Prediction of Nuclear Power Plant Operating Parameters Based on Transfer Learning between Simulation and Measurement Data
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摘要: 核电厂安全运行的关键是实现其运行参数的精准预测。近年来，数据驱动方法表现出了强大的预测能力，然而，测量数据的不充分限制了其预测性能。本研究将基于迁移学习框架，开发了一种以多组仿真工况预训练，再利用测量数据微调的预测模型构建方法。首先通过仿真数据训练门控循环单元（GRU）神经网络，再使用部分测量数据微调模型，以预测运行工况的未来状态。使用PKL Ⅲ热工水力台架的B3.1实验的测量数据，及与之相近的9组RELAP5仿真数据，验证了方法的可行性。运用该方法预测得出蒸汽压力、蒸汽温度、下降管流体温度、出口温度、入口温度和质量流量的相对误差分别能够达到0.358%、0.065%、0.020%、0.065%、0.028%和1.705%。最后通过5组数值实验对比说明了方法各模块的有效性。
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关键词:
- 迁移学习 /
- 运行参数预测 /
- 门控循环单元（GRU）神经网络
Abstract: The key to the safe operation of nuclear power plants is to achieve accurate prediction of their operating parameters. In recent years, data-driven methods have shown strong predictive capabilities. However, insufficient measurement data limits their predictive performance. Based on the transfer learning framework, this study develops a prediction model construction method that is pre-trained with multiple sets of simulation conditions and then fine-tuned with measured data. First, the Gated Recurrent Unit (GRU) neural network is trained with simulation data, and then the model is fine-tuned using part of the measurement data to predict the future state of the operating conditions. The feasibility of the method is verified using the measurement data of the B3.1 experiment on the PKL Ⅲ thermal hydraulic bench and 9 sets of similar RELAP5 simulation data. Using this method, the relative errors of steam pressure, steam temperature, downcomer fluid temperature, outlet temperature, inlet temperature and mass flow rate can reach 0.358%, 0.065%, 0.020%, 0.065%, 0.028% and 1.705%, respectively. Finally, five sets of numerical experiments are used to compare and illustrate the effectiveness of each module of the method. -
图 1 “预训练—微调”的迁移学习框架
Figure 1. “Pre-training to Fine-tuning” Transfer Learning Framework
图 4 多工况数据训练损失“平均化”的训练流程
Figure 4. Training Process of “Averaging” Training Loss for Data of Multiple Operating Conditions
图 7 PKL Ⅲ热工水力台架实验B3.1的测量数据曲线
Figure 7. Measured Data Curves of Experiment B3.1 at PKL Ⅲ
图 8 9组仿真工况数据与实验测量数据的数据曲线对比
图中图例均参照子图a
Figure 8. Comparison of 9 Sets of Simulation Data and Experimental Data
图 10 预训练模型在ZBS仿真工况上的预测结果
红色竖线为训练集和验证集的分割线
Figure 10. Prediction Results of Pre-trained Model under ZBS Simulation Conditions
图 11 预训练模型经过微调后在测量数据上的预测结果
蓝色竖线为验证集和测试集的分割线
Figure 11. Prediction Results of Pre-trained Model after Fine-tuning with Measured Data
图 12 5组对比实验在测试集上预测结果
Figure 12. Prediction Results of 5 Groups of Comparative Experiments with Test Set
图 13 不同数量的仿真工况在微调过程中的损失曲线对比
Figure 13. Comparison of Loss Curves for Different Numbers of Simulation Conditions during Fine-tuning
表 1 PKL Ⅲ热工水力台架实验B3.1的实验测量物理量
