Propagation of epistemic uncertainty in the fragility function used for bayesian estimation of failure probability

Abstract eng:
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.

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