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.

通过频率响应测量对动力系统进行数据驱动建模的一个重要工具是基础有理传递函数的重心形式。在这项工作中，我们提出了结构化重心形式，用于使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，系统的传递函数可以使用不同的参数化以不同的重心形式重写。类似 Loewner 的算法是为了根据基于已开发的重心形式的数据对二阶系统进行显式计算而开发的。数值实验表明，与文献中其他基于插值的数据驱动建模技术相比，这些新的结构化数据驱动建模方法的性能。