Abstract
In this paper, we consider the problem of data-driven modeling for systems containing nonlinear sensors. The issue is explored via an established nonlinear benchmark in the system identification community, referred to as the “coupled electric drives.” In the benchmark system, nonlinearity emerges in the pulse transducer used to measure the angular velocity of a pulley, which is invariant to the direction of rotation. In order to model the nonlinear dynamics without the use of extensive prior knowledge, we estimate a nonparametric Volterra series model using a regularized basis function approach. While the Volterra series is typically an impractical modeling tool due to the large number of parameters required, we obtain accurate models using only a short estimation dataset, by directly regularizing the basis function expansions of each Volterra kernel in a Bayesian framework.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Birpoutsoukis, G., Marconato, A., Lataire, J., Schoukens, J.: Regularized nonparametric Volterra kernel estimation. Automatica 82, 324–327 (2017)
Boyd, S., Chua, L.O.: Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circ. Syst. 32(11), 1150–1161 (1985)
Campello, R., Favier, G., do Amaral, W.: Optimal expansions of discrete-time Volterra models using Laguerre functions. Automatica 40, 815–822 (2004)
Ljung, L.: System Identification: Theory for the User. Prentice Hall Information and System Sciences Series, Prentice Hall PTR (1999)
Pillonetto, G., De Nicolao, G.: A new kernel-based approach for linear system identification. Automatica 46(1), 81–93 (2010)
Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., Ljung, L.: Kernel methods in system identification, machine learning and function estimation: a survey. Automatica 50(3), 657–682 (2014)
Pintelon, R., Schoukens, J.: System Identification: A Frequency Domain Approach. Wiley, New York (2012)
Rugh, W.J.: Nonlinear System Theory: The Volterra-Wiener Approach. Johns Hopkins University Press, Baltimore (1980)
Schetzen, M.: The Volterra and Wiener Theories of Nonlinear Systems. Wiley, New York (1980)
Stoddard, J.G., Welsh, J.S.: Volterra kernel identification using regularized orthonormal basis functions (2018). https://arxiv.org/abs/1804.07429
Stoddard, J.G., Welsh, J.S., Hjalmarsson, H.: EM-based hyperparameter optimization for regularized Volterra kernel estimation. IEEE Control Syst. Lett. 1(2), 388–393 (2017)
Wahlberg, B.: System identification using Laguerre models. IEEE Trans. Autom. Control AC–36(5), 551–562 (1991)
Wellstead, P.E.: Introduction to Physical System Modelling. Academic Press, London (1979)
Wigren, T., Schoukens, M.: Coupled electric drives data set and reference models. Technical report, Department of Information Technology, Uppsala University (2017). http://www.it.uu.se/research/publications/reports/2017-024/2017-024-nc.pdf
Wu, C.F.J.: On the convergence properties of the EM algorithm. Ann. Stat. 11(1), 95–103 (1983)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Stoddard, J.G., Welsh, J.S. (2018). Data-Driven Modeling of a Coupled Electric Drives System Using Regularized Basis Function Volterra Kernels. In: Chen, Z., Mendes, A., Yan, Y., Chen, S. (eds) Intelligent Robotics and Applications. ICIRA 2018. Lecture Notes in Computer Science(), vol 10984. Springer, Cham. https://doi.org/10.1007/978-3-319-97586-3_43
Download citation
DOI: https://doi.org/10.1007/978-3-319-97586-3_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97585-6
Online ISBN: 978-3-319-97586-3
eBook Packages: Computer ScienceComputer Science (R0)