Fractional spectral moments for digital simulation of multivariate wind velocity fields

Abstract

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. * Publication info: Cottone G., Di Paola M., Fractional spectral moments for digital simulation of multivariate wind velocity fields,

Treatment of arbitrarily autocorrelated load functions in the scope of parameter identification

“…without any restriction to the functional form of the PSD and it is efficient also in case of long-memory processes; ii) the coefficients of the model for the process are known in analytical form and their number can be arbitrarily increased to achieve higher accuracy without recalculation; iii) it is efficiently combined to the Extended Kalman filter; iv) it is easily extendible to multivariate loads, see [10,13].…”

“…The method is called 'H-fractional spectral moments decomposition' as the coefficients for the noise simulation are calculated from the FSMs of the linear transfer function H(ω). In [10,13] it is applied for the simulation of univariate/multivariate wind velocity fields, respectively. Based on the H-FSMs decomposition the new issue presented in this paper is the derivation of a state space representation of arbitrarily correlated load processes in analytical form which neither require the factorization of the PSD nor any optimization procedure and which can be easily combined with common state space model based system identification methods such as the well known and widely used Kalman filter algorithm.…”

“…Furthermore in deriving the latter equation it was considered that the AC, and consequently the PSD, are symmetric and real functions. This representation is valid for any Fourier pair, originally was proposed for probability density and characteristic function in [12], and extended to multidimensional random variables [14] and multivariate processes [10,13].…”

“…Applying a finite Fourier transform finally leads to a reconstruction of the correlated noise process {F (t)} in terms of the H-FSMs given by (26) where E [F k (t, T )] is the expected value operation over the ensemble index k. In [13] a computational efficient algorithm for the digital simulation of wind loads based on Eq. (26) is introduced.…”

Exact Closed-Form Fractional Spectral Moments for Linear Fractional Oscillators Excited by a White Noise

“…The advantage of these complex quantities is that they are able to reconstruct both the PSD and the correlation functions, and, therefore, can be seen as an alternative representation of the process itself [22,23]. Additionally, Cottone and Di Paola [24] have shown that FSMs can be used as coefficients of a time series defined in terms of the Riesz fractional derivatives of a white noise for the digital simulation of realizations of a stochastic process with assigned PSD. In this paper, the SMs and FSMs of a fractional oscillator excited by a Gaussian stationary white noise are evaluated in exact closed-form solution.…”