Identification of Instantaneous Modal Parameter of Time-Varying Systems via a Wavelet-Based Approach and Its Application

This work presents an efficient approach using time-varying autoregressive with exogenous input (TVARX) model and a substructure technique to identify the instantaneous modal parameters of a linear time-varying structure and its substructures. The identified instantaneous natural frequencies can be used to identify earthquake damage to a building, including the specific floors that are damaged. An appropriate TVARX model of the dynamic responses of a structure or substructure is established using a basis function expansion and regression approach combined with continuous wavelet transform. The effectiveness of the proposed approach is validated using numerically simulated earthquake responses of a five-storey shear building with time-varying stiffness and damping coefficients. In terms of accuracy in determining the instantaneous modal parameters of a structure from noisy responses, the proposed approach is superior to typical basis function expansion and regression approach. The proposed method is further applied to process the dynamic responses of an eight-storey steel frame in shaking table tests to identify its instantaneous modal parameters and to locate the storeys whose columns yielded under a strong base excitation.