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可靠性全局灵敏度指标能够有效地分析输入变量的不确定性对结构系统失效概率的影响程度,为提高该灵敏度指标求解数字模拟法的效率,提出了一种基于密度权重及连续无重叠区间全方差公式的空间分割高效方法。所提方法通过连续无重叠区间上的全方差公式来加快该指标计算的收敛速度,利用密度权重法在输入变量可能的取值区间内进行均匀抽样,并以均匀样本点的联合概率密度函数的权重来保证计算的等价性,这使得所构造的方法不需要寻找失效域的设计点,因此其可以有效解决非线性程度较高难以找到设计点及多设计点的问题。除此之外,应用空间分割技术,使得本文所提方法仅需重复利用一组样本点,就可同时得到各个输入变量的可靠性全局灵敏度指标,消除了计算量与输入变量维数的相关性,大大地提高了样本的利用率和计算效率。验证算例的计算结果,说明了本文方法对计算功能函数非线性程度较高及多设计点问题的高效性。
The reliability global sensitivity index can effectively analyze the degree of influence of the uncertainty of input variables on the failure probability of the structural system. To improve the efficiency of the digital simulation method for the sensitivity index, a new method based on the density weight and the total variance Spatial partition efficient formula method. The proposed method accelerates the calculation of convergence rate by means of the total variance formula in the continuous non-overlapping interval. The method uses the density weight method to uniformly sample the input variables in a range of possible values, and uses the joint probability density function of the uniform sample points Therefore, the constructed method does not need to find the design point of the invalid domain, so it can effectively solve the problem that the non-linearity is hard to find the design point and the multi-design point. In addition, the application of spatial segmentation technology makes the proposed method only need to repeatedly use a set of sample points to obtain the reliability global sensitivity index of each input variable at the same time, which eliminates the correlation between the computation and the dimension of input variables , Greatly improving the sample utilization and computational efficiency. The calculation results of the verified example illustrate the high efficiency of the proposed method for calculating the non-linearity of the functional function and the multi-design point problem.