Abstract
This entry is an extension of the nonparametric techniques presented in “Nonparametric Techniques in System Identification”, by Rik Pintelon and Johan Schoukens, to time- and parameter-varying systems and missing data problems. To increase its readability, we first briefly recall in the introduction some definitions given in “Nonparametric Techniques in System Identification”, by Rik Pintelon and Johan Schoukens, and clarify the leakage contribution to nonparametric frequency response function (FRF) estimation. Given its importance in the nonparametric estimation of time- and parameter-varying dynamics, the entry starts by describing the newest developments in advanced techniques for estimating FRFs. Next, the time-varying, parameter-varying, and missing data cases are handled.
As a main result the reader will learn about (i) the detection and quantification of time-varying effects and nonlinear distortions in FRF estimates, (ii) the estimation of time- and parameter-varying FRFs, and (iii) the estimation of (time-varying) FRFs in the presence of missing data. All results are valid for discrete- and continuous-time systems operating in open or closed loop.
Similar content being viewed by others
Bibliography
Bamieh B, Giarré L (2002) Identification of linear parameter varying models. Int J Robust Nonlinear Control 12(9):841–853
Birpoutsoukis G, Marconato A, Lataire J, Schoukens J (2017) Regularized nonparametric Volterra kernel estimation. Automatica 82:324–327
Brillinger DR (1981) Time series: data analysis and theory. McGraw-Hill, New York
Darwish MAH, Cox PB, Proimadis I, Pillonetto G, Toth R (2018) Prediction-error identification of LPV systems: a nonparametric Gaussian regression approach. Automatica 97:92–103
Enqvist M, Ljung L (2005) Linear approximations of nonlinear FIR systems for separable input processes. Automatica 41(3):459–473
Lataire J, Louarroudi E, Pintelon R (2012) Detecting a time-varying behavior in frequency response function measurements. IEEE Trans Instrum Meas 61(8):2132–2143
Ljung L (2001) Estimating linear time-invariant models of nonlinear time-varying systems. Eur J Control 7(2–3):203–219
McKelvey T, Guérin G (2012) Non-parametric frequency response estimation using a local rational model. IFAC Proc Vol 45(16):49–54. Brussels
Pillonetto G, Chiuso A, De Nicolao G (2011) Prediction error identification of linear systems: a nonparametric Gaussian regression approach. Automatica 47(2):291–305
Peumans D, Busschots C, Vandersteen G, Pintelon R (2018) Improved FRF measurements of lightly damped systems using local rational models. IEEE Trans Instrum Meas 67(7):1749–1759
Peumans D, De Vestel A, Busschots C, Rolain Y, Pintelon R, Vandersteen G (2019) Accurate estimation of the non-parametric FRF of lightly-damped mechanical systems using arbitrary excitations. Mech Syst Signal Process 130(1):545–564
Pintelon R, Schoukens J (2012) System identification: a frequency domain approach, 2nd edn. Wiley/IEEE Press, Hoboken
Pintelon R, Louarroudi E, Lataire J (2013) Detecting and quantifying the nonlinear and time-variant effects in FRF measurements using periodic excitations. IEEE Trans Instrum Meas 62(12):3361–3373
Pintelon R, Louarroudi E, Lataire J (2015) Nonparametric time-variant frequency response function estimates using arbitrary excitations. Automatica 51(1):308–317
Pintelon R, Ugryumova D, Vandersteen G, Louarroudi E, Lataire J (2017) Time-variant frequency response function measurement in the presence of missing data. IEEE Trans Instrum Meas 66(11):3091–3099
Rizvi SZ, Velni JM, Abbasi F, Toth R, Meskin N. (2018) State-space LPV model identification using kernelized machine learning. Automatica 88:38–47
Rugh W.J. (1996) Linear system theory, 2nd edn. Prentice Hall, Upper Saddle River.
Tóth R (2010) Modeling and identification of linear parameter-varying systems. Springer, Berlin
Ugryumova D, Pintelon R, Vandersteen G (2015) Frequency response matrix estimation from missing input-output data. IEEE Trans Instrum Meas 64(11):3124–3136
van der Maas R, van der Maas A, Oomen T (2017) Accurate FRF identification of LPV systems: nD-LPM with application to a medical X-ray system. IEEE Trans Contr Syst Techn 25(5):1724–1735
Voorhoeve R, van der Maas A, Oomen T (2018) Non-parametric identification of multivariable systems: a local rational modeling approach with application to a vibration isolation benchmark. Mech Syst Signal Process 105:120–152
Zadeh LA (1950a) Frequency analysis of variable networks. Proc I.R.E. 38:291–299
Zadeh LA (1950b) The determination of the impulsive response of variable networks. J Appl Phys 21:642–645
Acknowledgements
This work is sponsored in part by the Research Foundation Flanders (FWO-Vlaanderen) and in part by the Flemisch Government (Methusalem Fund, METH1).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2019 Springer-Verlag London Ltd., part of Springer Nature
About this entry
Cite this entry
Pintelon, R., Lataire, J. (2019). Nonparametric Techniques in System Identification: The Time-Varying and Missing Data Cases. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100164-1
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5102-9_100164-1
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5102-9
Online ISBN: 978-1-4471-5102-9
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering