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Annals of Operations Research

, Volume 275, Issue 2, pp 393–420 | Cite as

Optimally configuring a measurement system to detect diversions from a nuclear fuel cycle

  • Benjamin L. Johnson
  • Aaron T. Porter
  • Jeffrey C. King
  • Alexandra M. NewmanEmail author
Original - OR Modeling/Case Study
  • 37 Downloads

Abstract

The civilian nuclear fuel cycle is an industrial process that produces electrical power from the nuclear fission of uranium. Using a measurement system to accurately account for possibly dangerous nuclear material, such as uranium, in a fuel cycle is important because of its possible loss or diversion. A measurement system is defined by a set of measurement methods, or “devices,” used to account for material flows and inventory values at specific locations at facilities in the fuel cycle. We develop a simulation-optimization algorithm and an integer-programming model to find the best, or near-best, resource-limited measurement system with a high degree of confidence. The simulation-optimization algorithm minimizes a weighted sum of false positive and false negative diversion-detection probabilities while accounting for material quantities and measurement errors across a finite, discrete time horizon in hypothetical non-diversion and diversion contexts. In each time period, the estimated cumulative material unaccounted for is compared to a fixed or an optimized threshold value to assess if a “significant amount of material” is lost from a measurement system. The integer-programming model minimizes the population variance of the estimated material loss, i.e., material unaccounted for, in a measurement system. We analyze three potential problems in nuclear fuel cycle measurement systems: (i) given location-dependent device precisions, find the configuration of n devices at n locations (\(n=3\)) that provides the lowest corresponding objective values using the simulation-optimization algorithm and integer-programming model, (ii) find the location at which improving device precision reduces objective values the most using the simulation-optimization algorithm (given the device accuracy is 100%), and (iii) determine the effect of measurement frequency on measurement system configurations and objective values using the simulation-optimization algorithm. We obtain comparable results for each problem at least an order of magnitude faster than existing methods do. Using an optimized, rather than a fixed, detection threshold in the simulation-optimization algorithm reduces the weighted sum of false positive and false negative probabilities.

Keywords

Integer programming Simulation optimization Resource allocation Nuclear safeguards 

Notes

Acknowledgements

We acknowledge Nicolas Shugart, Ph.D. candidate in the Nuclear Engineering Department at the Colorado School of Mines, for developing relevant nuclear engineering problems and giving data support for our models. In addition, we are grateful for the insights provided by Dr. R. Kevin Wood, Distinguished Professor Emeritus of Operations Research at Naval Postgraduate School, and Dr. David Morton, Professor of Industrial Engineering and Management Sciences at Northwestern University. We thank the National Nuclear Security Administration for providing us support under Grant DE-NA0001730.

References

  1. Alesina, A., & La Ferrara, E. (2014). A test of racial bias in capital sentencing. The American Economic Review, 104(11), 3397–3433.CrossRefGoogle Scholar
  2. AMPL Optimization LLC (2013) AMPL Version 20130109.Google Scholar
  3. Avenhaus, R., & Jaech, J. (1981). On subdividing material balances in time and/or space. Nuclear Materials Management, 10(3), 24–33.Google Scholar
  4. Beedgen, R. (1988). Statistical near-real-time accountancy procedures applied to AGNS Minirun data using PROSA. Tech. rep., Los Alamos National Laboratory. https://www.osti.gov/scitech/servlets/purl/5534189. Accessed 2016.
  5. Bouchey, G., Koen, B., & Beightler, C. (1971). Optimization of nuclear materials safeguards sampling systems by dynamic programming. Nuclear Technology, 12(1), 18–25.CrossRefGoogle Scholar
  6. Bronshtein, I., & Semendyayev, K. (2015). Handbook of mathematics. Berlin: Springer.Google Scholar
  7. Burr, T. (1994). Material balance areas and frequencies for large reprocessing plants. Tech. rep., Los Alamos National Laboratory. http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/26/006/26006771.pdf?r=1. Accessed 2016.
  8. Burr, T., Croft, S., Jarman, K., Nicholson, A., Norman, C., & Walsh, S. (2016). Improved uncertainty quantification in nondestructive assay for nonproliferation. Chemometrics and Intelligent Laboratory Systems, 159, 164–173.CrossRefGoogle Scholar
  9. Burr, T., & Hamada, M. (2013). Revisiting statistical aspects of nuclear material accounting. Science and Technology of Nuclear Installations, 2013, 1–15.Google Scholar
  10. Cipiti, B., Duran, F., Middleton, B., & Ward, R. (2011). Fully integrated safeguards and security for reprocessing plant monitoring. Tech. rep., Sandia National Laboratories. http://prod.sandia.gov/techlib/access-control.cgi/2011/117292.pdf. Accessed 2016.
  11. Cipiti, B., & McDaniel, M. (2012). Reprocessing plant scale model integration. Tech. rep., Sandia National Laboratories. http://prod.sandia.gov/techlib/access-control.cgi/2012/127779.pdf. Accessed 2016.
  12. Cipiti, B., & Zinaman, O. (2010a) The integration of process monitoring for safeguards. Tech. rep., Sandia National Laboratories. http://prod.sandia.gov/techlib/access-control.cgi/2010/106593.pdf. Accessed 2016.
  13. Cipiti, B., & Zinaman, O. (2010b). Separations and safeguards model integration. Tech. rep., Sandia National Laboratories. http://prod.sandia.gov/techlib/access-control.cgi/2010/105962.pdf. Accessed 2016.
  14. de Montmollin, J., & Weinstock, E. (1979). Goals of measurement systems for international safeguards. Transactions of the American Nuclear Society, 33(1), 53.Google Scholar
  15. DeGroot, M., & Schervish, M. (2012). Probability and statistics (4th ed.). Reading: Addison-Wesley.Google Scholar
  16. Efron, B., & Tibshirani, R. (1994). An introduction to the bootstrap. Boca Raton: CRC Press.Google Scholar
  17. European Federation of National Associations of Measurement, Testing and Analytical Laboratories. (2006). Guide to the evaluation of measurement uncertainty for quantitative test results. Tech. rep. http://www.eurolab.org/documents/EL_11_01_06_387%20Technical%20report%20-%20Guide%20Measurement%20uncertainty.pdf. Accessed 2016.
  18. Fourer, R., Gay, D., & Kernighan, B. (2003). AMPL—a modeling language for mathematical programming. Pacific Grove, CA: Thomson Brooks/Cole.Google Scholar
  19. Free Software Foundation. (2014). GNU Compiler Collection Version 4.8.4.Google Scholar
  20. Gale, R. (1987). CIMACT: An operating data management system for near real time materials accountancy. In Nuclear safeguards technology 1986, (vol 1, pp. 385–398).Google Scholar
  21. IBM. (2014). CPLEX Version 12.6.0.1.Google Scholar
  22. IBM ILOG AMPL. (2010). Version 12.2 user’s guide: Standard (Command-line) version including CPLEX directives.Google Scholar
  23. International Atomic Energy Agency. (2002). IAEA safeguards glossary, 2001 edn. Tech. rep. https://www.iaea.org/sites/default/files/iaea_safeguards_glossary.pdf. Accessed 2016.
  24. International Atomic Energy Agency. (2007). Combating illicit trafficking in nuclear and other radioactive material. Tech. rep., http://www-pub.iaea.org/MTCD/publications/PDF/pub1309_web.pdf. Accessed 2016.
  25. International Atomic Energy Agency. (2008). Nuclear materials accounting handbook. Tech. rep. http://www-pub.iaea.org/MTCD/Publications/PDF/svs_015_web.pdf. Accessed 2016.
  26. International Atomic Energy Agency. (2015). IAEA incident and trafficking database. Tech. rep., https://www-ns.iaea.org/downloads/security/itdb-fact-sheet.pdf. Accessed 2016.
  27. International Atomic Energy Agency. (2016). IAEA safeguards overview. https://www.iaea.org/publications/factsheets/iaea-safeguards-overview. Accessed 2016.
  28. Jacobson, J. (1992). Automated statistical modeling of analytical measurement systems. Tech. rep., Westinghouse Idaho Nuclear Company Incorporated. https://www.osti.gov/scitech/servlets/purl/10164281/. Accessed 2016.
