{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T12:11:35Z","timestamp":1790424695743,"version":"4.1.0"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,20]],"date-time":"2022-02-20T00:00:00Z","timestamp":1645315200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51078311"],"award-info":[{"award-number":["51078311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under stochastic earthquakes based on adaptive Gaussian process regression (GPR) metamodeling is proposed in this study. In this method, the uncertainties of ground motions are described by the record-to-record variation and the randomness of intensity measure (IM). A GPR model is constructed to obtain the approximations of the engineering demand parameter (EDP), and an active learning (AL) strategy is presented to adaptively update the design of experiments (DoE) of this metamodel. Based on the reliability of design variables calculated by Monte Carlo simulation (MCS), an optimal solution can be obtained by an efficient global optimization (EGO) algorithm. To validate the effectiveness and efficiency of the developed method, it is applied to the optimization problems of a steel frame and a reinforced concrete frame and compared with the existing methods. The results show that this method can provide accurate reliability information for seismic design and can deal with the problems of minimizing costs under the probabilistic constraint and problems of improving the seismic reliability under limited costs.<\/jats:p>","DOI":"10.3390\/axioms11020081","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T08:14:46Z","timestamp":1645431286000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Reliability-Based Design Optimization of Structures Considering Uncertainties of Earthquakes Based on Efficient Gaussian Process Regression Metamodeling"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5152-6243","authenticated-orcid":false,"given":"Yanjie","family":"Xiao","sequence":"first","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4054-1560","authenticated-orcid":false,"given":"Feng","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinwei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xun\u2019an","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,20]]},"reference":[{"key":"ref_1","unstructured":"(2000). 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