Real Variance Estimation using Spectral Analysis Method in Monte Carlo Criticality Calculation with p-CMFD Feedback

The effects of the MC/p-CMFD are 1) acceleration of the convergence speed in the fission source distributions (FSDs) and 2) real variance reduction in the local MC tallies by reducing the inter-cycle correlation. On the other hand, the estimation of the real variance of the sample mean has been a big challenge in the MC criticality calculation. The conventional way to estimate variance from a single batch run neglects the inter-cycle correlation, which leads to the significant underestimation. To estimate the real variance, the intercycle covariance of a MC tally should be considered. Depending on the number of periodograms used in the local average, there is a trade-off between the bias and the variance of the real variance. In this paper, the spectral analysis method is applied to estimate the real variances of the local MC tallies in the MC/p-CMFD. In numerical results, it is shown that the p-CMFD feedback not only reduces the real variance itself, but also makes it possible to reduce the variance of the estimated real variance by the spectral analysis method without losing significant accuracy. The spectral analysis method was applied to estimate the real variances of the local MC tallies in the MC/p- CMFD. It was shown that the p-CMFD feedback not only reduces the real variance itself, but also makes it possible to reduce the variance of the spectral SD by averaging the periodogram near frequency zero without losing significant accuracy. In the time domain (cycle), the p-CMFD feedback efficiently accelerates the convergence of the FSDs by reducing slowly decaying error component, which is the low frequency error component in the frequency domain. As further studies, the cycle length control in terms of the accuracy of the spectral SD will be performed. Of course, a synergetic application of the p-CMFD feedback and the spectral analysis method will be investigated in the continuous-energy whole-core problem. Furthermore, the investigation of the appropriate filter for the spectral analysis method is also viable.