Usually the parameters of a system are not know exactly, and one has to distinguish between aleatoric and epistemic uncertainties.
Aleatoric uncertainties are random and natural fluctuations, which can be described by stochastic distribution functions. These can be accounted for in simulations by the stochastic finite element method or Monte Carlo techniques.
However, epistemic uncertainties stem from a lack of knowledge, like a not yet fixed design parameter at the start of a development cycle. These can be modelled by methods of interval and fuzzy arithmetic.
Since both Monte Carlo methods and fuzzy arithmetic necessitate a large number of system evaluations, efficient model reduction methods are a central topic of research.
The overarching goal of the proposed project at the methodological side is to establish a computationally tractable numerical method that is suited to capture polymorphic uncertainties in large-scale problems (as arising from the numerical analysis of heterogeneous materials microstructures). On the one hand the method will allow for fuzzy probability distributions of the random parameters (describing a microstructures geometry) and on the other hand the method will be based on only a few reduced…