一种基于插值的快速频域系统辨识方案
An Interpolation-based Scheme for Rapid Frequency-Domain System Identification
AI总结：
本研究提出一种基于重心插值与权重优化的频域系统辨识方案，采用自适应频率点选择与瞬态数据优化权重，构建凸优化问题可保证系统稳定性，能减少正弦测试次数，在高阶低阻尼结构系统上验证了有效性。
摘要：
我们提出了一种基于重心插值与权重优化的频域系统辨识方案。该方案与用于模型降阶的Adaptive Antoulas-Anderson（AAA）算法相关，但采用自适应算法选择用于探测系统响应的频率点，这是辨识相较于模型降阶的必需要求。该方案尤其适用于单次正弦响应测试耗时久或成本高的系统，因此有减少此类测试总次数的需求。我们算法的两个核心特性是：利用正弦测试中的瞬态数据来优化重心权重，以及在自适应网格上自动选择下一个频率点。两者分别采用对应系统$H^2$范数和$H^\infty$范数的误差准则实现。此外，我们构建的优化问题是凸的，还可选择保证辨识系统的稳定性。在一个高阶、低阻尼结构系统上的计算结果验证了该方案的有效性。
英文摘要：
We present a frequency-domain system identification scheme based on barycentric interpolation and weight optimization. The scheme is related to the Adaptive Antoulas-Anderson (AAA) algorithm for model reduction, but uses an adaptive algorithm for selection of frequency points for interrogating the system response, as would be required in identification versus model reduction. The scheme is particularly suited for systems in which any one sinusoidal response run is long or expensive, and thus there is an incentive to reduce the total number of such runs. Two key features of our algorithm are the use of transient data in sinusoidal runs to both optimize the barycentric weights, and automated next-frequency selection on an adaptive grid. Both are done with error criteria that are proxies for a system's $H^2$ and $H^\infty$ norms respectively. Furthermore, the optimization problem we formulate is convex, and can optionally guarantee stability of the identified system. Computational results on a high-order, lightly damped structural system highlights the efficacy of this scheme.
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