基于敏感性分析的核数据调整模块开发与验证

邹晓阳; 梁亮; 徐嘉隆

doi:10.11884/HPLPB202638.250234

基于敏感性分析的核数据调整模块开发与验证

doi: 10.11884/HPLPB202638.250234

西安智核云谷科技有限公司，西安 710021

详细信息

作者简介:
邹晓阳，1968940059@qq.com

中图分类号: TL32
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- 被引次数: 0
出版历程
- 收稿日期: 2025-07-24
- 修回日期: 2025-12-18
- 录用日期: 2025-12-18
- 网络出版日期: 2026-01-04

Development and validation of a nuclear data adjustment module based on sensitivity analysis

Xi'an Nuclear Intelligence Valley Co., Ltd. Xi'an 710021, China

摘要

摘要: 随着中子学计算方法的发展和精确建模能力的提高，核反应堆物理计算程序中模型近似和离散方法带来的误差逐渐减小，而核数据因其测量难度高，成为影响计算精度的关键输入参数。因此，基于自主研发的敏感性和不确定性分析平台SUPES，开发了基于敏感性分析和广义线性最小二乘算法的核数据调整模块。首先，由敏感性分析获取响应关于输入参数的变化规律；其次，通过相似性分析筛选中子学层面上相似程度高的实验装置参与核数据调整；最后，采用广义线性最小二乘算法使得计算值与实测值之间的误差最小，获得核数据调整量。根据临界基准题HEU-MET-FAST-078中的22个算例，对ACE格式连续能量数据库进行调整，数值结果表明，有效增殖因子k_eff的均方根误差从3.10×10⁻³降低到1.53×10⁻³。通过数值结果对比分析，验证了所开发的核数据调整模块的正确性。
- 敏感性分析 /
- 相似性分析 /
- 核数据调整 /
- ACE数据库
Abstract: Background
With the development of neutron calculation methods and improved modeling capabilities, the errors introduced by model approximations and discretization methods in nuclear reactor physics calculations have gradually decreased. However, nuclear data, due to the challenges in measurement, have become the key input parameter affecting computational accuracy.
Purpose
In this study, a nuclear data adjustment module based on sensitivity analysis and the generalized linear least squares algorithm was developed within the self-developed sensitivity and uncertainty analysis platform, SUPES.
Methods
First, sensitivity analysis was used to determine the relationship between system responses and input parameter variations. Next, similarity analysis was applied to select experimental setups with high similarity at the neutron physics level. Finally, the generalized linear least squares algorithm was employed to minimize the error between computed and measured values, resulting in nuclear data adjustments.
Results
The adjustment of the ACE format continuous energy database was performed on 22 cases from the critical benchmark HEU-MET-FAST-078. The numerical results show that the root mean square error of the effective multiplication factor (k_eff) was reduced from 3.10×10⁻³ to 1.53×10⁻³.
Conclusions
The comparison and analysis verified the correctness of the developed nuclear data adjustment module.
- sensitivity analysis /
- similarity analysis /
- nuclear data adjustment /
- ACE database

HTML全文

图 1 SUPES程序功能介绍

Figure 1. Introduction to SUPES program functions

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图 2 核数据调整模块流程图

Figure 2. Flowchart of nuclear data adjustment module

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图 3 HEU-MET-FAST-078基准题结构示意图

Figure 3. Schematic diagram of HEU-MET-FAST-078 benchmark structure

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图 4 临界实验装置k_eff对核数据的相对灵敏度系数

Figure 4. Relative sensitivity coefficients of k_eff to nuclear data for critical experiment device

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图 5 HEU-MET-FAST-078基准题算例之间的相似性系数

Figure 5. Similarity coefficients among HEU-MET-FAST-078 benchmark cases

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图 6 主要反应道核数据的相对调整系数

Figure 6. Relative adjustment coefficients of nuclear data for major reaction channels

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图 7 核数据调整前后k_eff计算值与基准值的对比

Figure 7. Comparison of k_eff calculation values before and after nuclear data adjustment with benchmark values

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图 8 核数据调整前后²³⁵U主要反应道核数据相对标准差的变化

