Parametric Model Order Reduction via Balanced Truncation with Taylor Series Representation
Parametric Model Order Reduction via Balanced Truncation with Taylor Series Representation
复制标题
通过泰勒级数表示的平衡截断来降低参数模型阶数
DOI：
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发表时间：
2016
影响因子：
6.8
通讯作者：
O. Sawodny
中科院分区：
文献类型：
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作者：
P. Wittmuess;C. Tarín;A. Keck;E. Arnold;O. Sawodny
提出了一种基于平衡截断的参数化模型降阶方法。参数模型降阶旨在从更大的模型生成低阶模型，而不失去对参数的依赖。利用原系统的泰勒展开式，可以得到平衡系统的泰勒展开式。与求解参数模型降阶问题的基于插值的方法相比，该方法可以计算降阶后的系统以及不同参数值对应的投影矩阵，且计算量减少。这绕过了在基于插值的方法中可能出现的来自不同快照点的不兼容子空间的问题，这些问题可能导致意外行为导致不稳定。该方法可以处理多维参数空间。给出了基于全纯函数的平衡系统泰勒级数收敛的充分条件。讨论了截断步骤和误差范围。以伯努利光束模型为例，验证了该方法的有效性。
This paper presents a new method for parametric model order reduction based on balanced truncation. Parametric model order reduction seeks to generate low-order models from larger models without losing the dependence on a parameter. Using a Taylor expansion of the original system, a Taylor expansion of the balanced system can be obtained. In contrast to interpolation-based approaches for the solution of the parametric model order reduction problem, the proposed approach permits calculation of the reduced system as well as the corresponding projection matrix for different parameter values with reduced computation power. This bypasses the problem of incompatible subspaces from different snapshot points potentially occurring in interpolation based approaches that can lead to unexpected behavior up to instability. The presented method can handle multidimensional parameter spaces. Sufficient conditions for the convergence of the Taylor series of the balanced system based on holomorphic functions are derived. The truncation step as well as error bounds are discussed. A Bernoulli beam model is used as an example to demonstrate the performance of the technique.