基于Kriging代理模型的铅铋反应堆智能优化方法

李琼; 刘紫静; 肖豪; 肖英杰; 赵鹏程; 王昌; 于涛

doi:10.11884/HPLPB202234.210560

基于Kriging代理模型的铅铋反应堆智能优化方法

doi: 10.11884/HPLPB202234.210560

李琼^{1, 2,},
刘紫静^{1, 2, ,},
肖豪¹,
肖英杰^{1, 2},
赵鹏程^{1, 2},
王昌¹,
于涛^{1, 2}

1.
南华大学核科学技术学院, 湖南衡阳 421001
2.
南华大学湖南省数字化反应堆工程技术研究中心, 湖南衡阳 421001

基金项目: 国家自然科学基金青年项目（12005097）；中央军委装备发展部预研项目（6142A07190106）；湖南省自然科学基金青年项目（2020JJ5465）；湖南省教育厅优秀青年项目（19B494)；湖南省科技创新团队项目（2020RC4053）

详细信息

作者简介:
李　琼，liqiong3646@163.com

通讯作者:
刘紫静，liuzijing1123@163.com

中图分类号: TL334
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- 文章访问数: 938
- HTML全文浏览量: 410
- PDF下载量: 64
- 被引次数: 0
出版历程
- 收稿日期: 2021-12-14
- 修回日期: 2022-01-14
- 网络出版日期: 2022-02-14
- 刊出日期: 2022-05-15

Intelligent optimization method for lead-bismuth reactor based on Kriging surrogate model

Li Qiong^{1, 2
,},
Liu Zijing^{1, 2
, ,},
Xiao Hao¹,
XiaoYingjie^{1, 2},
Zhao Pengcheng^{1, 2},
Wang Chang¹,
Yu Tao^{1, 2}

1.
School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
2.
Hunan Engineering and Technology Research Center for Virtual Nuclear Reactor, University of South China, Hengyang 421001, China

摘要

摘要: 铅铋反应堆广泛应用的需求要求研究人员在现有堆芯方案的基础上开展大量优化设计工作。针对铅铋反应堆多物理、多变量、多约束耦合影响的多维非线性约束优化设计问题，基于Kriging代理模型、正交拉丁超立方抽样和SEUMRE空间搜索技术构建铅铋反应堆智能优化方法，耦合物理蒙卡计算/热工分析程序，开发包含抽样、耦合程序前后处理、反应堆优化分析功能的优化平台，并以铅铋反应堆SPALLER-4，URANUS为原型分别开展最小燃料装载量的方案寻优与参数优化验证。验证结果表明，该智能优化方法用于铅铋反应堆设计方案寻优和堆芯参数优化可行、有效，相比传统蒙卡程序计算寻优，在保证预测精度前提下极大地降低了计算成本，与URANUS初始模型比较，燃料装载量、堆芯总质量、活性区体积、堆芯总体积分别优化10.8%，11.5%，18.1%，17.1%，为基于代理模型的智能优化方法应用于铅铋反应堆的优化设计提供参考。
- 铅铋反应堆 /
- 智能优化 /
- Kriging代理模型 /
- SEUMRE空间搜索 /
- 正交拉丁超立方抽样
Abstract: The extensive application requirements of lead-bismuth reactors require researchers to carry out a lot of optimization design work on the basis of existing core schemes. Aiming at the multi-dimensional nonlinear constrained optimization design problem of lead-bismuth reactor with multi-physical, multi-variable and multi-constraint coupling effects, an intelligent optimization method for lead-bismuth reactor was constructed based on Kriging surrogate model, orthogonal Latin hypercube sampling and SEUMRE spatial search technology. Coupled with physical Monte Carlo calculation/thermal ranalysis code, an optimization platform including sampling, pre-and post-processing of coupling program and reactor optimization analysis function was developed. Taking SPALLER-4 and URANUS as prototypes, the scheme optimization and parameter optimization verification of minimum fuel load were carried out respectively. The verification results show that the core intelligent optimization method is feasible and effective for the optimization of lead-bismuth reactor design scheme and core parameters. Compared with the traditional Monte Carlo calculation optimization, the calculation cost is greatly reduced under the premise of ensuring the prediction accuracy. Compared with the URANUS initial model, the fuel loading, the total mass of the core, the volume of the active zone and the total volume of the core are optimized by 10.8%, 11.5%, 18.1% and 17.1% respectively, which provides a reference for the intelligent optimization method based on the surrogate model applied to the optimization design of lead-bismuth reactor.
- lead-bismuth reactor /
- intelligent optimization /
- Kriging surrogate model /
- SEUMRE spatial search /
- orthogonal Latin hypercube sampling

