Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

Perfetti, Christopher M.; Rearden, Bradley T.; Marshall, William J.

doi:10.13182/NSE16-54

Title: Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

Abstract

Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin ^{$$\hat{R}_c$$} diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.

Authors:

Perfetti, Christopher M. ^[1]; Rearden, Bradley T. ^[1]; Marshall, William J. ^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Wed Feb 08 00:00:00 EST 2017

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1376296

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Science and Engineering

Additional Journal Information:: Journal Volume: 185; Journal Issue: 1; Journal ID: ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Monte Carlo; undersampling biases; convergence metrics; SCALE Code System

Citation Formats


                    Perfetti, Christopher M., Rearden, Bradley T., and Marshall, William J. Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates.  United States: N. p., 2017. 
Web.  doi:10.13182/NSE16-54.

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                    Perfetti, Christopher M., Rearden, Bradley T., & Marshall, William J. Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates.  United States.  https://doi.org/10.13182/NSE16-54

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                    Perfetti, Christopher M., Rearden, Bradley T., and Marshall, William J. Wed .  
"Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates".  United States.  https://doi.org/10.13182/NSE16-54.  https://www.osti.gov/servlets/purl/1376296.

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@article{osti_1376296,

  title        = {Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates},

  author       = {Perfetti, Christopher M. and Rearden, Bradley T. and Marshall, William J.},

  abstractNote = {Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin $\hat{R}_c$ diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.},

  doi          = {10.13182/NSE16-54},

  journal      = {Nuclear Science and Engineering},

  number       = 1,

  volume       = 185,

  place        = {United States},

  year         = {Wed Feb 08 00:00:00 EST 2017},

  month        = {Wed Feb 08 00:00:00 EST 2017}

}

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Works referenced in this record:

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Brissenden, R. J.; Garlick, A. R.
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Uncertainty Underprediction in Monte Carlo Eigenvalue Calculations
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Nuclear Science and Engineering, Vol. 173, Issue 3
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FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations
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Title: Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

Abstract

Citation Formats

Biases in the estimation of Keff and its error by Monte Carlo methods journal, January 1986

Stationarity Modeling and Informatics-Based Diagnostics in Monte Carlo Criticality Calculations journal, January 2005

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method journal, July 1993

A Mathematical Theory of Communication journal, October 1948

Inference from Iterative Simulation Using Multiple Sequences journal, November 1992

Uncertainty Underprediction in Monte Carlo Eigenvalue Calculations journal, March 2013

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations journal, January 2014

“K-effective of the World” and Other Concerns for Monte Carlo Eigenvalue Calculations journal, January 2011

Biases in the estimation of Keff and its error by Monte Carlo methods
journal, January 1986

Stationarity Modeling and Informatics-Based Diagnostics in Monte Carlo Criticality Calculations
journal, January 2005

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method
journal, July 1993

A Mathematical Theory of Communication
journal, October 1948

Inference from Iterative Simulation Using Multiple Sequences
journal, November 1992

Uncertainty Underprediction in Monte Carlo Eigenvalue Calculations
journal, March 2013

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations
journal, January 2014

“K-effective of the World” and Other Concerns for Monte Carlo Eigenvalue Calculations
journal, January 2011