Uncertainty quantification of large-scale dynamical systems using parametric model order reduction

Abstract

The finite element method is a widely used tool for the discretization and modeling of complex engineering structures. The output quantities of analyses conducted with finite element models are given as sharp values. This misleads about the fact that model input parameters used to define the finite element model are usually only imprecisely known, either due to aleatory uncertainty and/or due to epistemic uncertainty. Therefore, a meaningful quantification and analysis of these polymorphic uncertainties is indispensable to obtain robust simulation results. Very often, an uncertainty quantification (UQ) scheme involves multiple simulation model evaluations where the imprecisely known model parameters are varied in order to rate the impact of the uncertain model parameters on the simulation results. However, the underlying systems of ordinary differential equations of industrial finite element models usually exhibit hundreds of thousands degrees of freedom making repeated model evaluations in dynamical analyses computationally infeasible. This article proposes a novel simulation workflow for the efficient UQ of large-scale dynamical systems. Its fundamental idea is to combine parametric modeling and parametric model order reduction in order to drastically reduce the number of degrees of freedom of the underlying systems of ordinary differential equations. This allows for a very efficient UQ of large-scale finite element models with almost no loss of accuracy. The workflow is successfully applied to an industrial finite element model of a helicopter airframe structure in a possibilistic UQ. In this contribution, numerical speedups by a factor of 1630 compared to a conventional simulation workflow can be reached.