Identification of modal parameter of nonlinear system from seismic response data using amplitude-dependent time series model

The present work develops a novel procedure of establishing an amplitude-dependent time series model for a nonlinear system and estimating the instantaneous modal parameters of the system from the dynamical responses. The undetermined coefficient in an amplitude-dependent autoregressive with exogenous input (amplitude-dependent ARX) model are assumed as functions of amplitude and are expanded by shape functions constructing by moving least-squares with polynomial basis functions. The amplitude of dynamical responses could be obtained by Hilbert transform. The instantaneous modal parameters of the system are directly estimated from the coefficient in the amplitude-dependent ARX model. The feasibility of the procedure is demonstrated by processing numerically simulated dynamic responses of a nonlinear system. The proposed scheme is demonstrated to be superior to time-varying ARX model and recursive method in identifying modal parameters. Finally, the proposed approach is applied to process measured data for a frame specimen subjected to a series of base excitations in shaking table tests. The specimen was damaged during testing. The identified modal parameters are consistent with observed physical phenomena.