Research on Construction Method of a Machine Learning-Based Fuel Rod Temperature Distribution Surrogate Model
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摘要: 为提高大规模燃料棒性能模拟的计算效率，以燃料棒温度预测为例，研究了燃料棒温度分布预测代理模型（简称“代理模型”）的构建方法。以燃料棒性能分析程序COPERNIC的计算结果作为数据源，采用k-means聚类算法筛选代表性的训练数据，训练了4个全连接前馈神经网络，分别能够考虑冷却剂流动传热及氧化膜生长影响的包壳外表面温度预测、包壳径向温度分布预测、燃料芯块和包壳间隙变化影响的燃料芯块外表面温度预测、燃料芯块径向温度分布预测。通过这些神经网络的组合，可以根据输入的燃料棒功率史快速预测出燃料棒不同时刻的温度分布。数值试验表明：构建的代理模型相比COPERNIC程序计算速度提升约204倍，同时具有较高精度。在整个数据集上，包壳温度和燃料芯块温度预测的平均偏差分别为0.07℃、0.44℃。Abstract: In order to improve the computational efficiency of large-scale fuel rod performance simulation, the construction method of fuel rod temperature distribution surrogate model (referred to as "surrogate model") is studied by taking fuel rod temperature prediction as an example. The calculation results of the fuel rod performance analysis code COPERNIC are used as the data source, and the representative training data are selected by using the k-means clustering algorithm. Four fully connected feedforward neural networks are trained to predict the outer surface temperature of the cladding considering the effects of coolant flow heat transfer and oxide film growth, the radial temperature distribution of the cladding, the outer surface temperature of the fuel pellet considering the effects of the gap variation between the fuel pellet and cladding, and the radial temperature distribution of the fuel pellet. By combining these neural networks, the temperature distribution of the fuel rod at different times can be quickly predicted based on the input fuel rod power history. Numerical experiments show that the calculation speed of the surrogate model is about 204 times faster than that of the COPERNIC code, and it has high accuracy. The mean deviations of fuel cladding and pellet temperature prediction on the whole data set are about 0.07°C and 0.44°C respectively.
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Key words:
- Neural network /
- Fuel rod temperature /
- Surrogate model /
- Fuel behavior
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图 1 多神经网络组合的温度分布预测示意图
Tco—包壳外表面温度；Tclad—包壳不同径向位置温度；Tpellet—燃料芯块不同径向位置温度
Figure 1. Schematic Diagram of Temperature Distribution Prediction Based on Multiple Neural Networks
图 2 代理模型预测值与参考值的对比
Figure 2. Comparison between Predicted Value and Reference Value of Surrogate Model
表 1 燃料棒温度分布预测神经网络的架构参数
Table 1. Architecture Parameters of Neural Networks for Prediction of Fuel Rod Temperature Distribution
神经网络 输入参数 输出参数 隐含层每层
神经元个数NNTco $ {\tilde q_{\text{l}}},{\textit{z}},t,\bar B $ Tco [30,30,30,30] NNTclad $ {q_{\text{l}}},{T_{{\text{co}}}},r $ Tclad [5] NNTpo $ {q_{\text{l}}},{T_{{\text{ci}}}},t,\bar B $ Tpo [30,30,30] NNTpellet $ {q_{\text{l}}},{T_{{\text{po}}}},\bar B,r $ Tpellet [30,30] $ {\tilde q_{\text{l}}} $—轴向功率分布离散点 
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表 2 计算时间对比
Table 2. Comparison of Calculation Time
COPERNIC程序
计算时间/s代理模型计算时间/s 加速比 NNTco NNTclad NNTpo NNTpellet 总计 93.964 0.084 0.025 0.023 0.305 0.460 204
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