Gaussian process regression for the estimation of generalized frequency response functions
Gaussian process regression for the estimation of generalized frequency response functions
复制标题
用于估计广义频率响应函数的高斯过程回归
DOI：
10.1016/j.automatica.2019.05.010
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
J. Welsh
中科院分区：
文献类型：
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作者：
Jeremy G. Stoddard;Georgios Birpoutsoukis;J. Schoukens;J. Welsh
贝叶斯学习技术最近在系统识别领域引起了极大的关注。这个概念最初是为了线性脉冲响应模型的低方差估计而引入的，后来扩展到了时间域中Volterra级数估计的非线性设置。本文从频域的角度讨论了非线性系统的估计问题，其中Volterra级数具有由广义频率响应函数(GFRF)组成的表示形式。受针对线性频域情况开发的技术的启发，GFRF被建模为具有与相应Volterra级数的时域特性相关的先验协方差的实/复高斯过程。给出了周期激励情况下的高斯过程回归方法，数值算例表明了该方法的有效性，以及在带限激励情况下该方法优于时间域法的优点。
Bayesian learning techniques have recently garnered significant attention in the system identification community. Originally introduced for low variance estimation of linear impulse response models, the concept has since been extended to the nonlinear setting for Volterra series estimation in the time domain. In this paper, we approach the estimation of nonlinear systems from a frequency domain perspective, where the Volterra series has a representation comprised of Generalized Frequency Response Functions (GFRFs). Inspired by techniques developed for the linear frequency domain case, the GFRFs are modelled as real/complex Gaussian processes with prior covariances related to the time domain characteristics of the corresponding Volterra series. A Gaussian process regression method is developed for the case of periodic excitations, and numerical examples demonstrate the efficacy of the proposed method, as well as its advantage over time domain methods in the case of band-limited excitations.