Figure 8. The change in relative standard deviation of ²³⁵U reaction channel before and after nuclear data adjustment

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图 9 核数据调整前后²³⁵U主要反应道对k_eff不确定度的贡献

Figure 9. The contribution of ²³⁵U reaction channels to k_eff uncertainty before and after adjustment

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表 1 HEU-MET-FAST-078基准题的材料和尺寸信息

Table 1. Material and dimension information of HEU-MET-FAST-078 benchmark cases

case	²³⁵U mass fraction/%	fuel density/ (g/cm³)	diameter D/cm	fuel height H_c/cm	reflector material	top thickness H_t/cm	bottom thickness H_b/cm	reflector density/ (g/cm³)
#1	93.3	17.9	38.1	5.7562	water	15.24	0.0	0.9982
#3	93.3	17.9	38.1	6.7331	polyethylene	2.54	0.0	0.925
#5	93.3	17.9	38.1	5.9663	polyethylene	5.08	0.0	0.925
#7	93.3	17.9	38.1	3.8392	polyethylene	5.08	5.08	0.925
#9	93.3	17.9	38.1	5.7404	polyethylene	7.62	0.0	0.925
#11	93.3	17.9	38.1	5.6984	polyethylene	10.16	0.0	0.925
#13	93.3	17.9	38.1	5.7089	polyethylene	15.24	0.0	0.925
#15	93.3	17.9	38.1	5.6984	polyethylene	20.32	0.0	0.925
#17	93.3	17.9	38.1	5.6984	polyethylene	25.40	0.0	0.925
#19	93.3	17.9	38.1	5.5881	Lucite	15.24	0.0	1.18
#21	93.3	17.9	38.1	5.7352	paraffin	15.24	0.0	0.87
#23	93.3	17.9	38.1	7.1165	paraffin	2.54	0.0	1.79
#25	93.3	17.9	38.1	6.5860	paraffin	5.08	0.0	1.79
#27	93.3	17.9	38.1	6.0346	paraffin	15.24	0.0	1.70
#29	93.3	17.9	38.1	3.9600	paraffin	15.24	15.24	1.70
#31	93.3	17.9	38.1	5.9820	paraffin	17.78	0.0	1.71
#33	93.3	17.9	38.1	3.8340	paraffin	17.78	17.78	1.70
#35	93.3	17.9	38.1	5.9453	paraffin	20.32	0.0	1.72
#37	93.3	17.9	38.1	5.9558	paraffin	30.48	0.0	1.70
#39	93.3	17.9	38.1	5.9505	paraffin	35.56	0.0	1.71
#41	93.3	17.9	38.1	8.1564	none	/	/	/
#43*	93.3	17.9	38.1	6.7751	polyethylene	15.24	0.0	0.925
Note：*case #43 has a 0.0381 cm thick cadmium sheet between the polyethylene reflector and the fuel cylinder.

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表 3 核数据调整前后k_eff计算值与基准值的误差

Table 3. Error of k_eff calculation values before and after nuclear data adjustment from benchmark values

