Estimation of Correlation Functions by the Random Decrement Technique

The Random Decrement (RDD) Technique is a versatile technique for characterization of random signals in the time domain. In this paper a short review of the theoretical basis is given, and the technique is illustrated by estimating auto-correlation functions and cross-correlation functions on modal responses simulated by two SDOF ARMA models loaded by the same bandlimited white noise. The speed and the accuracy of the RDD technique is compared to the Fast Fourier Transform (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. Comparison 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 cross-correlations functions for stochastic processes with
low mutual correlation, the FFT technique might be more accurate.