Interval and Ellipsoid Intersection Model for Structural Uncertainty Analysis

The nonprobabilistic convex model is suitable for handling many engineering structures with limited information. Recently, the generalization of the conventional interval and ellipsoidal models has received more attention, which provides more flexibility and may possess more compact uncertainty domain. In this paper, a novel generalization of both the interval model and the ellipsoidal model, namely the interval and ellipsoid intersection model, is proposed to achieve more accurate approximation for experimental data. The proposed model can provide a smaller uncertainty domain and can achieve a better balance between accuracy and efficiency than both the interval model and the ellipsoidal model. Based on the proposed model, a semi-analytical method is developed to efficiently obtain the bounds of linear or weak nonlinear response functions, and a nonprobabilistic reliability index is proposed to rationally assess the safety degree of structures. Three numerical examples are provided to demonstrate the effectiveness of the proposed model, to illustrate the superiority of the semi-analytical method over the interior-point method and the rationality of the proposed nonprobabilistic reliability index.