Efficient evaluation of structural reliability under imperfect knowledge about probability distributions

We investigate the evaluation of structural reliability under imperfect knowledge about the probability distributions of random variables, with emphasis on the uncertainties of the distribution parameters. When these uncertainties are considered, the failure probability becomes a random variable that is referred to as the conditional failure probability. For the sake of transparency in communicating risk, it is necessary to determine not only the mean but also the quantile of the conditional failure probability. A novel method is proposed for estimating the quantile of the conditional failure probability by using the probability distribution of the corresponding conditional reliability index, in which a point-estimate method based on bivariate dimension-reduction integration is first suggested to compute the first three moments (i.e., mean, standard deviation and skewness) of the conditional reliability index. The probability distribution of the conditional reliability index is then approximated by a three-parameter square normal distribution. Numerical studies show that the computational efficiency of the proposed method was well above that of Monte Carlo simulations without loss of accuracy, and also show that neglecting parameter uncertainties will lead to the structural reliability being overestimated. The developed methodology provides a complete picture of structural reliability evaluation under imperfect knowledge about probability distributions.