Table 1. Experimental Measurement of Physical Quantities in Experiment B3.1 at PKL Ⅲ
物理量 符号 蒸汽发生器二次侧蒸汽压力/Pa Pdm 蒸汽发生器二次侧蒸汽温度/K Tdm 蒸汽发生器二次侧下降管流体温度/K Tdc 蒸汽发生器一次侧出口温度/K Tout 蒸汽发生器一次侧入口温度/K Tin 蒸汽发生器一次侧质量流量/(kg·s−1) M 
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表 2 9组仿真工况的描述
Table 2. Description of 9 Sets of Simulation Conditions
工况名称 参数调整 ZBS 基准计算 BCM1 质量流量整体提升5% BCM2 质量流量整体降低5% BCT1 入口温度整体降低2 K BCT2 入口温度整体提升2 K PA1 瞬态二次侧散热系数整体提升5% PA2 瞬态二次侧散热系数整体降低5% PA3 瞬态二次侧散热系数整体提升10% PA4 瞬态二次侧散热系数整体降低10%
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表 3 超参数优化范围
Table 3. Hyperparameter Optimization Range
超参数 取值范围 网络层数 1~5 隐藏层节点数 1~1000 初始学习率 10−7~10−1 小批量大小 1~50 正则化系数 10−7~10−1 SGD优化器的平方梯度衰减因子 0.8~1.0
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表 4 最优超参数的取值
Table 4. Optimal Hyperparameter Values
超参数 最优取值 网络层数 1 隐藏层节点数 332 初始学习率 0.0034 小批量大小 11 正则化系数 1.13×10−7 SGD优化器的平方梯度衰减因子 0.99
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表 5 预训练模型在ZBS仿真工况上的预测结果的误差和拟合优度
Table 5. Error and Goodness of Fit of Prediction Results of Pre-trained Model under ZBS Simulation Conditions
物理量 训练集 验证集 MAPE/% RMSE R2 MAPE/% RMSE R2 Pdm 0.062 2338 Pa 0.999 0.109 2822 Pa 0.999 Tdm 0.007 0.045 K 0.999 0.046 0.259 K 0.993 Tdc 0.018 0.107 K 0.999 0.059 0.314 K 0.999 Tout 0.015 0.098 K 0.999 0.102 0.550 K 0.989 Tin 0.014 0.092 K 0.999 0.044 0.239 K 0.998 M 0.605 0.002 kg/s 0.999 0.588 0.002 kg/s 0.998
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表 6 预训练模型在9个仿真工况上预测结果的整体归一化RMSE平均值
Table 6. Overall Normalized RMSE Average of Prediction Results of Pre-trained Model under 9 Simulation Conditions
工况名称 训练集$\overline {{\mathrm{RMSE}}} $ 验证集$\overline {{\mathrm{RMSE}}} $ ZBS 0.00216 0.00651 BCM1 0.00221 0.00651 BCM2 0.00216 0.00659 BCT1 0.00223 0.00649 BCT2 0.00221 0.00660 PA1 0.00217 0.00585 PA2 0.00214 0.00637 PA3 0.00221 0.00610 PA4 0.00223 0.00610
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表 7 预训练模型经过微调后在测量数据上的预测结果的误差和拟合优度
Table 7. Error and Goodness of Fit of Prediction Results of Pre-trained Model after Fine-tuning with Measured Data
物理量 训练集 验证集 测试集 MAPE/% RMSE R2 MAPE/% RMSE R2 MAPE/% RMSE R2 Pdm 0.042 1638 Pa 0.999 0.180 4816 Pa 0.991 0.358 9588 Pa 0.995 Tdm 0.007 0.045 K 0.999 0.022 0.112 K 0.989 0.065 0.444 K 0.974 Tdc 0.007 0.050 K 0.999 0.005 0.037 K 0.999 0.020 0.124 K 0.999 Tout 0.020 0.127 K 0.999 0.017 0.097 K 0.993 0.065 0.424 K 0.994 Tin 0.011 0.073 K 0.999 0.028 0.146 K 0.984 0.028 0.155 K 0.999 M 0.179 0.001 kg/s 0.999 0.140 0.001 kg/s 0.999 1.705 0.008 kg/s 0.986
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表 8 5组对比实验在测试集上预测结果的整体归一化均方根误差平均值
Table 8. Overall Normalized RMSE Average of Prediction Results of 5 Groups of Comparative Experiments with Test Set
对比实验 $\overline {{\mathrm{RMSE}}} $ 实验一 0.0085 实验二 0.0083 实验三 0.0093 实验四 0.0252 实验五 0.0625
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