An E_PGPT-based approach for uncertainty quantification

Generalized Perturbation Theory (GPT) has been widely used by many scientific disciplines to perform sensitivity analysis and uncertainty quantification. This manuscript employs recent developments in GPT theory, collectively referred to as Exact-to-Precision Generalized Perturbation Theory (E_PGPT), to enable uncertainty quantification for computationally challenging models, e.g. nonlinear models associated with many input parameters and many output responses and with general non-Gaussian parameters distributions. The core difference between E_PGPT and existing GPT is in the way the problem is formulated. GPT formulates an adjoint problem that is dependent on the response of interest. It tries to capture via the adjoint solution the relationship between the response of interest and the constraints on the state variations. E_PGPT recasts the problem in terms of a smaller set of what is referred to as the 'active' responses which are solely dependent on the physics model and the boundary and initial conditions rather than on the responses of interest. The objective of this work is to apply an E_PGPT methodology to propagate cross-sections variations in typical reactor design calculations. The goal is to illustrate its use and the associated impact for situations where the typical Gaussian assumption for parameters uncertainties is not valid and when nonlinear behavior must be considered. To allow this demonstration, exaggerated variations will be employed to stimulate nonlinear behavior in simple prototypical neutronics models.