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基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶

赖学方 王晓龙 聂玉峰

赖学方, 王晓龙, 聂玉峰. 基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶[J]. 应用数学和力学, 2021, 42(6): 551-561. doi: 10.21656/1000-0887.410230
引用本文: 赖学方, 王晓龙, 聂玉峰. 基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶[J]. 应用数学和力学, 2021, 42(6): 551-561. doi: 10.21656/1000-0887.410230
LAI Xuefang, WANG Xiaolong, NIE Yufeng. Nonlinear Model Reduction Based on the Mori-Zwanzig Scheme and Partial Least Squares[J]. Applied Mathematics and Mechanics, 2021, 42(6): 551-561. doi: 10.21656/1000-0887.410230
Citation: LAI Xuefang, WANG Xiaolong, NIE Yufeng. Nonlinear Model Reduction Based on the Mori-Zwanzig Scheme and Partial Least Squares[J]. Applied Mathematics and Mechanics, 2021, 42(6): 551-561. doi: 10.21656/1000-0887.410230

基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶

doi: 10.21656/1000-0887.410230
基金项目: 

国家自然科学基金(11871400;11971386)

详细信息
    作者简介:

    赖学方(1988—),男,博士生(E-mail: xfanglai@mail.nwpu.edu.cn);聂玉峰(1968—),男,教授,博士,博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).

    通讯作者:

    聂玉峰(1968—),男,教授,博士,博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).

  • 中图分类号: O242.2

Nonlinear Model Reduction Based on the Mori-Zwanzig Scheme and Partial Least Squares

Funds: 

The National Natural Science Foundation of China(11871400;11971386)

  • 摘要: 本征正交分解及Galerkin投影是解决复杂非线性系统模型降阶问题常用的方法.然而,该方法在构造降阶系统过程中只截取基函数的部分模态,这通常会使得降阶系统不准确.针对该问题,提出了对降阶系统误差进行快速校正的方法.首先应用Mori-Zwanzig格式对降阶系统的误差进行分析,理论上得到误差模型的形式和有效预测变量.再通过偏最小二乘方法构造预测变量和系统误差的多元回归模型,建立误差预测模型.将所构造的误差预测模型直接嵌入到原降阶系统,得到新的降阶系统在形式上等价于对原模型的右端采用Petrov-Galerkin投影.最后给出了新的降阶系统的误差估计.数值结果进一步说明了所提方法能有效地提高降阶系统的稳定性和准确性,且具有较高计算效率.
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出版历程
  • 收稿日期:  2020-08-05
  • 修回日期:  2021-01-06

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