Uncertainty Analysis Method for Activation Neutron Spectra Based on Random Sampling
-
摘要: 为提升活化法测量中子能谱的精度并解决不确定度分析的关键问题，本文针对基于迭代法开发的SD解谱程序，提出一种基于实验测量的活化率、截面协方差和预置谱的中子测量不确定度随机抽样分析方法。通过开发迭代法驱动的SD解谱程序，系统量化了活化率、截面协方差和预置谱对解谱不确定度的影响，并基于随机抽样原理构建了多因素耦合分析模型，结合中国实验快堆（CEFR）中子能谱实验数据进行验证。结果表明：中子能谱不确定度在全能区呈非均匀分布，热区解谱最大不确定度达24%，快区则低于8%；预置谱是解谱不确定度的主要来源（占比超90%），截面协方差和活化率的贡献不足5%。与传统方法相比，基于随机抽样的分析方法能够更全面解析不确定度来源，可为提升中子能谱测量精度提供可靠依据，还可作为评估解谱程序性能的有效工具。Abstract: To improve the accuracy of neutron spectrum measurement via activation method and address the critical issue of uncertainty analysis, this study proposed a random sampling-based uncertainty analysis method integrating experimentally measured activation rates, cross-section covariance, and preset spectra for the SD spectrum unfolding program developed using an iterative method. By developing an iterative method-driven SD spectrum unfolding program, the impacts of activation rates, cross-section covariance, and preset spectra on spectrum unfolding uncertainties were systematically quantified by the system. A multi-factor coupling analysis model was constructed based on the principles of random sampling and validated using neutron spectrum experimental data from the China Experimental Fast Reactor (CEFR). The results demonstrate that: Neutron spectrum uncertainties exhibit non-uniform distribution across the full energy range, with the maximum uncertainty of spectrum unfolding in the thermal region reaching 24%, while uncertainties in the fast region remain below 8%. The preset spectrum dominates the unfolding uncertainties (contributing over 90%), whereas cross-section covariance and activation rates have negligible effects (contributing less than 5%). Compared to traditional methods, the random sampling-based analysis method provides a more comprehensive analysis of uncertainty sources, offering not only a reliable reference for enhancing neutron spectrum measurement accuracy but also serving as an effective tool for evaluating the performance of spectrum unfolding programs.
-
Key words:
- Spectrum unfolding /
- Activation method /
- Uncertainty /
- Iterative method /
- Random sampling
-
图 1 迭代法解谱基本原理
k—迭代次数；C—修正因子。
Figure 1. Basic Principle of Iterative Method for Spectrum Unfolding
图 2 截面不确定度分析方法的逻辑图
Figure 2. Logic Diagram of Cross-section Uncertainty Analysis Method
图 6 238U(n,f)反应截面的相对协方差
Figure 6. Relative Covariance of 238U(n,f) Reaction Cross-section
图 8 中子能谱调整前后活化率计算值与实验值的比较
Figure 8. Comparison between Calculated and Experimental Activation Rate before and after Neutron Spectrum Adjustment
表 1 CEFR 2-2 组件8个反应道的单核活化率
Table 1. Activation Rate of 8 Reaction Channels in CEFR 2-2 Assembly
序号 反应道 中子能量阈值/MeV 单核活化率/(cm−3·s−1) 1 238U(n,f) 1.5 5.60×10−14 2 47Ti(n,p)47Sc 2.2 2.43×10−15 3 58Ni(n,p)58Co 1.0 1.44×10−14 4 64Zn(n,p)64Cu 3.0 5.14×10−15 5 54Fe(n,p)54Mn 3.1 1.01×10−14 6 46Ti(n,p)46Sc 3.9 1.27×10−15 7 48Ti(n,p)48Sc 7.6 3.23×10−17 8 235U(n,f) 7.87×10−13 
下载: 导出CSV
表 2 调整谱计算与实验测量的单核活化率相对偏差
Table 2. Deviation between the Adjusted Spectrum and the Experimentally Measured Single-nuclide Activation Rates
