Nonparametric kernel-based modelling of dynamical systems offers important advantages over other nonparametric techniques; the estimate is a continuous function, the model complexity is continuously tuneable, and stability, causality and smoothness are imposed on the impulse response estimate. However, for lightly damped systems, most of the existing kernel-based approaches for estimating the impulse- or frequency response function fail because classical kernels are not appropriate for describing lowly damped resonances. Smoothness is imposed on the entire frequency axis with the diagonal correlated or stable spline kernel, with as a result that resonances cannot be captured well. By introducing the superposition of different kernels, carrying prior knowledge about the resonant poles of the system, we make the kernel-based modelling of lightly-damped systems possible with high-accuracy. We use a frequency domain local rational modelling technique as preprocessing step to determine the most dominant poles, and include these as prior knowledge in the kernels. The performance of the new kernel is demonstrated on a highly resonating simulated system and compared to the state of the art nonparametric frequency domain approaches.
Hallemans, N, Pintelon, R, Joukovsky, BJ, Peumans, D & Lataire, J 2022, 'FRF estimation using multiple kernel-based regularisation', Automatica, vol. 136, no. 2, 110056, pp. 1-12. <https://doi.org/10.1016/j.automatica.2021.110056>
Hallemans, N., Pintelon, R., Joukovsky, B. J., Peumans, D., & Lataire, J. (2022). FRF estimation using multiple kernel-based regularisation. Automatica, 136(2), 1-12. Article 110056. https://doi.org/10.1016/j.automatica.2021.110056
@article{5f4fe4bcd35c4c398ae4c390be72c0bf,
title = "FRF estimation using multiple kernel-based regularisation",
abstract = "Nonparametric kernel-based modelling of dynamical systems offers important advantages over other nonparametric techniques; the estimate is a continuous function, the model complexity is continuously tuneable, and stability, causality and smoothness are imposed on the impulse response estimate. However, for lightly damped systems, most of the existing kernel-based approaches for estimating the impulse- or frequency response function fail because classical kernels are not appropriate for describing lowly damped resonances. Smoothness is imposed on the entire frequency axis with the diagonal correlated or stable spline kernel, with as a result that resonances cannot be captured well. By introducing the superposition of different kernels, carrying prior knowledge about the resonant poles of the system, we make the kernel-based modelling of lightly-damped systems possible with high-accuracy. We use a frequency domain local rational modelling technique as preprocessing step to determine the most dominant poles, and include these as prior knowledge in the kernels. The performance of the new kernel is demonstrated on a highly resonating simulated system and compared to the state of the art nonparametric frequency domain approaches.",
keywords = "Data-driven modelling, Kernel-based modelling, local rational modelling, Gaussian Process regression, Machine learning, Lightly damped systems",
author = "Noel Hallemans and Rik Pintelon and Joukovsky, {Boris Joseph} and Dries Peumans and John Lataire",
note = "Funding Information: This research was supported in part by the Fund for Scientific Research (FWO Belgium, Ph.D. fellowship strategic basic research 1SB5721N), in part by the Vrije Universiteit Brussel (SRP-19), and in part by the Flemish Government (Methusalem Grant METH1). The material in this paper was presented at the 19th IFAC Symposium on System Identification, July 13–16 2021, Padova, Italy. This paper was recommended for publication in revised form by Associate Editor Gianluigi Pillonetto under the direction of Editor Torsten S{\"o}derstr{\"o}m. Funding Information: Boris Joukovsky received a Master degree in Electrical Engineering in 2019 from the Universit{\'e} Libre de Bruxelles (ULB) and the Vrije Universiteit Brussel (VUB), Belgium. Since 2019, he is a Ph.D. student with the Department of Electronics and Informatics (ETRO), VUB, under the supervision of Prof. Nikos Deligiannis. In 2020, he obtained a Ph.D. Strategic Basic Research Fellowship from the Research Foundation Flanders (FWO), Belgium. His research focuses on interpretable deep learning with applications in image and video processing, as well as theoretical machine learning concepts and convex optimisation. Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",
year = "2022",
month = feb,
day = "1",
language = "English",
volume = "136",
pages = "1--12",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",
number = "2",
}