基于β面的截断重要抽样法可以用来求解单失效模式可靠性灵敏度.该方法在设计点处作失效面的虚拟切面β面,而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区域对可靠性灵敏度的贡献来分配,并通过迭代模拟计算来得到.本文推导了基于β面截断重要抽样法的可靠性灵敏度估计值方差和变异系数的计算公式,并将该方法推广应用到并联系统中.算例结果表明:在估计值相对误差小于2%、可靠性灵敏度估计值变异系数相同时,基于β面的截断重要抽样法的可靠性灵敏度估计所需的样本数比传统重要抽样法、β球截断重要抽样法计算量少.%A novel β hyper-plane based importance sampling method is presented to estimate reliability sensitivity of a structure. By introducing a virtual hyper-plane tangent to the failure surface, the variable space is separated into an importance region R and a 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 contribution of the reliability sensitivity, which is determined by the iterative simulations. The formulae of the reliability sensitivity 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 reliability sensitivity estimation of both the single failure mode and the multiple failure mode in parallel. Examples show that the proposed method is more efficient than the traditional importance sampling method and the β hyper-sphere importance sampling method, in the case that the variation coefficients of three estimations keep the same quantity and the relative errors of the reliability sensitivity estimations are less than 2％.
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