抽样法与灵敏度法keff不确定度量化

胡泽华; 叶涛; 刘雄国; 王佳

doi:10.7498/aps.66.012801

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摘要

核反应堆的中子学模拟计算中，核数据的不确定度导致的积分量计算结果的不确定度，通常采用基于微扰理论的灵敏度与不确定度分析方法（简称灵敏度法）量化.灵敏度分析法原则上只适用于线性模型，且一般输运计算程序难以直接进行灵敏度分析.而抽样法直接抽样核数据输入中子学计算程序进行计算，通过对计算结果的统计分析评估计算量的不确定度.抽样法易于实现、计算精确、且适用性强.在灵敏度分析与不确定度量化程序SURE中，增加了抽样法不确定度的量化功能.为将抽样法不确定度量化应用于复杂问题的模拟计算，需对其进行细致的考核.为此，选取简单的临界基准实验模型，分别采用灵敏度分析法和抽样法进行不确定度量化，得到了各核素各反应道核数据导致的keff计算不确定度.对比显示，两种方法的不确定度计算结果有很好的符合，验证了SURE程序抽样法功能的正确性.抽样法计算的keff符合正态分布，说明在一般核数据的不确定度范围内，keff与核数据近似成线性关系，利用灵敏度分析法评估keff计算值的不确定度是适用的.

关键词:

作者及机构信息

1.
北京应用物理与计算数学研究所, 北京 100094;

2.
中国工程物理研究院高性能数值模拟软件中心, 北京 100088

通信作者: 胡泽华, hu_zehua@iapcm.ac.cn

基金项目: 中国物理研究院中子物理学重点实验室基金（批准号：2013AA02）、能源局06重大专项（批准号：2015ZX06002008）和国家磁约束核聚变能研究专项（批准号：2015GB108002）资助的课题.

参考文献

[1]	USDOE 2002 A Technology Roadmap for Generation-IV Nuclear Energy Systems USDOE/GIF-002-00（Washington:USDOE) p1
[2]	Salvatores M, Jacqmin R 2008 Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations NEA/WPEC-26（Paris:OECD/NEA) p1
[3]	Marable J H, Weisbin C R 1979 Theory and Application of Sensitivity and Uncertainty Analysis（Oak Ridge:Oak Ridge National Laboratory) p16
[4]	Gilli L, Lathouwers D, Kloosterman J L, van der Hagen T H J J 2013 Nucl. Sci. Eng. 175 172
[5]	Kim D H, Gil C S, Lee Y O 2008 International Conference on Nuclear Data for Science and Technology Nice, France, April 22-27, 2007 p289
[6]	Kodeli I 2008 Sci. Technol. Nucl. Instll. 2008 659861
[7]	Pusa M 2012 Sci. Technol. Nucl. Instll. 2012 157029
[8]	Williams M L, Rearden B T 2008 Nucl. Data Sheets 109 5
[9]	Hu Z H, Wang J, Sun W L, Li M S 2013 Atom. Energy Sci. Technol. 47 25 （in Chinese)[胡泽华, 王佳, 孙伟力, 李茂生2013原子能科学技术47 25]
[10]	Dossantos-Uzarralde P J, Guittet A 2008 Nucl. Data Sheets 109 2894
[11]	Gilli L, Lathouwers D, Kloosterman J L, van der Hagen T H J J, Koning A J, Rochman D 2013 Ann. Nucl. Energy 56 71
[12]	Williams M M R 2007 Nucl. Sci. Eng. 155 109
[13]	Wieselquist W, Zhu T, Vasiliev A, Ferroukhi H 2013 Sci. Technol. Nucl. Instll. 2013 549793
[14]	Zhu T, Vasiliev A, Ferroukhi H, Pautz A 2014 Nucl. Data Sheets 118 453
[15]	Zhu T, Vasiliev A, Ferroukhi H, Pautz A 2015 Ann. Nucl. Energy 75 713
[16]	Zhu T, Vasiliev A, Ferroukhi H, Pautz A, Tarantola S 2015 J. Nucl. Sci. Technol. 52 8
[17]	Chadwick M B, Herman M, Oblozinsky P 2011 Nucl. Data Sheets 112 110
[18]	Engle W W J 1967 A User's Manual for ANISN:A One-Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering（Oak Ridge:Oak Ridge Gaseous Diffusion Plant Computing Technology Center) p1
[19]	Macfarlane R E, Muir D W, Boicourt R M, Kahler A C 2012 The NJOY Nuclear Data Processing System (Los Alamos:Los Alamos National Laboratory) p1
[20]	Kiedrowski B C, Brown F B 2013 Nucl. Sci. Eng. 174 227
[21]	Briggs J B 2004 International Handbook of Evaluated Criticality Safety Benchmark Experiments（Paris:Nuclear Energy Agency) p1

