Multisine multiexcitation in frequency response function estimation

Abstract

Introduction T RUE random single excitation has been widely used in frequency response function (FRF) estimation. It reduces test times when compared to swept or stepped sinusoidal excitation. Transient excitation presents the same advantage, but it has handicaps related to digital signal processing difficulties and difficulties in supplying enough energy in a short period of time without causing nonlinear behavior due to high force amplitudes. When true random excitation is used, averaging is mandatory due to the stochastic character of the signals. Furthermore, some sort of windowing is necessary to reduce leakage in the discrete Fourier transform (DFT). In vibration analysis problems where stochastic phenomena are present, random signal processing techniques are unavoidable. However, this is usually not the case in modal testing, where multifrequency excitation, rather than random excitation, is desired. For this purpose, it is much more reasonable to synthesize an excitation signal by adding sinusoids of arbitrary amplitudes. Synthesized excitation signals may be generated numerically and then sent to a digital-to-analog converter, which produces an analog signal to drive a shaker. This signal may be made periodic with a period equal to the observation window, so that its DFT is leakage-free. It can also be made transient, in which case it is desirable that both the excitation and the response signals vanish within the observation window. Such signals have been called pseudorandom, periodic random, or chirp in the former case, and burst random or burst chirp in the latter. More recently, a generalized approach was given to this problem after the work of Schroeder, which was first used in mechanical system identification by Burrows. True random signals have nonetheless continued to be used in FRF estimation in the case of simultaneous broadband multiexcitation. Otherwise, in modern stepped sine multiexcitation methods, the phase is usually random. It will be shown in this paper that the same results can be obtained using Schroeder-phased multisine excitation signals with linearly independent sets of constant phases.