An efficient reliability evaluation method involving correlated random variables under distribution parameter uncertainty

To fully describe the safety of the structure involving correlated random variables under the distribution parameter uncertainty, it is necessary to obtain not only the mean value of the conditional failure probability, but also to grasp its complete probability characteristics. Due to the large variability of the conditional failure probability, it is difficult to directly use an explicit function to fit its probability distribution. Therefore, the focus of this paper is to first approximate the distribution of the conditional reliability index involving correlated random variables, and then obtain the quantile of the conditional failure probability in form of an explicit formula. For this purpose, the limit state function involving the correlated random variables should be first transformed into the standard normal space based on the three-parameter lognormal transformation, and then the first-three central moments of the conditional reliability index can be calculated by combining the bivariate dimensionreduction integration method combined with the point-estimate method, so that the distribution of the conditional reliability index can be obtained. Finally, an explicit expression of the quantile values of the conditional failure probability can be derived from the distribution of the corresponding conditional reliability index. Two illustrative examples show that the results obtained from the proposed method are almost similar to those of the Monte Carlo simulations, and the proposed method has a wide range of applications.