Uncertainty quantification in high dimensional problems

Abstract

Uncertainties are predominant in the world that we know. Referring therefore to a nominal value is too restrictive, especially when it comes to complex systems. Understanding the nature and the impact of these uncertainties has become an important aspect of engineering work. On a societal point of view, uncertainties play a role in terms of decision-making. From the European Commission through the Better Regulation Guideline, impact assessments are now advised to take uncertainties into account. In order to understand the uncertainties, the mathematical field of uncertainty quantification has been formed. UQ encompasses a large palette of statistical tools and it seeks to link a set of input perturbations on a system (design of experiments) towards a quantity of interest. The purpose of this work is to propose improvements on various methodological aspects of uncertainty quantification applied to costly numerical simulations. This is achieved by using existing methods with a multi-strategy approach but also by creating new methods. In this context, novel sampling and resampling approaches have been developed to better capture the variability of the physical phenomenon when dealing with a high number of perturbed inputs. These allow to reduce the number of simulation required to describe the system. Moreover, novel methods are proposed to visualize uncertainties when dealing with either a high dimensional input parameter space or a high dimensional quantity of interest. The developed methods can be used in various fields like hydraulic modelling and aerodynamic modelling. Their capabilities are demonstrated in realistic systems using well established computational fluid dynamics tools. Lastly, they are not limited to the use of numerical experiments and can be used equally for real experiments