施引文献

[1]	USDOE 2002 A Technology Roadmap for Generation-IV Nuclear Energy Systems USDOE/GIF-002-00（Washington:USDOE) p1
[2]	Salvatores M, Jacqmin R 2008 Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations NEA/WPEC-26（Paris:OECD/NEA) p1
[3]	Marable J H, Weisbin C R 1979 Theory and Application of Sensitivity and Uncertainty Analysis（Oak Ridge:Oak Ridge National Laboratory) p16
[4]	Gilli L, Lathouwers D, Kloosterman J L, van der Hagen T H J J 2013 Nucl. Sci. Eng. 175 172
[5]	Kim D H, Gil C S, Lee Y O 2008 International Conference on Nuclear Data for Science and Technology Nice, France, April 22-27, 2007 p289
[6]	Kodeli I 2008 Sci. Technol. Nucl. Instll. 2008 659861
[7]	Pusa M 2012 Sci. Technol. Nucl. Instll. 2012 157029
[8]	Williams M L, Rearden B T 2008 Nucl. Data Sheets 109 5
[9]	Hu Z H, Wang J, Sun W L, Li M S 2013 Atom. Energy Sci. Technol. 47 25 （in Chinese)[胡泽华, 王佳, 孙伟力, 李茂生2013原子能科学技术47 25]
[10]	Dossantos-Uzarralde P J, Guittet A 2008 Nucl. Data Sheets 109 2894
[11]	Gilli L, Lathouwers D, Kloosterman J L, van der Hagen T H J J, Koning A J, Rochman D 2013 Ann. Nucl. Energy 56 71
[12]	Williams M M R 2007 Nucl. Sci. Eng. 155 109
[13]	Wieselquist W, Zhu T, Vasiliev A, Ferroukhi H 2013 Sci. Technol. Nucl. Instll. 2013 549793
[14]	Zhu T, Vasiliev A, Ferroukhi H, Pautz A 2014 Nucl. Data Sheets 118 453
[15]	Zhu T, Vasiliev A, Ferroukhi H, Pautz A 2015 Ann. Nucl. Energy 75 713
[16]	Zhu T, Vasiliev A, Ferroukhi H, Pautz A, Tarantola S 2015 J. Nucl. Sci. Technol. 52 8
[17]	Chadwick M B, Herman M, Oblozinsky P 2011 Nucl. Data Sheets 112 110
[18]	Engle W W J 1967 A User's Manual for ANISN:A One-Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering（Oak Ridge:Oak Ridge Gaseous Diffusion Plant Computing Technology Center) p1
[19]	Macfarlane R E, Muir D W, Boicourt R M, Kahler A C 2012 The NJOY Nuclear Data Processing System (Los Alamos:Los Alamos National Laboratory) p1
[20]	Kiedrowski B C, Brown F B 2013 Nucl. Sci. Eng. 174 227
[21]	Briggs J B 2004 International Handbook of Evaluated Criticality Safety Benchmark Experiments（Paris:Nuclear Energy Agency) p1

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抽样法与灵敏度法keff不确定度量化

1. 北京应用物理与计算数学研究所, 北京 100094;

2. 中国工程物理研究院高性能数值模拟软件中心, 北京 100088

通信作者: 胡泽华, hu_zehua@iapcm.ac.cn

基金项目:

中国物理研究院中子物理学重点实验室基金（批准号：2013AA02）、能源局06重大专项（批准号：2015ZX06002008）和国家磁约束核聚变能研究专项（批准号：2015GB108002）资助的课题.

