Predicting Correlation Coefficients for Monte Carlo Eigenvalue Simulations
Name
Forget_Predicting correlation.pdf
Size
228.43 KB
Format
Adobe PDF
Checksum (MD5)
c52be599a11c2d88f35589327e287964
Author(s)
Miao, Jilang
Forget, Benoit Robert Yves
Smith, Kord S.
Date Issued
November 2016
Journal
Proceedings of the 2016 American Nuclear Society Winter Meeting and Nuclear Technology Expo
Publisher
American Nuclear Society
Citation
Miao, Jilang, Benoit Forget and Kord Smith. "Predicting Correlation Coefficients for Monte Carlo Eigenvalue Simulations." 2016 American Nuclear Society Winter Meeting and Nuclear Expo, 6-10 November, 2016, Las Vegas, Nevada, USA.
Version
Author's final manuscript
Abstract
Monte Carlo methods are most often considered as a reference for neutron transport simulations since very limited approximations are made abount nuclear data and system geometry. To report uncertainty of any tally evaluated as generation averages, the sample variance is divided by the number of active generations, which is based on the assumption that
the neutron generations are independent. Correlation effects between neutrons in multiplying systems, particularly when performing power iteration to evaluate eigenvalues have been observed in previous work. Neglecting the correlation effect results in an underestimate of uncertainty
reported by Monte Carlo calculations. Previous work has also proposed methods to predict the underestimation ratio. Yamamoto et al expanded the fission source distribution with diffusion equation modes, performed numerical simulation of
the AR(autoregressive) process of the expansion coefficients
and used the correlation of the AR process to predict that of the Monte Carlo eigenvalue simulation. Sutton applied the discretized phase space (DPS) approach to predict the underestimation ratio but the method cannot predict the ratio when one neutron generates offspring in different phase space regions or generates a random number of offspring. This paper presents a method to predict the correlation effect with the model of multitype branching processes (MBP). The method requires simulations for one generation of neutrons without knowing the source distribution and
can predict the underestimation ratio for the cases where the traditional DPS approach does not work. The generation-to-generation correlation determines the convergence rate of active generations, the bias of variance estimator for each generation and the underestimation ratio of variance estimator for tallies averaged over active generations. The generation-to-generation correlation is characterized by the Auto-Correlation Coefficients (ACC) between tallies from different generations.
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://www.ans.org/meetings/m_147
