Estimating frequency response functions by using transient responses of systems to simple excitations

Abstract

This study develops an efficient method using input–output data on estimating non-parametric and then parametric frequency response functions (FRFs) associated with a dynamic system. Contrary to most existing FRF estimation methods that have been theoretically based on the steady-state or stationary responses, the proposed method uses the transient responses that are induced by simple, such as sinusoidal or two-exponential, excitations instead. Its numerical procedure for obtaining a non-parametric FRF is nothing more than solving a set of linear equations in which the unknown variables are individual components of the sought FRF. Furthermore, from the non-parametric FRF, its corresponding poles and residues are extracted through a procedure that involves a usage of the inverse discrete Fourier transform and the Prony-SS method; afterwards, a partial fraction FRF in terms of poles and residues can be achieved. Three numerical examples, including computer simulations and lab experiment, are provided to demonstrate the superior performance of the developed method.