{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T07:05:51Z","timestamp":1779519951330,"version":"3.53.1"},"reference-count":50,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012154","name":"Graduate Research and Innovation Projects of Jiangsu Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012154","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Industrial Engineering"],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1016\/j.cie.2026.112102","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:05:11Z","timestamp":1777993511000},"page":"112102","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["An efficient reliability-based design optimization approach based on probability quantile estimation and structural constraint integration"],"prefix":"10.1016","volume":"217","author":[{"given":"Yuwei","family":"Shi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0430-1553","authenticated-orcid":false,"given":"Chenglong","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-9594-0837","authenticated-orcid":false,"given":"Mingyu","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingyuan","family":"Shen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ikjin","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1589-8050","authenticated-orcid":false,"given":"Yizhong","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cie.2026.112102_b0005","doi-asserted-by":"crossref","first-page":"2459","DOI":"10.2514\/1.34321","article-title":"Efficient global reliability analysis for nonlinear implicit performance functions","volume":"46","author":"Bichon","year":"2008","journal-title":"AIAA Journal"},{"key":"10.1016\/j.cie.2026.112102_b0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110491","article-title":"A reliability-based design optimization strategy using quantile surrogates by improved PC-kriging","volume":"253","author":"Chen","year":"2025","journal-title":"Reliability Engineering & System Safety"},{"key":"10.1016\/j.cie.2026.112102_b0015","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00158-013-0988-4","article-title":"A local adaptive sampling method for reliability-based design optimization using Kriging model","volume":"49","author":"Chen","year":"2014","journal-title":"Struct Multidisc Optim"},{"key":"10.1016\/j.cie.2026.112102_b0020","doi-asserted-by":"crossref","first-page":"1294","DOI":"10.1080\/24725854.2023.2275166","article-title":"Robust expected improvement for Bayesian optimization","volume":"56","author":"Christianson","year":"2024","journal-title":"IISE Transactions"},{"key":"10.1016\/j.cie.2026.112102_b0025","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.matcom.2009.09.005","article-title":"Monte Carlo algorithms for evaluating Sobol\u2019 sensitivity indices","volume":"81","author":"Dimov","year":"2010","journal-title":"Mathematics and Computers in Simulation"},{"key":"10.1016\/j.cie.2026.112102_b0030","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1115\/1.1649968","article-title":"Sequential optimization and reliability assessment method for efficient probabilistic design","volume":"126","author":"Du","year":"2004","journal-title":"Journal of Mechanical Design"},{"key":"10.1016\/j.cie.2026.112102_b0035","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.strusafe.2011.01.002","article-title":"AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation","volume":"33","author":"Echard","year":"2011","journal-title":"Structural Safety"},{"key":"10.1016\/j.cie.2026.112102_b0040","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.paerosci.2008.11.001","article-title":"Recent advances in surrogate-based optimization","volume":"45","author":"Forrester","year":"2009","journal-title":"Progress in Aerospace Sciences"},{"key":"10.1016\/j.cie.2026.112102_b0045","doi-asserted-by":"crossref","unstructured":"Forrester, A.I.J., S\u00f3bester, A., Keane, A.J. Engineering design via surrogate modelling: A practical guide. 1st ed. Wiley; 2008. https:\/\/doi.org\/10.1002\/9780470770801.","DOI":"10.1002\/9780470770801"},{"key":"10.1016\/j.cie.2026.112102_b0050","first-page":"1809","article-title":"Entropy search for information-efficient global optimization","volume":"13","author":"Hennig","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"10.1016\/j.cie.2026.112102_b0055","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.109939","article-title":"A sequential sampling-based Bayesian numerical method for reliability-based design optimization","volume":"244","author":"Hong","year":"2024","journal-title":"Reliability Engineering & System Safety"},{"key":"10.1016\/j.cie.2026.112102_b0060","doi-asserted-by":"crossref","DOI":"10.1007\/s00158-024-03884-x","article-title":"Reliability-based design optimization: A state-of-the-art review of its methodologies, applications, and challenges","volume":"67","author":"Hu","year":"2024","journal-title":"Struct Multidisc Optim"},{"key":"10.1016\/j.cie.2026.112102_b0065","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109810","article-title":"A novel quantile-based sequential optimization and reliability assessment method for safety life analysis","volume":"243","author":"Jiang","year":"2024","journal-title":"Reliability Engineering & System Safety"},{"key":"10.1016\/j.cie.2026.112102_b0070","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1023\/A:1008306431147","article-title":"Efficient global optimization of expensive black-box functions","volume":"13","author":"Jones","year":"1998","journal-title":"Journal of Global Optimization"},{"key":"10.1016\/j.cie.2026.112102_b0075","first-page":"3","article-title":"Systematic Reliability Optimization (ASRO). Babylonian","volume":"50","author":"Kim","year":"2023","journal-title":"Journal of Mathematics"},{"key":"10.1016\/j.cie.2026.112102_b0080","doi-asserted-by":"crossref","DOI":"10.1061\/(ASCE)EM.1943-7889.0001910","article-title":"Reliability-based design optimization using quantile surrogates by adaptive Gaussian process","volume":"147","author":"Kim","year":"2021","journal-title":"Journal of Engineering Mechanics"},{"key":"10.1016\/j.cie.2026.112102_b0085","unstructured":"Kun, Z., Guangwu, L., Wen, S., An upper confidence bound approach to estimating the maximum mean. arXiv Preprint arXiv:240804179 2024."