Uncertainty propagation of p-boxes using sparse polynomial chaos expansions

TL;DR

This paper introduces a two-level sparse polynomial chaos expansion method for efficiently propagating p-box uncertainties through complex engineering models, reducing computational costs while maintaining accuracy.

Contribution

It presents a novel non-intrusive meta-modeling approach for uncertainty propagation with p-boxes, combining efficiency and accuracy in high-fidelity simulations.

Findings

Accurately estimates output statistics with few model evaluations

Effective for both benchmark and real engineering problems

Reduces computational costs in uncertainty quantification

Abstract

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making efficient quantification and propagation of uncertainties an important aspect. In this context, a typical workflow includes the characterization of the uncertainty in the input variables. In this paper, input variables are modelled by probability-boxes (p-boxes), accounting for both aleatory and epistemic uncertainty. The propagation of p-boxes leads to p-boxes of the output of the computational model. A two-level meta-modelling approach is proposed using non-intrusive sparse polynomial chaos expansions to surrogate the exact computational model and, hence, to facilitate the uncertainty quantification analysis. The capabilities of the proposed approach are illustrated through applications using a benchmark analytical function and two realistic engineering problem settings. They show that the proposed two-level approach allows for an accurate estimation of the statistics of the response quantity of interest using a small number of evaluations of the exact computational model. This is crucial in cases where the computational costs are dominated by the runs of high-fidelity computational models.