8. Time-Frequency Domain Modal Parameter Estimation of Time-Varying Structures Using a Two-Step Least Square Estimator

Under natural stochastic excitations, responses of time-varying structures are always nonstationary stochastic signals, of which spectra change with time. This paper studies the time-dependent power spectrum density based on time-frequency analysis. Based on the time-dependent power spectrum density, a mathematical model of the time-frequency-domain two-step least square modal parameter estimator for time-varying structures is presented. In the first-step estimation, the modal parameters at each time instant are estimated using the least square complex frequency-domain method. Furthermore, the estimated modal parameters are sifted and sorted. Based on the sifted and sorted modal parameters, the time-varying resonance frequency, damping ratio and operational mode shapes are estimated in the second-step estimation. A numerical simulation example and a group of experiments validate this two-step least square modal parameter estimator for time-varying structures.