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Efficient evaluation of structural reliability under imperfect knowledge about probability distributions

机译：在不完善的概率分布知识下对结构可靠性进行有效评估

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摘要

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. (C) 2018 Elsevier Ltd. All rights reserved.
机译：我们在对随机变量的概率分布不完全了解的情况下调查结构可靠性的评估，重点是分布参数的不确定性。当考虑这些不确定性时，故障概率变为一个随机变量，称为条件故障概率。为了透明地传达风险，有必要确定条件失败概率的均值和分位数。提出了一种利用条件可靠性指标的概率分布来估计条件失效概率的分位数的新方法，该方法首先提出了一种基于二元降维积分的点估计方法来计算前三个矩（条件可靠性指标的平均值，标准差和偏度）。然后，通过三参数平方正态分布来近似条件可靠性指标的概率分布。数值研究表明，所提方法的计算效率远高于蒙特卡洛模拟方法，而没有损失精度，并且表明忽略参数不确定性会导致结构可靠性被高估。在不完善的概率分布知识下，开发的方法可以提供结构可靠性评估的完整信息。 （C）2018 Elsevier Ltd.保留所有权利。

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