Dimension-reduced cross-section adjustment method based on minimum variance unbiased estimation |
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| Authors: | Kenji Yokoyama Akio Yamamoto Takanori Kitada |
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| Affiliation: | 1. Nuclear Science and Engineering Center, Japan Atomic Energy Agency, Ibaraki, Japan;2. Department of Applied Energy, Graduate School of Engineering, Nagoya University, Nagoya, Japan;3. Division of Sustainable Energy and Environmental Engineering, Graduate School of Engineering, Osaka University, Osaka, Japan |
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| Abstract: | A new formulation of the cross-section adjustment methodology with the dimensionality-reduction technique has been derived in the light of the fact that it is often used under the condition of ill-posed problem, where the number of integral experimental quantities is less than the number of adjusted nuclear data parameters. This new formulation is proposed as the dimension-reduced conventional cross-section adjustment method (DRCA). The derivation of DRCA is based on the minimum variance unbiased estimation (MVUE), and the assumption of normal distribution is not used. The result of DRCA depends on a user-defined matrix that determines the dimension-reduced feature subspace. We examined three variations of DRCA, namely, DRCA1, DRCA2, and DRCA3, which employ (1) the nuclear data covariance matrix as the user-defined matrix, (2) the sensitivity coefficient matrix postmultiplied by the nuclear data covariance matrix, and (3) the sensitivity coefficient matrix, respectively. Mathematical investigation and numerical verification revealed that DRCA2 is equivalent to the currently widely used cross-section adjustment method. Moreover, DRCA3 is found to be identical to the cross-section adjustment method based on MVUE, which has been proposed in the previous study. |
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| Keywords: | Cross-section adjustment dimensionality reduction minimum variance unbiased estimation Bayes theorem normal distribution uncertainty quantification nuclear data covariance |
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