Fourier Analysis on the Symmetric Group for a Repositioning Plan Optimization Problem

The placement of the stops for refueling is an important challenge for the economic aspect in nuclear energy production industry. In this paper, we intend to study, in the context of the so-called PWR1300—a pressurized water reactor of 1300 MW, how economical criteria, including the mean core burnup, and safety criteria, such as hot power factor (which are often not correlated) are sensitive to repositioning. Given the huge number of possible combinations and the very expensive CPU cost of a steady-cycle simulation, we have set a methodology based on a surrogate model using Fourier expansion of the criterion function on the symmetric group Sn. We address this problem in an efficient way, taking into account the limited computational resources; thus, we restrict our analysis to the permutation operating only on the Uox gadolinium assemblies as UGd. The criteria functions are evaluated by using the Minos Solver of APOLLO3® neutronics simulation code along the last converged depletion cycle. As a result, we establish a design of experiments from which is derived an expansion Fourier surrogate model of the first and second degree, with very good accuracy. In fact, for most of the criteria, the surrogate model of the second degree has a coefficient of determination greater than 0.8. We then study the sensitivity of the criteria from the substitution model and present, as a result, an intensity map that attests to the importance of specific repositioning of the UGd. These first results show that the criteria are repositioning-sensitive and call for further investigation into the application of more complex permutation, including Uox and UGd simultaneously.