System reliability-based design optimization of structures using non-probabilistic ellipsoidal convex model

Abstract

This paper proposes a system non-probabilistic reliability-based design optimization (SNRBDO) framework for engineering structural systems. In view of the limitations of traditional probabilistic methods due to insufficient uncertainty information, the ellipsoidal convex model is used to quantify the uncertainty while considering the parameter correlation. The non-probabilistic credible set uncertainty method is employed to quantify the ellipsoidal uncertainty domain of uncertain parameters. A system non-probabilistic reliability index, defined as the volume ratio of safe regions to uncertainty domains, is introduced to evaluate structural safety under multiple failure modes. To enhance computational efficiency, Kriging surrogate model is utilized to replace the finite element analysis during optimization, and a localized sampling strategy is developed to refine accuracy near critical design points. The method is validated through a mathematical example and two engineering applications. The results demonstrate significant improvements in computational efficiency and design precision compared to conventional methods.