An essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling dynamical systems with second-order time derivatives using their frequency domain input-output data. By imposing a set of interpolation conditions, the systems' transfer functions are rewritten in different barycentric forms using different parametrizations. Loewner-like algorithms are developed for the explicit computation of second-order systems from data based on the developed barycentric forms. Numerical experiments show the performance of these new structured data driven modeling methods compared to other interpolation-based data-driven modeling techniques from the literature.
翻译:摘要:基于频率响应测量数据的数据驱动建模中,重心有理传输函数是一个重要的工具。本文提出了结构化重心形式来建模具有二阶时间导数的动态系统;使用不同的参数化形式,通过一组插值条件来重新编写系统的传输函数。基于类Loewner算法,通过所提出的重心形式显式计算二阶系统。数值实验表明,这些新的结构化数据驱动建模方法在性能上要优于文献中其他基于插值的数据驱动建模技术。