核数据敏感性与不确定性分析及其在目标精度评估中的应用
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摘要
核数据作为反应堆物理计算不确定性的重要来源,量化由核数据引入的不确定性,是反应堆不确定性分析的重要内容。另一方面,降低核数据的不确定性,有利于提高反应堆计算结果的可靠性,对于反应堆的经济性和安全性的提升有重要意义。基于敏感性与不确定性分析的目标精度评估,是给出核数据精度要求,从而降低计算结果不确定性的重要途径。本文提出了两步法的敏感性计算策略,针对快堆基准题BN-600,进行了有效增殖因数的敏感性分析,并量化了其不确定性的主要来源。通过建立目标精度评估问题对应的优化问题数学模型,采用差分进化算法,给出了有效增殖因数的目标精度为0.3%时核数据应达到的不确定性要求。
The nuclear data are one of the most important uncertainty sources for the reactor physics calculation. The quantification of the uncertainty introduced by the nuclear data is an important aspect in reactor uncertainty analysis. On the other hand, it is significant to improve the accuracy of the nuclear data for the reliability of reactor calculation results as well as the economy and safety of the reactor. The target accuracy assessment is one of the most effective approaches to give the accuracy requirement of the nuclear data to reduce calculation result uncertainties based on the sensitivity and uncertainty analysis. In this work, a two-step approach was proposed for sensitivity calculation. The k_(eff) sensitivity and uncertainty analysis was performed based on the fast reactor benchmark BN-600. The optimization mathematical model related to the target accuracy assessment was built and the differential evolution algorithm was applied to solve the optimization problems. The uncertainty requirements of the nuclear data were given when the target accuracy of k_(eff) was set to 0.3%.
The nuclear data are one of the most important uncertainty sources for the reactor physics calculation. The quantification of the uncertainty introduced by the nuclear data is an important aspect in reactor uncertainty analysis. On the other hand, it is significant to improve the accuracy of the nuclear data for the reliability of reactor calculation results as well as the economy and safety of the reactor. The target accuracy assessment is one of the most effective approaches to give the accuracy requirement of the nuclear data to reduce calculation result uncertainties based on the sensitivity and uncertainty analysis. In this work, a two-step approach was proposed for sensitivity calculation. The k_(eff) sensitivity and uncertainty analysis was performed based on the fast reactor benchmark BN-600. The optimization mathematical model related to the target accuracy assessment was built and the differential evolution algorithm was applied to solve the optimization problems. The uncertainty requirements of the nuclear data were given when the target accuracy of k_(eff) was set to 0.3%.
引文
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[15] 杨冰. 实用最优化方法及计算机程序[M]. 哈尔滨:哈尔滨船舶工程学院出版社,1994.
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[19] MacFARLANE R E, MUIR D W, BOICOURT R M, et al. The NJOY nuclear data processing system version 2012[R]. US: Los Alamos National Laboratory, 2012.
[20] SUGANTHAN P N, HANSEN N, LIANG J J, et al. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization[R]. Singapore: Nanyang Technological University, 2005.
[2] SUGAWARA T, STANKOVSKIY A, SAROTTO M, et al. Impact of nuclear data uncertainties on neutronics parameters of MYRRHA/XT-ADS[C]//NEMEA-6. Krakow, Poland: [s. n.], 2010.
[3] ZU T, YANG C, CAO L, et al. Nuclear data uncertainty propagation analysis for depletion calculation in PWR and FR Pin-cells[J]. Annals of Nuclear Energy, 2016(94): 399-408.
[4] WAN C, CAO L, WU H, et al. Uncertainty analysis for the assembly and core simulation of BEAVRS at the HZP conditions[J]. Nuclear Engineering and Design, 2017, 315: 11-19.
[5] SALVATORES M, JACQMIN R. International evaluation co-operation volume 26: Uncertainty and target accuracy assessment for innovative systems using recent covariance data evaluations[R]. [S. l.]: OECD/NEA, 2008.
[6] DU X, CAO L, ZHENG Y, et al. Developments of the sodium fast reactor analysis code SARAX: Methods and verification[C]//M&C 2017. Jeju, Korea: [s. n.], 2017.
[7] KIM Y. BN-600 fully MOX fuelled core benchmark analyses (phase4)[R]. Vienna: IAEA, 2004.
[8] CACUCI D G. Handbook of nuclear engineering[M]. New York: Springer, 2010.
[9] 谢仲生,邓力. 中子输运理论数值计算方法[M]. 西安:西北工业大学出版社,2005.
[10] TAKEDA T, ASANO K, KITADA T. Sensitivity analysis based on transport theory[J]. Journal of Nuclear Science and Technology, 2006, 43(7): 743-749.
[11] BALL M R. Uncertainty analysis in lattice reactor physics calculations[D]. Canada: McMaster University, 2012.
[12] WIESELQUIST W, ZHU T, VASILIEV A, et al. PSI methodologies for nuclear data uncertainty propagation with CASMO-5M and MCNPX: Results for OECD/NEA UAM benchmark phase I[J]. Science and Technology and Nuclear Installations, 2013(1): 129-132.
[13] ALIBERTI G, PALMIOTTI G, SALVATORES M, et al. Nuclear data sensitivity, uncertainty and target accuracy assessment for future nuclear systems[J]. Annals of Nuclear Energy, 2006, 33: 700-733.
[14] PALMIOTTI G, SALVATORES M. Impact of nuclear data uncertainties on innovative fast reactors and required target accuracies[J]. Journal of Nuclear Science and Technology, 2011, 48(4): 612-619.
[15] 杨冰. 实用最优化方法及计算机程序[M]. 哈尔滨:哈尔滨船舶工程学院出版社,1994.
[16] 肖婧. 差分进化算法的改进及应用研究[D]. 哈尔滨:哈尔滨工程大学,2011.
[17] 董明刚. 基于差分进化的优化算法及应用研究[D]. 杭州:浙江大学,2012.
[18] SCHLüTER M, GERDTS M. The oracle penalty method[J]. Journal of Global Optimization, 2010, 47(2): 293-325.
[19] MacFARLANE R E, MUIR D W, BOICOURT R M, et al. The NJOY nuclear data processing system version 2012[R]. US: Los Alamos National Laboratory, 2012.
[20] SUGANTHAN P N, HANSEN N, LIANG J J, et al. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization[R]. Singapore: Nanyang Technological University, 2005.
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