Frequency-based methods have been successfully employed in creating high fidelity data-driven reduced order models (DDROMs) for linear dynamical systems. These methods require access to values (and sometimes derivatives) of the frequency-response function (transfer function) in the complex plane. These frequency domain values can at times be costly or difficult to obtain (especially if the method of choice requires resampling); instead one may have access to only time-domain input-output data. The data informativity approach to moment matching provides a powerful new framework for recovering the required frequency data from a single time-domain trajectory. In this work, we analyze and extend upon this framework, resulting in vastly improved conditioning of the associated linear systems, an error indicator, and removal of an assumption that the system order is known. This analysis leads to a robust algorithm for recovering frequency information from time-domain data, suitable for large scale systems. We demonstrate the effectiveness of our algorithm by forming frequency based DDROMs from time-domain data of several dynamical systems.

翻译：频率方法已成功应用于构建线性动力系统的高保真数据驱动降阶模型。这些方法需要获取复平面上频率响应函数（传递函数）的值（有时还包括其导数）。在特定情况下，获取这些频域值可能代价高昂或困难重重（尤其是当所选方法需要重新采样时）；相反，我们可能仅能获取时域输入输出数据。数据信息性方法为矩匹配提供了一种强大的新框架，能够从单条时域轨迹中恢复所需的频率数据。本研究分析并扩展了这一框架，显著改善了关联线性系统的条件数，提出了误差指标，并消除了对系统阶数已知这一假设的依赖。该分析衍生出一种鲁棒算法，可从时域数据中恢复频率信息，适用于大规模系统。我们通过若干动力系统的时域数据构建基于频率的降阶模型，验证了算法的有效性。