Analysis of mixed uncertainty through possibilistic inference by using error estimation of reduced order surrogate models

Abstract

In the context of solving inverse problems, such as in statistical inference, an efficient repeated evaluability of a system can be achieved through methods of model order reduction. However, quantifying and adequately representing the emerging reduction error requires special techniques for combining different sources of uncertainty. In this paper, parametric finite element models are reduced through parametric model order reduction. The induced approximation error, an epistemic uncertainty, is reasonably estimated with the help of modern estimators for formulating statistical statements about the parameters to be identified. Measurement noise is also taken into account as a source of aleatory uncertainty. As a novel extension to analyzing a single source of uncertainty, the construction of a basic workflow for parameter identification in the face of both epistemic and aleatory uncertainties is presented, combining efficient error estimation techniques and possibilistic inference. The general applicability of this procedure is highlighted by two illustrative applications.