{"id":"https://openalex.org/W1985745141","doi":"https://doi.org/10.1061/(asce)0733-9399(1991)117:6(1289)","title":"Equivalent Statistical Quadratization for Nonlinear Systems","display_name":"Equivalent Statistical Quadratization for Nonlinear Systems","publication_year":1991,"publication_date":"1991-06-01","ids":{"openalex":"https://openalex.org/W1985745141","doi":"https://doi.org/10.1061/(asce)0733-9399(1991)117:6(1289)","mag":"1985745141"},"language":"en","primary_location":{"id":"doi:10.1061/(asce)0733-9399(1991)117:6(1289)","doi":"https://doi.org/10.1061/(asce)0733-9399(1991)117:6(1289)","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)0733-9399(1991)117:6(1289)","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/A5110431873","display_name":"Pol D. Spanos","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. D. Spanos","raw_affiliation_strings":["L. B. Ryon Chair in Engrg., Rice Univ., P.O. Box 1892, Houston, TX 77251"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"L. B. Ryon Chair in Engrg., Rice Univ., P.O. Box 1892, Houston, TX 77251","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110299249","display_name":"Mark G. Donley","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. G. Donley","raw_affiliation_strings":["Sr. Project Engr., Struct. Dynamics Res. Corp., 2000 Eastman Dr., Milford, OH 45150"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sr. Project Engr., Struct. Dynamics Res. Corp., 2000 Eastman Dr., Milford, OH 45150","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4474,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.91435276,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"117","issue":"6","first_page":"1289","last_page":"1310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.6747999787330627,"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":0.6747999787330627,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.2660999894142151,"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/T10160","display_name":"Seismic Performance and Analysis","score":0.014700000174343586,"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/equivalent-linearization","display_name":"equivalent linearization","score":0.9509999752044678},{"id":"https://openalex.org/keywords/nonlinear-random-vibration","display_name":"nonlinear random vibration","score":0.8190000057220459},{"id":"https://openalex.org/keywords/volterra-series","display_name":"Volterra series","score":0.9290000200271606},{"id":"https://openalex.org/keywords/single-degree-of-freedom-oscillator","display_name":"single-degree-of-freedom oscillator","score":0.8980000019073486},{"id":"https://openalex.org/keywords/gram-charlier-expansion","display_name":"Gram-Charlier expansion","score":0.9539999961853027}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6983883380889893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6947672367095947},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6870813369750977},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5984036326408386},{"id":"https://openalex.org/C2778532037","wikidata":"https://www.wikidata.org/wiki/Q3957891","display_name":"Volterra series","level":3,"score":0.5537934899330139},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5358383059501648},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5263239741325378},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5115547776222229},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.46978798508644104},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4370363652706146},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.4260580539703369},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.343363881111145},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20798438787460327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10492604970932007},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1061/(asce)0733-9399(1991)117:6(1289)","doi":"https://doi.org/10.1061/(asce)0733-9399(1991)117:6(1289)","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)0733-9399(1991)117:6(1289)","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W570957880","https://openalex.org/W1512158565","https://openalex.org/W1595848081","https://openalex.org/W1976047396","https://openalex.org/W1978270876","https://openalex.org/W1991777572","https://openalex.org/W2009854079","https://openalex.org/W2028697190","https://openalex.org/W2029864616","https://openalex.org/W2052636318","https://openalex.org/W2107192240","https://openalex.org/W2108555859","https://openalex.org/W2284995748","https://openalex.org/W2333240428","https://openalex.org/W2480173016","https://openalex.org/W2736830216","https://openalex.org/W2797066837","https://openalex.org/W6721849768"],"related_works":["https://openalex.org/W44342674","https://openalex.org/W2072849988","https://openalex.org/W4240505046","https://openalex.org/W2097313859","https://openalex.org/W2168119960","https://openalex.org/W2067896713","https://openalex.org/W4242348036","https://openalex.org/W1579471891","https://openalex.org/W2069014081","https://openalex.org/W782577448"],"abstract_inverted_index":{"The":[0,92,112,131,157],"statistical":[1,60],"linearization":[2,57,181],"method":[3,62,113,175,182],"is":[4,18,63,80,114,136,170,176],"often":[5],"inadequate":[6],"for":[7,49,99,116,153,183],"estimating":[8],"spectral":[9],"properties":[10],"of":[11,14,27,29,37,55,68,147],"random":[12],"responses":[13,28,43],"nonlinear":[15,50,70,93,118],"systems.":[16,51,156,186],"This":[17],"due":[19],"to":[20,89,179],"the":[21,24,34,38,56,66,69,84,101,108,145,148,173,180,184],"fact":[22],"that":[23,172],"power":[25],"spectra":[26],"linear":[30],"systems":[31],"span":[32],"only":[33],"frequency":[35],"range":[36,46],"excitation":[39],"spectrum,":[40],"whereas":[41],"significant":[42],"outside":[44],"this":[45],"are":[47,72,129,151],"possible":[48],"As":[52],"an":[53,75],"extension":[54],"method,":[58,149],"a":[59,97,117,139],"\u201cquadratization\u201d":[61],"presented.":[64],"Specifically,":[65],"statistics":[67,128],"system":[71,95],"obtained":[73,152],"from":[74],"\u201cequivalent\u201d":[76],"quadratic":[77,90],"system,":[78],"which":[79,100],"constructed":[81],"by":[82,86,106,138],"replacing":[83],"nonlinearity":[85],"polynomials":[87],"up":[88],"order.":[91],"equivalent":[94],"has":[96],"form":[98],"solution":[102],"can":[103],"be":[104],"approximated":[105,137],"using":[107],"Volterra":[109],"series":[110],"method.":[111],"formulated":[115],"single\u2010degree\u2010of\u2010freedom":[119],"oscillator":[120],"under":[121],"stationary,":[122],"Gaussian":[123],"excitation.":[124],"Stationary,":[125],"non\u2010Gaussian":[126,132],"response":[127,133],"obtained.":[130],"probability":[134],"distribution":[135],"third\u2010order":[140],"Gram\u2010Charlier":[141],"expansion.":[142],"To":[143],"demonstrate":[144],"applicability":[146],"solutions":[150],"two":[154],"sample":[155],"corresponding":[158],"results":[159],"compare":[160],"well":[161],"with":[162],"relevant":[163],"Monte":[164],"Carlo":[165],"simulation":[166],"data.":[167],"Further,":[168],"it":[169],"shown":[171],"quadratization":[174],"notably":[177],"superior":[178],"considered":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}