Parameter Estimation for Randomly Excited Non-Linear Systems
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.
KeywordsMoment Equation Stiffness Parameter Sample Function Stochastic Average Ship Roll
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