{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T02:59:22Z","timestamp":1778641162103,"version":"3.51.4"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"S5","license":[{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"aviation science foundation for the aviation key laboratory of science and technology on life-support technology","award":["201929053001"],"award-info":[{"award-number":["201929053001"]}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51975473"],"award-info":[{"award-number":["51975473"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s00366-021-01484-7","type":"journal-article","created":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T06:02:30Z","timestamp":1627884150000},"page":"4367-4385","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters"],"prefix":"10.1007","volume":"38","author":[{"given":"Pan","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunyu","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuchao","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanyuan","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,2]]},"reference":[{"issue":"15","key":"1484_CR1","doi-asserted-by":"publisher","first-page":"4349","DOI":"10.1080\/03610926.2014.901369","volume":"45","author":"JC Fort","year":"2016","unstructured":"Fort JC, Klein T, Rachdi N (2016) New sensitivity analysis subordinated to contrast. Commun Stat Theory Methods 45(15):4349\u20134364","journal-title":"Commun Stat Theory Methods"},{"key":"1484_CR2","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1111\/0272-4332.00040","volume":"22","author":"S Andrea","year":"2002","unstructured":"Andrea S (2002) Sensitivity analysis for importance assessment. Risk Anal 22:579\u2013590","journal-title":"Risk Anal"},{"key":"1484_CR3","first-page":"101","volume":"59","author":"G Dellino","year":"2015","unstructured":"Dellino G, Meloni C (2015) Uncertainty management in simulation-optimization of complex systems: algorithms and applications. Oper Res 59:101\u2013122","journal-title":"Oper Res"},{"key":"1484_CR4","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1016\/j.ress.2015.05.018","volume":"142","author":"P Wei","year":"2015","unstructured":"Wei P, Lu Z, Song S (2015) Variable importance analysis: a comprehensive review. Reliab Eng Syst Saf 142:399\u2013432","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR5","first-page":"398","volume":"101","author":"A Saltelli","year":"2004","unstructured":"Saltelli A, Tarantola S, Campolongo F et al (2004) Sensitivity analysis in practice: a guide to assessing scientific models. J R Stat Soc Ser A 101:398\u2013399","journal-title":"J R Stat Soc Ser A"},{"key":"1484_CR6","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1016\/j.ress.2005.11.017","volume":"91","author":"JC Helton","year":"2006","unstructured":"Helton JC, Johnson JD, Sallaberry CJ et al (2006) Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91:1175\u20131209","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR7","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1016\/j.ress.2009.05.007","volume":"94","author":"CB Storlie","year":"2009","unstructured":"Storlie CB, Swiler LP, Helton JC et al (2009) Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models. Reliab Eng Syst Saf 94:1735\u20131763","journal-title":"Reliab Eng Syst Saf"},{"issue":"1","key":"1484_CR8","doi-asserted-by":"publisher","first-page":"90","DOI":"10.3390\/sym13010090","volume":"13","author":"S Song","year":"2021","unstructured":"Song S, Wang L (2021) A novel global sensitivity measure based on probability weighted moments. Symmetry 13(1):90","journal-title":"Symmetry"},{"issue":"2","key":"1484_CR9","doi-asserted-by":"publisher","first-page":"263","DOI":"10.3390\/sym13020263","volume":"13","author":"Z Kala","year":"2021","unstructured":"Kala Z (2021) Global sensitivity analysis of quantiles: new importance measure based on superquantiles and subquantiles. Symmetry 13(2):263","journal-title":"Symmetry"},{"issue":"2","key":"1484_CR10","doi-asserted-by":"publisher","first-page":"984","DOI":"10.1785\/0120160185","volume":"107","author":"C Molkenthin","year":"2017","unstructured":"Molkenthin C, Scherbaum F, Griewank A et al (2017) Derivative-based global sensitivity analysis: upper bounding of sensitivities in seismic-hazard assessment using automatic differentiation. Bull Seismol Soc Amer 107(2):984\u20131004","journal-title":"Bull Seismol Soc