A wavelet-based approach for the identification of damping in non-linear oscillators

A special class of non-linear damping models is studied in which the damping force is proportional to the product of positive powers of the absolute values of displacement and velocity. For a single degree of freedom system, the Krylov–Bogoliubov averaging method is used to determine the approximate free response. The wavelet transform of this response is used as a time-scale representation for parameter identification: two methods based on this wavelet transform are presented to estimate instantaneous frequency, damping and envelope of the system. The first method uses cross-sections of the wavelet transform. The second method uses ridges and skeletons of the wavelet transform. This second method is general and gives accurate results in the case of noisy non-linear oscillators. These methods are illustrated using a simulated example.