Propagation of Uncertainties Modelled by Parametric P-boxes Using Sparse Polynomial Chaos Expansions

Advanced simulations, such as finite element methods, are routinely used to model the behaviour of physical systems and processes. At the same time, awareness is growing on concepts of structural reliability and robust design. This makes efficient quantification and propagation of uncertainties in computation models a key challenge. For this purpose, surrogate models, and especially Polynomial Chaos Expansions (PCE), have been used intensively in the last decade. In this paper we combine PCE and probability-boxes (p-boxes), which describe a mix of aleatory and epistemic uncertainty. In particular , parametric p-boxes allow for separation of the latter uncertainties in the input space. The introduction of an augmented input space in PCE leads to a new uncertainty propagation algorithm for p-boxes. The proposed algorithm is illustrated with two applications: a benchmark analytical function and a realistic truss structure. The results show that the proposed algorithm is capable of predicting the p-box of the response quantity extremely efficiently compared to double-loop Monte Carlo simulation. 1. INTRODUCTION In modern engineering sciences, computational simulations, such as finite element modelling, have become wide spread. The goal is to predict the response of a system with respect to a set of parameters , e.g. the deflection of a beam under variable loads. The parameters (e.g. geometries, mechanical properties, loads) are mapped to the quantity of interest through a computational model, e.g. through the governing equations of the process. It is only in recent times that the traditionally deterministic model parameters have been gradually substituted with probability distributions that account for their uncertainty. In practice though, data available for calibrating such distributions are often too sparse, thus resulting in an extra layer of uncertainty in their parameters. Different frameworks have been proposed to quantify the latter lack of knowledge (epistemic uncertainty) as well as the natural variability of the process (aleatory