A general nonlinear system identification method based upon time-varying trend of instantaneous frequencies and amplitudes

Nonlinear phenomena are widely encountered in practical applications. The presence of nonlinearity makes a system exhibit different dynamic behaviours from its linear counterpart. A typical example is that free-vibration frequencies of nonlinear systems are amplitude-dependent, resulting in the variation of free-vibration frequencies with time. Therefore, Fourier spectrum which has been widely used in linear systems cannot completely represent dynamic characteristics of nonlinear systems. On the contrary, the time-varying trend of instantaneous frequencies and vibration amplitudes can completely capture dynamic characteristics of nonlinear systems. In this study, a general system identification method based on curving-fitting the time-varying trend of instantaneous frequencies and amplitudes is proposed for nonlinear systems. Herein Hilbert transform is employed to extract instantaneous frequencies and amplitudes from the measured responses. By taking the relationships between instantaneous vibration characteristics and structural physical parameters as regression models, structural physical parameters can be estimated by a least-squares estimation or an optimization method. The combination of the instantaneous information in time domain and frequency domain leads to high accuracy of identification results. The determination of model structure of nonlinearities is solved by assuming a generalized model which involves as many types of nonlinearities as possible. The proposed method has been demonstrated by numerical simulations.