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Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability

机译:主动学习Kriging结合基于方差减少的采样方法的有效方法,用于与时间有关的故障概率

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摘要

For efficiently estimating the time-dependent failure probability, two new methods named as the active learning Kriging (AK) coupled with importance sampling (AK-co-IS) and AK coupled with subset simulation (AK-co-SS) are proposed. The proposed methods are based on the fact that the AK coupled with Monte Carlo simulation (AKMCS) method has been proved to be a very efficient method. However, for problem with small time-dependent failure probability or long service time, the size of candidate sample pool generated by MCS would be so large that the efficiency of AK-MCS is reduced. Therefore, the AK-co-IS and AK-co-SS are proposed to highly enhance the computational efficiency by greatly reducing the candidate sample pool size. And these two methods reduce the candidate sample pool size respectively by searching the optimal time-dependent design point to increase the ratio of failure samples and converting a rare event simulation problem into sequence of more frequent event ones. Through iteratively constructing the AK model to be convergent by the U-learning function in the IS and SS sample pools, respectively, the computational cost of estimating the time-dependent failure probability would reduce drastically compared with AK-MCS. Several examples are used to illustrate the efficiency and accuracy of the proposed methods.
机译:为了有效地估计与时间有关的故障概率,提出了两种新方法,分别称为主动学习克里格(AK)结合重要性采样(AK-co-IS)和AK结合子集模拟(AK-co-SS)。所提出的方法基于以下事实:已证明AK与蒙特卡洛模拟(AKMCS)方法相结合是一种非常有效的方法。但是,对于时间依赖性失败概率较小或服务时间较长的问题,由MCS生成的候选样本池的大小将太大,以致AK-MCS的效率降低。因此,提出了AK-co-IS和AK-co-SS通过大大减小候选样本池大小来高度提高计算效率。这两种方法分别通过搜索最佳时变设计点以增加故障样本的比例并将稀有事件模拟问题转换为频率更高的事件序列来分别减小候选样本池的大小。通过分别在IS和SS样本池中迭代构造AK模型以通过U学习函数收敛,与AK-MCS相比,估计与时间有关的故障概率的计算成本将大大降低。几个例子用来说明所提出方法的效率和准确性。

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