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Uncertainty widely exists in practical engineering problems, which are commonly related to material properties, loads, etc. Non-probabilistic convex models need to be provided only the variation interval bounds of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is inadequate for probability modelling. Convex model utilizes a convex set to quantify the uncertainty domain of the uncertain-but-bounded parameters. It is not a single mathematical model; it means a series of models. The ellipsoid model and the parallelepiped models are convex models which could take correlation between uncertain parameters into consideration. In this work, a unified method for construction of these convex models—one ellipsoid model and five parallelepiped models, is proposed. The analytic mathematical expression of each convex model can be formulated once the correlation matrix of the uncertain-but-bounded parameters is obtained. Two kinds of correlation coefficient between uncertain parameters are utilized to construct a convex model, and the comparisons are made. A concept of “unbiasedness” is proposed to evaluate the adaptability of each convex model to a certain group of samples. The indexes such as “fitness” and “ratio of uncertainty volume” are presented as a reference for decision making among the various kinds of convex models. For some certain group of uncertain-but-bounded parameters and corresponding sample points, the construction procedure of a convex model quantifying the uncertainty is discussed in detail by several numerical examples. With the convex uncertainty domain, such as a multidimensional ellipsoid or parallelepiped obtained, subsequent uncertainty analysis such as reliability analysis, optimization design, etc. can be carried out.

non-probabilistic; convex model; correlation quantification; uncertainty analysis