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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">glonucsec</journal-id><journal-title-group><journal-title xml:lang="ru">Глобальная ядерная безопасность</journal-title><trans-title-group xml:lang="en"><trans-title>Global Nuclear Safety</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2305-414X</issn><issn pub-type="epub">2499-9733</issn><publisher><publisher-name>National Research Nuclear University "MEPhI"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26583/GNS-2022-04-03</article-id><article-id custom-type="elpub" pub-id-type="custom">glonucsec-168</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ПРОЕКТИРОВАНИЕ, ИЗГОТОВЛЕНИЕ И ВВОД В ЭКСПЛУАТАЦИЮ ОБОРУДОВАНИЯ ОБЪЕКТОВ АТОМНОЙ ОТРАСЛИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>DESIGN, MANUFACTURE AND COMMISSIONING COMMISSIONING OF EQUIPMENT NUCLEAR INDUSTRY FACILITIES</subject></subj-group></article-categories><title-group><article-title>РЕЗУЛЬТАТЫ ТЕСТИРОВАНИЯ МЕТОДОВ ПОНИЖЕНИЯ ДИСПЕРСИИ В ЗАДАЧЕ НА ГЛУБОКОЕ ПРОХОЖДЕНИЕ ИЗЛУЧЕНИЯ</article-title><trans-title-group xml:lang="en"><trans-title>Test Results of Variance Reduction Techniques Applied to Deep Penetration Problem</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8184-2124</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Богданова</surname><given-names>Екатерина Владимировна</given-names></name><name name-style="western" xml:lang="en"><surname>Bogdanova</surname><given-names>E. V.</given-names></name></name-alternatives><email xlink:type="simple">evbogdanova@mephi.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5332-7272</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тихомиров</surname><given-names>Георгий Валентинович</given-names></name><name name-style="western" xml:lang="en"><surname>Tikhomirov</surname><given-names>G. V.</given-names></name></name-alternatives><email xlink:type="simple">gvtikhomirov@mephi.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный исследовательский ядерный университет «МИФИ»</institution></aff><aff xml:lang="en"><institution>National Research Nuclear University (MEPhI)</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>11</day><month>11</month><year>2022</year></pub-date><volume>45</volume><issue>4</issue><fpage>25</fpage><lpage>39</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Богданова Е.В., Тихомиров Г.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Богданова Е.В., Тихомиров Г.В.</copyright-holder><copyright-holder xml:lang="en">Bogdanova E.V., Tikhomirov G.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://glonucsec.elpub.ru/jour/article/view/168">https://glonucsec.elpub.ru/jour/article/view/168</self-uri><abstract><p>В настоящее время существует проблема нехватки компьютерных мощностей для проведения высокоточного анализа реакторных установок. При моделировании полномасштабных моделей активных зон ядерных реакторов стохастическим методом Монте-Карло существует ряд факторов, увеличивающих чрезмерную вычислительную нагрузку и затрудняющих проведение расчетов. Среди них можно выделить наличие большого ослабления потока, которое наблюдается в задачах на глубокое прохождение излучения. Для повышения эффективности расчетов методом Монте-Карло используются различные техники понижения дисперсии, которые позволяют уменьшить статистическую неопределенность оценки функционала без увеличения числа моделируемых историй. Данная работа посвящена исследованию и тестированию методов понижения дисперсии в задаче на глубокое прохождение излучения. Сформулирована тестовая задача, решение которой позволит продемонстрировать возможность использования различных техник неаналогового моделирования. Для определения количественной эффективности применения методов понижения дисперсии рассматривается характеристика FOM, выступающая в роли функции от относительного отклонения оценки функционала и времени счета. В работе рассмотрены методы неаналогового моделирования, реализованные в программных комплексах MCU и OpenMC. В рамках исследования разработан модуль программы OpenMC, позволяющий автоматически генерировать значения весовых окон. Показано, что использование методов понижения дисперсии позволяет повысить эффективность расчета в несколько раз, в частности, с помощью метода весового окна в программе OpenMC удалось достичь повышения эффективности оценки потока нейтронов в 7 раз при неизменном количестве моделируемых историй. Сформулированные рекомендации в дальнейшем могут быть использованы при расчете полномасштабных моделей активных зон инновационных ядерный реакторов.