Noise Leakage Suppression in Multivariate FRF Measurements Using Periodic Excitations

Due to the non-periodic nature of noise, the steady state response of a dynamic system to a periodic input is still subject to noise transients (noise leakage errors). For lightly damped systems these noise transients (significantly) increase the variance of frequency response function (FRF) measurements Pintelon MSSP10c]. This paper presents a method for suppressing the noise transients in FRF measurements using periodic excitations. It is based on a local polynomial approximation of the noise leakage error and is an extension of the results of [Pintelon MSSP10c] to multivariable systems. Compared with the local polynomial method for random excitations [Pintelon MSSP10a, Pintelon MSSP10b], no local polynomial approximation of the frequency response matrix is made. Irrespective of the number of inputs and outputs, it is shown in this paper that 2 periods of the state state response are enough to suppress the noise transients and to estimate the input-output noise covariance matrix. Since no distinction can be made between the system and noise transients, the presented method is also applicable to the first 2 periods of the transient response of the system to a periodic input. For lightly damped systems this results in a significant reduction of the measurement time.