An efficient Bayesian updating framework for characterizing the posterior failure probability

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dc.contributor.authorLi, Pei-Pei
dc.contributor.authorZhao, Yan-Gang
dc.contributor.authorDang, Chao
dc.contributor.authorBroggi, Matteo
dc.contributor.authorValdebenito, Marcos A.
dc.contributor.authorFaes, Matthias G. R.
dc.date.accessioned2025-11-20T08:26:50Z
dc.date.available2025-11-20T08:26:50Z
dc.date.issued2024-08-06
dc.description.abstractBayesian updating plays an important role in reducing epistemic uncertainty and making more reliable predictions of the structural failure probability. In this context, it should be noted that the posterior failure probability conditional on the updated uncertain parameters becomes a random variable itself. Hence, characterizing the statistical properties of the posterior failure probability is important, yet challenging task for risk-based decision-making. In this study, an efficient framework is proposed to fully characterize the statistical properties of the posterior failure probability. The framework is based on the concept of Bayesian updating and keeps the effect of aleatory and epistemic uncertainty separated. To improve the efficiency of the proposed framework, a weighted sparse grid numerical integration is suggested to evaluate the first three raw moments of the corresponding posterior reliability index. This enables the reuse of evaluation results stemming from previous analyses. In addition, the proposed framework employs the shifted lognormal distribution to approximate the probability distribution of the posterior reliability index, from which the mean, quantile, and even the distribution of the posterior failure probability can be easily obtained in closed form. Four examples illustrate the efficiency and accuracy of the proposed method, and results generated with Markov Chain Monte Carlo combined with plain Monte Carlo simulation are employed as a reference.en
dc.identifier.urihttp://hdl.handle.net/2003/44266
dc.language.isoen
dc.relation.ispartofseriesMechanical systems and signal processing; 222
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.subjectBayesian updatingen
dc.subjectPosterior failure probabilityen
dc.subjectSparse grid numerical integrationen
dc.subjectShifted lognormal distributionen
dc.subject.ddc620
dc.subject.rswkBayes-Verfahren
dc.subject.rswkAusfallwahrscheinlichkeit
dc.subject.rswkNumerische Integration
dc.subject.rswkDünnes Gitter
dc.subject.rswkLogarithmische Normalverteilung
dc.titleAn efficient Bayesian updating framework for characterizing the posterior failure probabilityen
dc.typeText
dc.type.publicationtypeArticle
dcterms.accessRightsopen access
eldorado.dnb.deposittrue
eldorado.doi.registerfalse
eldorado.secondarypublicationtrue
eldorado.secondarypublication.primarycitationPei-Pei Li, Yan-Gang Zhao, Chao Dang, Matteo Broggi, Marcos A. Valdebenito, Matthias G.R. Faes, An efficient Bayesian updating framework for characterizing the posterior failure probability, Mechanical Systems and Signal Processing, Volume 222, 2025, 111768, https://doi.org/10.1016/j.ymssp.2024.111768
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1016/j.ymssp.2024.111768

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