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结合源偏倚和权窗的蒙特卡罗全局减方差方法

张显 刘仕倡 魏军侠 李树 王鑫 上官丹骅

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结合源偏倚和权窗的蒙特卡罗全局减方差方法

张显, 刘仕倡, 魏军侠, 李树, 王鑫, 上官丹骅

Monte Carlo global variance reduction method combining source bias and weight window

Zhang Xian, Liu Shi-Chang, Wei Jun-Xia, Li Shu, Wang Xin, Shangguan Dan-Hua
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  • 全局计数问题在反应堆pin-by-pin模型蒙特卡罗模拟和多物理耦合计算中动态粒子输运蒙特卡罗模拟等重大研究领域中都有广泛的应用场景. 大量的全局减方差算法研究立足于全局计数误差分布的展平, 由此提高全局计数的整体效率. 本工作针对两种高效全局减方差算法, 即均匀计数密度算法(属于源偏倚算法的一种)和权窗算法的结合展开研究, 提出利用均匀计数密度算法的偏倚因子调整权窗下限, 由此实现两种算法的有机结合. 基于Hoogenboom-Martin压水堆全堆基准题中开展了一系列对比测试, 验证了混合全局减方差算法更优于单一权窗算法或均匀计数密度算法, 尤其是在降低最大误差方面. 同时, 基于新的指标, 验证了均匀计数密度算法较经典的均匀裂变源算法具有更好的表现. 研究结果表明, 本文提出的混合全局减方差算法能高效求解全局计数问题, 进一步促进了相关领域的研究.
    The global tally problem has a wide range of applications in major research fields such as Monte Carlo simulations of pin-by-pin reactor models and time-dependent particle transport problems in multi-physics coupling calculations. Due to the uneven power distribution of the simulated system, the statistical errors of all tallies are unevenly distributed, resulting in some low global efficiency. For this kind of problem with global characteristics, it is necessary to develop global variance reduction techniques to obtain the accurate distribution of target tallies in the entire space. A large number of global variance reduction algorithms have been studied based on the consideration of flattening global tally error distribution, so as to improve global efficiency. This work focuses on the combination of two efficient global variance reduction algorithms, namely, the uniform tally density algorithm and the weight window algorithm, which belong to source bias and transport process bias, respectively. In tally, a method is proposed to adjust the weight window parameters by using the bias factor of the uniform tally density algorithm. Then, the weight window method will be used to reduce the weight fluctuation caused by the uniform tally density method. In this way, an organic combination of these two algorithms can be realized. A series of comparative tests are carried out based on the Hoogenboom-Martin pressurized water reactor benchmark, and it is verified that the hybrid global variance reduction algorithm proposed in this work is better than the single weight window algorithm or the uniform tally density algorithm. In terms of reducing the maximum error, the global efficiency of the hybrid algorithm is 2.6 times and 3 times that of the weight window algorithm and the uniform tally density algorithm, respectively. In addition, through the comparative analysis of computational asymmetry degree and computational efficiency, it is verified that the uniform tally density algorithm has better performance than the classical uniform fission site algorithm, and the performance advantages of the uniform tally density algorithm are quantitatively evaluated based on some new indicators. The results show that the hybrid global variance reduction algorithm proposed in this work can solve the global tally problem efficiently, thereby further promoting research in related fields.
      通信作者: 上官丹骅, sgdh@iapcm.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 12175067, 12035002, 12375164)、河北省自然科学基金(批准号: A2022502008)、中央高校基本科研业务费专项资金(批准号: 2022JG002)和中国工程物理研究院创新发展基金(批准号: CX20210045, CX20200028)资助的课题.
      Corresponding author: Shangguan Dan-Hua, sgdh@iapcm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12175067, 12035002, 12375164), the Natural Science Foundation of Hebei Province, China (Grant No. A2022502008), the Fundamental Research Funds for the Central Universities of China (Grant No. 2022JG002), and the Innovation Development Foundation of China Academy of Engineering Physics, China (Grant Nos. CX20210045, CX20200028).
    [1]

    张滕飞, 吴宏春, 曹良志, 李云召, 刘晓晶, 熊进标, 柴翔 2019 原子能科学技术 53 1160Google Scholar

    Zhang T F, Wu H C, Cao L Z, Li Y Z, Liu X J, Xiong J B, Chai X 2019 At. Energy Sci. Technol. 53 1160Google Scholar

    [2]

    李刚, 雷伟, 张宝印, 邓力, 马彦, 李瑞, 上官丹骅, 付元光, 胡小利 2014 核动力工程 35 228

    Li G, Lei W, Zhang B Y, Deng L, Ma Y, Li R, Shangguan D H, Fu Y G, Hu X L 2014 Nucl. Power Eng. 35 228

    [3]

    上官丹骅, 闫威华, 魏军侠, 高志明, 陈艺冰, 姬志成 2022 物理学报 71 090501Google Scholar

    Shangguan D H, Yan W H, Wei J X, Gao Z M, Chen Y B, Ji Z C 2022 Acta Phys. Sin. 71 090501Google Scholar

    [4]