</p></abstract><trans-abstract xml:lang="en"><p>Nowadays, there is a problem of a lack of computer power to conduct high-precision reactor analysis. There are several factors that increase the excessive computational load and make it difficult to calculate nuclear reactor full-scale models using Monte Carlo method. Among them is the large neutron-flux attenuation, which is observed in deep penetration problems. Various reduction techniques are used to increase the efficiency of Monte Carlo calculations in such tasks. It allows to reduce the statistical uncertainty of the functional evaluation without increasing the number of neutron histories. This work is devoted to study and testing of variance reduction techniques in the deep penetration problem. To demonstrate the possibility of using non-analogue Monte Carlo modeling a test problem was formulated. To quantify the efficacy of applying the variance reduction methods, FOM characteristic is considered, which is a function of the relative error in a flux estimate and the computational time of the simulation. The article considers non-analogue techniques implemented in the MCU (Monte Carlo Univarsal) and OpenMC codes. As part of the study, a module of the OpenMC code was developed that allows to automatically generate weight windows. It is shown that variance reduction techniques increase the calculation efficiency by several times, particularly, the weight windows method in OpenMC make it possible to achieve a 7-fold increase in the efficiency of neutron flux estimation with the same number of simulated histories. The formulated recommendations can be used in the calculation of innovative nuclear reactors full-scale models.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>метод Монте-Карло</kwd><kwd>математическое моделирование</kwd><kwd>тестовая задача</kwd><kwd>глубокое прохождение излучения</kwd><kwd>неаналоговое моделирование</kwd><kwd>методы понижения дисперсии</kwd><kwd>метод расщепления/русская рулетка</kwd><kwd>метод весового окна</kwd><kwd>FOM</kwd><kwd>внешний источник</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Monte Carlo method</kwd><kwd>mathematical modeling</kwd><kwd>test problem</kwd><kwd>deep penetration problem</kwd><kwd>non-analogue modeling</kwd><kwd>variance reduction techniques</kwd><kwd>splitting/russian roulette</kwd><kwd>weight windows</kwd><kwd>FOM</kwd><kwd>external source</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Edward W. Larsen (2006) An Overview of Neutron Transport Problems and Simulation Techniques. In: Graziani F. (eds) Computational Methods in Transport. Lecture Notes in Computational Science and Engineering, vol 48. Springer, Berlin, Heidelberg.</mixed-citation><mixed-citation xml:lang="en">Edward W. Larsen (2006) An Overview of Neutron Transport Problems and Simulation Techniques. In: Graziani F. (eds) Computational Methods in Transport. Lecture Notes in Computational Science and Engineering, vol 48. Springer, Berlin, Heidelberg.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Paul Kollath Romano. Parallel Algorithms for Monte Carlo Particle TransportSimulation on Exascale Computing Architectures. Massachusetts Institute of Technology, - 2013.</mixed-citation><mixed-citation xml:lang="en">Paul Kollath Romano. Parallel Algorithms for Monte Carlo Particle TransportSimulation on Exascale Computing Architectures. Massachusetts Institute of Technology, - 2013.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Kord Smith, «Reactor Core Methods», Invited lecture at the M&amp;C 2003 International Conference, April 6-10, 2003, Gatlinburg, TN, USA, 2003.</mixed-citation><mixed-citation xml:lang="en">Kord Smith, «Reactor Core Methods», Invited lecture at the M&amp;C 2003 International Conference, April 6-10, 2003, Gatlinburg, TN, USA, 2003.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Чистяков, В.П. Курс теории вероятностей / В.П. Чистяков. - Москва : Наука, 1982.</mixed-citation><mixed-citation xml:lang="en">Чистяков, В.П. Курс теории вероятностей / В.П. Чистяков. - Москва : Наука, 1982.