{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T22:28:14Z","timestamp":1776119294934,"version":"3.50.1"},"reference-count":83,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T00:00:00Z","timestamp":1714521600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T00:00:00Z","timestamp":1714521600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T00:00:00Z","timestamp":1714521600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Earthquake Spectra"],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:p>This study presents a two\u2010step hybrid (model\u2010data fusion) method for reconstructing the seismic response of instrumented buildings at their non\u2010instrumented floors. Over the past couple of decades, seismic data recorded within instrumented buildings have yielded invaluable insights into the behavior of civil structures, which were arguably impossible to obtain through numerical simulations, laboratory\u2010scale experiments, or even in\u2010situ testing. Recently, advances in sensing technology have opened new pathways for structural health monitoring (SHM) and rapid post\u2010earthquake assessment. However, data\u2010driven techniques tend to lack accuracy when structures have sparse instrumentation. In addition, creating detailed numerical models for the monitored structures is labor\u2010intensive and time\u2010consuming, often unsuitable for rapid post\u2010event assessments. The common approach to address these challenges has been to use simple interpolation techniques over the sparse measurements. However, uncertainties associated with such estimates are usually overlooked, and these methods have certain physical limitations. In this study, we propose a two\u2010step approach for reconstructing seismic responses. In the initial step, a coupled shear\u2013flexural beam model is calibrated using data collected from instrumented floors. Next, the residual, representing the difference between measurements and the beam model\u2019s predictions, is used to train a Gaussian process regression model. The combination of these two models provides both the mean and variance of the response at the non\u2010instrumented floors. This new approach is verified by using simulated acceleration responses of a tall building. Validation is attained by using real seismic data recorded in two tall buildings and comparing the method\u2019s predictions with actual measurements on floors not used for training. Finally, data recorded in a 52\u2010story building during multiple earthquakes are used for demonstrating the practical application of the proposed approach in real\u2010world scenarios.<\/jats:p>","DOI":"10.1177\/87552930241231686","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T00:07:27Z","timestamp":1710115647000},"page":"1235-1268","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["A hybrid model\u2010data method for seismic response reconstruction of instrumented buildings"],"prefix":"10.1002","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3847-5277","authenticated-orcid":false,"given":"Farid","family":"Ghahari","sequence":"first","affiliation":[{"name":"Civil and Environmental Engineering Department University of California Los Angeles CA USA"},{"name":"California Geological Survey Sacramento CA USA"}]},{"given":"Daniel","family":"Swensen","sequence":"additional","affiliation":[{"name":"California Geological Survey Sacramento CA USA"}]},{"given":"Hamid","family":"Haddadi","sequence":"additional","affiliation":[{"name":"California Geological Survey Sacramento CA USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9618-1210","authenticated-orcid":false,"given":"Ertugrul","family":"Taciroglu","sequence":"additional","affiliation":[{"name":"Civil and Environmental Engineering Department University of California Los Angeles CA USA"}]}],"member":"311","published-online":{"date-parts":[[2024,5]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.1513"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1193\/031712EQS093M"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)EM.1943-7889.0000990"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1193\/1.2084232"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.3915"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)EM.1943-7889.0000851"},{"key":"e_1_2_6_8_1","unstructured":"ATC\u201020(2005)Building Safety Evaluation Forms and Placards. Available at:https:\/\/www.atcouncil.org\/atc\u201020"},{"key":"e_1_2_6_9_1","volume-title":"Numerical issues in maximum likelihood parameter estimation for Gaussian Process interpolation (Lecture Notes in Computer Science)","author":"Basak S","year":"2022"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstl.1763.0053"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.3636"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1193\/1.2359702"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1785\/0220190220"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1177\/8755293020906836"},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1193\/092713EQS260M"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1193\/052114EQS071M"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.1193\/122216eqs249m"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.1193\/1.1735987"},{"key":"e_1_2_6_19_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120220005"},{"key":"e_1_2_6_20_1","volume-title":"Dynamics of Structures","author":"Clough RW","year":"2013"},{"key":"e_1_2_6_21_1","doi-asserted-by":"publisher","DOI":"10.1137\/0806023"},{"key":"e_1_2_6_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2018.08.017"},{"key":"e_1_2_6_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6333-3"},{"key":"e_1_2_6_24_1","doi-asserted-by":"publisher","DOI":"10.2172\/249299"},{"key":"e_1_2_6_25_1","doi-asserted-by":"publisher","DOI":"10.3390\/buildings13010028"},{"key":"e_1_2_6_26_1","unstructured":"FEMA P\u201058(2018)Seismic performance assessment of buildings volume 1\u2014methodology. Technical Report FEMA\u2010P 58\u20101. Available at:https:\/\/www.atcouncil.org\/docman\/fema\/246\u2010fema\u2010p\u201058\u20101\u2010seismic\u2010performance\u2010assessment\u2010of\u2010buildings\u2010volume\u20101\u2010methodology\u2010second\u2010edition\/file"},{"key":"e_1_2_6_27_1","volume-title":"Finite Element Model Updating in Structural Dynamics (Solid Mechanics and Its Applications)","author":"Friswell MI","year":"1995"},{"key":"e_1_2_6_28_1","first-page":"1","article-title":"Gaussian process regression for seismic fragility assessment of building Portfolios","volume":"87","author":"Gentile R","year":"2019","journal-title":"Conference of Earthquake Risk and Engineering Towards a Resilient World"},{"key":"e_1_2_6_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.1925"},{"key":"e_1_2_6_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10518-017-0253-0"},{"key":"e_1_2_6_31_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.1803"},{"key":"e_1_2_6_32_1","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.2268"},{"key":"e_1_2_6_33_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.1593"},{"key":"e_1_2_6_34_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120210224"},{"key":"e_1_2_6_35_1","doi-asserted-by":"publisher","DOI":"10.3390\/s22031278"},{"key":"e_1_2_6_36_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.3078"},{"key":"e_1_2_6_37_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/58.2.255"},{"key":"e_1_2_6_38_1","volume-title":"Proceedings \u2010 6th International Conference on New Trends in Information Science, Service Science and Data Mining (NISS, ICMIA and NASNIT), Taipei, 23\u201325 October","author":"Hong S","year":"2012"},{"key":"e_1_2_6_39_1","first-page":"17","article-title":"Structure instrumentation in the California strong motion instrumentation program","volume":"373","author":"Huang MJ","year":"2011","journal-title":"Strong Motion Instrumentation for Civil Engineering Structures"},{"key":"e_1_2_6_40_1","doi-asserted-by":"publisher","DOI":"10.1193\/1.4000091"},{"key":"e_1_2_6_41_1","doi-asserted-by":"publisher","DOI":"10.1002\/2475-8876.12155"},{"issue":"6","key":"e_1_2_6_42_1","first-page":"4792","article-title":"A statistical approach to some basic mine valuation problems on the Witwatersrand","volume":"52","author":"Krige DG","year":"1951","journal-title":"Journal of Southern African Institute of Mining and Metallurgy"},{"key":"e_1_2_6_43_1","doi-asserted-by":"publisher","DOI":"10.1198\/004017004000000671"},{"key":"e_1_2_6_44_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10518-022-01461-5"},{"key":"e_1_2_6_45_1","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.262"},{"key":"e_1_2_6_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2011.06.012"},{"key":"e_1_2_6_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-13976-6"},{"key":"e_1_2_6_48_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2006.1932"},{"key":"e_1_2_6_49_1","doi-asserted-by":"publisher","DOI":"10.3390\/buildings13020420"},{"key":"e_1_2_6_50_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-011-9274-8"},{"key":"e_1_2_6_51_1","doi-asserted-by":"publisher","DOI":"10.1193\/1.4000151"},{"key":"e_1_2_6_52_1","unstructured":"MartuscelliP MoehleJP(2019)Using CSMIP data to test FEMA P58 methodology and the potential for automated loss estimation. SMIP Seminar. Available at:https:\/\/www.semanticscholar.org\/paper\/USING\u2010CSMIP\u2010DATA\u2010TO\u2010TEST\u2010FEMA\u2010P58\u2010METHODOLOGY\u2010AND\u2010Martuscelli\u2010Moehle\/a085233a0a87cf5799234efc26bb042f08fb33d4"},{"key":"e_1_2_6_53_1","unstructured":"MathWorks(2018).MATLAB version: 9.4.0 (R2018b) Natick Massachusetts: The MathWorks Inc.https:\/\/www.mathworks.com."