Nonlinear Induced Variance of Frequency Response Function Measurements

This paper analyzes the variance of the estimated frequency response function (FRF) GBLA of the best linear approximation GBLA to a nonlinear system that is driven by random excitations. GBLA 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 σGBLA2 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.