序号 核反应 实验测量
活化率/(cm−3·s−1)调整谱计算
活化率/(cm−3·s−1)单核活化率
相对偏差/%1 238U(n,f) 5.60×10−14 5.39×10−14 −3.75 2 47Ti(n,p) 2.43×10−15 2.46×10−15 1.23 3 58Ni(n,p) 1.44×10−14 1.43×10−14 −0.69 4 64Zn(n,p) 5.14×10−15 5.08×10−15 −1.17 5 54Fe(n,p) 1.01×10−14 1.00×10−14 −0.99 6 46Ti(n,p) 1.27×10−15 1.24×10−15 −2.36 7 48Ti(n,p) 3.23×10−17 3.26×10−17 0.93 8 235U(n,f) 7.87×10−13 7.86×10−13 −0.13
下载: 导出CSV
-
[1] 黄迁明,刘斌,陆婷,等. 中子能谱测量中的解谱技术研究进展[J]. 辐射防护,2023, 42(4): 265-279. [2] HOSSEINI S A. Neutron spectrum unfolding using artificial neural network and modified least square method[J]. Radiation Physics and Chemistry, 2016, 126: 75-84. doi: 10.1016/j.radphyschem.2016.05.010 [3] HEYDARZADE A, KASESAZ Y, MOHAMMADI S. Coupling the SAND-II and MCNPX codes for neutron spectrum unfolding[J]. Journal of Instrumentation, 2018, 13(8): P08010. doi: 10.1088/1748-0221/13/08/P08010 [4] YANG J K, WANG P Q, REN Z G, et al. Comparison of neutron energy spectrum unfolding methods and evaluation of rationality criteria[J]. Nuclear Science and Techniques, 2022, 33(12): 164. doi: 10.1007/s41365-022-01139-2 [5] SEGHOUR A, SEGHOUR F Z. Unfolding neutron energy spectra from foil activation detector measurements with the gold algorithm[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2001, 457(3): 617-626. [6] MCELORY W N, BERG S, CROCKETT T, et al. Computer-automated iterative method for neutron flux spectra determination by foil activation[R]. New Mexico: Air Force Weapons Laboratory, Research and Technology Division, Air Force Systems Command, Kirtland Air Force Bose, 1967. [7] BRIESMEISTER J F. MCNP: A General Monte Carlo N-Particle transport code: LA-12625-M[R]. USA: LANL, 1997. [8] MUIR D W, BOICOURT M R, KAHLER A C, et al. The NJOY nuclear data processing system, version 2016: UR-17-20093[R]. New Mexico: Los Alamos National Laboratory, 2019. [9] 邓勇军. 活化箔方法测量中子能谱[D]. 北京: 中国原子能科学研究院,2006. [10] 吴治华. 原子核物理实验方法[M]. 第二版. 北京: 中国原子能出版社,1997: 7. [11] 施兆民,施朝晖,芦涵林. 核反应截面协方差矩阵计算[J]. 核科学与工程,1990, 10(3): 284-288,276. [12] BALL M R. Uncertainty analysis in lattice reactor physics calculations[D]. Hamilton: MaMaster University, 2012. [13] WISESLQUIST W VASILIEV A, FERROUKHI H. Nuclear data uncertainty propagation in a lattice physics code using stochastic sampling: PHYSOR 2012[R]. Illinois: American Nuclear Society, Inc. , 2012. [14] KLEIN M, GALLNER L, KRZYKACZ-HAUSMANN B, et al. Influence of nuclear data uncertainties on reactor core calculations[J]. Kerntechnik, 2011, 76(3): 174-178. doi: 10.3139/124.110148 [15] QUARTEMONT N J, BICKLEY A A, BEVINS J E. Nuclear data covariance analysis in radiation-transport simulations utilizing SCALE sampler and the IRDFF nuclear data library[J]. IEEE Transactions on Nuclear Science, 2020, 67(3): 482-491. doi: 10.1109/TNS.2020.2970700 [16] DONG D, FANG P, BOCK Y, et al. Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis[J]. Journal of Geophysical Research: Solid Earth, 2006, 111(B3): B03405. [17] 陈晓亮. 基于探测片活化法的中国实验快堆中子能谱测量实验研究及其应用[D]. 北京: 中国原子能科学研究院,2014. -
下载:
计量
- 文章访问数: 17
- HTML全文浏览量: 8
- PDF下载量: 0
- 被引次数: 0
