A spectral method for estimation of non-linear system parameters from measured response

The problem of estimating the parameters in a randomly excited single degree of freedom non-linear system, from measurements of the response alone, is addressed. It is shown that, in the case where the bandwidth of the excitation is significantly greater than that of the response, it is possible to estimate the overall damping, as measured by the equivalent linear damping factor, and the linear and non-linear stiffness parameters, using a spectral technique. To separate the contributions from linear and non-linear damping terms a further estimation stage is required, based on an analysis of the probability distribution of the energy envelope. To validate the proposed estimation method it is applied to some simulated data, corresponding to both white noise and correlated noise inputs.