},{"key":"10.1016\/j.cie.2026.112102_b0090","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1016\/j.compstruc.2007.05.023","article-title":"A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: Constraint boundary sampling","volume":"86","author":"Lee","year":"2008","journal-title":"Computers & Structures"},{"key":"10.1016\/j.cie.2026.112102_b0095","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.116456","article-title":"A novel sampling method for adaptive gradient-enhanced Kriging","volume":"418","author":"Lee","year":"2024","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.cie.2026.112102_b0100","article-title":"A novel low-fidelity-guided design of experiments for multi-fidelity surrogate modeling","volume":"69","author":"Lee","year":"2026","journal-title":"Advanced Engineering Informatics"},{"key":"10.1016\/j.cie.2026.112102_b0105","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.compstruc.2015.09.004","article-title":"A local Kriging approximation method using MPP for reliability-based design optimization","volume":"162","author":"Li","year":"2016","journal-title":"Computers & Structures"},{"key":"10.1016\/j.cie.2026.112102_b0110","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s00366-020-01135-3","article-title":"A multi-constraint failure-pursuing sampling method for reliability-based design optimization using adaptive Kriging","volume":"38","author":"Li","year":"2022","journal-title":"Engineering with Computers"},{"key":"10.1016\/j.cie.2026.112102_b0115","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s00158-019-02384-7","article-title":"A new efficient decoupled reliability-based design optimization method with quantiles","volume":"61","author":"Li","year":"2020","journal-title":"Struct Multidisc Optim"},{"key":"10.1016\/j.cie.2026.112102_b0120","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1115\/1.2779884","article-title":"A single-loop approach for system reliability-based design optimization","volume":"129","author":"Liang","year":"2007","journal-title":"Journal of Mechanical Design"},{"key":"10.1016\/j.cie.2026.112102_b0125","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1109\/TR.2022.3200137","article-title":"An overview of adaptive-surrogate-model-assisted methods for reliability-based design optimization","volume":"72","author":"Ling","year":"2023","journal-title":"IEEE Trans Rel"},{"key":"10.1016\/j.cie.2026.112102_b0130","volume":"vol. 2","author":"Lophaven","year":"2002"},{"key":"10.1016\/j.cie.2026.112102_b0135","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1016\/j.camwa.2015.07.004","article-title":"A new learning function for Kriging and its applications to solve reliability problems in engineering","volume":"70","author":"Lv","year":"2015","journal-title":"Computers & Mathematics with Applications"},{"key":"10.1016\/j.cie.2026.112102_b0140","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109386","article-title":"Reliability-based design optimization using adaptive Kriging-A single-loop strategy and a double-loop one","volume":"237","author":"Ma","year":"2023","journal-title":"Reliability Engineering & System Safety"},{"key":"10.1016\/j.cie.2026.112102_b0145","doi-asserted-by":"crossref","DOI":"10.1115\/1.4040883","article-title":"An adaptive directional boundary sampling method for efficient reliability-based design optimization","volume":"140","author":"Meng","year":"2018","journal-title":"Journal of Mechanical Design"},{"key":"10.1016\/j.cie.2026.112102_b0150","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.116704","article-title":"Optimum-pursuing method for constrained optimization and reliability-based design optimization problems using Kriging model","volume":"420","author":"Meng","year":"2024","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.cie.2026.112102_b0160","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1007\/s00158-016-1504-4","article-title":"Quantile-based optimization under uncertainties using adaptive Kriging surrogate models","volume":"54","author":"Moustapha","year":"2016","journal-title":"Struct Multidisc Optim"},{"key":"10.1016\/j.cie.2026.112102_b0165","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.istruc.2023.04.006","article-title":"Metamodel-assisted design optimization in the field of structural engineering: A literature review","volume":"52","author":"Negrin","year":"2023","journal-title":"Structures"},{"key":"10.1016\/j.cie.2026.112102_b0170","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1016\/0045-7949(88)90418-X","article-title":"Reliability based optimization: A safety index approach","volume":"28","author":"Nikolaidis","year":"1988","journal-title":"Computers & Structures"},{"key":"10.1016\/j.cie.2026.112102_b0175","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/24725854.2025.2491492","article-title":"Double-robust Bayesian variable selection and model prediction with spherically symmetric error","volume":"58","author":"Ouyang","year":"2026","journal-title":"IISE Transactions"},{"key":"10.1016\/j.cie.2026.112102_b0180","doi-asserted-by":"crossref","DOI":"10.1016\/j.strusafe.2024.102453","article-title":"Life safety in the Reliability-Based design and assessment of structures","volume":"113","author":"Pandey","year":"2025","journal-title":"Structural Safety"},{"key":"10.1016\/j.cie.2026.112102_b0185","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1080\/0305215X.2022.2145604","article-title":"Using