8704,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.94576987,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"10","first_page":"1347","last_page":"1363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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":0.9998999834060669,"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/T11357","display_name":"Risk and Safety Analysis","score":0.9962999820709229,"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/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.9904999732971191,"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/multivariate-statistics","display_name":"Multivariate statistics","score":0.7439163327217102},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6495419144630432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6113860607147217},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5671896934509277},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5664584040641785},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5353586673736572},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5219578146934509},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.45993947982788086},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35033196210861206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.256555438041687},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2327858805656433},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14033949375152588},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12140804529190063},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10725834965705872}],"concepts":[{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7439163327217102},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6495419144630432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6113860607147217},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5671896934509277},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5664584040641785},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5353586673736572},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5219578146934509},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.45993947982788086},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35033196210861206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.256555438041687},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2327858805656433},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14033949375152588},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12140804529190063},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10725834965705872},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2014.2310712","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2014.2310712","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6299999952316284}],"awards":[{"id":"https://openalex.org/G8494091128","display_name":"CPS: Small: Collaborative Research: Dynamical-Network Evaluation and Design Tools for Strategic-to-Tactical Air Traffic Flow Management","funder_award_id":"1035386","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306108","display_name":"U.S. Department of Transportation","ror":"https://ror.org/02xfw2e90"},{"id":"https://openalex.org/F4320332390","display_name":"Federal Aviation Administration","ror":"https://ror.org/05q0y0j38"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1580682816","https://openalex.org/W1599009198","https://openalex.org/W1603888081","https://openalex.org/W1939945791","https://openalex.org/W1981270896","https://openalex.org/W1983156129","https://openalex.org/W2000315490","https://openalex.org/W2045996814","https://openalex.org/W2055455718","https://openalex.org/W2089792964","https://openalex.org/W2097264805","https://openalex.org/W2103452908","https://openalex.org/W2105737698","https://openalex.org/W2116841475","https://openalex.org/W2118545485","https://openalex.org/W2128069253","https://openalex.org/W2133924802","https://openalex.org/W2138930243","https://openalex.org/W2146480545","https://openalex.org/W2147252093","https://openalex.org/W2155726536","https://openalex.org/W2167747641","https://openalex.org/W2319464764","https://openalex.org/W2323086495","https://openalex.org/W2324644391","https://openalex.org/W2329298432","https://openalex.org/W2333105625","https://openalex.org/W2335443803","https://openalex.org/W2417112726","https://openalex.org/W4239335912","https://openalex.org/W4243645092","https://openalex.org/W4301253858","https://openalex.org/W4302769929","https://openalex.org/W6635782744","https://openalex.org/W6636072753","https://openalex.org/W6650429709","https://openalex.org/W6679192538","https://openalex.org/W6681698204","https://openalex.org/W6716981725"],"related_works":["https://openalex.org/W2370840338","https://openalex.org/W2388641108","https://openalex.org/W2368317224","https://openalex.org/W2370651559","https://openalex.org/W2383177152","https://openalex.org/W3000893075","https://openalex.org/W2349694428","https://openalex.org/W2384630579","https://openalex.org/W2358919722","https://openalex.org/W3000494655"],"abstract_inverted_index":{"Modern":[0],"large-scale":[1],"infrastructure":[2],"systems":[3],"have":[4],"typical":[5],"complicated":[6],"structure":[7],"and":[8,10,48,145],"dynamics,":[9],"extensive":[11],"simulations":[12],"are":[13],"required":[14],"to":[15,27,87,109,133],"evaluate":[16],"their":[17],"performance.":[18],"The":[19],"probabilistic":[20],"collocation":[21],"method":[22],"(PCM)":[23],"has":[24],"been":[25],"developed":[26],"effectively":[28],"simulate":[29],"a":[30,54],"system's":[31],"performance":[32,50,169],"under":[33,170],"parametric":[34],"uncertainty.":[35],"In":[36,76],"particular,":[37],"it":[38],"allows":[39],"reduced-order":[40],"representation":[41,61],"of":[42,57,62,73,84,114,123,129,148,154,161],"the":[43,59,63,70,81,88,112,124,134,149,152,155,159],"mapping":[44],"between":[45],"uncertain":[46,93],"parameters":[47,94],"system":[49,65,116,168],"measures/outputs,":[51],"using":[52],"only":[53],"limited":[55],"number":[56],"simulations;":[58],"resultant":[60],"original":[64,115],"is":[66],"provably":[67],"accurate":[68],"over":[69],"likely":[71],"range":[72],"parameter":[74,143],"values.":[75],"this":[77],"paper,":[78,156],"we":[79,102,157],"extend":[80],"formal":[82],"analysis":[83],"single-variable":[85],"PCM":[86,108,163],"multivariate":[89,107,125,162],"case,":[90],"where":[91],"multiple":[92],"may":[95,97],"or":[96],"not":[98],"be":[99],"independent.":[100],"Specifically,":[101],"provide":[103],"conditions":[104],"that":[105],"permit":[106],"precisely":[110],"predict":[111],"mean":[113],"output.":[117],"We":[118],"also":[119],"explore":[120],"additional":[121],"capabilities":[122],"PCM,":[126],"in":[127,164],"terms":[128],"cross-statistics":[130],"prediction,":[131],"relation":[132],"minimum":[135],"mean-square":[136],"estimator,":[137],"computational":[138],"feasibility":[139],"for":[140],"large":[141],"dimensional":[142],"sets,":[144],"sample-based":[146],"approximation":[147],"solution.":[150],"At":[151],"end":[153],"demonstrate":[158],"application":[160],"evaluating":[165],"air":[166],"traffic":[167],"weather":[171],"uncertainties.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}