论文标题
通过本地子集近似值估计故障概率
Estimation of Failure Probabilities via Local Subset Approximations
论文作者
论文摘要
我们在这里考虑使用嵌套中间故障事件的减小序列接近故障事件的子集仿真方法。该方法类似于重要性抽样，它通过使用Markov Chain Monte Carlo（MCMC）算法对先前评估进行下一次评估来积极探索概率空间。马尔可夫链通常需要许多步骤来估计目标分布，这对于昂贵的数值模型是不切实际的。因此，我们建议使用高斯过程（GP）回归局部近似马尔可夫链的每个步骤。基准的可靠性分析示例表明，局部近似显着提高了子集仿真的总体效率。他们将昂贵的限额评估的数量减少超过$ 80 \％$。但是，随着维度的增加，GP回归在计算上不切实际。因此，为了使我们使用GP可行，我们采用了部分最小二乘（PLS）回归，这是一种无梯度还原方法，在本地探索和利用马尔可夫链中的低维子空间。数值实验说明了具有足够准确性的显着计算增益。
We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by conditioning the next evaluation on the previous evaluations using a Markov chain Monte Carlo (MCMC) algorithm. A Markov chain typically requires many steps to estimate the target distribution, which is impractical with expensive numerical models. Therefore, we propose to approximate each step of a Markov chain locally with Gaussian process (GP) regression. Benchmark examples of reliability analysis show that local approximations significantly improve overall efficiency of subset simulation. They reduce the number of expensive limit-state evaluations by over $80\%$. However, GP regression becomes computationally impractical with increasing dimension. Therefore, to make our use of a GP feasible, we employ the partial least squares (PLS) regression, a gradient-free reduction method, locally to explore and utilize a low-dimensional subspace within a Markov chain. Numerical experiments illustrate a significant computational gain with maintained sufficient accuracy.
