{"id":"https://openalex.org/W2058736576","doi":"https://doi.org/10.1061/(asce)em.1943-7889.0000047","title":"Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions","display_name":"Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions","publication_year":2009,"publication_date":"2009-05-02","ids":{"openalex":"https://openalex.org/W2058736576","doi":"https://doi.org/10.1061/(asce)em.1943-7889.0000047","mag":"2058736576"},"language":"en","primary_location":{"id":"doi:10.1061/(asce)em.1943-7889.0000047","doi":"https://doi.org/10.1061/(asce)em.1943-7889.0000047","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)em.1943-7889.0000047","pdf_url":null,"source":{"id":"https://openalex.org/S160934207","display_name":"Journal of Engineering Mechanics","issn_l":"0733-9399","issn":["0733-9399","1943-7889"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315747","host_organization_name":"American Society of Civil Engineers","host_organization_lineage":["https://openalex.org/P4310315747"],"host_organization_lineage_names":["American Society of Civil Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Engineering Mechanics","raw_type":"journal-article"},"volume":null,"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/A5100782801","display_name":"Sharif Rahman","orcid":"https://orcid.org/0000-0003-0837-9871","observed_orcids":["https://orcid.org/0000-0003-0837-9871"]},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sharif Rahman","raw_affiliation_strings":["College of Engineering, The Univ. of Iowa, Iowa City, IA 52242"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Engineering, The Univ. of Iowa, Iowa City, IA 52242","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100782801"],"corresponding_institution_ids":["https://openalex.org/I126307644"],"apc_list":null,"apc_paid":null,"fwci":7.0126,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.97009548,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"135","issue":"12","first_page":"1439","last_page":"1451"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9961000084877014,"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":0.9961000084877014,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.0003000000142492354,"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/arbitrary-probability-distributions","display_name":"arbitrary probability distributions","score":0.890999972820282},{"id":"https://openalex.org/keywords/recursion-coefficients","display_name":"recursion coefficients","score":0.7250000238418579},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.8790000081062317},{"id":"https://openalex.org/keywords/tail-probability-estimation","display_name":"tail probability estimation","score":0.6610000133514404},{"id":"https://openalex.org/keywords/reliability-analysis","display_name":"reliability analysis","score":0.7070000171661377},{"id":"https://openalex.org/keywords/stochastic-response","display_name":"stochastic response","score":0.6520000100135803},{"id":"https://openalex.org/keywords/convergence-acceleration","display_name":"convergence acceleration","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.780045747756958},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.7107351422309875},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.608972430229187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5595897436141968},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.5560092926025391},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49377140402793884},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.4872931241989136},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.47578513622283936},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4658874571323395},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.4622907340526581},{"id":"https://openalex.org/C158557763","wikidata":"https://www.wikidata.org/wiki/Q5166603","display_name":"Convolution of probability distributions","level":4,"score":0.4153786301612854},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.3923541307449341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.307555615901947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2940722405910492},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27658194303512573},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.1291782259941101},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1061/(asce)em.1943-7889.0000047","doi":"https://doi.org/10.1061/(asce)em.1943-7889.0000047","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)em.1943-7889.0000047","pdf_url":null,"source":{"id":"https://openalex.org/S160934207","display_name":"Journal of Engineering Mechanics","issn_l":"0733-9399","issn":["0733-9399","1943-7889"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315747","host_organization_name":"American Society of Civil Engineers","host_organization_lineage":["https://openalex.org/P4310315747"],"host_organization_lineage_names":["American Society of Civil Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Engineering Mechanics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W79383899","https://openalex.org/W1513751997","https://openalex.org/W1593505867","https://openalex.org/W1972955129","https://openalex.org/W1992068214","https://openalex.org/W2020328455","https://openalex.org/W2093145699","https://openalex.org/W2119835964","https://openalex.org/W2120062331","https://openalex.org/W2123562397","https://openalex.org/W2143547713","https://openalex.org/W2163244656","https://openalex.org/W2601436066","https://openalex.org/W3016843226","https://openalex.org/W4214736987","https://openalex.org/W4236269093"],"related_works":["https://openalex.org/W2333364686","https://openalex.org/W2163244656","https://openalex.org/W2317449888","https://openalex.org/W7098715554","https://openalex.org/W2082005075","https://openalex.org/W2158285576","https://openalex.org/W2022104168","https://openalex.org/W2143714414","https://openalex.org/W7099140399","https://openalex.org/W2158288611"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3,19],"extended":[4,92,119],"polynomial":[5,33],"dimensional":[6],"decomposition":[7,93],"method":[8,24,94,120],"for":[9,38,51,59],"solving":[10],"stochastic":[11,85],"problems":[12],"subject":[13],"to":[14],"independent":[15],"random":[16,107],"input":[17],"following":[18],"arbitrary":[20],"probability":[21,54,105],"distribution.":[22],"The":[23,64,115],"involves":[25],"Fourier-polynomial":[26],"expansions":[27],"of":[28,43,76,79,83,102,106,112,117],"component":[29],"functions":[30,109],"by":[31],"orthogonal":[32,44,69,126],"bases,":[34,71],"the":[35,40,47,61,80,91,103,118],"Stieltjes":[36],"procedure":[37],"generating":[39],"recursion":[41],"coefficients":[42],"polynomials":[45,70],"and":[46,56,98],"Gauss":[48],"quadrature":[49],"rule":[50],"a":[52,73,84],"specified":[53],"measure,":[55],"dimension-reduction":[57],"integration":[58],"calculating":[60],"expansion":[62],"coefficients.":[63],"extension,":[65],"which":[66],"subsumes":[67],"nonclassical":[68],"generates":[72],"convergent":[74],"sequence":[75],"lower-variate":[77],"estimates":[78,101],"probabilistic":[81],"characteristics":[82],"response.":[86],"Numerical":[87],"results":[88],"indicate":[89],"that":[90],"provides":[95],"accurate,":[96],"convergent,":[97],"computationally":[99],"efficient":[100],"tail":[104],"mathematical":[108],"or":[110],"reliability":[111],"mechanical":[113],"systems.":[114],"convergence":[116],"accelerates":[121],"significantly":[122],"when":[123],"employing":[124],"measure-consistent":[125],"polynomials.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":7}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}
