On parametric model order reduction by matrix interpolation
On parametric model order reduction by matrix interpolation
复制标题
基于矩阵插值的参数模型降阶研究
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
B. Lohmann
中科院分区：
文献类型：
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作者：
M. Geuß;H. Panzer;B. Lohmann
针对高阶参数相关线性定常系统，提出了一种模型降阶的一般框架。该过程是基于矩阵插值和由六个步骤组成。首先，针对不同的参数向量，计算一组高阶非参数系统。由此产生的局部高阶系统，然后减少基于投影的减少方法。从而，正确的右和左子空间的约化系统的计算。其次，对简化系统的右子空间的基进行自适应，并调整左子空间的基。为此，引入了对偶性的概念。最后，用插值方法将局部系统的预计算矩阵插值到矩阵流形中。在本文中的六个步骤的算法和其中出现的自由度。此外，自由度的选择的优点和困难指出。它还表明，现有的两种方法参数模型降阶矩阵插值的特殊情况下，所提出的一般程序，因为它们-往往隐含-确定限制选择的自由度。
A general framework for model order reduction is proposed for high-order parameter-dependent, linear time-invariant systems. The procedure is based on matrix interpolation and consists of six steps. At first a set of high-order nonparametric systems is computed for different parameter vectors. The resulting local high-order systems are then reduced by a projection-based reduction method. Thereby, proper right and left subspaces for the reduced systems are calculated. Next the bases of the right subspaces of the reduced systems are adapted and the bases of the left subspaces are adjusted. For that the concept of duality is introduced. Finally, the precomputed matrices of the local systems are interpolated in a matrix manifold with an interpolation method. In this paper the six steps of the algorithm and the degrees of freedom which arise therein are presented. Furthermore, advantages and difficulties in the selection of the degrees of freedom are pointed out. It is additionally shown that two existing methods for parametric model order reduction by matrix interpolation are special cases of the proposed general procedure as they - often implicitly - determine a limiting selection of the degrees of freedom.