Enhancing the variability of simulated random processes using the spectral representation method

Abstract

Listen

Translate article

In this paper, the traditional spectral representation method for simulating stochastic processes is revisited. The main goal is to introduce various approaches to enhance the variability of the generated sample functions to better reflect variabilities observed in field measurements and experimental data, while keeping the ensemble-averaged power spectra unchanged. The general idea, gradually developed over the last decade, is to randomize the power spectral density function of the uncertain physical quantities by modeling certain parameters as random variables calibrated from experimental data. The potential of such approaches has not been fully explored yet. This work explores the pros and cons of using power spectral density functions with random parameters in the simulation of highly variable, stationary and nonstationary, Gaussian stochastic processes. The main characteristics of a stochastic process, such as distribution of maxima and variability in time and frequency, are examined. The use of a pass-band Butterworth filter to control the variability of the Fourier spectrum of the simulated samples is studied. The Butterworth filter is selected so that the ensemble-averaged power spectral density matches the target power spectrum, but each individual generated sample function possesses different amplitude and frequency distributions. Comparisons between samples generated using the traditional spectral representation method and those generated with enhanced variability are made through a series of illustrative examples. Results show that with the proposed enhanced-variability spectral representation method, certain characteristics of the stochastic process, such as the distribution of maxima, will be significantly different (while the ensemble-averaged power spectra will remain the same). The implications in reliability studies are obvious.