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：基于频率的方法已成功应用于为线性动力系统构建高保真数据驱动降阶模型(DDROMs)。这些方法需要获取复平面上频率响应函数（传递函数）的数值（有时还需其一阶导数）。然而，此类频域数值有时获取成本较高或存在困难（尤其当所选方法需要重采样时）；相比之下，研究者可能仅能获取时域输入-输出数据。矩匹配的数据信息量方法为从单一时域轨迹恢复所需频率数据提供了强大的新框架。本文对该框架进行深入分析与扩展，显著改善了相关线性系统的条件数，提出了误差指标，并消除了系统阶数已知这一假设条件。该分析最终形成了一种鲁棒算法，能够从时域数据恢复频率信息，适用于大规模系统。我们通过多个动力系统的时域数据构建基于频率的DDROMs，验证了所提算法的有效性。