Fractional calculus approach for the representation of power spectral densities and correlation functions in wind engineering

Abstract

The paper deals with the digital simulation of wind velocity samples by Fractional Spectral Moment function. It is shown that such a function represents a third useful way to characterize a stationary Gaussian stochastic process, alongside the power spectral density and the correlation function. The method is applied to wind velocity fields whose power spectra is given by the Kaimal’s, the Davenport’s and the Solari’s representation. It is shown that by constructing a digital filter whose coefficients are the fractional spectral moments, it is possible to simulate samples of the target process as superposition of Riesz fractional derivatives of Gaussian white noise processes.