物理方程约束的机器学习流场时程表征方法  

PHYSICAL CONSTRAINED MACHINE LEARNING MODEL FOR FLOW TIME HISTORY REPRESENTATION

作　　者：战庆亮 刘鑫 白春锦 葛耀君[3] ZHAN Qing-liang;LIU Xin;BAI Chun-jin;GE Yao-jun(College of Transportation and Engineering,Dalian Maritime University,Dalian 116026,China;Liaoning Provincial Transportation Planning and Design Institute Co.,Ltd.,Shenyang 110111,China;Key Laboratory of Transport Industry of Wind Resistant Technology for Bridge Structures,Tongji University,Shanghai 200092,China)

机构地区：[1]大连海事大学交通运输工程学院,大连116026 [2]辽宁省交通规划设计院有限责任公司,沈阳110111 [3]同济大学桥梁结构抗风技术交通行业重点实验室,上海200092

出　　处：《工程力学》2025年第4期38-45,共8页Engineering Mechanics

基　　金：大连海事大学博联科研基金项目(3132023619);国家自然科学基金项目(51778495,51978527);桥梁结构抗风技术交通行业重点实验室(上海)开放课题项目(KLWRTBMC21-02);辽宁教育厅研究计划项目(LJ212410151014)。

摘　　要：机器学习是流场表征的有效研究手段,基于数据驱动的神经网络模型缺乏物理机制的可解释性,且在可用训练样本较少时数据驱动的训练方法难以获得准确的模型。针对此问题,该文构建了流场测点时程的人工神经网络模型,并辅以流体的控制方程修正模型的输出,提出了考虑物理约束的流场时程机器学习表征方法。采用神经网络方法来表征不同位置处的流场时程,并用已知测点处的样本时程进行模型训练;使用模型的输出计算流动控制方程的误差,用以修正数据驱动的模型参数。以低雷诺数方柱绕流场为例,讨论了流场时程特征表征模型的可行性和物理约束方法的精度。结果表明:该文提出的方法通过引入流动控制方程的约束,使得模型可在较少已知测点数据的情况下获得更准确、更符合物理规律的流场时程表征模型。Machine learning is an effective method for flow representation.Data-driven machine learning models lack the interpretability of physical mechanisms,and it is difficult to obtain accurate models when there are few training samples available.An artificial neural network model using flow time history data of measurement point is proposed.The output of the model is further improved using flow governing equations,resulting a machine learning model of the flow time history considering physical constraints.The neural network model is proposed to represent the flow time history data at different locations,and the model is trained with known measurement point samples;then the model output is used to calculate the loss of the Naïve-stokes equations to improve the purely data-driven model parameters.The model is verified using flow time history data around square cylinder at low Reynolds number,and it is demonstrated that the physical constraint method can improve the accuracy of the results.The method proposed in this paper is applicable to the analysis of flow data based on measurement points,and the model accuracy is improved by introducing constraints on the flow governing equations,making the model more accurate and more consistent with the physical laws for the flow time history representation with limited available measurement data.

关 键 词：时程深度学习 物理方程约束 稀疏已知信息 时程重构 人工神经网络 流场表征 

分 类 号：O357[理学—流体力学]