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基于物理信息神经网络的管道瞬变流模型
梅力方, 李小纲, 杨思琪, 乔潘诗霈, 张菁, 赵苑汝, 马轶
长江科学院院报 ›› 2026, Vol. 43 ›› Issue (7) : 153-160.
PDF(1325 KB)
PDF(1325 KB)
基于物理信息神经网络的管道瞬变流模型
Numerical Model of Pipeline Transient Flow Based on Physics-Informed Neural Networks
为提升管道系统水锤波压力变化过程的预测精度,提出基于物理信息神经网络(PINNs)的管道瞬变流动压力预测框架,将连续性方程与动量方程嵌入神经网络损失函数,利用自动微分(AD)求解偏微分方程,从而实现有限标注数据条件下的高精度压力模拟。同时,基于传统局部自适应激活函数(LAAF)加入可学习的偏移参数β,并结合小批量梯度下降策略,提高了模型预测的稳定性和精度。结果表明:提出的M-LAAF2-PINNs模型能较好地捕捉水锤压力特性,在预测精度方面显著优于Baseline-PINNs模型与LAAF2-PINNs模型,L2相对误差分别降低了37.32%和23.83%;此外,波速敏感性分析、多初始流速工况验证及泛化性分析结果表明了改进模型具有更强的泛化能力与鲁棒性,可为工业管道系统的压力监测提供更优的技术手段。
[Objective] To address the limited adaptability of traditional numerical methods for water hammer under complex boundary and uncertain conditions, as well as the constrained convergence efficiency and prediction accuracy of Physics-Informed Neural Networks (PINNs) in strongly nonlinear transient flows, this study proposes a PINNs-based framework for transient pressure prediction in pipelines aiming to enhance the prediction accuracy of pressure variations in pipeline hydraulic transients. [Methods] In this framework, the continuity and momentum equations are embedded into the neural network loss function, and automatic differentiation is employed to solve the governing partial differential equations, enabling high-accuracy pressure simulation under limited labeled data conditions. Furthermore, an improved Locally Adaptive Activation Function (LAAF) is introduced by incorporating a trainable offset parameter β, while a mini-batch gradient descent strategy is adopted to enhance the model’s training stability and prediction robustness. [Results] Numerical case studies demonstrate that the proposed model effectively captures the transient characteristics of water hammer pressure. Compared with the Baseline-PINNs model and LAAF2-PINNs model, it achieves significantly higher predictive accuracy, with the relative L2 error reduced by 37.32% and 23.83%, respectively. In addition, sensitivity analysis of wave velocity, verification under multiple initial flow velocity conditions and generalization ability analysis demonstrate that the improved model has superior generalization ability and robustness. [Conclusions] The proposed M-LAAF2-PINNs model provides a novel and effective approach for achieving high-precision water hammer transient analysis under limited observational data and uncertain boundary conditions, offering superior technical support for pressure monitoring, parameter inversion, and intelligent scheduling in long-distance pipeline systems.
水锤 / 瞬变流 / M-LAAF2-PINNs / 管道 / 压力预测
water hammer / transient flow / M-LAAF2-PINNs / pipeline / pressure prediction
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