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">W.R. MARTIN, «Advances in Monte Carlo Methods for Global Reactor Analysis», Proc. Joint International Topical Meeting on Mathematics &amp; Computation and Supercomputing in Nuclear Applications, Monterey, California, April 15-19, 2007, Invited Lecture.</mixed-citation><mixed-citation xml:lang="en">W.R. MARTIN, «Advances in Monte Carlo Methods for Global Reactor Analysis», Proc. Joint International Topical Meeting on Mathematics &amp; Computation and Supercomputing in Nuclear Applications, Monterey, California, April 15-19, 2007, Invited Lecture.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">D. Legrady, A. Claret, B. Molnar, G. Tolnai, Verification of the interaction physics of GUARDYAN a novel GPU-based Monte Carlo code for short scale reactor transients, in Proceedings of the PHYSOR, Reactor Physics Paving the Way Towards More Efficient Systems (Cancun, Mexico, 2018), p. 2018.</mixed-citation><mixed-citation xml:lang="en">D. Legrady, A. Claret, B. Molnar, G. Tolnai, Verification of the interaction physics of GUARDYAN a novel GPU-based Monte Carlo code for short scale reactor transients, in Proceedings of the PHYSOR, Reactor Physics Paving the Way Towards More Efficient Systems (Cancun, Mexico, 2018), p. 2018.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Gross, R., Tomatis, D. &amp; Gilad, E. High-accuracy neutron diffusion calculations based on integral transport theory. Eur. Phys. J. Plus 135, 235 (2020).</mixed-citation><mixed-citation xml:lang="en">Gross, R., Tomatis, D. &amp; Gilad, E. High-accuracy neutron diffusion calculations based on integral transport theory. Eur. Phys. J. Plus 135, 235 (2020).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Kleijnen, J.P.C. Statistical Techniques in Simulation, Part 1. Marcel Dekker, New York (1974).</mixed-citation><mixed-citation xml:lang="en">Kleijnen, J.P.C. Statistical Techniques in Simulation, Part 1. Marcel Dekker, New York (1974).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Кольчужкин, А.М. Введение в теорию прохождения частиц через вещество / А.М. Кольчужкин, В.В. Учайкин. - Москва : Атомиздат, 1978, - 256 с.</mixed-citation><mixed-citation xml:lang="en">Кольчужкин, А.М. Введение в теорию прохождения частиц через вещество / А.М. Кольчужкин, В.В. Учайкин. - Москва : Атомиздат, 1978, - 256 с.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Figure of merit. Merriam-Webster.com Dictionary, Merriam-Webster [Электронный ресурс]. - URL : https://www.merriam-webster.com/dictionary/figure%20of%20merit (дата обращения: 26.02.2021).</mixed-citation><mixed-citation xml:lang="en">Figure of merit. Merriam-Webster.com Dictionary, Merriam-Webster [Электронный ресурс]. - URL : https://www.merriam-webster.com/dictionary/figure%20of%20merit (дата обращения: 26.02.2021).</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">«MCNPTM-A General Purpose Monte Carlo N-Particle Transport Code», Version 4C, LA-13709-M, J. F. BRIESMEISTER, Ed. (Dec. 2000).</mixed-citation><mixed-citation xml:lang="en">«MCNPTM-A General Purpose Monte Carlo N-Particle Transport Code», Version 4C, LA-13709-M, J. F. BRIESMEISTER, Ed. (Dec. 2000).</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">S.P. Pederson, R.A. Forster, and T.E. Booth. Confidence Interval Procedures for Monte Carlo Transport Simulations. Nucl. Sci. Eng., 127, 54 (1997).</mixed-citation><mixed-citation xml:lang="en">S.P. Pederson, R.A. Forster, and T.E. Booth. Confidence Interval Procedures for Monte Carlo Transport Simulations. Nucl. Sci. Eng., 127, 54 (1997).</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">J. Kenneth Shultis and Richard E. Faw. An MCNP Primer. Dept. of Mechanical and Nuclear Engineering, Kansas State University. December, 2011.</mixed-citation><mixed-citation xml:lang="en">J. Kenneth Shultis and Richard E. Faw. An MCNP Primer. Dept. of Mechanical and Nuclear Engineering, Kansas State University. December, 2011.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">S.N. Cramer, J.S. Tang. Variance reduction methods applied to deep-penetration Monte Carlo problems. Engineering Physics and Mathematics Division. ORNL/TM-9643, DE86 007080, 1986.</mixed-citation><mixed-citation xml:lang="en">S.N. Cramer, J.S. Tang. Variance reduction methods applied to deep-penetration Monte Carlo problems. Engineering Physics and Mathematics Division. ORNL/TM-9643, DE86 007080, 1986.