小失效概率情况下的全局可靠性灵敏度分析的高效方法
收稿日期: 2015-09-16
修回日期: 2015-11-22
网络出版日期: 2016-03-08
基金资助
国家自然科学基金（51475370）；中央高校基本科研业务费专项资金（3102015BJ（II）CG009）
Efficient method for global reliability sensitivity analysis with small failure probability
Received date: 2015-09-16
Revised date: 2015-11-22
Online published: 2016-03-08
Supported by
National Natural Science Foundation of China (51475370); the Fundamental Research Funds for the Central Universities (3102015BJ(II)CG009)
针对目前很多算法都无法准确、高效地计算小失效概率（10-4，甚至更小）情况下的全局可靠性灵敏度问题，本文提出了一种高效求解小失效概率情况下的全局可靠性灵敏度新算法。所提算法通过扩大标准差构造重要抽样密度函数来进行空间分割（SP），再与无迹变换（UT）结合，利用函数在分割后的子空间内非线性程度的降低和无迹变换方法可以高效计算低非线性程度函数的前二阶矩，来高效准确地计算小失效概率情况下的全局可靠性灵敏度。所提算法的优点有：重要抽样密度函数的选择可以使得空间分割时向重要区域偏移，并且在分割区域内功能函数的复杂性被降低，从而可以利用无迹变换方法高效计算失效概率，进而高效求得全局可靠性灵敏度。与已有的算法相比，算例说明了本文所提方法的优势。
柳诗雨 , 吕震宙 , 员婉莹 , 肖思男 . 小失效概率情况下的全局可靠性灵敏度分析的高效方法[J]. 航空学报, 2016 , 37(9) : 2766 -2774 . DOI: 10.7527/S1000-6893.2016.0029
At present, there are many methods for the estimation of global reliability sensitivity. However, these methods cannot efficiently and accurately estimate the global reliability probability in case of small failure probability (10-4 or smaller). In this work, a highly efficient method to compute the global reliability sensitivity is proposed for the small failure probability. The proposed method combines the space-partition (SP) with unscented transformation (UT) which can obtain the first two moments of lowly nonlinear response function. The importance sampling density function, which is constructed by increasing the standard deviation, is employed to partition the input space into a series of subspaces, and thus the subspaces partitioned by the constructed importance sampling density function can move to the important area for the failure probability. Because the complexity of response function is reduced in the partitioned subspace, in which UT can estimate effectively the failure probability, the proposed method can estimate the global reliability sensitivity indices efficiently. All the above contribute to the efficiency and accuracy of the proposed method to compute the global reliability sensitivity. In this paper, the proposed method is compared with the existing methods and examples, and it is shown that the proposed method outperforms the others.
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