区域和参数化可靠性灵敏度指标及其解法

New regional and parametric reliability sensitivities and their computational methods

针对基于方差的全局可靠性灵敏度指标,分别提出基于方差的区域和参数化可靠性灵敏度指标,以衡量输入变量的取值区域发生变化时或输入变量的方差减小时整个输入变量系统对失效概率不确定性贡献的变化情况。然后从Pearson相关系数的视角分别将所提指标表述成无条件失效域指示函数与固定某一随机输入时的条件失效域指示函数之间的相关系数。在此转换的基础上,提出基于Pearson相关系数的两种求解方法,一种采用蒙特卡洛方法重复抽样进行循环计算,另一种借鉴重要抽样的思想。功能函数的计算样本可重复使用而不增加任何额外的计算代价,故后者大大提高了求解所提区域和参数化灵敏度指标的计算效率。算例结果验证了所提指标的合理性,同时也证明了所提方法的准确性与高效性。

Based on the variance-based global reliability sensitivity index, new regional and parametric sensitivity indices were defined respectively to measure how the sensitivity indices of the whole inputs change when the distribution range of one input is changed or its variance is decreased. Then these two proposed indices were described by PCC （ Pearson correlation coefficient） between the unconditional failure indicator and its pick-frozen replication. Based on the transformation, two methods based on PCC were proposed to compute the proposed regional and parametric sensitivity indices. One method was based on Monte Carlo method and iterating sampling, whereas the other one was based on IS （importance sampling） and reusing the samples without extra computational cost, so the computational efficiency of the second method was much higher. The feasibility of the proposed regional and parametric indices, the accuracy and high efficiency of the proposed methods were demonstrated by the results of several examples.