Abstract For more and more complicated engineering structures, it is a challenge to efficiently estimate the profust failure probability based on the probability inputs and fuzzy state assumption. By combining active learning Kriging with Monte Carlo simulation (AK-MCS), an efficient method is proposed to estimate the profust failure probability. Firstly, the profust failure probability is transformed into an integral of the classical failure probability by introducing a variable related to the fuzzy state assumption. This integral is further reorganized as a weighted sum of a series of classical failure probabilities by Gaussian quadrature, and the series of the classical failure probabilities have the similar limit state function constructions constrained by different thresholds. Secondly, MCS is used according to the probability input distribution to generate the sample pool, in which the active learning Kriging is used to establish the surrogates of the series of similar limit state functions with different thresholds. An improved learning function is proposed by minimizing the U-learning function minima corresponding to all limit state functions, so that the candidate with the largest effect on the surrogating quality of all limit states can be selected as a training point to update the Kriging model. Once the updating process of the Kriging model converges, all limit state functions can be identified by the Kriging model, and the profust failure probability can be estimated by using the Kriging model without any extra model evaluation. Several examples are used to demonstrate the feasibility of the proposed strategy for estimating the profust failure probability.

中文翻译：

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一种结合主动学习克里金法和蒙特卡洛模拟的有效方法，用于预测故障概率

摘要 对于越来越复杂的工程结构，基于概率输入和模糊状态假设有效地估计profust失效概率是一个挑战。通过将主动学习克里金法与蒙特卡罗模拟（AK-MCS）相结合，提出了一种有效的估计故障概率的方法。首先，通过引入与模糊状态假设相关的变量，将profust失效概率转化为经典失效概率的积分。该积分通过高斯求积被进一步重组为一系列经典失效概率的加权和，并且经典失效概率序列具有相似的受不同阈值约束的极限状态函数构造。第二，MCS根据概率输入分布生成样本池，其中使用主动学习克里金法建立具有不同阈值的一系列相似极限状态函数的代理。提出了一种改进的学习函数，通过最小化所有极限状态函数对应的U-learning函数最小值，从而可以选择对所有极限状态的替代质量影响最大的候选者作为训练点来更新克里金模型。一旦 Kriging 模型的更新过程收敛，Kriging 模型就可以识别出所有的极限状态函数，无需任何额外的模型评估，就可以使用 Kriging 模型来估计 profust 失效概率。