Estimation of Frequency Response Functions by Random Decrement

A &had for estimating frequency response functions by the Random Decrement technique is investigated in this paper. The method is based on the auto and cross Random Decrement functions of the input process and the output process of a linear system. The Fourier transformation of these functions is used to calculate the frequency response functions. The Random Decrement functions are obtained by averaging time segments of the processes under given initial conditions. The method will reduce the leakage problem, because of the natural decay of the Random Decrement functions. Also, the influence of noise will be reduced since the FFT is applied to the signatures, where the noise is reduced by averaging. Finally, the proposed technique will typically be faster than the traditional method, where the FFT is applied to every data segment in stead of applying the FFT just one time on the final Random Decrement function. The method is demonstrated by a simulation study. Nomenclature L DYY DXY h,h H,H L Value of time series. Trig condition on Y. Auto RDD function. Crass RDD function. Impulse response function/matrix. Frequency response function/matrix. RDD function length and length of input time segments to FFT. Number of points in FRF. Number of trig points. Discrete time point. Stochastic processes. Realizations of Y, X Time derivative of Y ,X Value of time-derivative of timeseries. Fourier transformation of D. Standard deviation of Y RDD function length