Amer"},{"key":"1484_CR11","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/j.ast.2015.11.019","volume":"48","author":"L Li","year":"2016","unstructured":"Li L, Lu Z, Chen C (2016) Moment-independent importance measure of correlated input variable and its state dependent parameter solution. Aerosp Sci Technol 48:281\u2013290","journal-title":"Aerosp Sci Technol"},{"issue":"2","key":"1484_CR12","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1080\/00401706.1991.10484804","volume":"33","author":"MD Morris","year":"2012","unstructured":"Morris MD (2012) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161\u2013174","journal-title":"Technometrics"},{"key":"1484_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ress.2016.07.014","volume":"156","author":"S Xiao","year":"2016","unstructured":"Xiao S, Lu Z, Xu L (2016) A new effective screening design for structural sensitivity analysis of failure probability with the epistemic uncertainty. Reliab Eng Syst Saf 156:1\u201314","journal-title":"Reliab Eng Syst Saf"},{"issue":"2","key":"1484_CR14","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/0951-8320(90)90065-U","volume":"28","author":"A Saltelli","year":"1990","unstructured":"Saltelli A, Marivoet J (1990) Non-parametric statistics in sensitivity analysis for model output: a comparison of selected techniques. Reliab Eng Syst Saf 28(2):229\u2013253","journal-title":"Reliab Eng Syst Saf"},{"issue":"6","key":"1484_CR15","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1016\/j.ress.2006.04.015","volume":"92","author":"E Borgonovo","year":"2007","unstructured":"Borgonovo E (2007) A new uncertainty importance measure. Reliab Eng Syst Saf 92(6):771\u2013784","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR16","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1111\/rssb.12052","volume":"76","author":"E Borgonovo","year":"2014","unstructured":"Borgonovo E, Tarantola S, Plischke E et al (2014) Transformations and invariance in the sensitivity analysis of computer experiments. J R Stat Soc Ser B 76:925\u2013947","journal-title":"J R Stat Soc Ser B"},{"key":"1484_CR17","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.envsoft.2012.04.017","volume":"38","author":"W Castaings","year":"2012","unstructured":"Castaings W, Borgonovo E, Morris MD et al (2012) Sampling strategies in density-based sensitivity analysis. Environ Modell Softw 38:13\u201326","journal-title":"Environ Modell Softw"},{"issue":"2","key":"1484_CR18","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1137\/15M1025621","volume":"6","author":"F Gamboa","year":"2018","unstructured":"Gamboa F, Klein T, Lagnoux A (2018) Sensitivity analysis based on cramer-von mises distance. SIAM\/ASA J Uncertain Quantif 6(2):522\u2013548","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"issue":"1","key":"1484_CR19","first-page":"53","volume":"47","author":"Q Liu","year":"2012","unstructured":"Liu Q, Homma T (2012) A new importance measure for sensitivity analysis. Taylor & Francis Group 47(1):53\u201361","journal-title":"Taylor & Francis Group"},{"key":"1484_CR20","doi-asserted-by":"publisher","first-page":"1200","DOI":"10.1080\/00949655.2013.873039","volume":"85","author":"P Lema\u00eetre","year":"2015","unstructured":"Lema\u00eetre P, Sergienko E, Arnaud A et al (2015) Density modification-based reliability sensitivity analysis. J Stat Comput Simul 85:1200\u20131223","journal-title":"J Stat Comput Simul"},{"key":"1484_CR21","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.envsoft.2013.05.003","volume":"47","author":"P Wei","year":"2013","unstructured":"Wei P, Lu Z, Wu D et al (2013) Moment-independent regional sensitivity analysis: application to an environmental model. Environ Modell Softw 47:55\u201363","journal-title":"Environ Modell Softw"},{"key":"1484_CR22","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.probengmech.2015.04.003","volume":"41","author":"G Greegar","year":"2015","unstructured":"Greegar G, Manohar CS (2015) Global response sensitivity analysis using probability distance measures and generalization of Sobol\u2019s analysis. Probabilistic Eng Mech 41:21\u201333","journal-title":"Probabilistic Eng Mech"},{"issue":"3\u20135","key":"1484_CR23","doi-asserted-by":"publisher","first-page":"390","DOI":"10.3846\/jcem.2018.5194","volume":"24","author":"J Stefanak","year":"2018","unstructured":"Stefanak J, Kala Z, Mica L et al (2018) Global sensitivity analysis for