Identification of Time-varying Modal Parameters Using a Time-varying Autoregressive Approach

A time-varying autoregressive model with time-varying coefficients is introduced in this paper for parameter extraction from non-stationary vibration signals. With this model, the relationship between linear time-varying modal parameters, i.e., instantaneous frequencies and damping factors, and time-varying autoregressive model coefficients is established. The time-varying autoregressive modeling is employed in order to obtain good time and frequency resolution of the time-frequency distribution of non-stationary responses. A new algorithm is presented by combining the use of base functions with the time-frequency transform of signals, in which the base functions have shift the time-varying modeling to a linear time-invariant identification problem. A simulated linear time-varying system of three degrees of freedom with time-varying stiffness is presented to validate the proposed time-varying autoregressive method, and the simulated results have demonstrated that the method based on time-varying autoregressive modeling is effective in identifying time-varying modal parameters.