Uncertainty and global sensitivity analysis of neutron survival and extinction probabilities using polynomial chaos

Abstract

Generalised Polynomial Chaos (GPC) in conjunction with sparse grid stochastic collocation and High Dimensional Model Representation (HDMR) is used to perform uncertainty and global sensitivity analysis for the neutron chain survival and extinction probabilities, with and without an intrinsic random source. Starting with a lumped backward Master equation formulation, uncertainty is introduced by allowing the factorial moments of the fission multiplicity distribution, the neutron lifetime, and strength of the intrinsic source to be independent and uniformly distributed random variables. A multidimensional Legendre chaos representation of the random survival and extinction probabilities is used to achieve optimal numerical convergence in the stochastic dimension and the relative variance contributions from each random parameter are then quantified using High Dimensional Model Representation (HDMR).The underlying deterministic results of the model are found to closely match analytical benchmarks and, once uncertainty is introduced, the GPC results match both Monte Carlo simulations and analytical results for polynomial order greater than two. The GPC method is found to require significantly less computational time to achieve a given accuracy on the survival and extinction probabilities than the Monte Carlo method. It is found that, the probabilities are most sensitive to χi for lower i and have a significant sensitivity to χ2 in all cases. A chain’s survival probability is moderately sensitive to the neutron lifetime early in simulation. In the subcritical case this sensitivity increases as the simulation continues whilst it decreases in the supercritical case. The extinction probability is sensitive to the source strength.