Identification of Time-Varying Structural Parameters Based on Hilbert Transform: Numerical Simulations

This paper mainly focuses on the parameter identification of time-varying structural system via numerical simulation. Definitions of instantaneous frequency based on Hilbert Transform in time-varying system are first introduced. Followed are the definition of Hilbert damping spectrum. Identification procedures for both instantaneous frequency and damping ratios based on their definition are then introduced. Applicability of the identification algorithm is investigated through several numerical simulations, in which time-varying frequency and time-varying damping ratios are identified respectively both in SDOF and MDOF systems under different excitations. The results demonstrate that when the system modal parameters are slowly varying, the instantaneous frequency could be easily and well identified for all cases. However, the instantaneous damping ratio could be extracted only when the system is lightly damped, and the results are more convincing for free vibration cases. When the system is under sine waves or white noise excitation, only the variation tendency of the structural damping ratio could be tracked even for noise-free situation. It is also shown that the method based on Hilbert could easily track the abrupt change of system modal parameter under free vibration.