Performing uncertainty analysis of a nonlinear Point-Kinetics/Lumped Parameters problem using Polynomial Chaos techniques

Uncertainty analysis methodologies represent an important tool in the field of reactor physics with applications which span from the design phase to the safety analysis, as a support to “best estimate” models. A major source of uncertainty in reactor simulations is the input data set of the problem which is propagated, throughout the model, to the final simulation output. In this paper we perform such a propagation for a nonlinear point-kinetic model coupled to a lumped parameters system using a spectral technique, based on the Polynomial Chaos Expansion (PCE). We present two different ways to implement this technique, together with an overview of standard methods, and we apply them to a positive reactivity insertion transient. We show that for low-dimensional coupled problems PCE methods achieve the precision of Monte Carlo approaches at a significantly reduced computational cost.

► Two spectral techniques are applied to a stochastic nonlinear point-kinetic model.
► Polynomial Chaos approaches are presented and compared to standard UQ methodologies.
► PCE techniques achieve the accuracy of Monte Carlo where perturbation methods fail.
► Perturbation theory can be used to reduce the cost of nonintrusive PCE techniques.