The Universal reduced order fuzzy-stochastic FEM for a general class of polymorphic uncertainties

• Applicant: Dr.-Ing. Dmytro Pivovarov
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 506419890

The realistic simulation of any engineering structure or any dynamic system cannot be performed without considering different sources of uncertainties. Uncertainties originates from insufficient accuracy of measurements, model assumptions, lack of precise data, or from natural variability and randomness in some processes. It has been shown that effect of uncertainties can be strongly nonlinear and hard to predict. Correspondingly, the modeling of uncertainties is an important and emerging topic.Despite the number of promising results in stochastic and fuzzy modelling, there is no general approach towards uncertainties yet. All existing methods are actually developed and tested only for one particular type of models or one particular type of uncertainties. There is no universal solver suitable for the most realistic engineering problem, where all kinds of uncertainties are affecting the model.Another challenge is the high computational costs of uncertainty propagation. There are two groups of methods. The first group presents methods which are based on some significant simplifications. They are fast and overperform in terms of accuracy, but drastically lack the generic nature. The second group can potentially be generalized to the most general setting, but they are extremely expensive. This problem can be solved only by using the most advanced order reduction approach – low-rank tensor decomposition.Thus the main goal of our research is to provide a universal reduced order solver built of deeply connected and working in the synergy methods, which will be efficient, accurate, and applicable to the most general problem setting. The core of the new solver is built of the spectral non-deterministic FEM augmented with the adaptive sampling and the low-rank tensor decomposition.

• DFG Programme: Research Grants