Model reduction for dynamical systems with quadratic output
Model reduction for dynamical systems with quadratic output
复制标题
具有二次输出的动力系统的模型简化
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
K. Meerbergen
中科院分区：
文献类型：
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作者：
R. Van Beeumen;K. Van Nimmen;G. Lombaert;K. Meerbergen
结构和振动的有限元模型通常导致具有大型稀疏矩阵的二阶动力系统。对于大型有限元模型，计算频率响应函数和结构对动态载荷的响应可能会带来相当大的计算成本。Padé via Krylov方法被广泛使用，并且是具有线性输出的线性动力系统的基于投影的模型降阶技术。本文将Krylov方法的框架扩展到线性二次型最优控制或随机振动问题中具有二次输出的系统。三种不同的双边模型降阶方法基于Krylov方法。对于所有方法，控制（或右）Krylov空间是相同的。因此，方法之间的区别在于观察（或左）Krylov空间的选择。算法和理论的发展，特别重要的情况下，结构阻尼。我们还给出了对应于简支板和现有人行桥的强迫振动的大规模系统的数值例子。在这种情况下，使用块形式的Padé via Krylov方法。版权所有© 2012约翰威利父子有限公司.
Finite element models for structures and vibrations often lead to second order dynamical systems with large sparse matrices. For large‐scale finite element models, the computation of the frequency response function and the structural response to dynamic loads may present a considerable computational cost. Padé via Krylov methods are widely used and are appreciated projection‐based model reduction techniques for linear dynamical systems with linear output. This paper extends the framework of the Krylov methods to systems with a quadratic output arising in linear quadratic optimal control or random vibration problems. Three different two‐sided model reduction approaches are formulated based on the Krylov methods. For all methods, the control (or right) Krylov space is the same. The difference between the approaches lies, thus, in the choice of the observation (or left) Krylov space. The algorithms and theory are developed for the particularly important case of structural damping. We also give numerical examples for large‐scale systems corresponding to the forced vibration of a simply supported plate and of an existing footbridge. In this case, a block form of the Padé via Krylov method is used. Copyright © 2012 John Wiley & Sons, Ltd.