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图 1 堆芯智能优化方法主要技术原理

Figure 1. Main technical principle of core intelligent optimization method

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图 2 两种抽样结果比较

Figure 2. Comparison of two sampling results

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图 3 SEUMRE空间搜索算法流程框图

Figure 3. Flow diagram of SEUMRE spatial search algorithm

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图 4 铅铋反应堆优化设计平台实现流程框图

Figure 4. Realization flowchart of DOPPLER

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图 5 SPALLER-4结构简图

Figure 5. SPARLER-4 structure diagram

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图 6 URANUS结构简图

Figure 6. URANUS structure diagram

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图 7 Kriging代理模型预测K_eff、燃耗与蒙卡程序RMC计算值对比图

Figure 7. Comparison of K_eff, burnup predicted by Kriging surrogate model and RMC calculated value

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图 8 SPALLER-4燃料装载量寻优迭代图

Figure 8. Iterative graph of fuel loading optimization for SPALLER-4

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图 9 Kriging代理模型预测K_eff、燃耗与蒙卡程序RMC计算值对比图

Figure 9. Comparison of K_eff, burnup predicted by Kriging surrogate model and RMC calculated value

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图 10 URANUS燃料装载量寻优迭代图

Figure 10. Iterative graph of fuel loading optimization for URANUS

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表 1 Kriging代理模型常用相关函数及其表达式

Table 1. Commonly used related functions of Kriging surrogate model and their expressions

correlation function	expression
exponential function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\exp(-{\theta }_{k}{d}_{k})$
Gaussian function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\exp(-{\theta }_{k}{d}_{k}^{2})$
linear function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\mathrm{m}\mathrm{a}\mathrm{x}\{\mathrm{0,1}-{\theta }_{k}{d}_{k}\}$
cubic spline function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\left\{\begin{array}{l}1-15{\zeta }_{k}+30{\zeta }_{k}^{3},\quad 0\leqslant {\zeta }_{k}\leqslant 0.2\\ 1.25{(1-15{\zeta }_{k})}^{3},\quad 0.2 < {\zeta }_{k} < 1\\ 0,\quad{\zeta }_{k}\geqslant 1,{\zeta }_{k}={\theta }_{k}{d}_{k}\end{array}\right.$

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表 2 SPALLER-4设计参数及其材料与优化变量取值区间

Table 2. Materials used for the design parameters of SPALLER-4 and the interval value of optimization variables

design scheme	thermal power/MW	fuel loading/kg	equivalent diameter of active region/cm	height of active area/cm	average volume power density of active region/(W·cm⁻³)	fuel (mass fraction of Pu)/%	coolant and reflector	shielding layer
SPALLER-4	4	577.89	95.4	80	6.99	PuN-ThN (31/48)	²⁰⁸Pb-Bi(90)	B₄C(126)
URANUS	100	17580	97.02	180	19.18	UO₂(9.55/17.09)	²⁰⁸Pb-Bi(27.11 cm)	B₄C(15 cm)

design scheme	solid moderator (thickness/cm)	gate diameter ratio	fuel rod core radius/cm	air gap of fuel rod (thickness/cm)	cladding of fuel rod (thickness/cm)	upper/lower end plug of fuel rod (height/cm)	gas cavity/ spring area of fuel rod (height/cm)	top/bottom insulation of fuel rod (height/cm)
SPALLER-4	BeO (3.5)	1.20	0.60	He (0.015)	TH-9(0.06)	TH-9(3/3)	He(48/14)	He(1/1)
URANUS	—	1.35	0.72	He (0.010)	TH-9(0.06)	TH-9(30/30)	He(130/30)	—

