To reduce the cost of estimating the probability of a rare event involving a very large number of random parameters, we propose a new strategy for dimension reduction coupled with a surrogate model for the expensive part of the algorithm. To this end, we extend the Ordinary Kriging Active Subspace (OK-AS) method into a sequential version. Our approach consists of iteratively re-estimating the active subspace using a Kriging surrogate trained in a rotated coordinate system until the active subspace stabilises. This method allows for a reduction in prediction error and a better approximation of the active subspace on a benchmark of test problems. Furthermore, we integrate our algorithm into an efficient pre-existing approach for estimating the probability of a rare event. This approach is based on learning the active subspace associated with the random event whose probability is to be estimated. The sequential learning of an importance sampling density is necessary and corresponds to the expensive part of this strategy. To circumvent this issue, we integrate our sequential OK-AS version into the estimation of the importance sampling density. The numerical results indicate that our method allows for reducing the cost required to obtain a precise estimate of the rare event probability.

翻译：为降低涉及大量随机参数的稀有事件概率估计的计算成本，我们提出一种新的降维策略，并将其与代理模型相结合以处理算法中的昂贵部分。为此，我们将普通克里金主动子空间（OK-AS）方法扩展为序贯版本。该方法通过旋转坐标系下训练的克里金代理迭代重新估计主动子空间，直至主动子空间趋于稳定。在测试问题基准上，该方法能降低预测误差，并更精确地逼近主动子空间。进一步地，我们将该算法集成到一种高效的稀有事件概率估计预存方法中。该预存方法通过学习与待估概率随机事件相关的主动子空间实现降维。其中，重要性采样密度的序贯学习是必要环节，且对应于该策略中的昂贵部分。为解决此问题，我们将序贯OK-AS版本集成到重要性采样密度的估计中。数值结果表明，该方法能有效降低精确估计稀有事件概率所需的计算成本。