A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds
A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds
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DOI：
10.1002/nme.4408
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发表时间：
2013-02
影响因子：
2.9
通讯作者：
N. T. Son
中科院分区：
文献类型：
--
作者：
N. T. Son
模型降阶有助于减少处理大型动态系统的计算时间，例如，在仿真，控制，优化期间。在许多情况下，所考虑的模型依赖于参数;因此，模型降阶技术是优选的，以象征性地保持这种依赖性或适应于由参数值的变化引起的模型的变化。在本文中，我们首先提出应用格拉斯曼流形上的插值技术，这个问题。在分析奇异值分解和结构的基础上，将整个过程分解为离线和在线两个阶段，对系统矩阵依赖于参数的模型进行了改进，大大降低了计算复杂度。数值算例说明了该方法的有效性。版权所有© 2012约翰威利父子有限公司.
Model order reduction helps to reduce the computational time in dealing with large dynamical systems, for example, during simulation, control, optimization. In many cases, the considered model depends on parameters; Model order reduction techniques are, therefore, preferred to symbolically preserve this dependence or to be adaptive to the change of the model caused by the variation in the values of the parameters. In this paper, we first present the application of the interpolation technique on Grassmann manifolds to this problem. We then improve the method for the models whose system matrices depend affinely on parameters by considerably reducing the computational complexity on the basis of analyzing the structure of sums of singular value decompositions and decomposing the whole procedure into offline and online stages. A numerical example is shown to illustrate the method as well as to prove its effectiveness. Copyright © 2012 John Wiley & Sons, Ltd.