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An efficient method combining active learning Kriging and Monte Carlo simulation for profust failure probability

机译：主动学习Kriging和Monte Carlo模拟相结合的有效方法来确定失败概率

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摘要

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. (C) 2019 Elsevier B.V. All rights reserved.
机译：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来有效估计profust失效概率是一个挑战。通过将主动学习克里格法与蒙特卡洛模拟（AK-MCS）相结合，提出了一种有效的方法来估计profust失败概率。首先，通过引入与模糊状态假设有关的变量，将过去的失败概率转换为经典失败概率的整数。该积分通过高斯正交进一步重组为一系列经典失效概率的加权和，并且一系列经典失效概率具有受不同阈值约束的相似极限状态函数构造。其次，根据概率输入分布使用MCS生成样本池，其中主动学习Kriging用于建立一系列具有不同阈值的相似极限状态函数的替代。通过最小化与所有极限状态函数相对应的U学习函数最小值，提出了一种改进的学习函数，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作为训练点来更新克里格模型。一旦Kriging模型的更新过程收敛，就可以通过Kriging模型识别所有极限状态函数，并且可以通过使用Kriging模型来估计发生失效的可能性，而无需进行任何额外的模型评估。几个例子被用来证明所提出的策略来估计profust失败概率的可行性。 （C）2019 Elsevier B.V.保留所有权利。

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