Time-Varying Linear and Nonlinear Structural Identification with Analytical Mode Decomposition and Hilbert Transform

Analytical mode decomposition (AMD) of a time series concerning any preselected bisecting frequency with Hilbert transform has been developed for closely spaced multicomponent signal decomposition. For this class of structures, it is often challenging, if not impossible, to apply empirical mode decomposition. In this study, the instantaneous structural frequencies are directly derived from the decomposed modal responses for systems with single and multiple degrees of freedom with both free and force vibrations, based on AMD combined with Hilbert transform analysis. The results show that the slow varying component of the instantaneous frequency of the signal is approximately equal to the instantaneous frequency of the systems for slowly time varying linear or weakly nonlinear structures. Both numerical simulations and experimental tests show that the proposed method is capable of tracking the frequency variations with high accuracy for time varying linear structures or weakly nonlinear structures.