Hybrid Time-Variant Frequency Response Function Estimates Using Multiple Sets of Basis Functions

A new method for estimating the nonparametric time-variant frequency response function (TV-FRF) and its variance of a hybrid time-varying system is proposed. By parameterizing the hybrid time variation using Legendre polynomials and Haar multiresolution wavelets, the TV-FRF identification problem is reduced to a time-invariant FRF estimation problem. The stepwise regression method and Akaike information criterion are applied to select the significant basis functions without manual intervention. This method can achieve high estimation accuracy and small uncertainty without requiring prior knowledge of the time variation of system dynamics. Simulations and an experiment are included to illustrate the method.