遗传算法在中子-γ混合辐射场屏蔽材料优化设计中的应用

doi:10.19596/j.cnki.1001-246x.8714

摘要/Abstract

摘要：

针对中子-γ混合辐射场, 对屏蔽材料中的金属氧化物填料组分进行优化, 通过蒙特卡罗程序模拟获得WO₃/Bi₂O₃/Gd₂O₃/B₄C混合填料对低能中子与不同能量γ射线的综合屏蔽性能, 采用遗传算法和神经网络寻找填料组分的最优配比。通过对总剂量当量的计算和优化, 发现不同辐射环境下最优配比是不同的, 在中子(热中子麦氏分布能谱)通量与γ射线(0.5~3 MeV)通量相同时, 当添加屏蔽填料总质量一定, Bi₂O₃与B₄C质量比为9:1的混合填料综合屏蔽性能达到最优。将几种混合辐射环境下得到的最优解代入蒙特卡罗程序验证, 误差在可接受范围内, 表明该屏蔽填料组分的优化设计是可行的, 节省计算时间, 为屏蔽材料的设计和制备提供了理论依据。

关键词: 蒙特卡罗, 遗传算法, 神经网络, 屏蔽设计, 中子-γ混合辐射场

Abstract:

Based on the neutron-γ mixed radiation field, the metal oxide filler components in the material are optimized, and the comprehensive shielding performance of WO₃/Bi₂O₃/Gd₂O₃/B₄C mixed filler against low energy neutrons and different energy γ rays is obtained by Monte Carlo simulation. The optimal ratio of filler components is found by using genetic algorithm and neural network. Through the calculation and optimization of the total dose equivalent, it is found that the optimal ratio is different under different radiation environments. And the comprehensive shielding performance can be optimized by using Bi₂O₃ and B₄C (9:1) mixed fillers when the neutron (thermal neutron Maxwell distribution spectrum) flux is equal to γ ray (0.5-3 MeV) flux and the total mass of the shielding filler is constant. The results of Monte Carlo program show that the error is within an acceptable range, which indicates that the optimal design of the shielding filler is feasible. It can save a lot of calculation time and provide a theoretical basis for the design and preparation of shielding materials.

Key words: Monte Carlo, genetic algorithm, neural network, shielding design, neutron-γ mixed radiation field

中图分类号:

TL71
TL99

韩文敏, 戴耀东, 姚初清, 田家祥, 蒋丹枫, 周一帆. 遗传算法在中子-γ混合辐射场屏蔽材料优化设计中的应用[J]. 计算物理, 2024, 41(3): 357-366.

Wenmin HAN, Yaodong DAI, Chuqing YAO, Jiaxiang TIAN, Danfeng JIANG, Yifan ZHOU. Application of Genetic Algorithm to Optimal Design of Shielding Materials for Neutron-γ Mixed Radiation Fields[J]. Chinese Journal of Computational Physics, 2024, 41(3): 357-366.

图/表 17

图1 WinXCom中几种金属氧化物对γ射线的质量衰减系数对比

Fig.1 Linear attenuation coefficients of several metal oxides to γ rays in WinXCom

图2 采用的优化方法及流程

Fig.2 Methods and process of optimization

图3 MCNP模型

Fig.3 Model of MCNP

图4 热中子麦氏分布谱归一化分布

Fig.4 Normalized distribution of Maxwell thermal neutron

图5 BPNN模型结构

Fig.5 Model structure of BPNN

表1 神经网络参数设置

Table 1 Setting of neural network parameters

Parameter type	Set
Number of layers	4(Two hidden layers)
Training function	Trainlm
Transfer function	Tansig、logsig、purelin
Training sets∶Verification set∶Testing sets	7∶1.5∶1.5
Learning rate	0.1

表2 复合辐射环境的定义

Table 2 The definition of composite radiation environment

辐射环境	源数据
gn0.05	热中子源+0.05 MeV γ射线
gn0.1	热中子源+0.1 MeV γ射线
gn0.5	热中子源+0.5 MeV γ射线
gn1	热中子源+1 MeV γ射线
gn1.5	热中子源+1.5 MeV γ射线
gn2	热中子源+2 MeV γ射线
gn2.5	热中子源+2.5 MeV γ射线
gn3	热中子源+3 MeV γ射线
gn	热中子源+0.05、0.1、0.5、1、1.5 MeV γ射线