收稿日期: 2016-07-07

修回日期: 2016-09-30

刊出日期: 2017-01-05

摘要: 核反应堆的中子学模拟计算中，核数据的不确定度导致的积分量计算结果的不确定度，通常采用基于微扰理论的灵敏度与不确定度分析方法（简称灵敏度法）量化.灵敏度分析法原则上只适用于线性模型，且一般输运计算程序难以直接进行灵敏度分析.而抽样法直接抽样核数据输入中子学计算程序进行计算，通过对计算结果的统计分析评估计算量的不确定度.抽样法易于实现、计算精确、且适用性强.在灵敏度分析与不确定度量化程序SURE中，增加了抽样法不确定度的量化功能.为将抽样法不确定度量化应用于复杂问题的模拟计算，需对其进行细致的考核.为此，选取简单的临界基准实验模型，分别采用灵敏度分析法和抽样法进行不确定度量化，得到了各核素各反应道核数据导致的keff计算不确定度.对比显示，两种方法的不确定度计算结果有很好的符合，验证了SURE程序抽样法功能的正确性.抽样法计算的keff符合正态分布，说明在一般核数据的不确定度范围内，keff与核数据近似成线性关系，利用灵敏度分析法评估keff计算值的不确定度是适用的.

关键词:

Uncertainty quantification in the calculation of keff using sensitity and stochastic sampling method

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;

2.
Software Center for High Performance Numerical Simulation, China Academy of Engineering Physics, Beijing 100088, China

Fund Project:

Project supported by the Key Laboratory of Neutron Physics of China Academy of Engineering Physics（Grant No. 2013AA02), Sub-item of Special Project of the National Energy Bureau, China（Grant No. 2015ZX06002008), National Magnetic Confinement Fusion Energy Research Project, China（Grant No. 2015GB108002).

Received Date: 07 July 2016

Accepted Date: 30 September 2016

Published Online: 05 January 2017

Abstract: The sensitivity and uncertainty analysis(S/U) method based on the first order perturbation theory is commonly employed to calculate the uncertainties in-nuclear reactor's integral parameters, such as the neutron effective multiplication factor(keff), due to uncertainties in nuclear data. However, this method is only theoretically suitable for the linear model because of its first order approximation. Moreover, S/U method is difficult to incorporate into a neutronics code, because the adjoint angular flux is needed to obtain the sensitivity coefficient of an integral parameter to nuclear data. Meanwhile, the sampling approach based on parametric random sampling of input parameters, an easy implemented method, evaluates the uncertainties in the integral parameters by performing a set of neutronics simulations inputted with a set of stochastic nuclear data sampled from a multinomial normal distribution with nuclear cross section mean values and covariance data. The sampling approach is considered as a more exact method, as linear approximation is not needed. With the increase of computational power, the sampling methods with consuming more time are now possible. The sampling approach is incorporated into SURE, a sensitivity and uncertainty analysis code developed in IAPCM, as a functional module. A careful verification of the new function is necessary before it is used to analyze complicated problems, such as multi-physical coupling calculations of nuclear reactor. Two simple fast criticality benchmark experiments, namely Godiva(HEU-MET-FAST-001) and Jezebel(PU-MET-FAST-001), are selected to verify the sampling module of SURE. The uncertainties in nuclear data are given by multigroup covariance matrices processed from ENDF/B-VⅡ. 1 data. The uncertainties in the computed value of keff resulting from uncertainties in the nuclear data are calculated with both S/U and sampling methods. The uncertainties due to reaction cross sections for each nuclide in two benchmarks given by two methods with the multigroup covariance matrices are in good agreement. Since the S/U module of SURE code is verified extensively, the correctness of the sampling function of the code is confirmed as well. The distribution of the keff from the sampling approach obeys the normal distribution pretty well, which indicates that keff varies linearly with the nuclear data under its uncertainty range, since the nuclear data used in calculations are assumed to be normal distribution in the sampling method. The results from the sampling method also support the S/U method with linear approximation as a suitable uncertainty quantification method for keff calculation.

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