case	benchmark k_eff (±1σ)	ENDF/B-VII.1 ACE MCNP result (±1σ)	error before adjustment/10⁻⁵	after adjustment MCNP result (±1σ)	error after adjustment/10⁻⁵
#1	0.9995±0.0018	0.99460±0.00007	−490	0.99799±0.00007	−151
#3	0.9994±0.0022	0.99597±0.00007	−343	0.99781±0.00007	−159
#5	0.9991±0.0019	0.99619±0.00007	−291	0.99864±0.00007	−46
#7	1.0000±0.0019	0.99857±0.00008	−143	1.00147±0.00008	147
#9	0.9997±0.0022	0.99580±0.00007	−390	0.99815±0.00007	−155
#11	0.9995±0.0015	0.99582±0.00007	−368	0.99845±0.00007	−105
#13	1.0000±0.0017	0.99735±0.00007	−265	0.99996±0.00008	−4
#15	0.9991±0.0018	0.99670±0.00007	−240	0.99925±0.00007	15
#17	0.9995±0.0018	0.99668±0.00007	−282	0.99928±0.00007	−22
#19	0.9995±0.0016	0.99560±0.00008	−390	0.99842±0.00007	−108
#21	0.9995±0.0020	0.99624±0.00007	−326	0.99885±0.00008	−65
#23	0.9992±0.0022	0.99804±0.00006	−116	0.99947±0.00006	27
#25	0.9992±0.0025	0.99739±0.00007	−181	0.99896±0.00007	−24
#27	0.9992±0.0021	0.99597±0.00007	−323	0.99733±0.00006	−187
#29	1.0000±0.0025	1.00235±0.00007	235	1.00292±0.00007	292
#31	0.9994±0.0020	0.99513±0.00007	−427	0.99668±0.00007	−272
#33	0.9996±0.0026	0.99591±0.00007	−369	0.99677±0.00007	−283
#35	0.9991±0.0022	0.99452±0.00007	−458	0.99592±0.00007	−318
#37	0.9986±0.0021	0.99624±0.00007	−236	0.99777±0.00006	−83
#39	0.9989±0.0021	0.99676±0.00007	−214	0.99835±0.00007	−55
#41	0.9992±0.0025	0.99678±0.00006	−242	0.99860±0.00006	−60
#43	1.0000±0.0019	0.99895±0.00007	−105	1.00044±0.00008	44

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表 2 敏感性分析包含的核素反应道

Table 2. Nuclide reaction channels included in the sensitivity analysis

reaction symbol	instruction	involved nuclides
σ_elas	elastic scattering reaction	¹H ¹²C ¹⁶O ²³⁴U ²³⁵U ²³⁸U
σ_inel	inelastic scattering reaction	²³⁴U ²³⁵U ²³⁸U
σ_f	fission reaction	²³⁴U ²³⁵U ²³⁸U
σ_γ	capture reaction	¹H ¹²C ¹⁶O ²³⁴U ²³⁵U ²³⁸U
ν_p	prompt fission neutron yield	²³⁴U ²³⁵U ²³⁸U
χ_p	prompt fission neutron spectrum	²³⁵U

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表 4 核数据调整前后有效增殖因子k_eff不确定度的变化

Table 4. The change in k_eff uncertainty of eigenvalues before and after nuclear data adjustment

case	benchmark k_eff (±1σ)	ENDF/B-VII.1 ACE MCNP result (±1σ)	before adjustment k_eff uncertainty/10⁻⁵	after adjustment k_eff uncertainty/10⁻⁵
#1	0.9995±0.0018	0.99460±0.00007	1130	482
#3	0.9994±0.0022	0.99597±0.00007	1145	516
#5	0.9991±0.0019	0.99619±0.00007	1135	478
#7	1.0000±0.0019	0.99857±0.00008	1321	462
#9	0.9997±0.0022	0.99580±0.00007	1128	464
#11	0.9995±0.0015	0.99582±0.00007	1119	460
#13	1.0000±0.0017	0.99735±0.00007	1123	464
#15	0.9991±0.0018	0.99670±0.00007	1126	471
#17	0.9995±0.0018	0.99668±0.00007	1117	463
#19	0.9995±0.0016	0.99560±0.00008	1136	471
#21	0.9995±0.0020	0.99624±0.00007	1117	462
#23	0.9992±0.0022	0.99804±0.00006	1039	531
#25	0.9992±0.0025	0.99739±0.00007	1098	533
#27	0.9992±0.0021	0.99597±0.00007	1199	539
#29	1.0000±0.0025	1.00235±0.00007	1538	525
#31	0.9994±0.0020	0.99513±0.00007	1204	534
#33	0.9996±0.0026	0.99591±0.00007	1574	536
#35	0.9991±0.0022	0.99452±0.00007	1206	532
#37	0.9986±0.0021	0.99624±0.00007	1211	534
#39	0.9989±0.0021	0.99676±0.00007	1212	539
#41	0.9992±0.0025	0.99678±0.00006	994	567
#43	1.0000±0.0019	0.99895±0.00007	1141	504

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