Simulation of high variable random processes through the spectral- representation-based approach

Abstract: In this paper the traditional spectral-representation-method for simulating stochastic processes is revisited. A modification aimed to control the variability of the simulated samples of the random process is proposed. Specifically, in order to avoid that the simulated samples possess similar Fourier spectrum, it is proposed to randomize the power spectral density function through a pass band filter with random parameters. The filters is selected in such a way the ensemble averaged power spectral density determined by the samples will match the original power spectrum, but each individual sample will possess different frequency distributions. Comparison between the traditional simulation technique and the new one proposed in this paper will be also discussed. Results show that despite the ensemble averaged power spectral density is the same, related quantities, such as the distribution of peaks, will be significantly different highlighting the needing to consider the variability of frequency distributions when stochastic models are calibrated from experimental data.