    Davis A, Turner A 2011 Fusion Eng. Des. 86 2689Google Scholar

    [5]

    Wijk A J V, Eynde G V D, Hoogenboom J E 2011 Ann. Nucl. Energy 38 2496Google Scholar

    [6]

    Hunter J L, Sutton T M 2013 M&C 2013 Sun Valley, Idaho, USA, May 5–9, 2013 p2780

    [7]

    Kelly D J, Sutton T M, Wilson S C 2012 Proceedings of PHYSOR 2012-Advances in Reactor Physics-Linking Research, Industry, and Education Knoxville, Tennessee, USA, April 15–20, 2012

    [8]

    上官丹骅, 姬志成, 邓力, 李瑞, 李刚, 付元光 2019 物理学报 68 122801Google Scholar

    Shangguan D H, Ji Z C, Deng L, Li R, Li G, Fu Y G 2019 Acta Phys. Sin. 68 122801Google Scholar

    [9]

    Shangguan D H, Li G, Zhang B Y, Deng L, Ma Y, Fu Y G, Li R, Hu X L 2017 Nucl. Sci. Eng. 182 555Google Scholar

    [10]

    李新梅, 郑华庆, 郝丽娟, 宋婧, 胡丽琴, 江平 2017 核科学与工程 37 577Google Scholar

    Li X M, Zheng H Q, Hao L J, Song Q, Hu L Q, Jiang P 2017 Nucl. Sci. Eng. 37 577Google Scholar

    [11]

    Cooper M A, Larsen E W 2001 Nucl. Sci. Eng. 137 1Google Scholar

    [12]

    Wang K, Li Z G, She D, Liang J G, Xu Q, Qiu Y S, Yu J K, Sun J L, Fan X, Yu G L 2015 Ann. Nucl. Energy 82 121Google Scholar

    [13]

    余慧, 全国萍, 秦瑶, 严伊蔓, 陈义学 2021 核动力工程 42 218Google Scholar

    Yu H, Quan G P, Qin Y, Yan Y M, Chen Y X 2021 Nucl. Power Eng. 42 218Google Scholar

    [14]

    Zhang X, Liu S C, Yan Y M, Qin Y, Chen Y X 2020 Fusion Eng. Des. 159 111875Google Scholar

    [15]

    Kelly D J, Aviles B N, Herman B R 2013 M&C 2013 Sun Valley Idaho, USA, May 5–9, 2013 p2962

    [16]

    Hoogenboom J E, Martin W R 2009 M&C 2009 Saratoga Springs, NY, USA, May 3–7, 2009

    [17]

    刘鸿飞, 张彬航, 张澍, 孙光耀, 郝丽娟, 宋婧, 龙鹏程 2016 核技术 39 040604Google Scholar

    Liu H F, Zhang B H, Zhang S, Sun G Y, Hao L J, Song Q, Long P C 2016 Nucl. Tech. 39 040604Google Scholar

    [18]

    张显, 刘仕倡, 强胜龙, 张文鑫, 尹强, 崔显涛, 陈义学 2021 原子能科学技术 55 66Google Scholar

    Zhang X, Liu S C, Qiang S L, Zhang W X, Yin Q, Cui X T, Chen Y X 2021 Atomic Energy Sci. Technol. 55 66Google Scholar

    [19]

    Kiedrowski B C, Ibrahim A 2011 Trans. Am. Nucl. Soc. 104 325

    [20]

    上官丹骅, 李刚, 邓力, 张宝印, 李瑞, 付元光 2015 物理学报 64 052801Google Scholar

    Shangguan D H, Li G, Deng L, Zhang B Y, Li R, Fu Y G 2015 Acta Phys. Sin. 64 052801Google Scholar

  • 图 1  权窗原理

    Fig. 1.  Working principle of weight window.

    图 2  Hoogenboom-Martin基准题 (a) 几何横截面; (b) 功率分布(MW); (c) 统计误差分布

    Fig. 2.  Hoogenboom Martin benchmark: (a) Geometric cross-section; (b) power distribution (MW); (c) statistical error distribution.

    图 3  变异系数分布 (a) Basic; (b) UFS; (c) UTD

    Fig. 3.  Distribution of the coefficient of variation: (a) Basic; (b) UFS; (c) UTD.

    图 4  偏倚因子的方差分布

    Fig. 4.  Variance distribution of bias factors.

    图 5  统计误差的累积分布

    Fig. 5.  Cumulative distribution of statistical errors.

    表 1  UTD算法和UFS算法的计算结果对比

    Table 1.  Comparison of calculation results of UTD and UFS.

    计算条件RemaxRe95计算时间

    T/min
    FOM_
    MAX
    FOM_95
    Basic0.25910.096913.051.14148.1610
    UFS0.14860.055813.063.467524.5917
    UTD0.12710.053213.154.707426.8690
    下载: 导出CSV

    表 2  计算结果对比

    Table 2.  Comparison of calculation results.

