Novel bootstrap-based ellipsoidal convex model for non-probabilistic reliability-based design optimization with insufficient input data

Abstract

Performing reliability-based design optimization with insufficient input data is a significant and challenging issue as accurately quantifying epistemic uncertainty can be difficult in such scenarios. Non-probabilistic models can marginally alleviate the need for a large sample size by constructing the boundaries of uncertainty parameters. However, most of the existing non-probabilistic models account for only the available or known samples. For cases with insufficient data, the compact uncertainty domain may result in considerably hazardous results, particularly for the problems that require high reliability. Therefore, a novel bootstrap-based ellipsoidal convex model (BECM) is proposed herein to account for both known and unknown data. Herein, the bootstrap method is introduced to non-probabilistic convex models for the first time to quantify the ellipsoidal shape uncertainty caused by insufficient input data. Further, the proposed BECM is also integrated into non-probabilistic reliability-based design optimization. The entire framework of uncertainty quantification and reliability optimization design for insufficient input data is established. Marginally conservative results can finally be achieved in a rational and objective manner by partially sacrificing the ellipsoid volume. Comprehensive comparisons and detailed discussions on aspects, including the problem complexity, initial sample size, and distribution type, are also conducted. The numerical results show that the BECM displays the best performance in terms of accuracy and robustness. It can achieve an approximate balance between being conservative and taking risks. The significant advantages are also illustrated by an engineering example of linear buckling analysis of stiffened cylindrical shells.