核反应堆中极高参数条件下换热系数(Coefficient of Heat Transfer,HTC)的准确预测对反应堆的设计及运行至关重要,但因涉及不同流型的多重因素影响的复杂情形,物理机理仍不完全明晰.由于缺乏满足实际反应堆高温高压下的参数实验数据,而严重依赖实验数据的半经验关系式很难满足核反应堆高精度数值计算的要求.深度学习算法能够有效预测和解决复杂的非线性问题,但存在外推性能差以及过拟合等不足.本研究采用先验物理信息Jens-Lottes关系式、Thom关系式与机器学习算法中多层感知机(Multi-layer Perceptron,MLP)、反向传播神经网络(Backpropagation Neural Network,BPNN)和随机森林(Random Forest,RF)相结合的方式开发HTC预测模型,基于圆管通道HTC实验数据训练神经网络并进行验证,对6种不同的物理信息机器学习(Physical Information Machine Learning,PIML)算法模型的适用性以及预测精度进行评估.结果表明:(1)基于Jens-Lottes关系式与RF相结合的模型为最佳预测模型,对实验数据的预测平均相对误差为3.17%,且模型可扩展范围占总适用范围的63.6%,具有良好的外推适用性;(2)使用基于物理信息机器学习算法能够有效提高关系式的计算准确度,基于Jens-Lottes关系式与RF相结合的模型相比于经验关系式评价相对误差降低了24.5%.本研究结果为说明采用物理信息机器学习算法对核反应堆热工参数经验关系式的计算可提高精度并扩大适用范围提供了参考依据.
Prediction of heat transfer parameters of nuclear reactor based on physical information machine learning algorithm
[Background]Accurate prediction of the coefficient of heat transfer(HTC)under extremely high parameter conditions in nuclear reactors is crucial for the design and operation of reactors,but the HTC is influenced by many factors,and there are issues such as unclear physical model and lack of experimental data.Traditional empirical relations often struggle to meet the demands of high-precision numerical calculations.Machine learning algorithms can effectively address the complex nonlinear problems,but some results do not conform to physical laws.[Purpose]This study aims to propose a physical information machine learning(PIML)algorithm model that can calculate thermal parameters more accurately.[Methods]Firstly,HTC experimental data were collected from a circular tube and subjected to preprocessing.Then,the HTC model was developed by combining the Jens-Lottes formula and the Thom formula with Multi-layer Perceptron(MLP),Backpropagation Neural Network(BPNN),and Random Forest(RF).Following this,the preprocessed data were partitioned into training and testing sets,with the training set utilized for model training and the testing set employed for model validation.Finally,six algorithms in the HTC models were evaluated and compared against empirical correlations.[Results]Evaluation results show that the calculation accuracy of Jens-Lottes formula combined with RF in the HTC model is the highest,with average relative error of predicting experimental data of 3.17%.The expandable range of the model accounts for 63.6%of the total applicable range,demonstrating good extrapolation capabilities.At the same time,using the PIML algorithm significantly enhances the computational accuracy of the physical model.The model based on the Jens-Lottes relationship combined with RF reduces the relative error of evaluation by 24.5%compared to the empirical relationship.[Conclusions]The PIML algorithm proposed in this study provides a framework for a high precision calculation model for HTC.It also provides a reference for expanding the scope of application.
Coefficient of heat transferPhysical information machine learningMulti-layer Perceptron(MLP)Backpropagation Neural Network(BPNN)Random Forest(RF)
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