基于PINN-HEM混合框架的SCO2临界流模型研究

Research on SCO2 Critical Flow Prediction Model Based on PINN-HEM Hybrid Framework

  • 摘要: 超临界二氧化碳(SCO2)反应堆系统的临界流量高精度预测是失压事故安全分析的关键,但现有实验数据有限且集中于低温低压区,缺乏高精度宽参数范围预测的SCO2临界流模型。理论计算模型和纯数据驱动模型存在着计算效率和泛化性的失衡,而物理信息神经网络(PINN)因将包含物理规律的方程引入到深度神经网络的构造中,提升了模型的可解释性和泛化性。因此本研究基于PINN算法,将均相平衡模型(HEM)的守恒方程嵌入损失函数以构造PINN-HEM框架,通过扩展的高温高压试验数据集(130~500 ℃、压力12~15 MPa),利用超参数优化后的数据驱动模型初始化PINN-HEM网络参数来加速训练收敛速度等方法,建立了宽参数范围、高精度的PINN-HEM SCO2临界流模型。结果表明,考虑不同数据集特性,PINN-HEM对比经验公式下PINN-EF模型,平均相对误差降低了62.65%,输入特征的贡献度更符合物理规律。

     

    Abstract: The accurate prediction of critical flow in supercritical carbon dioxide (SCO2) reactor systems is a crucial aspect of pressure drop accident safety analysis. However, the availability of current experimental data is limited and primarily focused on low-temperature and low-pressure regions. This limitation leads to a lack of high-precision, wide-parameter-range models for SCO2 critical flow. Traditional theoretical models and purely data-driven approaches are characterized by an inherent trade-off between computational efficiency and generalization capability. In contrast, physics-informed neural networks (PINN) integrate physical laws into the neural network framework, which improves both the interpretability and generalization of the model. Within this study, the PINN algorithm was adopted, and the conservation equations of the homogeneous equilibrium model (HEM) were embedded into the loss function to construct the PINN-HEM framework. The HEM framework was chosen for its physical completeness, broad applicability across single-phase, two-phase, short-tube, and long-tube flow regimes, and its foundation in fundamental physical principles rather than numerous simplifying assumptions typical of empirical correlations. By leveraging an extended high-temperature and high-pressure experimental dataset (130-500 ℃, 12-15 MPa), the network parameters of the PINN-HEM model were initialized using a purely data-driven model. Furthermore, the hyperparameters of this purely data-driven model (including the number of hidden layers, the number of nodes per layer, and the L2 regularization coefficient) have been rigorously optimized. This optimized initialization results in a significant reduction in the number of training epochs required for convergence. Consequently, a high-precision PINN-HEM SCO2 critical flow model applicable across a wide range of parameters was developed. Results demonstrate that, when evaluated across diverse test sets (including long-tube experimental data D1, high-parameter experimental data D2, and numerically generated broad-parameter data D3), a substantial reduction in average relative error is achieved by the PINN-HEM model. Specifically, compared to the PINN-EF model, the average relative error is reduced by 62.65%, 81.00%, and 62.65% on datasets D1, D2 and D3, respectively, by the PINN-HEM model. Furthermore, the contribution of input features within the PINN-HEM model is found to be in closer alignment with fundamental physical principles, resulting in enhanced model interpretability. The potential of PINN in solving complex thermodynamic problems is demonstrated by this research, providing a more accurate and efficient tool for predicting SCO2 critical flow in reactor systems. The integration of physical constraints ensures that the model not only fits the data but also adheres to the governing physical laws. Consequently, robustness and generalization performance across a broader parameter space are enhanced. For enhanced understanding of PINN model characteristics, subsequent research could explore the influence of individual feature values on the PINN-HEM model’s predictive contributions through SHAP value analysis. Based on SHAP analysis, network hyperparameters could be optimized to improve physical interpretability and generalization capability.

     

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