Time-frequency analysis of nonlinear systems: The skeleton linear model and the skeleton curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.