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表 3 Kriging代理模型预测K_eff、燃耗的精度验证结果

Table 3. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

contrast group	thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	third-year K_eff			burnup/(MW·d·kg⁻¹)
contrast group	thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
1	4.6555	47.2024	0.2911	112.1659	1.3710	1.0502	1.0503	−0.0154	22.9477	22.7960	0.6654
2	4.8222	45.4101	0.2776	115.2353	1.3773	1.0352	1.0352	0.0006	24.6610	24.4460	0.8794
3	4.9908	48.9315	0.2608	118.1860	1.4117	1.0325	1.0334	−0.0846	26.8646	26.8940	0.1093
4	4.5899	48.8228	0.2117	103.6606	1.3534	1.0164	1.0174	−0.0987	46.3528	46.5440	0.4108
5	4.7828	46.6647	0.2173	116.5918	1.3548	1.0244	1.0234	0.0994	39.1589	39.3960	0.6019

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表 4 SPALLER-4堆芯设计方案寻优结果

Table 4. Optimization results of SPALLER-4 core design scheme

thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	third-year K_eff			burnup/(MW·d·kg⁻¹)
thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
4.5732	49.8686	0.2003	100.0818	1.3131	1.0057	1.0052	0.0550	53.7021	53.7990	−0.0018

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表 5 Kriging代理模型预测K_eff、燃耗的精度验证结果

Table 5. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

contrast group	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	twentieth-year K_eff			burnup/(MW·d·kg⁻¹)
contrast group	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
1	0.7287	164.3119	1.3207	1.0010	1.0018	−0.0809	44.0797	44.4100	−0.7438
2	0.7373	157.4453	1.3208	1.0004	1.0007	−0.0338	45.2746	45.2710	0.0080
3	0.7388	156.9933	1.3211	1.0005	1.0009	−0.0409	45.2266	45.2130	0.0301
4	0.7410	153.9331	1.3205	0.9994	0.9999	−0.0585	43.5830	43.5540	0.0666
5	0.7374	157.4387	1.3203	1.0006	1.0003	0.0297	45.2645	45.2560	0.0187

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表 6 URANUS堆芯设计参数优化结果

Table 6. Optimization results of design parameters for URANUS core

URANUS core	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	initial K_eff	twentieth-year K_eff			burnup/(MW·d·kg⁻¹)
URANUS core	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	initial K_eff	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
initial	0.7200	180.0000	1.3500	1.0289	—	1.0031	—	—	41.5240	—
optimization	0.7314	155.5838	1.2893	1.0307	1.0007	1.0010	−0.0229	46.5773	46.5530	0.0523

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URANUS core	refueling interval/ EFPY	fuel loading/kg	total mass of core (including reflector)/kg	volume of the active area/m³	average volume power density of the active area/(W·cm⁻³)	total volume of core (including reflector)/m³	maximum temperature of fuel cladding/K	maximum temperature of fuel core/K
initial	20	17580.0925	175459.3633	5.2138	19.1800	8.5734	600.6219	770.3892
optimization	20	15681.0697	155309.9496	4.2697	23.4208	7.1059	604.1702	796.0589

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参考文献(29)

