It has been recognized that the uncertainty of distribution parameters has a significant effect on the outcome of structural reliability analysis. In this study, an efficient and accurate method is proposed to fully quantify failure probability, considering the uncertainty of the distribution parameters. This method obtains predictive failure probability by integrating the probability space of the conditional reliability index instead of directly utilizing the point-estimate method on the conditional failure probability as in previous studies. In the proposed method, a three-parameter lognormal distribution is suggested to approach the distribution of the conditional reliability index. The first three central moments of the conditional reliability index are estimated utilizing the point-estimate method combined with the bivariate dimension-reduction method. Based on this, the analytical solutions for the quantiles and probability distribution of the conditional failure probability can be readily derived without redundant calculations. Four illustrative examples were investigated to verify the efficiency and accuracy of the proposed method. The results show that the proposed method produces sufficiently accurate results in an efficient and simple way. It also presents a complete picture of the structural reliability evaluation results considering distribution parameter uncertainty in a wide range of applications.

已经认识到分布参数的不确定性对结构可靠性分析的结果有显着影响。在这项研究中，考虑到分布参数的不确定性，提出了一种有效且准确的方法来充分量化失效概率。该方法通过对条件可靠性指标的概率空间进行积分来获得预测失效概率，而不是像以往的研究那样直接利用条件失效概率的点估计方法。在所提出的方法中，三参数对数正态分布建议接近条件可靠性指数的分布。条件可靠性指标的前三个中心矩是利用点估计方法结合二元降维方法估计的。在此基础上，可以很容易地推导出条件失效概率的分位数和概率分布的解析解，而无需进行冗余计算。研究了四个说明性示例，以验证所提出方法的效率和准确性。结果表明，所提出的方法以一种有效且简单的方式产生了足够准确的结果。它还提供了在广泛应用中考虑分布参数不确定性的结构可靠性评估结果的全貌。