An interval uncertainty modeling method based on information granulation and improved multidimensional parallelepiped

Interval uncertainty modeling is essential for non-probabilistic reliability analysis of uncertain structures in the context of small samples, which confronts the difficulties of obtaining marginal intervals and characterizing variables correlation. A novel method for interval uncertainty modeling based on information granulation and improved multidimensional parallelepiped is proposed in this paper. Firstly, the method for constructing marginal intervals of uncertain variables is presented by integrating the up-sampling method based on kernel density estimation and information granulation theory (KDE-IG). Secondly, a relatively simple correlation coefficient expression based on the correlation angle is defined, and an improved multidimensional parallelepiped modeling method is proposed by optimizing the correlation coefficient within the marginal intervals. Additionally, two evaluation indexes are proposed to evaluate the robustness and accuracy of the constructed model. Finally, the applicability and effectiveness of the proposed method are demonstrated through two examples.