Non-Parametric Identification of Rotor-Bearing System through Volterra-Wiener Theories

  • Nalinaksh S. VyasEmail author
  • Animesh Chatterjee
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 1011)


The structure of the Volterra and Wiener series, which model the relationship between system response and input in terms of series of first and higher order convolution integrals, provide analytical platforms which can be utilized for parameter estimation. These are non-parametric forms of response representation. Non-parametric identification concerns modeling in a function space by input-output mapping, for systems where sufficient information on the mathematical structure or class is not available. Parametric identification, on the other hand, refers to systems where sufficient a-prioriinformation about the mathematical structure of the class to which the system belongs, is available. In the present study, structured Volterra and Wiener response representations are employed to develop identification and parameter estimation procedures for nonlinear rotor systems. Experimental investigations and validation of algorithms have been carried out on a laboratory test rig. Linear and nonlinear stiffness parameters are estimated and compared with approximate theoretical formulations and some previous experimental results.


Volterra series Wiener series Nonlinear system identification Rotor-bearing system 


  1. 1.
    Zhabanch, N., Jean, W.Z.: Nonlinear dynamic analysis of a rotor shaft system with viscoelastically supported bearings. ASME J. Vib. Acoust. 125, 290–298 (2004)Google Scholar
  2. 2.
    Harsha, S.P.: Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearings. Chaos, Solitons and Fractals 26(1), 47–66 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bonnelo, P., Brennan, M.J., Homes, R.: Nonlinear modelling of rotor dynamic systems with squeeze film dampers-an efficient integrated approach. J. Sound Vib. 249(4), 743–773 (2002)CrossRefGoogle Scholar
  4. 4.
    Tiwari, R., Vyas, N.S.: Nonlinear bearing stiffness parameter extraction from random response in flexible rotor-bearing systems. J. Sound Vib. 203(3), 389–408 (1997)CrossRefGoogle Scholar
  5. 5.
    Fretchet, M.: Sur les fonctionnels continues. Annls. Scient. Ec. Norm. Sup. 27, 193–219 (1910)Google Scholar
  6. 6.
    Volterra, V.: Theory of Functionals. Blackie & Sons, Glasgow (1930)Google Scholar
  7. 7.
    Schetzen, M.: The Volterra and Wiener Theories of Nonlinear Systems. Wiley, New York (1980)zbMATHGoogle Scholar
  8. 8.
    Lee, Y.W., Schetzen, M.: Measurement of Wiener kernels of nonlinear systems by cross correlation. Int. J. Control 2(3), 237–254 (1965)CrossRefGoogle Scholar
  9. 9.
    Harris, T.A.: Rolling Bearing Analysis. Wiley, New York (1984)Google Scholar
  10. 10.
    Ragulskis, K.M., Jurkauskas, A.Y., Atstupenas, V.V., Vitkute, A.Y., Kulvec, A.P.: Vibration in Bearings. Mintis Publishers, Vilnyus (1974)Google Scholar
  11. 11.
    Chatterjee, A., Vyas, N.S.: Nonlinear parameter estimation through Volterra series using method of recursive iteration through harmonic probing. J. Sound Vib. 268(4), 657–678 (2003)CrossRefGoogle Scholar
  12. 12.
    Khan, A.A., Vyas, N.S.: Nonlinear bearing stiffness parameter estimation in flexible rotor-bearing systems using Volterra and Wiener approach. Probab. Eng. Mech. 6(2), 137–157 (2001)CrossRefGoogle Scholar
  13. 13.
    Khan, A.A., Vyas, N.S.: Application of Volterra and Wiener theories for nonlinear parameter estimation in a rotor-bearing system. Nonlinear Dyn. 24(3), 285–304 (2001)zbMATHCrossRefGoogle Scholar
  14. 14.
    French, A.S., Butz, E.G.: Measuring the Wiener kernels of a nonlinear system using the Fast Fourier Transform algorithm. Int. J. Control 17(3), 529–539 (1973)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of TechnologyKanpurIndia
  2. 2.Department of Mechanical EngineeringVisvesvaraya National Institute of TechnologyNagpurIndia

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