Gaussian process regression for the estimation of generalized frequency response functions

Jeremy Stoddard; Georgios Birpoutsoukis; Johan Schoukens; James Welsh

doi:10.1016/j.automatica.2019.05.010

Gaussian process regression for the estimation of generalized frequency response functions

Jeremy Stoddard, Georgios Birpoutsoukis, Johan Schoukens (Corresponding author), James Welsh

Control Systems

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Abstract

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.

Original language	English
Pages (from-to)	161-167
Number of pages	7
Journal	Automatica
Volume	106
DOIs	https://doi.org/10.1016/j.automatica.2019.05.010
Publication status	Published - 1 Aug 2019

Funding

This work was supported in part by an Australian government Research Training Program (RTP) scholarship and the Priority Research Centre for Complex Dynamic Systems and Control (CDSC) at the University of Newcastle, Australia , and in part by the Fund for Scientific Research (FWO-Vlaanderen), the Flemish Government (Methusalem) , the Belgian Government through the Inter university Poles of Attraction (IAP VII) Program , and the ERC advanced grant SNLSID, under contract 320378 . Jeremy G. Stoddard was born in Newcastle, Australia in 1993. He received a B.E. degree (Hons. I and University Medal) in electrical engineering in 2015 from the University of Newcastle, Australia. He is currently completing his Ph.D. at the same university, where his research interests include estimation, analysis and control of nonlinear systems, and biomedical applications of system identification. Georgios Birpoutsoukis received the Diploma of Mechanical Engineering in 2010 from the Aristotle University of Thessaloniki (AUTH), Thessaloniki, Greece. In 2013 he received the Master of Science degree in Systems and Control from the Delft University of Technology (TU Delft), Delft, the Netherlands. In 2018 he received the degree of Doctor of Engineering Sciences from the Vrije Universiteit Brussel (VUB), Brussels, Belgium. Since 2017 he is a Post-Doctoral Researcher at the Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM) at the Université Catholique de Louvain (UCLouvain). His main research interests include data-driven modelling of nonlinear dynamical systems, optimal input design for linear and nonlinear dynamical systems, as well as time-series estimation for prediction and forecasting. Johan Schoukens received both the Masters degree in electrical engineering in 1980, and the Ph.D. degree in engineering sciences in 1985 from the Vrije Universiteit Brussel (VUB), Brussels, Belgium. In 1991 he received the degree of Geaggregeerde voor het Hoger Onderwijs from the VUB, and in 2014 the degree of Doctor of Science from The University of Warwick. From 1981 to 2000, he was a researcher of the Belgian National Fund for Scientific Research (FWO-Vlaanderen) at the Electrical Engineering Department of the VUB. From 2000 to 2018 he was a full-time professor in electrical engineering, and since 2018 he is emeritus professor at the department INDI of the VUB and at the Department of Electrical Engineering of the TU/e (The Netherlands). From 2009 to 2016, he was visiting professor at the Katholieke Universiteit Leuven (Belgium). His main research interests include system identification, signal processing, and measurement techniques. He has been a Fellow of IEEE since 1997. He was the recipient of the 2002 Andrew R. Chi Best Paper Award of the IEEE Transactions on Instrumentation and Measurement, the 2002 Society Distinguished Service Award from the IEEE Instrumentation and Measurement Society, and the 2007 Belgian Francqui Chair at the Université Libre de Bruxelles (Belgium). Since 2010, he is a member of Royal Flemish Academy of Belgium for Sciences and the Arts. In 2011 he received a Doctor Honoris Causa degree from the Budapest University of Technology and Economics (Hungary). Since 2013 he is an honorary professor of the University of Warwick. James S. Welsh was born in Maitland, Australia in 1965. He received a B.E. degree (Hons. I) in electrical engineering in 1997 and his Ph.D. in 2004, both from the University of Newcastle, Australia. His Ph.D. thesis analysed ill-conditioning problems arising in system identification. He spent more than 15 years working in industry before taking up his current position with the University of Newcastle, where, since 2004 he has been employed in the School of Electrical Engineering and Computing. His research interests include system identification, auto-tuning and process control. Most recently he has been actively involved in research projects in the areas of biomedical science, transformer monitoring and medical engineering. He is a member of the Priority Research Centre for Complex Dynamic Systems and Control at the University of Newcastle.

Keywords

Gaussian process regression
Generalized frequency response function
Nonlinear system identification

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Gaussian process regression for the estimation of generalized frequency response functions

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