基于PINN-GP混合模型的水泵叶片转角预测

Prediction of pump blade angle based on PINN-GP hybrid model

摘要

为提升水泵叶片转角在小样本与强非线性工况下的预测精度，提出一种基于物理先验与高斯过程的混合预测模型（physics-informed neural network-Gaussian process，PINN-GP）。该模型采用一种两阶段预测修正策略：构建物理信息神经网络（physics-informed neural network，PINN），融合数据驱动损失与物理先验约束，以获取高精度的基础预测；引入高斯过程（Gaussian process，GP）对 PINN 的系统性误差进行建模修正，在提升精度的同时实现不确定性量化。以南水北调东线工程洪泽泵站为对象进行实例验证，结果表明：PINN-GP 模型性能全面占优，相较于传统多项式拟合模型，其决定系数（R²）提升 6.3%，平均绝对误差（mean absolute error，E_MA）显著降低 86.69%。可见该模型在小样本、强非线性及不确定性工况下表现出卓越的建模能力，可为泵站的调度优化提供更为鲁棒与可靠的决策支持。

Abstract

Significant deviations between factory performance curves and actual operating conditions consistently posed challenges to operational assessment, dispatch optimization, and energy efficiency management of large-scale pumping stations over time. The main causes of these deviations are complicated factors that have been seen in practice, such as aging equipment, different installation conditions, and long-term variations in water levels. As a critical mechanical parameter, the precise prediction of the blade angle was identified as the key to addressing these issues. However, the task was made more difficult by the strong non-linearity and small sample sizes present in pump operational data. Traditional data-driven models, such as polynomial fitting, frequently failed to capture complex coupling relationships in real-world applications, resulting in low accuracy. Additionally, even though conventional deep learning techniques provided better non-linear modeling, they suffered from a "black box" nature that made it difficult to measure prediction uncertainty and were prone to overfitting when training data was limited. As a result, there was a need for a robust modeling approach capable of combining mechanistic knowledge with data-driven techniques to improve decision support system reliability. To address the two issues of prediction accuracy and dependability, a hybrid prediction model called the physics-informed neural network combined with a Gaussian process was designed. The modeling framework was designed with a three-stage prediction-correction architecture. First, a physical prior model based on polynomial regression was utilized to decouple the global physical trends of the blade angle from the raw data. Second, a physics-informed neural network was constructed to learn the complex non-linear residual features that the physical prior model could not capture; this network incorporated a composite loss function that fused data-driven errors with physical constraints to ensure the output respected fundamental physical laws. Third, a Gaussian process regression was introduced to model the systematic prediction errors of the neural network. This final stage allowed for the precise correction of residuals and enabled the quantification of uncertainty by generating confidence intervals. The Hongze pumping station unit 3 on the East Route of the South-to-North Water Transfers Project was chosen as the research subject. Filtering and steady-state screening were used to pre-process operational data before applying a clustering algorithm to create a representative dataset covering various working conditions. The proposed model was then systematically compared against multiple benchmark models, including polynomial fitting, back propagation neural networks, and physics-informed neural networks. The experimental results demonstrated that the physics-informed neural network combined with a Gaussian process model achieved overall superiority compared with all reference models. In the evaluation of single-unit operation, high prediction accuracy was achieved. Compared to the traditional polynomial fitting model, the coefficient of determination ( R ²) increased by 6.3%, while the mean absolute error decreased by 86.69%. Furthermore, in the adaptability tests involving multiple operating units (ranging from single to quadruple unit parallel operations), the model displayed strong robustness. The model maintained high accuracy with minimal performance decay even when tested on untested multi-unit scenarios and trained exclusively on single-unit data, while traditional models demonstrated notable degradation. The Gaussian process component successfully provided a 95% confidence interval that effectively enveloped the true values, particularly reflecting higher uncertainty during transient state changes, which accurately represented the physical reality of the system. It was concluded that the proposed hybrid model effectively addressed the challenges associated with limited sample sizes and strong non-linear characteristics in pump station modeling. The integration of physical mechanisms with data-driven deep learning methods resulted in significantly improved prediction accuracy while also quantifying uncertainty. This capability was demonstrated to provide more robust and reliable decision support for the optimal dispatch and intelligent management of large-scale pumping stations, thereby contributing to safer and more efficient operation under complex engineering conditions.

关键词

水泵机组 / 叶片转角 / 物理信息神经网络 / 高斯过程 / 混合预测模型

Key words

water pump unit / blade angle / physics-informed neural network / Gaussian process / hybrid prediction model

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基金资助

中国科协青年人才托举工程项目(YESS20240288)