Abstract As a typical convex model, the parallelepiped plays an important role in the non-probabilistic uncertainty quantification with simultaneous dependent and independent variables. To overcome the complexity of the conventional geometric design-based method, this paper proposes a more efficient sample-driven procedure to construct the explicit mathematical expression of parallelepiped model. Instead of the geometric characteristics of minimum-volume parallelepiped, the statistical characteristics of available samples are employed to directly evaluate the marginal intervals and correlation coefficients of uncertain variables. Especially for the inconstant uncertainty problem with dispersed samples, a sub-parallelepiped modeling method is further presented by means of the sample clustering analysis, which can effectively decrease the invalid domains in uncertainty quantification. Besides, in order to improve the computing efficiency of uncertainty propagation analysis under the parallelepiped model, the radial basis function-based surrogate model is introduced as an approximation of the original time-consuming computational model. Finally, two numerical examples verify the effectiveness of the proposed model and method.

中文翻译：

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用于非概率不确定性量化和传播分析的改进平行六面体模型

摘要 作为典型的凸模型，平行六面体在因变量和自变量同时存在的非概率不确定性量化中起着重要作用。为了克服传统的基于几何设计的方法的复杂性，本文提出了一种更有效的样本驱动程序来构建平行六面体模型的显式数学表达式。代替最小体积平行六面体的几何特征，利用可用样本的统计特征直接评估不确定变量的边际区间和相关系数。特别是针对离散样本的不确定性不确定问题，通过样本聚类分析进一步提出了一种亚平行六面体建模方法，可以有效减少不确定性量化中的无效域。此外，为了提高平行六面体模型下不确定性传播分析的计算效率，引入了基于径向基函数的代理模型作为原始耗时计算模型的近似。最后，通过两个数值算例验证了所提出模型和方法的有效性。