可靠性全局灵敏度指标的空间分割高效方法

An efficient method for reliability global sensitivity index by space-partition

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 sensitivity index well analyzes how the failure probability of a model is affected by the different sources of uncertainty in the model inputs. In order to improve the efficiency of digital simula- tion in estimating this index, a method was proposed based on the weighted density, the law of total variance in the successive intervals without overlapping and the space partition. To accelerate the speed of conver- gence, the law of total variance in the successive intervals without overlapping was proved and used subse- quently, The weighted density method generates uniform samples in the possible interval of model inputs, and it can ensure the equivalence of estimation by the weighted density indices. The proposed method can avoid searching the design point; therefore, for the highly nonlinear problem which is difficult to find the design point and the problem of multiple design points, the proposed method can well deal with. In addition, by the idea of space-partition, the dependence of the computational cost on the input dimensionality is removed, and the proposed method only requires one set of input-output samples to obtain all the sensitivity indices, which greatly improves the utilization of samples and computational efficiency. Examples illustrate that the proposed method has higher efficiency, accuracy, convergence and robustness than the existing methods for the prob- lems of high nonlinearity and multiple design points.