Uncertainty quantification in nuclear criticality modelling using a high dimensional model representation

• Published in: Annals of nuclear energy Vol. 80; pp. 379 - 402
• Main Authors: Ayres, D., Eaton, M.D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2015
• Subjects: Covariance data nuclear criticality; High dimensional model representation; Polynomial chaos; High dimensional model representation; Covariance data nuclear criticality; Polynomial chaos
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2015.02.024

•We combine adaptive high dimensional model representation with adaptive sparse grid quadrature to build a polynomial chaos expansion.•The uncertainty in keff is calculated for problems with up to 988 uncertain input parameters.•The proposed method is an order of magnitude more accurate than Latin Hypercube sampling for the problems presented. An adaptive high dimensional model representation (HDMR) is used to decompose the response parameter keff into a superposition of lower dimensional subspaces which are in-turn projected on to a polynomial basis. These projections are evaluated using an adaptive quadrature scheme which is used to infer the polynomial orders of the basis. The combination of adaptive HDMR and adaptive quadrature techniques results in a sparse polynomial expansion which has been optimised to represent the variance of the response with the minimum number of polynomials. The combined application of these techniques is illustrated using UOX and MOX pin cell problems with evaluated nuclear covariance data. We show that this approach to calculating the variance in keff is an order of magnitude more efficient when compared to Latin Hypercube sampling with the same number of samples for problems involving up to 988 random dimensions.