失效概率矩独立全局灵敏度指标的高效算法

基于失效概率的矩独立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. 然而，目前以抽样方式来计算该灵敏度指标的方法都不能最大程度地利用样本. 因此，研究了在准确计算该指标的基础上如何提高样本的利用率. 基于所证明的连续区间上的全方差公式，提出了基于空间分割及重要抽样法来高效计算该指标的方法，其仅需一组样本，且计算量与输入变量的维数无关. 该方法首先通过重要抽样密度抽取一组样本，使得抽取到的样本以较大的概率落入失效域从而加快计算的收敛速度，其次，通过重复利用这一组样本来计算出各个输入变量的基于失效概率的矩独立全局灵敏度指标，大大提高了样本的利用率和计算效率. 验证算例的计算结果，说明了所提方法在计算效率、计算精度、收敛性及稳健性方面都较已有同类方法高，具有更好的工程适用性. 

AN EFFICIENT METHOD FOR FAILURE PROBABILITY-BASED MOMENT-INDEPENDENT SENSITIVITY ANALYSIS

The failure probability-based moment-independent sensitivity index well analyzes how uncertainty in the failure probability of a model can be apportioned to different sources of uncertainty in the model inputs. At present, the existing sampling-based methods to estimate this index can not make full use of samples. Therefore, in this paper, we mainly concern how to improve the utilization of samples to accurately estimate this index. Based on the law of total variance in the successive intervals without overlapping proved in this paper, we propose an efficient method to estimate the failure probability-based moment-independent sensitivity index by combining the idea of space-partition and importance sampling, which only requires one set of input-output samples and the computational cost is independent of the dimensionality of inputs. The proposed method firstly uses importance sampling density function which can promise that a large number of samples will drop into the failure domain to generate a set of samples and then simultaneously obtain the sensitivity indices for all the input variables by repeatedly using this single set of samples. It is because of this that proposed method greatly improves the utilization of samples. Examples in this paper illustrate that our proposed method has higher efficiency, accuracy, convergence and robustness than the existing ones, and demonstrate its good prospect in engineering applications.