Abstract The efficiency of existing stochastic analysis method depends on the discretization of the random variables domain. The number theoretical method has been proposed to discretize the random variable space and solve the generalized density evolution equation via sampling strategy. This method traditionally involves hyper-ball sieving (HS) algorithm to sample the representative point set. However, the sieving radius of the hyper-ball is determined subjectively, and the efficiency and accuracy of the analysis depend on the selected radius. To avoid this subjective selection, an equal volume hyper-ball sieving method is presented in this paper. By transforming the hypercube spatial volume of random variables into that of an equivalent hyper-ball, the radius of the equal volume hyper-ball is obtained analytically. This radius is further optimized with a minimum star discrepancy in the representative point set. The performance and accuracy of the proposed method are checked in four numerical examples, and the representative point set such obtained is more uniform with smaller NRP leading to more accurate and efficient subsequent stochastic analysis than the HS method.

中文翻译：

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结构可靠性分析的改进筛点法

摘要 现有随机分析方法的效率取决于随机变量域的离散化。提出了数论方法对随机变量空间进行离散化，并通过采样策略求解广义密度演化方程。这种方法传统上涉及超球筛分 (HS) 算法来对代表性点集进行采样。但是，超球的筛分半径是主观确定的，分析的效率和准确性取决于所选的半径。为了避免这种主观选择，本文提出了一种等体积超球筛分方法。通过将随机变量的超立方体空间体积转化为等效超球的空间体积，解析得到等体积超球的半径。该半径通过代表性点集中的最小星差进一步优化。在四个数值例子中检查了所提出方法的性能和准确性，并且这样获得的代表性点集更均匀，NRP更小，导致后续随机分析比HS方法更准确和有效。