Research on Data-driven Intelligent Optimization Design of Mobile Microreactor Shielding
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摘要: 为快速获得满足工程偏好的移动式微型核反应堆（微堆）轻量化屏蔽设计方案，本研究采用基于数据驱动的代理模型和多目标智能优化算法，对陆基移动式微堆的运行屏蔽开展具有多约束和工程偏好的多目标优化设计。首先通过对先进屏蔽材料参数和屏蔽几何参数采样构建变规模优化空间下的数据集，其次基于此数据集训练多频率尺度神经网络MscaleDNN，并耦合基于图形处理器（GPU）并行的一维离散纵标法（SN）中子-光子耦合输运求解器，以建立稳定的高效高精度剂量率预测代理模型SN-MscaleDNN，之后与引入罚函数法和工程偏好模型的第二代非支配排序（NSGA-II）遗传算法耦合，实现满足剂量率安全、材料和力学限制等多约束以及工程偏好的屏蔽优化设计。研究结果表明，代理模型在变规模优化空间下可实现单个屏蔽方案毫秒级评估且预测泛化误差整体在10%以内，其与优化算法耦合后优化得到的多个屏蔽方案满足各项指标限值和工程偏好，本研究建立的方法能够用于变规模优化空间下移动式微堆的轻量化屏蔽优化设计。Abstract: In order to quickly obtain the lightweight shielding design scheme of mobile microreactor (microreactor) that meets the engineering preferences, a multi-objective intelligent optimization algorithm coupled with the data-driven surrogate model is employed to optimize the operational shielding of a land-based mobile microreactor based on multiple constraints and engineering preferences. We initially construct the dataset by sampling advanced shielding material and geometry’s parameters in the variable-scale optimization space and train the surrogate model (SN-MscaleDNN), which consists of the multi-frequency scale neural network called MscaleDNN and the GPU-parallel 1-D neutron-photon coupling transport SN solver, to achieve stable, accurate, and efficient dose rate prediction. This model is then coupled with the NSGA-II genetic algorithm, incorporating penalty functions and engineering preference models, to achieve the final shielding optimization that satisfies multiple constraints such as dose rate safety, material and mechanical limitations and engineering preferences. The results confirm the surrogate model's ability to accurately predict dose rates of one shielding scheme at a millisecond level with its generalization error under 10%. Furthermore, the coupled optimization algorithm enables the efficient search for more shielding schemes that meet engineering constraints and preferences. The method established in this study can be used for lightweight shielding optimization design of mobile microreactor in a variable-scale optimization space.
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图 2 剂量率代理模型框架及多频率尺度神经网络架构
xi—第i个神经元对应的输入特征；y—剂量率校正因子；$ {\bf{NMF}}{{\bf{P}}_{\text{a}}} $—吸收平均自由程数，$ {\bf{NMF}}{{\bf{P}}_{\text{a}}} $=[x1, x2,…, x67]T；$ {\bf{NMF}}{{\bf{P}}_{\text{t}}} $—总的平均自由程数，$ {\bf{NMF}}{{\bf{P}}_{\text{t}}} $=[x68, x69,…, x134]T；Φ1D—目标点处一维SN计算得到的各能群通量，Φ1D=[x135, x136,…, x201]T
Figure 2. Framework of Dose Rate Prediction Surrogate Model and Multi-frequency Scale Neural Network Architecture
图 3 代理模型预测相对误差统计分布
μ—相对误差的正态分布近似对应的平均值；σ—相对误差的正态分布近似对应的标准差
Figure 3. Statistical Distribution of Relative Error of the Surrogate Model Prediction
表 1 屏蔽材料库及相关材料参数
Table 1. Shielding Material Library and Corresponding Parameters
材料
类型材料
序号材料名称及符号
表示材料组分质量
分数范围最大使用
温度/℃直接屏蔽 1 碳化硼（B4C） 1.00 800 直接屏蔽 2 氮化硼（BN） 1.00 985 直接屏蔽 3 钨（W） 1.00 1925 直接屏蔽 4 聚醚醚酮
（PEEK）1.00 250 直接屏蔽 5 碳钢（CS） 1.00 870 直接屏蔽 6 硼铝材（B-Al） 1.00 482 二元复合 7 聚醚醚酮+碳化硼（PEEK+B4C） B4C：0.05~0.35 250 二元复合 8 聚醚醚酮+氮化硼（PEEK+BN） BN：0.05~0.40 250 二元复合 9 聚醚醚酮+钨
（PEEK+W）W：0.30~0.75 250 二元复合 10 含硼聚乙烯
（HDPE+B4C）B4C：0.05~0.40 100 多元复合 11 铅硼聚乙烯
（LBPE）1.00 80 多元复合 12 聚醚醚酮+碳化硼+钨（PEEK+B4C+W） B4C：0.05~0.20；
W：0.05~0.30250 多元复合 13 含硼环氧树脂
（EP-H+B4C+FR）B4C：0.05~0.50；
FR：0.55~0.10；
EP-H：0.40160 “+”表示均匀混合；“EP-H”为加入固化剂的双酚A型环氧树脂；“FR”为阻燃剂氢氧化铝；HDPE为高密度聚乙烯 
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表 2 选择算子伪代码
Table 2. Pseudocode of Selection Operator
算法：基于设计偏好和约束违反的二进制锦标赛选择杂交个体 输入 个体Sa和个体Sb分别对应的约束违反度向量a_cv、b_cv，偏好度a_p、b_p，目标向量Fa、Fb，拥挤距离a_cd、b_cd 输出 选择的个体Sa或个体Sb 1 if Sa和Sb至少一个解不可行 then 2 计算a_cv和b_cv的支配关系并返回占优个体； 3 if Sa和Sb约束违反度互不支配 then 4 比较a_p和b_p大小并返回偏好度大的个体； 5 else 6 计算Fa和Fb的支配关系并返回占优个体； 7 if Sa和Sb目标向量互不支配 then 8 个体Sa支配判断向量dom_a ← [−a_p, −a_cd]； 9 个体Sb支配判断向量dom_b ← [−b_p, −b_cd]； 10 计算dom_a和dom_b的支配关系并返回占优个体； 11 if dom_a和dom_b互不支配 then 12 从个体Sa和Sb中随机抽样返回
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表 3 最终优化得到的屏蔽方案
Table 3. Final Optimied Shielding Schemes
序号 层数 质量/t 体积/m3 偏好度 #1 6 96.478 37.853 0.78 #2 6 96.489 37.136 0.78 #3 6 96.526 36.420 0.77 #4 7 96.763 35.345 0.71 #5 8 96.997 33.857 0.66 #6 7 97.513 33.506 0.71 #7 6 99.541 32.749 0.78 #8 6 99.605 32.404 0.78
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表 4 优化算法平均性能对比
Table 4. Comparison of Average Performance of Optimization Algorithms
算法类型 耗时/h 质量/t 体积/m3 偏好度 本文方法 12.4 99.13 33.56 0.73 NSGA-II+CDP+CSO 13.5 98.25 32.90 0.60 NSGA-III+CDP 9.4 105.56 41.34 0.59
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