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：在频率响应测量数据驱动建模动力系统的基本工具是底层有理传递函数的重心形式。本文提出结构化重心形式，利用频域输入输出数据对具有二阶时间导数的动力系统进行建模。通过施加一组插值条件，系统的传递函数使用不同参数化方式被重写为多种重心形式。基于所发展的重心形式，开发了类似Loewner的算法，用于从数据显式计算二阶系统。数值实验展示了这些新型结构化数据驱动建模方法相对于文献中其他基于插值的数据驱动建模技术的性能。