图6 测试样本、数据未归一化和归一化网络预测的剂量当量

Fig.6 Comparison of dose equivalent of output, dose equivalent from predicted unnormalized and normalized network

图7 不同数量样本的神经网络训练误差结果

Fig.7 Neural network training error results of different number of samples

图8 不同隐含层节点数在三次训练中均方误差 (a) 第一隐含层; (b) 第二隐含层

Fig.8 Error from different numbers of S1 and S2 hidden layers in three training (a) the first hidden layer; (b) the second hidden laryer

图9 k值不同时gn0.1辐射环境下神经网络预测与蒙特卡罗方法计算所得的总剂量当量

Fig.9 The total dose equivalent predicted by the neural network and that calculated by MCNP in gn0.1 radiation environment with different k values

表3 遗传算法参数设置

Table 3 Setting of genetic algorithm parameters

Parameter type	Set
Population size	100
Number of iterations	100
Generation gap	0.9
Crossover rate	0.8
Mutation rate	0.01

图10 k=1时几种辐射环境剂量当量的优化过程及结果

Fig.10 Optimization process and results of several radiation environmental dose equivalents at k = 1

图11 (a) 各辐射环境中填料组分最优配比下神经网络预测剂量当量、蒙特卡罗程序计算剂量当量结果；(b) 各辐射环境中填料组分最优配比

Fig.11 (a) Results of the dose equivalent from neural network and Monte Carlo program under the optimal ratio of filler ratio in various radiation environments; (b) optimum ratio of filler in various radiation environments

图12 k值不同时，各辐射环境中优化得到的填料组分 (a) gn0.05; (b) gn0.1; (c) gn0.5; (d) gn1; (e) gn1.5; (f) gn2; (g) gn2.5; (h) gn3

Fig.12 The optimum ratio of filler in various radiation environments with different k values (a)gn0.05; (b) gn0.1; (c) gn0.5; (d) gn1; (e) gn1.5; (f) gn2; (g) gn2.5; (h) gn3

表4 放射性贯穿件位置实测各核素峰位能量及净计数

Table 4 The measured peak energy and net count of each nuclide in nuclear power environment

核素	峰位能量/keV	全能峰净计数
Co-60	1 332	1 106
I-134	884	557
Cs-137	662	1 204
Xe-133	81	3 873

表5 几种不同填料配比在蒙特卡罗方法输运中产生的几种剂量当量

Table 5 Several dose equivalents of different filler ratio in Monte Carlo method transport

WO₃/Bi₂O₃/Gd₂O₃/B₄C	H_n/10^-12Sv	H_n_γ/10^-12Sv	H_γ/10^-12Sv	H_总/10^-12Sv
0.9/0/0/0.1	1.130 × 10^-3	1.101 × 10^-2	1.273 × 10^-2	2.487 × 10^-2
0/0/0.9/0.1	5.398 × 10^-8	1.034 × 10^-1	1.278 × 10^-2	1.161 × 10^-1
0.4/0.5/0/0.1	9.214 × 10^-4	9.957 × 10^-3	1.262 × 10^-2	2.350 × 10^-2
0/0.5/0.4/0.1	6.206 × 10^-7	9.879 × 10^-2	1.265 × 10^-2	1.114 × 10^-1
0.3/0.3/0.3/0.1	1.644 × 10^-6	9.759 × 10^-2	1.268 × 10^-2	1.103 × 10^-1
0/0/0/1	1.910 × 10^-6	1.241 × 10^-2	1.443 × 10^-2	2.684 × 10^-2
0/0.7/0/0.3	4.232 × 10^-5	1.023 × 10^-2	1.310 × 10^-2	2.337 × 10^-2
0/0.8/0/0.2	1.333 × 10^-4	9.697 × 10^-3	1.286 × 10^-2	2.269 × 10^-2
0/0.89/0/0.11	6.145 × 10^-4	9.141 × 10^-3	1.263 × 10^-2	2.239 × 10^-2
0/0.9/0/0.1	7.630 × 10^-4	9.060 × 10^-3	1.261 × 10^-2	2.243 × 10^-2
0/1/0/0	1.965 × 10^-2	6.823 × 10^-6	1.231 × 10^-2	3.196 × 10^-2

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