An Interpolation-based Scheme for Rapid Frequency-Domain System Identification

Abstract: 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.