[1]	王建强, 戴志敏, 徐洪杰. 核能综合利用研究现状与展望[J]. 中国科学院院刊, 2019, 34(4):460-468. (Wang Jianqiang, Dai Zhimin, Xu Hongjie. Research status and prospect of comprehensive utilization of nuclear energy[J]. Bulletin of the Chinese Academy of Sciences, 2019, 34(4): 460-468
[2]	吴宜灿. 铅基反应堆研究进展与应用前景[J]. 现代物理知识, 2018, 30(4):35-39. (Wu Yican. Research progress and application prospects of lead-based reactors[J]. Modern Physics, 2018, 30(4): 35-39
[3]	Zameer A, Mirza S M, Mirza N M. Core loading pattern optimization of a typical two-loop 300 MWe PWR using Simulated Annealing (SA), novel crossover Genetic Algorithms (GA) and hybrid GA(SA) schemes[J]. Annals of Nuclear Energy, 2014, 65: 122-131. doi: 10.1016/j.anucene.2013.10.024
[4]	de Moura Meneses A A, Machado M D, Schirru R. Particle Swarm Optimization applied to the nuclear reload problem of a Pressurized Water Reactor[J]. Progress in Nuclear Energy, 2009, 51(2): 319-326. doi: 10.1016/j.pnucene.2008.07.002
[5]	Khoshahval F, Minuchehr H, Zolfaghari A. Performance evaluation of PSO and GA in PWR core loading pattern optimization[J]. Nuclear Engineering and Design, 2011, 241(3): 799-808. doi: 10.1016/j.nucengdes.2010.12.023
[6]	王成. 新型优化算法开发及其在核动力装置优化中的应用[D]. 哈尔滨: 哈尔滨工程大学, 2018 Wang Cheng. The development of new optimization algorithms and applications in optimal design for nuclear power plant[D]. Harbin: Harbin Engineering University, 2018
[7]	张扬. 多参数非线性系统全局敏感性分析与动态代理模型研究[D]. 长沙: 湖南大学, 2014 Zhang Yang. The study on global sensitivity analysis and dynamic metamodel of multiple-parameters nonlinear system[D]. Changsha: Hunan University, 2014
[8]	Kempf S, Forget B, Hu Linwen. Kriging-based algorithm for nuclear reactor neutronic design optimization[J]. Nuclear Engineering and Design, 2012, 247: 248-253. doi: 10.1016/j.nucengdes.2012.03.001
[9]	Zeng Kaiyue, Stauff N E, Hou J, et al. Development of multi-objective core optimization framework and application to sodium-cooled fast test reactors[J]. Progress in Nuclear Energy, 2020, 120: 103184. doi: 10.1016/j.pnucene.2019.103184
[10]	Kim K Y, Lee S M. Shape optimization of inlet plenum in a PBMR-type gas-cooled nuclear reactor[J]. Journal of Nuclear Science and Technology, 2009, 46(7): 649-652. doi: 10.1080/18811248.2007.9711571
[11]	李淞, 杨红义, 周志伟, 等. 基于克里金方法的快堆燃料组件设计[J]. 原子能科学技术, 2018, 52(7):1288-1293. (Li Song, Yang Hongyi, Zhou Zhiwei, et al. Design of fast reactor fuel assembly based on Kriging method[J]. Atomic Energy Science and Technology, 2018, 52(7): 1288-1293 doi: 10.7538/yzk.2017.youxian.0650
[12]	Pebesma E J, Heuvelink G B M. Latin hypercube sampling of Gaussian random fields[J]. Technometrics, 1999, 41(4): 303-312. doi: 10.1080/00401706.1999.10485930
[13]	Jin R, Chen W, Simpson T W. Comparative studies of metamodelling techniques under multiple modelling criteria[J]. Structural and Multidisciplinary Optimization, 2001, 23(1): 1-13. doi: 10.1007/s00158-001-0160-4
[14]	毛凤山, 陈昌富, 朱世民. 代理模型方法及其在岩土工程中的应用综述[J]. 地基处理, 2020, 2(4):295-306. (Mao Fengshan, Chen Changfu, Zhu Shimin. Surrogate model method and its application in geotechnical engineering[J]. Journal of Ground Improvement, 2020, 2(4): 295-306
[15]	Younis A, Dong Zuomin. Metamodelling and search using space exploration and unimodal region elimination for design optimization[J]. Engineering Optimization, 2010, 42(6): 517-533. doi: 10.1080/03052150903325540
