Search results for "fractional spectral moment"

Fractional Spectral Moments for Digital Simulation of Multivariate Wind Velocity Fields

2012

In this paper, a method for the digital simulation of wind velocity fields by Fractional Spectral Moment function is proposed. 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 a Gaussian white noise processes. The key of this simulation technique is the generalized Taylor expansion proposed by the authors. The method is extended to multivariate processes and practical issues on the implementation of the method are reported.

A new representation of power spectral density and correlation function by means of fractional spectral moments

2009

In this paper, a new perspective for the representation of both the power spectral density and the correlation function by a unique class of function is introduced. We define the moments of order gamma (gamma being a complex number) of the one sided power spectral density and we call them Fractional Spectral Moments (FSM). These complex quantities remain finite also in the case in which the ordinary spectral moments diverge, and are able to represent the whole Power Spectral Density and the corresponding correlation function.

CROSS-POWER SPECTRAL DENSITY AND CROSS-CORRELATION REPRESENTATION BY USING FRACTIONAL SPECTRAL MOMENTS

2012

A representation of wind velocity by means of fractional spectral moments

2009

This paper deals with the definition of a new function that is a link between Power Spectral Density (PSD) and correlation function, called the Fractional Spectral Moments function. This is defined as the moment of complex order g of the one-sided PSD. It is shown that by means of this complex function both the correlation function and PSD can be represented with great accuracy.

Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach

2011

In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.

Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables

2012

Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…

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

2010

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.