The Best Linear Approximation of MIMO Systems: First Results on Simplified Nonlinearity Assessment

  • Péter Zoltán CsurcsiaEmail author
  • Bart Peeters
  • Johan Schoukens
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Many mechanical structures are nonlinear and there is no unique solution for modeling nonlinear systems. When a single-input, single-output system is excited by special signals, it is easily possible to decide whether the linear framework is still accurate enough to be used, or a nonlinear framework must be used. However, for multiple-input, multiple-output (MIMO) systems, the design of experiment is not a trivial question since the input and output channels are not mutually independent. This paper shows the first results of an ongoing research project and it addresses the questions related to the user-friendly processing of MIMO measurements with respect to the design of experiment and the analysis of the measured data.

When the proposed framework is used, it is easily possible (a) to decide, if the underlying system is linear or not, (b) to decide if the linear framework is still accurate (safe) enough to be used, and (c) to tell the unexperienced user how much it can be gained using an advanced nonlinear framework. The proposed nonparametric industrial framework is illustrated on a ground vibration testing of an electrical airplane.


MIMO systems Nonlinearity Nonparametric estimation System identification Ground vibration testing 



This work was funded by the VLAIO Innovation Mandate project number HBC.2016.0235.


  1. 1.
    Lauwers, L., Schoukens, J., Pintelon, R., Enqvist, M.: Nonlinear structure analysis using the best linear. In: Proceedings of International Conference on Noise and Vibration Engineering, Leuven (2006)Google Scholar
  2. 2.
    Esfahani, A., Schoukens, J., Vanbeylen, L.: Using the best linear approximation with varying excitation signals for nonlinear system characterization. IEEE Trans Instrum Meas. 65, 1271–1280 (2016)CrossRefGoogle Scholar
  3. 3.
    Wong, H.K., Schoukens, J., Godfrey, K.: Analysis of best linear approximation of a wiener–hammerstein system for arbitrary amplitude distributions. IEEE Trans Instrum Meas. 61(3), 645–654 (2012)CrossRefGoogle Scholar
  4. 4.
    Schoukens, J., Pintelon, R.: Study of the variance of parametric estimates of the best linear approximation of nonlinear systems. IEEE Trans Instrum Meas. 59(12), 3156–3167 (2010)CrossRefGoogle Scholar
  5. 5.
    Pintelon, R., Schoukens, J.: System Identification: A Frequency Domain Approach, 2nd edn. Wiley. ISBN: 978-0470640371, Hoboken, NJ (2012)CrossRefGoogle Scholar
  6. 6.
    Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice-Hall., ISBN: 9780136566953, New Jersey (1999)zbMATHGoogle Scholar
  7. 7.
    Csurcsia, P.Z., Lataire, J.: Nonparametric estimation of time-variant systems using 2D regularization. IEEE Trans Instrum Meas. 65(5), 1259–1270 (2016)CrossRefGoogle Scholar
  8. 8.
    Csurcsia, P.Z.: Static nonlinearity handling using best linear approximation: an introduction. Pollack Periodica. 8(1), 153–165 (2013)CrossRefGoogle Scholar
  9. 9.
    Schoukens, J., Pintelon, R., Rolain, Y.: Mastering System Identification in 100 Exercises. Wiley. ISBN: 978047093698, Hoboken, NJ (2012)CrossRefGoogle Scholar
  10. 10.
    Solomou, M., Rees, D.: Measuring the best linear approximation of systems suffering nonlinear distortions: an alternative method. IEEE Trans Instrum Meas. 52(4), 1114–1119 (2003)CrossRefGoogle Scholar
  11. 11.
    Dobrowiecki, T., Schoukens, J.: Linear approximation of weakly nonlinear MIMO systems. In: IEEE International Instrumentation and Measurement Technology Conference (I2MTC), pp. 1607–1612 (2004)Google Scholar
  12. 12.
    Guillaume, P., Pintelon, R., Schoukens, J.: Accurate estimation of multivariable frequency response functions. 13th World Congress of IFAC. 29(1), 4351–4356 (1996)Google Scholar
  13. 13.
    Priemer, R.: Introductory Signal Processing. World Scientific, Singapore. ISBN: 9971509199 (1991)Google Scholar
  14. 14.
    Alvarez Blanco, M., Csurcsia, P.Z., Janssens, K., Peeters, B., Desmet, W.: Nonlinearity assessment of mimo electroacoustic systems on direct field environmental acoustic testing. In: International Conference on Noise and Vibration Engineering, Leuven (2018)Google Scholar
  15. 15.
    Peeters, B., El-Kafafy, M., Guillaume, P. Van der Auweraer, H.: Uncertainty propagation in experimental modal analysis. In: Conference Proceedings of the Society for Experimental Mechanics Series (2014)Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  • Péter Zoltán Csurcsia
    • 1
    • 2
    Email author
  • Bart Peeters
    • 1
  • Johan Schoukens
    • 2
  1. 1.Siemens Industry Software NVLeuvenBelgium
  2. 2.Department of Engineering Technology (INDI)Vrije Universiteit BrusselElseneBelgium

Personalised recommendations