  29. Jacobson, J., & Yacout, A. (2010). Verifiable fuel cycle simulation model (VISION): A tool for analyzing nuclear fuel cycle futures. Nuclear Technology, 172(2), 157–178.CrossRefGoogle Scholar
  30. Kirkpatrick, S., Gelatt, C., Vecchi, M., et al. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.CrossRefGoogle Scholar
  31. Land, A., & Doig, A. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520.CrossRefGoogle Scholar
  32. Leitner, E., Weh, R., Avenhaus, R., & Canty, M. (1987). Near real time material accountancy in an industrial scale reprocessing plant. In: Nuclear safeguards technology 1986, (vol 1, pp. 365–376).Google Scholar
  33. Neyman, J., & Pearson, E. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London Series A, 231, 289–337.CrossRefGoogle Scholar
  34. Python Software Foundation. (2013). Python Version 2.7.6.Google Scholar
  35. Riley, T., Pope, C., & Benedict, R. (2016). Safeguards performance model for evaluation of potential safeguards strategies applied to pyroprocessing facilities. Nuclear Engineering and Design, 301, 157–163.CrossRefGoogle Scholar
  36. Sanchez, S., & Wood, R. (2006). The “BEST” algorithm for solving stochastic mixed integer programs. In Proceedings of the winter simulation conference, 2006, WSC 06 (pp. 765–773). IEEE.Google Scholar
  37. Seifert, R. (1987). The GEMUF test: A new sequential test for detecting loss of material in a sequence of accounting periods. In Nuclear safeguards technology 1986 (vol 1, pp. 377–384).Google Scholar
  38. Shugart, N., & King, J. (2017). A new modeling technique to analyze safeguards measurements in large systems. Nuclear Technology, 199(2), 129–150.CrossRefGoogle Scholar
  39. Smith Jr., H. (1991). The measurement of uranium enrichment. Tech. rep., United States Nuclear Regulatory Commission. http://www.lanl.gov/orgs/n/n1/FMTTD/neut_mc/pdfs/LA_UR_90_0732.pdf. Accessed 2016.
  40. Srinivas, M., & Patnaik, L. (1994). Genetic algorithms: A survey. Computer, 27(6), 17–26.CrossRefGoogle Scholar
  41. Stewart, K. (1970). Statistical techniques for enhancing the role of material balance accounting in safeguards. Tech. rep., Pacific Northwest National Laboratory. https://www.osti.gov/scitech/servlets/purl/4131457. Accessed 2016.
  42. Suzuki, M., & Ihara, H. (2008). Development of safeguards system simulator composed of multi-functional cores. Journal of Power and Energy Systems, 2(2), 899–907.CrossRefGoogle Scholar
  43. Tange, O. (2011). GNU parallel–the command-line power tool. The USENIX Magazine, 36(1), 42–47.Google Scholar
  44. The MathWorks, Inc. (2014). MATLAB and statistics toolbox release 2014b.Google Scholar
  45. United States Nuclear Regulatory Commission. (2015). Spent fuel storage in pools and dry casks Key Points and Questions and Answers. http://www.nrc.gov/waste/spent-fuel-storage/faqs.html. Accessed 2016.
  46. United States Nuclear Regulatory Commission. (2016). Uranium enrichment. http://www.nrc.gov/materials/fuel-cycle-fac/ur-enrichment.html. Accessed 2016.
  47. US Congress, Office of Technology Assessment. (1995). Nuclear safeguards and the international atomic energy agency. Tech. rep. https://www.princeton.edu/~ota/disk1/1995/9530/9530.PDF. Accessed 2016.
  48. US Department of Energy (2011) Nuclear materials control and accountability. Tech. rep. https://nnsa.energy.gov/sites/default/files/nnsa/inlinefiles/m4704-6c1.pdf. Accessed 2016.
  49. Wilkey, D., & Whitty, W. (1995). Development of a near-real-time accountability system. Tech. rep., Los Alamos National Laboratory. https://www.osti.gov/scitech/servlets/purl/104291-ltidgL/webviewable/. Accessed 2016.
  50. Williams, M. (2014). On the importance of MC&A to nuclear security. Center for International & Security Studies at Maryland (Working paper).Google Scholar
  51. World Nuclear Association. (2016a). The nuclear fuel cycle. http://www.world-nuclear.org/information-library/nuclear-fuel-cycle/introduction/nuclear-fuel-cycle-overview.aspx. Accessed 2016.
  52. World Nuclear Association. (2016b). Radioactive waste management. http://www.world-nuclear.org/information-library/nuclear-fuel-cycle/nuclear-wastes/radioactive-waste-management.aspx. Accessed 2016.
  53. Zhao, M., Norman, C., Penkin, M., & Balsley, S. (2012). International target values 2010 for measurement uncertainties in safeguarding nuclear materials. ESARDA Bulletin, 48, 3–24.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Benjamin L. Johnson
    • 1
  • Aaron T. Porter
    • 2
  • Jeffrey C. King
    • 3
  • Alexandra M. Newman
    • 1
    Email author
  1. 1.Operations Research with Engineering ProgramColorado School of MinesGoldenUSA
  2. 2.Department of Applied Mathematics and StatisticsColorado School of MinesGoldenUSA
  3. 3.Nuclear Engineering ProgramColorado School of MinesGoldenUSA

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