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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。
In view of the fact that many algorithms are unable to accurately and efficiently calculate the global reliability sensitivity under the condition of small failure probability (10-4 or even smaller), this paper proposes a new global reliability sensitivity which can effectively solve the small failure probability algorithm. The proposed algorithm constructs an important sampling density function by expanding the standard deviation to perform spatial segmentation (SP), and then combines with unscented transformation (UT). Using the reduction of non-linearity of the function in the subspace after segmentation and the method of no-trace transformation Efficiently calculate the first two moments of a low degree of nonlinearity function to efficiently and accurately calculate the global reliability sensitivity for small failure probabilities. The advantages of the proposed algorithm are as follows: The selection of the important sampling density function can make the spatial division shift to the important region, and the complexity of the functional function in the segmentation region is reduced, so that the failure probability can be calculated efficiently by the unscented transformation method. Efficient global reliability and sensitivity. Compared with the existing algorithms, the examples illustrate the advantages of the proposed method.