论文标题
大规模二阶系统的频率和时间限制的平衡截断
Frequency- and Time-Limited Balanced Truncation for Large-Scale Second-Order Systems
论文作者
论文摘要
考虑到在实际应用中使用动态系统，通常仅在时间或频域中仅有限的区域。因此，它通常会偿还频率和时间域中使用的动态系统的局部近似值。在本文中，我们将频率和时间限制平衡截断方法的结构保存扩展到二阶动力学系统。我们提供了有关一阶有限平衡截断方法的完整概述，并通过使用文献中的不同二阶平衡截断公式将这些方法扩展到二阶系统。此外，我们提出了用于求解出现的大规模稀疏基质方程的数值方法，并给出数值修改以处理二阶系统的有问题情况。然后在三个数值示例中进行了说明。
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in the frequency and time domain. In this paper, we consider a structure-preserving extension of the frequency- and time-limited balanced truncation methods to second-order dynamical systems. We give a full overview about the first-order limited balanced truncation methods and extend those methods to second-order systems by using the different second-order balanced truncation formulas from the literature. Also, we present numerical methods for solving the arising large-scale sparse matrix equations and give numerical modifications to deal with the problematic case of second-order systems. The results are then illustrated on three numerical examples.
