基于密度权重的可靠性灵敏度分析方法

为了提高可靠性灵敏度求解数字模拟法的效率，提出了一种变量空间确定性低偏差均匀抽样与样本点处联合概率密度函数构造权重相结合的方法，来估计可靠性灵敏度。该方法通过均匀样本点处联合概率密度函数的权重保证了可靠性灵敏度的估计值收敛于真值，而由低偏差抽样代替原问题中的联合概率密度抽样则可以保证更低的误差阶以及在小失效概率条件下抽得的样本有更高的可能性落入失效域，从而保证了所提方法具有更高的收敛速度。另外，所提方法可以采用与独立变量相同的步骤来估计相关变量情况下的可靠性灵敏度，计算简便，适用范围广。算例充分证明了所提方法的优越性。

Reliability Sensitivity Analysis Method Based on Weight Index of Density

In order to improve the efficiency of digital simulation in approximating reliability sensitivity, a method is proposed which works by generating deterministic and low-discrepancy samples uniformly in the design space and applying the value of joint probability density function as a weight index at any sample. The weight indexes ensure the estimated values of the reliability sensitivity are converged to the true values. This way of getting points by low-discrepancy sampling instead of depending on a variable's probability density can ensure smaller error bounds and a higher possibility for the samples to fall into failure domain, so that the convergence speed becomes much higher for small failure probability events. Additionally, the steps to calculate the reliability sensitivity with related variables are the same as those with independent variables, which is another advantage that makes the method simpler and easily applicable. Several examples in this paper demonstrate the advantages of the proposed method sufficiently.