Automatic construction of a simplified burn-up chain model by the singular value decomposition

Nuclear reactor design analysis often requires a simplified, or reduced-order, burn-up chain model to reduce computation time. It is difficult to construct the reduced-order burn-up chain because it requires engineers to have highly skilled techniques and in-depth knowledge into burn-up processes. This paper develops an algorithm for automatically constructing a reduced-order burn-up chain model from a detailed model using the singular value decomposition (SVD). In our approach, we prepare a detailed burn-up chain matrix A, and an extraction matrix C, which extracts important nuclides for specific purposes such as the evaluation of neutron multiplication factor. First, the nuclides extracted by C are specified as the first candidate nuclides of the reduced-order burn-up model. Then, by applying the SVD to C, we can obtain the first information transfer matrix F₁₂⁽¹⁾, which defines the relationship between the first candidate nuclides and remaining nuclides. In the next place, by applying SVD to F₁₂⁽¹⁾, we can obtain additional candidate nuclides for the reduced-order burn-up chain model from the remaining nuclides. We repeat this process until the norm of the information transfer matrix is sufficiently close to zero. Finally, all candidate nuclides chosen through these simplification processes are adopted as a reduced-order burn-up chain model. As a test case, we reduce a detailed burn-up chain model consisting of 1421 nuclides to a model of 204 nuclides. We can use the resulting reduced-order model to calculate the burn-up of light water reactor fuel cells with a high degree of accuracy.