Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

Jin, Lei; Banerjee, Kaushik

doi:10.1080/00295639.2018.1471269

Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

Journal Article · Thu Jun 28 00:00:00 EDT 2018 · Nuclear Science and Engineering

DOI:https://doi.org/10.1080/00295639.2018.1471269· OSTI ID:1459299

Jin, Lei ^[1]; ^[2]

Texas A&M Univ.–Corpus Christi, Corpus Christi, TX (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Monte Carlo (MC) simulation is widely used to solve the eigenvalue form of the Boltzmann transport equation that mathematically represents the neutron transport process through complex multiplying (fissionable) systems. Monte Carlo eigenvalue simulation starts with an assumed fission source distribution and uses the fission sites from the previous iteration (cycle) as the starting source in the current iteration. Important system parameters (MC tallies) such as fuel pin-power distribution are estimated over several cycles after the convergence of the fission source distribution to a stationary distribution. However, the MC fission source iteration algorithm that uses fission source sites from the previous cycle introduces a cycle-to-cycle correlation. Monte Carlo simulations that do not account for the cycle-to-cycle correlation systematically underestimate the variance of the estimated system parameters (sample mean). This paper presents the relationship between the spectral density in the frequency domain at frequency zero and the variance of the sample mean. This paper introduces a novel method in the frequency domain for the MC variance estimation. For the three test problems used in this paper, researchers have observed that the new method results in an improvement of more than one order of magnitude to the standard deviation of the sample mean. The new method also compares favorably with the previously introduced batch, bootstrap, and covariance-adjusted methods when applied to the three test problems investigated in this paper. This new method does not require modification of the MC eigenvalue algorithm (power iteration), is code agnostic, and is therefore easy to use when implementing in any existing MC code. In conclusion, the new estimate can be calculated without saving tally results of all active/stationary cycles.

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1459299

Journal Information:: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 3 Vol. 191; ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Universal Methodology for Statistical Error and Convergence of Correlated Monte Carlo Tallies Ueki, Taro Nuclear Science and Engineering, Vol. 193, Issue 7 https://doi.org/10.1080/00295639.2018.1562779	journal	February 2019

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