基于β面的截断重要抽样法

A novel β hyper-plane based importance sampling method

提出一种基于β面的截断重要抽样法求解结构单失效模式的失效概率。该方法通过在设计点处作失效面的虚拟切面-β面,将变量空间分割成重要抽样区域R和非重要抽样区域S。在R和S区域分别建立相应的截断重要抽样密度函数hR(x)和hS(x),从hR(x)和hS(x)中抽取的样本量按照R和S区域对失效概率的贡献来分配,由迭代模拟计算得到。推导了基于β面截断重要抽样法的失效概率估计值的方差和变异系数计算公式,该方法还可推广应用到并联系统中。算例结果表明,在相同的计算精度下,基于β面的截断重要抽样法所需的样本数比传统重要抽样法计算量少。

A novel β hyper-plane based importance sampling method is presented to estimate failure probability of structure.Based on β section,a virtual hyper-plane tangent to the failure surface,the variable space is separated into the importance region R and the unimportance region S,on which the truncated importance sampling functions hR（x） and hS（x） are established respectively.The sampling numbers generated from hR（x） and hS（x） are dependent on the contributions of R and S to the failure probability,and they are determined by the iterative simulations.The formulae of the failure probability estimation,the variance and the coefficient of variation are derived for the presented β hyper-plane importance sampling method.The presented method is suitable for the failure probability estimation of both a single failure mode and multiple failure modes in parallel.The examples show that the presented method is more efficient than the traditional importance sampling method.