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耦合聚类的数据驱动稀薄流非线性本构计算方法(2022增刊2)

尧少波1,蒋励剑1,赵文文1,卢铮2,吴昌聚1,陈伟芳1   

  1. 1. 浙江大学
    2. 中国空间技术研究院
  • 收稿日期:2022-06-30 修回日期:2022-09-20 出版日期:2022-09-22 发布日期:2022-09-22
  • 通讯作者: 赵文文
  • 基金资助:
    国家自然科学基金;国家数值风洞项目

Numerical method of data-driven rarefied nonlinear constitutive relations coupled with clustering

  • Received:2022-06-30 Revised:2022-09-20 Online:2022-09-22 Published:2022-09-22

摘要: 临近空间环境下的稀薄流动具有典型非平衡特征,现有数值模拟方法在面对多尺度共存的复杂流动现象时难以同时高效、准确描述。结合近些年兴起的机器学习理论与建模方法,基于数据驱动非线性本构方程(DNCR,Data-driven Nonlinear Constitutive Relations)为稀薄非平衡流动快速求解提供了一种全新的物理建模思路。为进一步提升DNCR方法的泛化性能、模型训练与计算效率,本文在DNCR方法中首次引入高斯混合模型(GMM,Gaussian Mixture Model)与稀疏主成分分析(SPCA,Sparse Principal Component Analysis)在回归模型训练预测前对训练集与预测集数据进行聚类预处理,建立了耦合聚类模型的数据驱动非线性本构计算方法。相关算例预测结果表明:在DNCR可解释性方面,GMM与SPCA方法可以不依靠人工经验通过流场数据提取出不同流动中的主导物理量,提升了DNCR方法的可解释性与鲁棒性;在计算效率方面,GMM与SPCA方法能在大量流场样本下对数据点进行精准聚类,排除冗余信息的干扰,提高了方法的并行计算效率,降低了回归模型的训练预测时间,同时有利于后期添加新样本数据时模型的更新与维护;在计算精度方面,GMM与SPCA方法在简单特征流动预测中能够在保持现有预示精度的前提下提高计算效率,并在面对复杂流动特征耦合预测场景时有效提高DNCR方法预测精度。

关键词: 高斯混合模型, 稀疏主成分分析, 数据驱动, 树模型, 稀薄非平衡流

Abstract: Owing to the rarefied nonequilibrium effect encountered in near space environment, the existing numerical methods are difficult to describe the multi-scale flow phenomena efficiently and accurately at the same time. By integrating the machine learning methods rising in recent years, Data-driven nonlinear constitutive relations (DNCR) paved a new way for solving the nonequilibrium problem as a data-driven modeling approach. In order to further improve the generalization capability and model training efficiency of the DNCR method, Gaussian Mixture Model (GMM) and Sparse Principal Component Analysis (SPCA) for preprocessing the data of training set and prediction set are introduced into DNCR method for the first time in this paper. The prediction results of relevant cases show that the dominant parameters in different flow fields are extracted by GMM and SPCA without relying on artificial experience, which could improve the interpretability and robustness of DNCR. On the other hand, GMM and SPCA can accurately cluster the data points under a large number of flow field samples to eliminate the interference of redundant information and reduce the training and prediction time of the regression model, which is crucial to the updating and maintenance of the model when adding new sample data in future. For prediction accuracy, the coupled DNCR could improve the computational efficiency without losing accuracy in simple flows and further elevate the precision significantly in complex flows coupled with different flow characteristics.

Key words: Gaussian mixture model, Sparse principal component analysis, Data driven, Tree model, Rarefied non-equilibrium flow