Possibilistic Uncertainty Quantification for Parametrically Reduced Models of Dynamic Systems with Many Inputs

Abstract

This paper presents a novel and efficient simulative method for quantifying uncertain knowledge about outputs of mechanical systems caused by uncertain input parameters. For the purpose of efficiency, projection-based model order reduction based on Krylov subspaces is used, and an additional input reduction is proposed, making the approach suitable also for systems with many inputs. The uncertainty in input parameters is described with possibility theory, which is particularly suited to describe heterogeneous sources of uncertainty. Based on this description, the uncertainty in the output is determined with sampling-based methods. The industrial example of a finite element model of an eVTOL aircraft demonstrates the functionality of the approach. Large speed-ups are achieved by the use of parametric model order reduction while maintaining a high fidelity of the model. Four parameters are assumed to be only imprecisely known and their input on the transfer behavior of the system is investigated. Uncertain frequency output bands are obtained instead of one single crisp solution. Especially for higher frequencies, a significant uncertainty is visible. On the other hand, one can also identify regions that stay relatively unharmed from changes of the input parameters inside the given ranges.