Research on Prediction Method of In-core Capacity Factor Based on Graph Convolutional Network
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摘要: 堆芯节功率的分布直接影响到反应堆的安全运行。为了实现对堆芯节功率分布精准地预测，本文充分考虑功率量程探测器内各个敏感段分布的空间关系以及节功率物理模型的推导过程，根据中子传输矩阵的研究提出了一种适用于节功率分布预测的图数据结构，并利用图卷积网络（GCN）实现对堆芯节功率的预测。基于某二代压水堆机组的历史数据进行算例分析，结果表明本文提出的图数据结构能够有效地整合功率量程探测器采集信号的空间特征；结合GCN模型对节功率变化平稳与波动较大的2种情况进行预测，均能实现节功率分布的精准预测，解决了传统时序预测模型在功率波动较大情况下预测效果不理想的问题。本文所提出的堆芯节功率分布预测方法具有较好的适用性，对提高核反应堆运行的安全性与可靠性具有较高的参考价值。
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关键词:
- 核电厂 /
- 堆芯功率 /
- 节功率 /
- 图卷积网络（GCN）
Abstract: The distribution of capacity factor of core directly affects the safe operation of the reactor. In order to achieve accurate prediction of capacity factor distribution, the spatial relationship of the distribution of each sensitive segments in the power range detector and the derivation process of the capacity factor physical model are fully considered in the paper, which proposes a graph data structure by the research on the neutron transport matrix, which is suitable for capacity factor distribution prediction, and uses the graph convolutional network (GCN) to predict the capacity factor. Based on the historical data of a second-generation pressurized water reactor unit, analysis of examples is conducted and the result shows that the spatial characteristics of signal of the power range detector can be integrated effectively by the proposed graph data structure. Combining the GCN model to predict two different situations of stable and large fluctuations in the capacity factor, the result show that two different situations of capacity factor can be predicted accurately by GCN model, which solves the problem of unsatisfactory prediction results of traditional time series prediction models in situations under large fluctuations. Therefore, the method proposed in this paper is suitable for prediction of in-core capacity factor, which has a high reference value for improving the safety and reliability of nuclear reactor operation. -
图 2 功率量程探测器时空图数据构建
Figure 2. Spatial-temporal Graph Data Building of Power Range Detector
图 5 第一通道下部分电流与对应节功率示例
%FP 指在反应堆满功率运行状态下的百分比值。
Figure 5. Example of Current and Corresponding Capacity Factor of the Lower Part in the First Channel
图 6 第1段节功率预测值与真实值对比示例
Figure 6. Example of Comparison between Predicted Value and Actual Value of Capacity Factor of Section 1
图 7 各段节功率的平均绝对百分比误差
Figure 7. Mean Absolute Percentage Error of Capacity Factor of Each Section
图 9 测试集2上不同图结构预测的评价指标
Figure 9. Evaluation Indicators for Different Graph Structure Predictions on Test Set 2
图 10 不同模型各段节功率平均绝对百分比误差
Figure 10. Mean Absolute Percentage Error of Capacity Factor of Each Section of Different Models
表 1 GCN模型参数模型寻优结果
Table 1. Optimal Results of GCN Model Parameters
参数名称 参数范围 寻优结果 图卷积层数 [1,2,3,4,5] 3 图卷积层中隐含神经元个数 [16,32,48,64,96,128] 48 多层感知机中隐含神经元个数 [16,32,48,64,96,128] 96 学习率 [0.0001 0.001 0.005 0.01] 0.001 训练样本大小 [4,8,16,32,64] 16 
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表 2 GCN模型的整体评价指标
Table 2. Overall Evaluation Index of GCN Model
评价指标 ${\overline \delta _{\rm{RMSE}}}$/%FP $ {\overline \delta _{\rm{MAE}}} $/%FP ${\overline \delta _{\rm{MAPE}}}$/% 测试集1 0.05581 0.04431 0.268 测试集2 0.11439 0.06225 0.448 测试集3 0.06942 0.05371 0.329
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表 3 不同模型的整体评价指标
Table 3. Overall Evaluation Indicators of Different Models
模型 测试集1 测试集2 ${\overline \delta _{\rm{RMSE}}}$/%FP $ {\overline \delta _{\rm{MAE}}} $/%FP ${\overline \delta _{\rm{MAPE}}}$/% 响应时间/s ${\overline \delta _{\rm{RMSE}}}$/%FP $ {\overline \delta _{\rm{MAE}}} $/%FP ${\overline \delta _{\rm{MAPE}}}$/% 响应时间/s MLP 0.056538 0.044883 0.276 0.5505 0.17413 0.14671 1.001 0.5703 LSTM 0.072013 0.059513 0.391 0.6383 0.17509 0.14416 0.999 0.6452 CNN-LSTM 0.057499 0.045832 0.286 0.9285 0.17327 0.12938 0.893 0.9321 GCN 0.055811 0.044309 0.268 1.3663 0.11439 0.06225 0.448 1.3651
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