000013135 001__ 13135
000013135 005__ 20161114160328.0
000013135 04107 $$aeng
000013135 046__ $$k2009-06-22
000013135 100__ $$aVaidogas E., R.
000013135 24500 $$aPropagation of epistemic uncertainty in the fragility function used for bayesian estimation of failure probability

000013135 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013135 260__ $$bNational Technical University of Athens, 2009
000013135 506__ $$arestricted
000013135 520__ $$2eng$$aAccidental (abnormal) actions are among the main causes of structural failures. In this paper an estimation of probability of structural failure due to an accidental action is considered. Two sources of evidence are applied to this estimation: a small-size statistical sample and a fragility function. This function expresses aleatory and epistemic uncertainties related to the potential failure. The estimation of the failure probability is based on Bayesian reasoning. Bayesian prior and posterior distributions are applied to express the epistemic uncertainty in the failure probability. The prior distribution is developed by propagating epistemic uncertainty inherent in the fragility function and, if necessary, values of demand variables. The posterior distribution is estimated by carrying out Bayesian updating with uncertain (imprecise) data. Such updating is considered a sort of uncertainty propagation. The uncertain data is expressed by a set of continuous epistemic probability distributions of fragility function values. The distributions are generated by inserting elements of the small-size sample into the fragility function which is uncertain in the epistemic sense. The Bayesian updating with the new data represented by the set of continuous distributions is carried out by discretizing these distributions. The discretization yields a new sample which is entered into the Bayes theorem through likelihood function. The sample created by the discretization consists of fragility function values which have equal epistemic weights. The proposed scheme of discretization is considered an alternative to a posterior averaging approach. This approach is suitable for Bayesian updating with uncertain data; however, it is applicable to the case where data uncertainty is modeled by discrete distributions of epistemic uncertainty. Several aspects of numerical implementation of the proposed discretization approach and subsequent updating are discussed and illustrated by an example.

000013135 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013135 653__ $$aFailure probability, Fragility, Small-size sample, Imprecise data, Epistemic uncertainty, Bayesian updating. Abstract. Accidental (abnormal) actions are among the main causes of structural failures. In this paper an estimation of probability of structural failure due to an accidental action is considered. Two sources of evidence are applied to this estimation: a small-size statistical sample and a fragility function. This function expresses aleatory and epistemic uncertainties related to the potential failure. The estimation of the failure probability is based on Bayesian reasoning. Bayesian prior and posterior distributions are applied to express the epistemic uncertainty in the failure probability. The prior distribution is developed by propagating epistemic uncertainty inherent in the fragility function and, if necessary, values of demand variables. The posterior distribution is estimated by carrying out Bayesian updating with uncertain (imprecise) data. Such updating is considered a sort of uncertainty propagation. The uncertain data is expressed by a set of continuous epistemic probability distributions of fragility function values. The distributions are generated by inserting elements of the small-size sample into the fragility function which is uncertain in the epistemic sense. The Bayesian updating with the new data represented by the set of continuous distributions is carried out by discretizing these distributions. The discretization yields a new sample which is entered into the Bayes theorem through likelihood function. The sample created by the discretization consists of fragility function values which have equal epistemic weights. The proposed scheme of discretization is considered an alternative to a posterior averaging approach. This approach is suitable for Bayesian updating with uncertain data; however, it is applicable to the case where data uncertainty is modeled by discrete distributions of epistemic uncertainty. Several aspects of numerical implementation of the proposed discretization approach and subsequent updating are discussed and illustrated by an example.

000013135 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013135 720__ $$aVaidogas E., R.$$iJuocevicius, V.
000013135 8560_ $$ffischerc@itam.cas.cz
000013135 8564_ $$s248003$$uhttps://invenio.itam.cas.cz/record/13135/files/CD183.pdf$$yOriginal version of the author's contribution as presented on CD, section: Statistical and probabilistic methods in computational mechanics to treat aleatory and epistemic uncertainties in structural and/or geotechnical systems and their loading environment - iii (MS).
000013135 962__ $$r13074
000013135 980__ $$aPAPER