In this thesis we use polynomial chaos expansions to represent the response of criticality calculations when they are subject to large numbers (many hundreds) of correlated nuclear data uncertainties. 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. In the final chapter of this thesis, the adaptive HDMR and quadrature methods combined with polynomial chaos are applied to an industrially relevant problem; the computation of keff uncertainties due to evaluated covariance data. Uncertainties and first order sensitivities are computed from the polynomial chaos expansion which are compared to the results from the first order sensitivity method implemented in the Monte Carlo code MONK. We found that the local sensitivities and uncertainties derived from the PCE compare well with the MONK sensitivity method. These uncertainty quantification approaches were applied to fast spectrum uranium, plutonium and americium-241 critical assemblies. Comparisons between the uranium/plutonium and americium-241 uncertainties were made in the context of the 0.95 sub-critical limit. Suggestions for new sub-critical limits based on differing numbers of standard deviations below the mean values were proposed.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:668241 |
| Date | January 2015 |
| Creators | Ayres, Daniel |
| Contributors | Eaton, Matthew; Pain, Christopher |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/26993 |
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