the knowledge gradient acquisition function in Bayesian optimization when searching for robust solutions","volume":"56","author":"Phuong Le","year":"2024","journal-title":"Engineering Optimization"},{"key":"10.1016\/j.cie.2026.112102_b0190","series-title":"Global versus local search in constrained optimization of computer models. Institute of Mathematical Statistics Lecture Notes - Monograph Series","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1214\/lnms\/1215456182","author":"Schonlau","year":"1998"},{"key":"10.1016\/j.cie.2026.112102_b0195","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2025.113651","article-title":"An adaptive Kriging-assisted reliability-based design optimization framework with reliability assurance and high efficiency","volume":"242","author":"Shen","year":"2026","journal-title":"Mechanical Systems and Signal Processing"},{"key":"10.1016\/j.cie.2026.112102_b0200","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110007","article-title":"Active learning Kriging-based multi-objective modeling and optimization for system reliability-based robust design","volume":"245","author":"Shi","year":"2024","journal-title":"Reliability Engineering & System Safety"},{"key":"10.1016\/j.cie.2026.112102_b0205","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2025.112402","article-title":"A new fully decoupled strategy for reliability optimization based on adaptive Kriging with improved efficient global optimization and weighted K-means clustering","volume":"227","author":"Song","year":"2025","journal-title":"Mechanical Systems and Signal Processing"},{"key":"10.1016\/j.cie.2026.112102_b0210","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/00401706.2024.2336535","article-title":"Constrained Bayesian optimization with lower confidence bound","volume":"66","author":"Upadhye","year":"2024","journal-title":"Technometrics"},{"key":"10.1016\/j.cie.2026.112102_b0215","first-page":"1","article-title":"Recent advances in Bayesian optimization","volume":"55","author":"Wang","year":"2023","journal-title":"ACM Computing Surveys"},{"key":"10.1016\/j.cie.2026.112102_b0220","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1016\/j.swevo.2018.10.007","article-title":"Multi-objective Bayesian global optimization using expected hypervolume improvement gradient","volume":"44","author":"Yang","year":"2019","journal-title":"Swarm and Evolutionary Computation"},{"key":"10.1016\/j.cie.2026.112102_b0225","doi-asserted-by":"crossref","DOI":"10.1016\/j.strusafe.2023.102426","article-title":"An effective active learning strategy for reliability-based design optimization under multiple simulation models","volume":"107","author":"Yang","year":"2024","journal-title":"Structural Safety"},{"key":"10.1016\/j.cie.2026.112102_b0230","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2021.114462","article-title":"Efficient local adaptive Kriging approximation method with single-loop strategy for reliability-based design optimization","volume":"390","author":"Yang","year":"2022","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.cie.2026.112102_b0235","doi-asserted-by":"crossref","first-page":"874","DOI":"10.2514\/1.6648","article-title":"Enriched performance measure approach for reliability-based design optimization","volume":"43","author":"Youn","year":"2005","journal-title":"AIAA Journal"},{"key":"10.1016\/j.cie.2026.112102_b0240","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1080\/0305215X.2020.1800664","article-title":"A single-loop approach with adaptive sampling and surrogate Kriging for reliability-based design optimization","volume":"53","author":"Zhang","year":"2021","journal-title":"Engineering Optimization"},{"key":"10.1016\/j.cie.2026.112102_b0245","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2021.108020","article-title":"Reliability index function approximation based on adaptive double-loop Kriging for reliability-based design optimization","volume":"216","author":"Zhang","year":"2021","journal-title":"Reliability Engineering & System Safety"},{"key":"10.1016\/j.cie.2026.112102_b0250","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2023.109391","article-title":"Time-dependent reliability analysis under random and interval uncertainties based on Kriging modeling and saddlepoint approximation","volume":"182","author":"Zhao","year":"2023","journal-title":"Computers & Industrial Engineering"},{"key":"10.1016\/j.cie.2026.112102_b0255","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2024.110361","article-title":"Online adaptive selection of appropriate learning functions with parallel infilling strategy for Kriging-based reliability analysis","volume":"194","author":"Zhao","year":"2024","journal-title":"Computers & Industrial Engineering"}],"container-title":["Computers & Industrial Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0360835226003037?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0360835226003037?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T06:47:56Z","timestamp":1779518876000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0360835226003037"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":50,"alternative-id":["S0360835226003037"],"URL":"https:\/\/doi.org\/10.1016\/j.cie.2026.112102","relation":{},"ISSN":["0360-8352"],"issn-type":[{"value":"0360-8352","type":"print"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"An efficient reliability-based design optimization approach based on probability quantile estimation and structural constraint integration","name":"articletitle","label":"Article Title"},{"value":"Computers & Industrial Engineering","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cie.2026.112102","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"112102"}}