[16]	Wang Kan, Li Zeguang, She Ding, et al. RMC – A Monte Carlo code for reactor core analysis[J]. Annals of Nuclear Energy, 2015, 82: 121-129. doi: 10.1016/j.anucene.2014.08.048
[17]	Zhao Pengcheng, Liu Zijing, Yu Tao, et al. Code development on steady-state thermal-hydraulic for small modular natural circulation lead-based fast reactor[J]. Nuclear Engineering and Technology, 2020, 52(12): 2789-2802. doi: 10.1016/j.net.2020.05.023
[18]	赵鹏程. 小型自然循环铅冷快堆SNCLFR-100一回路主冷却系统热工安全分析[D]. 合肥: 中国科学技术大学, 2017 Zhao Pengcheng. Thermal-hydraulic safety analysis of primary cooling system for small modular natural circulation LFR SNCLFR-100[D]. Hefei: University of Science and Technology of China, 2017
[19]	刘紫静, 赵鹏程, 张斌, 等. 超长寿命小型自然循环铅铋快堆堆芯概念设计研究[J]. 原子能科学技术, 2020, 54(7):1254-1265. (Liu Zijing, Zhao Pengcheng, Zhang Bin, et al. Research on core concept design of ultra-long life small natural circulation lead-based fast reactor[J]. Atomic Energy Science and Technology, 2020, 54(7): 1254-1265 doi: 10.7538/yzk.2019.youxian.0720
[20]	刘紫静, 赵鹏程, 任广益, 等. 长寿命小型自然循环铅基快堆燃料选型[J]. 原子能科学技术, 2020, 54(5):944-953. (Liu Zijing, Zhao Pengcheng, Ren Guangyi, et al. Fuel selection of long life small natural circulation lead-based fast reactor[J]. Atomic Energy Science and Technology, 2020, 54(5): 944-953 doi: 10.7538/yzk.2019.youxian.0402
[21]	Jooeun Lee. Conceptual neutronic design of inverted core for lead-bismuth cooled small modular reactor[D]. Seoul: Graduate School of Seoul National University, 2017.
[22]	Kwak J, Kim H R. Development of innovative reactor-integrated coolant system design concept for a small modular lead fast reactor[J]. International Journal of Energy Research, 2018, 42(13): 4197-4205. doi: 10.1002/er.4177
[23]	Shin Y H, Choi S, Cho J, et al. Advanced passive design of small modular reactor cooled by heavy liquid metal natural circulation[J]. Progress in Nuclear Energy, 2015, 83: 433-442. doi: 10.1016/j.pnucene.2015.01.002
[24]	Shin Y H, Choi S, Cho J, et al. ICONE23-2135 design status of small modular reactor cooled by lead-bismuth eutectic natural circulation: Uranus[C]//Proceedings of ICONE-23 23rd International Conference on Nuclear Engineering. Chiba, Japan: 2015.
[25]	Driscoll N J, Hejzlar P. Reactor physics challenges in Gen-IV reactor design[J]. Nuclear Engineering and Technology, 2005, 37(1): 1-10.
[26]	Zhang Yan, Wang Chenglong, Lan Zhike, et al. Review of thermal-hydraulic issues and studies of lead-based fast reactors[J]. Renewable and Sustainable Energy Reviews, 2020, 120: 109625. doi: 10.1016/j.rser.2019.109625
[27]	Grasso G, Petrovich C, Mattioli D, et al. The core design of ALFRED, a demonstrator for the European lead-cooled reactors[J]. Nuclear Engineering and Design, 2014, 278: 287-301. doi: 10.1016/j.nucengdes.2014.07.032
[28]	Wallenius J, Suvdantsetseg E, Fokau A. ELECTRA: European lead-cooled training reactor[J]. Nuclear Technology, 2012, 177(3): 303-313. doi: 10.13182/NT12-A13477
[29]	杨红义, 过明亮. 中国实验快堆的设计创新与实现[J]. 原子能科学技术, 2020, 54(S1):199-205. (Yang Hongyi, Guo Mingliang. Design innovation and fulfillment of China experimental fast reactor[J]. Atomic Energy Science and Technology, 2020, 54(S1): 199-205