Parameter Estimation for Randomly Excited Non-Linear Systems

A Method based on Moment Equations and Measured Response
  • J. B. Roberts
  • J. F. Dunne
  • A. Debonos
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


The problem of estimating unknown parameters in a non-linear randomly excited dynamic system, when the excitation is unmeasurable, is considered. It is shown that, if the excitation is modelled stochastically as a Gaussian process, with a prescribed spectral form, it is possible to estimate the parameters from response data alone using either moment equations or a spectral input-output relationship. When applied to simulated data for a particular non-linear oscillator, as an example, it is found that the use of moment equations leads to a very good estimation of the stiffness parameters but is incapable of yielding estimates of the absolute level of damping. However the latter can be found accurately by applying a spectral relationship. Improvements in the accuracy of estimation for the damping parameters, and the input intensity, are achieved by using a theoretical expression for the distribution of the energy envelope of the response in combination with statistical linearisation.


Moment Equation Stiffness Parameter Sample Function Stochastic Average Ship Roll 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • J. B. Roberts
    • 1
  • J. F. Dunne
    • 1
  • A. Debonos
    • 1
  1. 1.School of Engineering, University of SussexFalmerUK

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