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基于数据驱动的流场控制方程的稀疏识别

江昊 王伯福 卢志明

江昊, 王伯福, 卢志明. 基于数据驱动的流场控制方程的稀疏识别[J]. 力学学报, 2021, 53(6): 1543-1551. doi: 10.6052/0459-1879-21-052
引用本文: 江昊, 王伯福, 卢志明. 基于数据驱动的流场控制方程的稀疏识别[J]. 力学学报, 2021, 53(6): 1543-1551. doi: 10.6052/0459-1879-21-052
Jiang Hao, Wang Bofu, Lu Zhiming. DATA-DRIVEN SPARSE IDENTIFICATION OF GOVERNING EQUATIONS FOR FLUID DYNAMICS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1543-1551. doi: 10.6052/0459-1879-21-052
Citation: Jiang Hao, Wang Bofu, Lu Zhiming. DATA-DRIVEN SPARSE IDENTIFICATION OF GOVERNING EQUATIONS FOR FLUID DYNAMICS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1543-1551. doi: 10.6052/0459-1879-21-052

基于数据驱动的流场控制方程的稀疏识别

doi: 10.6052/0459-1879-21-052
基金项目: 1)国家自然科学基金资助项目(12072185);国家自然科学基金资助项目(11732010);国家自然科学基金资助项目(11972220)
详细信息
    作者简介:

    2)卢志明, 教授, 主要研究方向: 湍流, 环境流体力学, 计算流体力学. E-mail: zmlu@shu.edu.cn

    通讯作者:

    卢志明

  • 中图分类号: O357

DATA-DRIVEN SPARSE IDENTIFICATION OF GOVERNING EQUATIONS FOR FLUID DYNAMICS

  • 摘要: 利用有限数据建立系统的非线性动力学模型是具有挑战性的重要课题. 数据驱动的稀疏识别方法是近年来发展的从数据识别动力系统控制方程的有效方法. 本文基于数据驱动稀疏识别方法对不同流场的控制方程进行了识别. 采用非线性动力学偏微分方程函数识别(partial differential equations functional identification of nonlinear dynamics, PDE-FIND)方法和最小绝对收缩和选择算子(least absolute shrinkage and selection operator, LASSO)方法对二维圆柱绕流、顶盖驱动方腔流、Rayleigh-Bénard (RB)对流和三维槽道湍流的控制方程进行了识别. 在稀疏识别过程中, 采用直接数值模拟得到的流场数据来计算过完备候选库中的每一项, 候选库中变量最高保留到二次, 变量导数最高保留到二阶, 非线性项最高保留到四阶. 结果发现PDE-FIND方法和LASSO方法对于不含有非线性项的控制方程, 如涡量输运方程、热输运方程和连续性方程, 都能准确识别. 对于含有强非线性项的控制方程, 如Navier-Stokes方程的识别, PDE-FIND方法正确地识别出了控制方程及流场的Rayleigh数和Reynolds数, 而LASSO方法识别结果不正确, 这是因为候选库中的项之间存在分组效应, LASSO方法通常只取分组中的一项. 本文还发现选择流动结构丰富的区域的数据进行控制方程的稀疏识别可以提高识别的准确性.

     

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出版历程
  • 收稿日期:  2021-01-29
  • 录用日期:  2021-06-18

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