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Суслов, И.Р. Гибридный метод расчета защиты ЯЭУ / И.Р. Суслов, И.А. Лямцев // Препринт ФЭИ-3267. - Обнинск, 2016. - 15 с.</mixed-citation><mixed-citation xml:lang="en">Суслов, И.Р. Гибридный метод расчета защиты ЯЭУ / И.Р. Суслов, И.А. Лямцев // Препринт ФЭИ-3267. - Обнинск, 2016. - 15 с.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Thomas E. Booth. A sample problem for variance reduction in MCNP. Technical Report, Los Alamos National Laboratory, LA-10363-MS, 1985.</mixed-citation><mixed-citation xml:lang="en">Thomas E. Booth. A sample problem for variance reduction in MCNP. Technical Report, Los Alamos National Laboratory, LA-10363-MS, 1985.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Статус MC -5 / Н.И. Алексеев, С.Н. Большагин, Е.А. Гомин [др.] // Вопросы атомной науки и техники. Сер.: Физика ядерных реакторов. - 2011. - № 4. - С. 4-23.</mixed-citation><mixed-citation xml:lang="en">Статус MC -5 / Н.И. Алексеев, С.Н. Большагин, Е.А. Гомин [др.] // Вопросы атомной науки и техники. Сер.: Физика ядерных реакторов. - 2011. - № 4. - С. 4-23.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Paul K. Romano and Benoit Forget, «The OpenMC Monte Carlo Particle Transport Code», Ann. Nucl. Energy, 51, 274-281 (2013).</mixed-citation><mixed-citation xml:lang="en">Paul K. Romano and Benoit Forget, «The OpenMC Monte Carlo Particle Transport Code», Ann. Nucl. Energy, 51, 274-281 (2013).</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Cristian G. Bucher. Adaptive sampling - an iterative fast Monte Carlo procedure. Structural Safety, (1998), Volume 5, pp. 119-126.</mixed-citation><mixed-citation xml:lang="en">Cristian G. Bucher. Adaptive sampling - an iterative fast Monte Carlo procedure. Structural Safety, (1998), Volume 5, pp. 119-126.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Booth, T.E. and J.S. Hendricks (1984), Importance Estimation in Forward Monte Carlo Calculations, Nucl. Techno U Fusion, 5, p. 90.</mixed-citation><mixed-citation xml:lang="en">Booth, T.E. and J.S. Hendricks (1984), Importance Estimation in Forward Monte Carlo Calculations, Nucl. Techno U Fusion, 5, p. 90.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Leppänen, J., et al. (2015) «The Serpent Monte Carlo code: Status, development and applications in 2013». Ann. Nucl. Energy, 82 (2015) 142-150.</mixed-citation><mixed-citation xml:lang="en">Leppänen, J., et al. (2015) «The Serpent Monte Carlo code: Status, development and applications in 2013». Ann. Nucl. Energy, 82 (2015) 142-150.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Cooper, M.A., Larsen, E.W. Automated weight windows for global Monte Carlo particles transport calculations. Nuclear Science and Engineering, 137, 1-13, 2001.</mixed-citation><mixed-citation xml:lang="en">Cooper, M.A., Larsen, E.W. Automated weight windows for global Monte Carlo particles transport calculations. Nuclear Science and Engineering, 137, 1-13, 2001.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">A.J. van Wijk, G. Van den Eynde, J.E. Hoogenboom. An easy to implement global variance reduction procedure for MCNP. Annals of Nuclear Energy 38 (2011) 2496-2503.</mixed-citation><mixed-citation xml:lang="en">A.J. van Wijk, G. Van den Eynde, J.E. Hoogenboom. An easy to implement global variance reduction procedure for MCNP. Annals of Nuclear Energy 38 (2011) 2496-2503.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Yuan Hu, Sha Yan, Yuefeng Qiu, Yu Zheng. Implementation and benchmarking of an automatic global variance reduction method on OpenMC. Fusion Engineering and Design, Volume 173, 2021, 112829.</mixed-citation><mixed-citation xml:lang="en">Yuan Hu, Sha Yan, Yuefeng Qiu, Yu Zheng. Implementation and benchmarking of an automatic global variance reduction method on OpenMC. Fusion Engineering and Design, Volume 173, 2021, 112829.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Christopher N. Culberts, JohnS. Hendricks. An Assessment of the MCNP4C Weight Window. LA-13668, 1999.</mixed-citation><mixed-citation xml:lang="en">Christopher N. Culberts, JohnS. Hendricks. An Assessment of the MCNP4C Weight Window. LA-13668, 1999.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
