An improved multidimensional parallelepiped non-probabilistic model for structural uncertainty analysis

The non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain parameters. Different with “interval model” and “ellipsoid model”, the parallelepiped convex model can include the dependent and independent interval variables in a unified framework to deal with the complex “multi-source uncertainty” problems. Based on the existing multidimensional parallelepiped (MP) model, this paper proposed an improved MP model for uncertainty quantification. The correlation coefficient between interval variables in this improved MP model is redefined and an explicit expression describing the uncertainty domain of the interval variables is derived based on the correlation matrix. Through matrix transformation, the parallelepiped-shaped uncertainty domain can be projected into a box. The improved MP model is then applied to the uncertainty propagation analysis and reliability analysis of structures. Several numerical examples are investigated to demonstrate the effectiveness of this model.