洪亮,金鑫,刘虓瀚,等.机器学习算法在燃料棒温度性能预测中的应用[J].深圳大学学报理工版,2022,39(5):515-520.[doi:10.3724/SP.J.1249.2022.05515] HONG Liang,JIN Xin,LIU Xiaohan,et al.Application of machine learning algorithm in the prediction of fuel rod temperature performance[J].Journal of Shenzhen University Science and Engineering,2022,39(5):515-520.[doi:10.3724/SP.J.1249.2022.05515]
In order to predict the fuel rod temperature performance effectively, we establish a series of machine learning models based on k-nearest neighbor, decision tree and AdaBoost algorithms. The input parameters and calculation results of fuel rod performance analysis software JASMINE and data feature engineering are used as the training and test data for the machine learning models. The models are trained by the training data set which includes the characteristic parameters such as pellet and cladding type, axial height, local power, cladding corrosion thickness and core inlet temperature. After training, the models use the test data to predict the cladding outside surface temperature and pellet center temperature. The prediction results show that the model based on AdaBoost algorithm has the best prediction performances, and the mean square errors of cladding outside surface temperature and pellet center temperature are 0. 605℃and 8. 347℃, respectively, and the average absolute errors are 0. 273℃and 3. 814 ℃, respectively. Comparing the predicted values with the target values, the maximum deviation of Adaboost algorithm for the cladding outside surface temperature is 3℃, and the most of the prediction deviation of the pellet center temperature is less than 10℃, indicating that the model based on AdaBoost algorithm has the high prediction accuracy for the temperature performance of fuel rods.
在核电领域，机器学习现已广泛用于堆芯物理参数计算、核素含量预测和堆芯事故诊断等过程．周剑东等[7]基于决策树的模式识别方法对堆芯物理参数进行预测，实现了参数的快速预测并取得了较好的预测精度．黄禹等[8]采用误差反向传播（back propagation，BP）算法基于堆芯核功率、入口温度、流量和压力等变量对堆芯偏离泡核沸腾比（de⁃parture from nucleate boiling ratio，DNBR）进行快速预测，并得到了较好的准确性．BAE等[9]采用神经网络在给定初始富集度和燃耗条件下预测压水堆（pressurized water reactor，PWR）的乏燃料的同位素成分．李仕鲜等[10]采用神经网络方法对核电厂的失水事故（loss of coolant accident，LOCA）进行诊断和预测，证明神经网络对破口位置和尺寸的诊断准确率较高且诊断稳定性较好．
燃料棒是反应堆的第1道安全屏障，也是反应堆产热的唯一源泉，其性能直接影响反应堆的安全性、可靠性和经济性，因此，正确预测燃料棒在堆内辐照行为是燃料设计和性能评价的基本要求．由于燃料棒在堆内行为复杂，且各种行为相互耦合，常需要开发专业的燃料棒性能分析软件来预测燃料棒的性能．此类软件的开发过程涉及大量试验数据、复杂的模型建立和模型验证与确认，开发周期通常在10 a左右．其中，包壳外表面温度和芯块中心温度是燃料棒设计需着重关注的重要性能参数．针对燃料棒性能分析软件开发投入巨大和研发周期漫长的特点，本研究采用机器学习算法构建基于芯块材料类型、包壳材料类型、燃料棒轴向高度、轴向局部功率、堆芯入口温度和包壳水侧腐蚀厚度6个物理特征参数的包壳外表面温度和芯块中心温度性能参数（目标参数）预测模型．采用机器学习方法不需要进行复杂的热力耦合模型开发，而是通过建立特征数据与性能数据之间的对应关系进行参数预测，从而缩短软件开发周期，节约研发成本．用于机器学习算法训练和测试的数据集要求的数据量大且维度多，一般实验数据无法满足该要求．因此，本研究主要关注基于机器学习算法的燃料棒温度模型的训练和测试，探讨机器学习算法在燃料棒性能分析中的应用，采用燃料棒性能分析软件JASMINE[11]的计算结果作为训练和测试数据集．所用机器学习算法分别为k近邻（k-nearest neigh⁃bor，kNN）[12]、决策树（decision tree，DT）[13]和集成学习算法AdaBoost[14]．kNN算法是基于距离样本特征最近的k个样本的目标平均值来进行预测，参数k对预测准确性有影响．DT算法是基于迭代二叉树3代（iterative dichotomiser 3，ID3）、C4. 5或分类回归树（classification and regression tree，CART）算法在每个节点上对特征进行判断，从而形成的一种树型结构，本研究采用CART算法．AdaBoost算法是一种有效且实用的提升（boosting）算法，其算法原理是通过调整样本权重和弱学习器权值，从训练出的弱学习器中筛选出权值系数最小的弱学习器组合成一个最终强学习器．
图1 基于JASMINE软件数据预测包壳外表面温度和芯块中心温度的模型框架Fig. 1 Model framework for prediction of cladding outside surface temperature and pellet center temperature based on JASMINE software.
图2 kNN算法参数k对（a）包壳外表面温度和（b）芯块中心温度预测的准确性趋势Fig. 2 Trend charts of parameter k to forecast accuracy R2 for (a) cladding outside surface temperature and (b) pellet center temperature.
图3 DT算法性能预测准确性R2随参数（a）max_depth、（b） min_sample_leaf和（c）min_impurity_decrease变化趋势Fig. 3 Trend charts of performance prediction accuracy R2 of DT algorithm with parameter (a) max_depth, (b) min_sample_leaf, and (c) min_impurity_decrease. The triangle is the cladding outside surface temperature, and the circle is the pellet center temperature.
表1 DT算法预测性能的最佳参数Table 1 Optimal parameters for predicting performance of DT algorithm
图4 AdaBoost算法性能预测准确性R2随参数（a）n_estimator和（b）learning_rate变化趋势Fig. 4 Trend charts of performance prediction accuracy R2 of AdaBoost algorithm with parameter (a) n_estimator and (b) learning_rate. The triangle is the cladding outside surface temperature and the circle is the pellet center temperature.
表2 三种算法的模型预测误差对比Table 2 Comparison of model prediction errors of the three algorithms
图5 AdaBoost算法对（a）包壳外表面温度和（b）芯块中心温度性能预测Fig. 5 Prediction of (a) cladding outer surface temperature and (b) pellet center temperature performance by AdaBoost algorithm. The square is target value, the triangle is predictive value, and the circle is the differente between predictive value and the target value.
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；v为总平方和，
；N为样本数量；i为数据样本编号；fi为模型预测值；yi为样本点i实际的数据标签（即包壳外表面温度或者芯块中心温度）；yˉ为实际数据标签的平均值．
