论文标题
广义和多尺模态分析
Generalized and Multiscale Modal Analysis
论文作者
论文摘要
本章介绍了矩阵因化框架中的模态分解。我们强调了经典的时空分解与2D离散变换之间的差异，并讨论了基础的一般体系结构\ emph {any}分解。然后，该设置用于得出简单的算法，从其空间或时间结构（碱基）中完成\ emph {任何}线性分解。离散的傅立叶变换，正确的正交分解（POD），动态模式分解（DMD）和本征函数扩展（EF）在此框架中进行了表达，并在简单的练习中进行了比较。最后，该概括用于分析光谱约束对经典豆荚的影响，并得出多尺度正交分解（MPOD）。该分解结合了多分辨率分析（MRA）和POD。本章包含四个练习和两个教程测试案例。 \ textsc {python}脚本与这些脚本相关联。
This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning \emph{any} decomposition. This setting is then used to derive simple algorithms that complete \emph{any} linear decomposition from its spatial or temporal structures (bases). Discrete Fourier Transform, Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Eigenfunction Expansions (EF) are formulated in this framework and compared on a simple exercise. Finally, this generalization is used to analyze the impact of spectral constraints on the classical POD, and to derive the Multiscale Proper Orthogonal Decomposition (mPOD). This decomposition combines Multiresolution Analysis (MRA) and POD. This chapter contains four exercises and two tutorial test cases. The \textsc{Python} scripts associated to these are provided on the book's website.
