Prediction of Spent Nuclear Fuel Decay Heat Based on GPR-SVR Co-training
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摘要: 在压水堆核电厂中，乏燃料组件的衰变热是堆芯余热的主要来源，准确预测衰变热对于反应堆冷却系统的设计和安全分析至关重要，但传统核素衰变模拟程序计算成本高，而机器学习模型由于数据不足可能存在过拟合问题。本文基于高斯过程回归（GPR）和支持向量回归（SVR）方法建立了协同训练的基础模型，生成了高质量的乏燃料衰变热虚拟数据，并与核电厂实测数据组成了混合数据集，采用混合数据集训练极限学习机（ELM）模型，对乏燃料衰变热进行了预测。结果表明，与常规的机器学习模型相比，协同训练显著提升了衰变热预测的稳定性和准确性。经过混合数据集训练后，ELM模型的预测稳定性提高了39.9%，衰变热预测结果的均方根误差（RMSE）比传统核素衰变模拟程序低25.7%。本研究提出的方法可为解决核工程领域存在的小数据集问题提供新思路。
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关键词:
- 衰变热预测 /
- 虚拟数据 /
- 协同训练 /
- 乏燃料 /
- 高斯过程回归（GPR） /
- 支持向量回归（SVR）
Abstract: The decay heat released by spent fuel assemblies is the main source of reactor core waste heat in PWR nuclear power plants. Accurate prediction of decay heat is crucial for the design and safety analysis of the nuclear power plant cooling system. However, the calculation cost of traditional nuclide decay simulation code is high, and the machine learning model may have over-fitting problems due to insufficient data. This study establishes a co-training model based on Gaussian Process Regression (GPR) and Support Vector Regression (SVR) to generate high-quality virtual decay heat samples. These virtual samples, combined with measured decay heat data, form a mixed dataset, which is used to train an Extreme Learning Machine (ELM) model for decay heat prediction. The results show that, compared with the conventional machine learning model, the co-training approach significantly enhances the stability and accuracy of decay heat predictions. After training on the mixed dataset, the prediction stability of the ELM model increased by 39.9%, and the RMSE of the predicted decay heat was 25.7% lower than that of the traditional nuclide decay simulation code. This research provides new insights for addressing the small sample problem in the field of nuclear engineering. -
图 1 各模型在测试集$ {V}_{0} $的预测结果
Figure 1. Predictions of Each Model on the Test Set $ {V}_{0} $
图 4 预测误差随协同训练次数变化情况
Figure 4. Prediction Error RMSE Changes with the Epoch of Co-training
图 5 ELM模型在测试集$ {V}_{0} $的预测结果
Figure 5. Predictions of ELM Model on the Test Set $ {V}_{0} $
图 7 ELM模型在所有测试集的预测结果对比
Figure 7. Comparison of Predictions of ELM Model in All Test Sets
图 8 衰变模拟程序计算值与ELM模型预测值对比
Figure 8. Comparison of Calculated Values by Decay Simulation Code and Predicted Values by ELM Model
表 1 乏燃料衰变热数据总结
Table 1. Summary of Spent Fuel Decay Heat Data
反应堆 组件排列 乏燃料组件富集度/% 初始铀质量/kg 燃耗深度/[MW·d·t−1(U)] 卸料后冷却时间/d Ringhals3 17×17 2.1~3.103 451.743~489.050 19699~47308 4717~7304 Ringhals2、Turkey Point 15×15 3.095~3.252 423.896~455.789 33973~50962 5804~8468 San Onofre1、Point Beach2 14×14 3.397~4.005 361.72~386.80 26540~39384 1078~3012 
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表 2 GPR和SVR预测误差汇总
Table 2. Summary of GPR and SVR Predictions
模型 RE/% RMSE/% MAPE/% 点1 点2 点3 $ {{\mathrm{M}}}_{{\mathrm{GPR}}0} $ 72.8 2.4 9.0 72.0 5.7 $ {{\mathrm{M}}}_{{\mathrm{SVR}}0} $ 10.5 32.9 1.3 76.3 3.8 神经网络 90.8 15.4
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表 3 衰变热预测误差汇总
Table 3. Summary of Decay Heat Prediction Errors
模型 最大RE/% 最小RE/% RMSE/% $ {\mathrm{M}}_{\mathrm{E}\mathrm{L}\mathrm{M}}^{\mathrm{c}\mathrm{o}} $ 4.54 0.01 12.05 $ {\mathrm{M}}_{\mathrm{E}\mathrm{L}\mathrm{M}}^{0} $ 10.39 0.35 39.42
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