    计算条件 Remax Re95 计算时间
    T/min
    FOM_
    MAX
    FOM_95
    WW 0.0874 0.0333 24.26 5.3962 37.1724
    UTD 0.1271 0.0540 13.61 4.5483 25.1973
    混合算法 0.0538 0.0324 24.40 14.1594 39.0409
    下载: 导出CSV
  • [1]

    张滕飞, 吴宏春, 曹良志, 李云召, 刘晓晶, 熊进标, 柴翔 2019 原子能科学技术 53 1160Google Scholar

    Zhang T F, Wu H C, Cao L Z, Li Y Z, Liu X J, Xiong J B, Chai X 2019 At. Energy Sci. Technol. 53 1160Google Scholar

    [2]

    李刚, 雷伟, 张宝印, 邓力, 马彦, 李瑞, 上官丹骅, 付元光, 胡小利 2014 核动力工程 35 228

    Li G, Lei W, Zhang B Y, Deng L, Ma Y, Li R, Shangguan D H, Fu Y G, Hu X L 2014 Nucl. Power Eng. 35 228

    [3]

    上官丹骅, 闫威华, 魏军侠, 高志明, 陈艺冰, 姬志成 2022 物理学报 71 090501Google Scholar

    Shangguan D H, Yan W H, Wei J X, Gao Z M, Chen Y B, Ji Z C 2022 Acta Phys. Sin. 71 090501Google Scholar

    [4]

    Davis A, Turner A 2011 Fusion Eng. Des. 86 2689Google Scholar

    [5]

    Wijk A J V, Eynde G V D, Hoogenboom J E 2011 Ann. Nucl. Energy 38 2496Google Scholar

    [6]

    Hunter J L, Sutton T M 2013 M&C 2013 Sun Valley, Idaho, USA, May 5–9, 2013 p2780

    [7]

    Kelly D J, Sutton T M, Wilson S C 2012 Proceedings of PHYSOR 2012-Advances in Reactor Physics-Linking Research, Industry, and Education Knoxville, Tennessee, USA, April 15–20, 2012

    [8]

    上官丹骅, 姬志成, 邓力, 李瑞, 李刚, 付元光 2019 物理学报 68 122801Google Scholar

    Shangguan D H, Ji Z C, Deng L, Li R, Li G, Fu Y G 2019 Acta Phys. Sin. 68 122801Google Scholar

    [9]

    Shangguan D H, Li G, Zhang B Y, Deng L, Ma Y, Fu Y G, Li R, Hu X L 2017 Nucl. Sci. Eng. 182 555Google Scholar

    [10]

    李新梅, 郑华庆, 郝丽娟, 宋婧, 胡丽琴, 江平 2017 核科学与工程 37 577Google Scholar

    Li X M, Zheng H Q, Hao L J, Song Q, Hu L Q, Jiang P 2017 Nucl. Sci. Eng. 37 577Google Scholar

    [11]

    Cooper M A, Larsen E W 2001 Nucl. Sci. Eng. 137 1Google Scholar

    [12]

    Wang K, Li Z G, She D, Liang J G, Xu Q, Qiu Y S, Yu J K, Sun J L, Fan X, Yu G L 2015 Ann. Nucl. Energy 82 121Google Scholar

    [13]

    余慧, 全国萍, 秦瑶, 严伊蔓, 陈义学 2021 核动力工程 42 218Google Scholar

    Yu H, Quan G P, Qin Y, Yan Y M, Chen Y X 2021 Nucl. Power Eng. 42 218Google Scholar

    [14]

    Zhang X, Liu S C, Yan Y M, Qin Y, Chen Y X 2020 Fusion Eng. Des. 159 111875Google Scholar

    [15]

    Kelly D J, Aviles B N, Herman B R 2013 M&C 2013 Sun Valley Idaho, USA, May 5–9, 2013 p2962

    [16]

    Hoogenboom J E, Martin W R 2009 M&C 2009 Saratoga Springs, NY, USA, May 3–7, 2009

    [17]

    刘鸿飞, 张彬航, 张澍, 孙光耀, 郝丽娟, 宋婧, 龙鹏程 2016 核技术 39 040604Google Scholar

    Liu H F, Zhang B H, Zhang S, Sun G Y, Hao L J, Song Q, Long P C 2016 Nucl. Tech. 39 040604Google Scholar

    [18]

    张显, 刘仕倡, 强胜龙, 张文鑫, 尹强, 崔显涛, 陈义学 2021 原子能科学技术 55 66Google Scholar

    Zhang X, Liu S C, Qiang S L, Zhang W X, Yin Q, Cui X T, Chen Y X 2021 Atomic Energy Sci. Technol. 55 66Google Scholar

    [19]

    Kiedrowski B C, Ibrahim A 2011 Trans. Am. Nucl. Soc. 104 325

    [20]

    上官丹骅, 李刚, 邓力, 张宝印, 李瑞, 付元光 2015 物理学报 64 052801Google Scholar

    Shangguan D H, Li G, Deng L, Zhang B Y, Li R, Fu Y G 2015 Acta Phys. Sin. 64 052801Google Scholar

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出版历程
  • 收稿日期:  2023-09-14
  • 修回日期:  2023-10-20
  • 上网日期:  2023-11-09
  • 刊出日期:  2024-02-20

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