Estimation of Correlation Functions by the Random Decrement Technique

The Random Decrement (RDD) Technique is aversatile technique for characterization of random signals in the time domain. In this paper a short review of the theoretical hasis is given, and the technique is illustrated hy estimating auto-correlation functions and cross-correlation functions on modal responses simulated by two SDOF ARMA models loaded by the sane bandlimited white noise. The speed and the accuracy of the RDD technique is compared to the Fast Fourier ‘Ikansform (FFT) technique. The RDD technique does not involve multiplications, but only additions. Therefore, the technique is very fast in some case up to 100 times faster that the FFT technique. Another important advantage is that if the RDD technique is implemented correctly, the correlation function estimates are unbiased. Comparkn with exact solutions for the correlation functions show that the RDD auto-correlation estimates suffer from smaller estimation errors than the corresponding FFT estimates. However, in the case of estimating crewscorrelations functions for stochastic processes with low mutual correlation, the FFT technique might be more accurate. t,7 : time i,j,rn : subsctipts X(t) : stochastic process z(t) : corhnous time series z,,, : sampled time series Dxy(~) : RDD signature Bx~(T) : RDD estimate variance on X(t) correlation function correlation function estimate number of trig points number of points in estimate sampling interval window variance variance on k(t) natural frequency m.turs.l period damping ratio ARMA paxaneters estimE%tio” errm