transformation of Hoek-Brown failure criterion for rock mass. J Civ Eng Manag 24(3\u20135):390\u2013398","journal-title":"J Civ Eng Manag"},{"key":"1484_CR24","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s40999-018-0302-3","volume":"17","author":"E Mahmoudi","year":"2019","unstructured":"Mahmoudi E, Holter R, Georgieva R, Konig M, Schanz T (2019) On the global sensitivity analysis methods in geotechnical engineering: a comparative study on a rock salt energy storage. Int J Civ Eng 17:131\u2013143","journal-title":"Int J Civ Eng"},{"key":"1484_CR25","doi-asserted-by":"publisher","first-page":"113656","DOI":"10.1016\/j.compstruct.2021.113656","volume":"263","author":"P Pitchai","year":"2021","unstructured":"Pitchai P, Jha NK, Nair RG, Guruprasad PJ (2021) A coupled framework of variational asymptotic method based homogenization technique and Monte Carlo approach for the uncertainty and sensitivity analysis of unidirectional composites. Compos Struct 263:113656","journal-title":"Compos Struct"},{"key":"1484_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-021-02909-z","author":"YZ Ma","year":"2021","unstructured":"Ma YZ, Li HS, Zhao ZZ (2021) Reliability sensitivity analysis of thermal protection system. Struct Multidiscip Optim. https:\/\/doi.org\/10.1007\/s00158-021-02909-z","journal-title":"Struct Multidiscip Optim"},{"key":"1484_CR27","doi-asserted-by":"publisher","DOI":"10.1109\/ICECTT50890.2020.00011","author":"Z Yang","year":"2020","unstructured":"Yang Z, Unsong P, Zhao H (2020) Reliability sensitivity analysis of stochastic resonance failure of vehicle drum brake. ICECTT. https:\/\/doi.org\/10.1109\/ICECTT50890.2020.00011","journal-title":"ICECTT"},{"issue":"11","key":"1484_CR28","doi-asserted-by":"publisher","first-page":"4788","DOI":"10.3390\/su12114788","volume":"12","author":"Z Kala","year":"2020","unstructured":"Kala Z (2020) Sensitivity analysis in probabilistic structural design: a comparison of selected techniques. Sustainability 12(11):4788","journal-title":"Sustainability"},{"key":"1484_CR29","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1007\/s11431-009-0386-8","volume":"53","author":"LJ Cui","year":"2010","unstructured":"Cui LJ, Lu ZZ, Zhao XP (2010) Moment-independent importance measure of basic random variable and its probability density evolution solution. Sci China Technol Sci 53:1138\u20131145","journal-title":"Sci China Technol Sci"},{"key":"1484_CR30","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.strusafe.2012.04.001","volume":"38","author":"L Li","year":"2012","unstructured":"Li L, Lu Z, Jun F et al (2012) Moment-independent importance measure of basic variable and its state dependent parameter solution. Struct Saf 38:40\u201347","journal-title":"Struct Saf"},{"key":"1484_CR31","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.ast.2017.09.009","volume":"71","author":"S Xiao","year":"2017","unstructured":"Xiao S, Lu Z (2017) Structural reliability sensitivity analysis based on classification of model output. Aerosp Sci Technol 71:52\u201361","journal-title":"Aerosp Sci Technol"},{"key":"1484_CR32","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.ress.2012.09.005","volume":"110","author":"P Wei","year":"2013","unstructured":"Wei P, Lu Z, Yuan X (2013) Monte Carlo simulation for moment-independent sensitivity analysis. Reliab Eng Syst Saf 110:60\u201367","journal-title":"Reliab Eng Syst Saf"},{"issue":"8","key":"1484_CR33","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1016\/j.cpc.2012.03.014","volume":"183","author":"P Wei","year":"2012","unstructured":"Wei P, Lu Z, Hao W et al (2012) Efficient sampling methods for global reliability sensitivity analysis. Comput Phys Commun 183(8):1728\u20131743","journal-title":"Comput Phys Commun"},{"key":"1484_CR34","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.jhydrol.2004.11.015","volume":"309","author":"B Merz","year":"2005","unstructured":"Merz B, Thieken AH (2005) Separating natural and epistemic uncertainty in flood frequency analysis. J Hydrol 309:114\u2013132","journal-title":"J Hydrol"},{"key":"1484_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ress.2004.03.001","volume":"85","author":"JC Helton","year":"2004","unstructured":"Helton JC (2004) Alternative representations of epistemic uncertainty. Reliab Eng Syst Saf 85:1\u201310","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR36","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1016\/j.ress.2010.11.010","volume":"96","author":"MS