An effective and efficient method for structural reliability considering the distributional parametric uncertainty

Abstract

In this study, the assessment of structural reliability considering distributional parametric uncertainty is investigated. If uncertainties of distribution parameters are considered in the evaluation of structural reliability, then the traditional failure probability turns into a random variable, which is defined as the conditional probability of failure. Correspondingly, the relevant reliability index is defined as the conditional reliability index. For the transparency of risk assessment, the Smolyak-type quadrature formula is first adopted to evaluate the expected value of the conditional probability of failure. Then, a new method constructed by integrating the Smolyak-type quadrature formula with the cubic normal distribution is used to determine the percentile value of the conditional probability of failure, which mainly included three steps: (1) the first four statistical moments of the conditional reliability index are estimated utilizing the Smolyak-type quadrature formula; (2) the probability density function of the conditional reliability index is fitted through the cubic normal distribution; and finally, the percentile value of the conditional probability of failure is determined from the cumulative distribution function of the conditional reliability index. Three illustrative examples are given to verify the efficiency and accuracy of the proposed method, in which Monte Carlo simulations are used as a benchmark for comparison study.