Nonlinear Induced Variance of Frequency Response Function Measurements

This paper analyzes the variance of the estimated frequency response function (FRF) Ĝ_BLA of the best linear approximation Ĝ_BLA to a nonlinear system that is driven by random excitations. Ĝ_BLA varies not only due to the disturbing measurement and process noise but also over different realizations of the random excitation because the nonlinear distortions depend on the input realization. It will be shown that the variance expression σ_ĜBLA² that is obtained in the linear framework can also be used to calculate the variance that is induced by the nonlinear distortions. This validates the common engineering practice, where the linear FRF methodology is often used under nonlinear conditions.