Eldred","year":"2011","unstructured":"Eldred MS, Swiler LP, Tang G (2011) Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation. Reliab Eng Syst Saf 96:1092\u20131113","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ress.2004.03.001","volume":"85","author":"JC Helton","year":"2004","unstructured":"Helton JC, Oberkampf WL (2004) Alternative representations of epistemic uncertainty. Reliab Eng Syst Saf 85:1\u201310","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR38","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1016\/j.jhydrol.2011.12.027","volume":"420","author":"S Sun","year":"2012","unstructured":"Sun S, Fu G, Djordjevic S et al (2012) Separating aleatory and epistemic uncertainties: probabilistic sewer flooding evaluation using probability box. J Hydrol 420:360\u2013372","journal-title":"J Hydrol"},{"key":"1484_CR39","doi-asserted-by":"publisher","first-page":"1114","DOI":"10.1016\/j.ress.2010.08.010","volume":"96","author":"A Urbina","year":"2011","unstructured":"Urbina A, Mahadevan S, Paez TL (2011) Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty. Reliab Eng Syst Saf 96:1114\u20131125","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR40","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.apm.2017.03.012","volume":"47","author":"P Wang","year":"2017","unstructured":"Wang P, Lu ZZ, Xiao SN (2017) A generalized separation for the variance contributions of input variables and their distribution parameters. Appl Math Model 47:381\u2013399","journal-title":"Appl Math Model"},{"issue":"10","key":"1484_CR41","doi-asserted-by":"publisher","first-page":"2244","DOI":"10.1016\/j.simpat.2011.08.003","volume":"19","author":"J Morio","year":"2011","unstructured":"Morio J (2011) Influence of input PDF parameters of a model on a failure probability estimation. Simul Model Pract Theory 19(10):2244\u20132255","journal-title":"Simul Model Pract Theory"},{"key":"1484_CR42","doi-asserted-by":"publisher","first-page":"1210","DOI":"10.1016\/j.ress.2005.11.019","volume":"91","author":"B Krzykacz-Hausmann","year":"2006","unstructured":"Krzykacz-Hausmann B (2006) An approximate sensitivity analysis of results from complex computer models in the presence of epistemic and aleatory uncertainties. Reliab Eng Syst Saf 91:1210\u20131218","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR43","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/S0951-8320(02)00056-X","volume":"77","author":"E Hofer","year":"2002","unstructured":"Hofer E, Kloos M, Krzykacz-Hausmann B et al (2002) An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties. Reliab Eng Syst Saf 77:229\u2013238","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR44","doi-asserted-by":"publisher","first-page":"6543","DOI":"10.1016\/j.apm.2013.01.019","volume":"37","author":"P Wang","year":"2013","unstructured":"Wang P, Lu Z, Tang Z (2013) An application of the kriging method in global sensitivity analysis with parameter uncertainty. Appl Math Model 37:6543\u20136555","journal-title":"Appl Math Model"},{"issue":"4","key":"1484_CR45","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1016\/j.camwa.2013.06.001","volume":"66","author":"P Wang","year":"2013","unstructured":"Wang P, Lu ZZ, Tang ZC (2013) Importance measure analysis with epistemic uncertainty and its moving least squares solution. Comput Math Appl 66(4):460\u2013471","journal-title":"Comput Math Appl"},{"key":"1484_CR46","doi-asserted-by":"publisher","first-page":"1232","DOI":"10.1016\/j.ress.2010.07.014","volume":"96","author":"S Sankararaman","year":"2011","unstructured":"Sankararaman S, Mahadevan S (2011) Model validation under epistemic uncertainty. Reliab Eng Syst Saf 96:1232\u20131241","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR47","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.ress.2012.11.024","volume":"112","author":"S Sankararaman","year":"2013","unstructured":"Sankararaman S, Mahadevan S (2013) Separating the contributions of variability and parameter uncertainty in probability distributions. Reliab Eng Syst Saf 112:187\u2013199","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR48","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1016\/j.ast.2017.07.016","volume":"69","author":"V Chabridon","year":"2017","unstructured":"Chabridon V, Balesdent M, Bourinet J-M et al (2017) Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment. Aerosp