},{"key":"e_1_2_6_54_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9445(1999)125:4(417)"},{"key":"e_1_2_6_55_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2010.10.012"},{"key":"e_1_2_6_56_1","doi-asserted-by":"publisher","DOI":"10.1002\/tal.345"},{"key":"e_1_2_6_57_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)ST.1943-541X.0001200"},{"key":"e_1_2_6_58_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/58.3.545"},{"key":"e_1_2_6_59_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2013.2250352"},{"key":"e_1_2_6_60_1","unstructured":"PorterKA(2003)An overview of PEER\u2019s performance\u2010based earthquake engineering methodology. In: 9th International Conference on Applications of Statistics and Probability in Civil Engineering San Francisco CA 6\u20139 July."},{"key":"e_1_2_6_61_1","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.3422"},{"key":"e_1_2_6_62_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2012.07.007"},{"key":"e_1_2_6_63_1","volume-title":"Gaussian Processes for Machine Learning","author":"Rasmussen CE","year":"2006"},{"key":"e_1_2_6_64_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02162161"},{"key":"e_1_2_6_65_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13349-020-00416-1"},{"key":"e_1_2_6_66_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.2373"},{"key":"e_1_2_6_67_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)ST.1943-541X.0003095"},{"key":"e_1_2_6_68_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2018.03.001"},{"key":"e_1_2_6_69_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(2000)126:12(1224)"},{"key":"e_1_2_6_70_1","doi-asserted-by":"publisher","DOI":"10.1002\/stc.2090"},{"key":"e_1_2_6_71_1","doi-asserted-by":"publisher","DOI":"10.1002\/0470045345"},{"key":"e_1_2_6_72_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2020.106837"},{"key":"e_1_2_6_73_1","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2008.923118"},{"key":"e_1_2_6_74_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1494-6"},{"key":"e_1_2_6_75_1","doi-asserted-by":"publisher","DOI":"10.1193\/072215EQS118M"},{"key":"e_1_2_6_76_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.soildyn.2016.09.041"},{"key":"e_1_2_6_77_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9445(2005)131:2(212)"},{"key":"e_1_2_6_78_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120210054"},{"key":"e_1_2_6_79_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"issue":"195","key":"e_1_2_6_80_1","first-page":"687","article-title":"Spline models for observational data","volume":"57","author":"Wahba G","year":"1991","journal-title":"Mathematics of Computation"},{"key":"e_1_2_6_81_1","doi-asserted-by":"publisher","DOI":"10.1193\/1.2923924"},{"key":"e_1_2_6_82_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120160069"},{"key":"e_1_2_6_83_1","doi-asserted-by":"publisher","DOI":"10.1080\/13632469.2021.1991860"},{"key":"e_1_2_6_84_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.soildyn.2021.106961"}],"container-title":["Earthquake Spectra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1177\/87552930241231686","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1177\/87552930241231686","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1177\/87552930241231686","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T14:14:14Z","timestamp":1769350454000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1177\/87552930241231686"},"secondary":[{"URL":"https:\/\/pubs.geoscienceworld.org\/earthquake-spectra\/article\/40\/2\/1235\/639007\/a-hybrid-model-data-method-for-seismic-response","label":"geoscienceworld"}]},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5]]},"references-count":83,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["10.1177\/87552930241231686"],"URL":"https:\/\/doi.org\/10.1177\/87552930241231686","archive":["Portico"],"relation":{},"ISSN":["8755-2930","1944-8201"],"issn-type":[{"value":"8755-2930","type":"print"},{"value":"1944-8201","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5]]}}}