Sci Technol 69:526\u2013537","journal-title":"Aerosp Sci Technol"},{"key":"1484_CR49","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.ress.2018.06.008","volume":"178","author":"V Chabridon","year":"2018","unstructured":"Chabridon V, Balesdent M, Perrin G, Morio J, Bourinet J-M, Gayton N (2018) Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty. Reliab Eng Syst Saf 178:164\u2013178","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR50","doi-asserted-by":"publisher","DOI":"10.1002\/9781119817635.ch7","volume-title":"Global reliability-oriented sensitivity analysis under distribution parameter uncertainty","author":"V Chabridon","year":"2021","unstructured":"Chabridon V, Balesdent M, Perrin G et al (2021) Global reliability-oriented sensitivity analysis under distribution parameter uncertainty. Wiley, Hoboken"},{"issue":"1","key":"1484_CR51","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s10910-011-9898-0","volume":"50","author":"G Li","year":"2012","unstructured":"Li G, Rabitz H (2012) General formulation of HDMR component functions with independent and correlated variables. J Math Chem 50(1):99\u2013130","journal-title":"J Math Chem"},{"key":"1484_CR52","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.strusafe.2011.01.002","volume":"33","author":"B Echard","year":"2011","unstructured":"Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining kriging and Monte Carlo simulation. Struct Saf 33:145\u2013154","journal-title":"Struct Saf"},{"key":"1484_CR53","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/j.ress.2012.10.008","volume":"111","author":"B Echard","year":"2013","unstructured":"Echard B, Gayton N, Lemaire M et al (2013) A combined Importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models. Reliab Eng Syst Saf 111:232\u2013240","journal-title":"Reliab Eng Syst Saf"},{"key":"1484_CR54","doi-asserted-by":"publisher","first-page":"2459","DOI":"10.2514\/1.34321","volume":"46","author":"BJ Bichon","year":"2012","unstructured":"Bichon BJ, Eldred MS, Swiler LP et al (2012) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46:2459\u20132468","journal-title":"AIAA J"},{"key":"1484_CR55","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.precisioneng.2012.07.007","volume":"37","author":"A Dumas","year":"2013","unstructured":"Dumas A, Echard B, Gayton N et al (2013) AK-ILS: an active learning method based on kriging for the inspection of large surfaces. Precis Eng 37:1\u20139","journal-title":"Precis Eng"},{"key":"1484_CR56","doi-asserted-by":"publisher","DOI":"10.1109\/ISUMA.1990.151285","author":"T Ishigami","year":"1990","unstructured":"Ishigami T, Homma T (1990) An importance quantification technique in uncertainty analysis for computer models, international symposium on uncertainty modeling & analysis. IEEE Xplore. https:\/\/doi.org\/10.1109\/ISUMA.1990.151285","journal-title":"IEEE Xplore"},{"key":"1484_CR57","doi-asserted-by":"publisher","first-page":"1182","DOI":"10.1016\/j.camwa.2015.07.004","volume":"70","author":"Z Lv","year":"2015","unstructured":"Lv Z, Lu Z, Wang P (2015) A new learning function for kriging and its applications to solve reliability problems in engineering. Comput Math Appl 70:1182\u20131197","journal-title":"Comput Math Appl"},{"key":"1484_CR58","doi-asserted-by":"publisher","first-page":"113336","DOI":"10.1016\/j.cma.2020.113336","volume":"372","author":"NC Xiao","year":"2020","unstructured":"Xiao NC, Zhan HY, Kai Y (2020) A new reliability method for small failure probability problems by combining the adaptive importance sampling and surrogate models. Comput Math Appl Mech Eng 372:113336","journal-title":"Comput Math Appl Mech Eng"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-021-01484-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-021-01484-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-021-01484-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,5]],"date-time":"2023-02-05T12:11:05Z","timestamp":1675599065000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-021-01484-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,2]]},"references-count":58,"journal-issue":{"issue":"S5","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["1484"],"URL":"https:\/\/doi.org\/10.1007\/s00366-021-01484-7","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,2]]},"assertion":[{"value":"3 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}