Simulacion Digital Del Viento

Journal of Wind Engineering and Industrial Aerodynamics 74—76 (1998) 91—109

Digital simulation of wind field velocity
Mario Di Paola
Dipartimento di Ingegneria Strutturale e Geotecnica, University of Palermo, Viale delle Scienze, I-90128 Palermo, Italy

Abstract In this paper some computational aspects on the generation procedure of n-variate wind velocity vectors are discussed in detail.Decompositions of the power spectral density matrix are also discussed showing the physical significance of eigenquantities of this matrix. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Multivariate processes; Wind velocity; Digital simulation

1. Introduction An effective approach for predicting the dynamic response to wind actions of structures such as tall buildings, long-spansuspended and cable-stayed bridges, towers, etc., is the Monte Carlo method. It mainly consists in generating sample functions having prescribed probabilistic characteristics, then for each sample function the linear or non-linear dynamic structural analysis is performed. From the time histories of the response the probabilistic analysis is made on the sample functions of the response for ensuringoverall safety of the various elements of the structure. The wind velocity at a given point location in the space is usually modeled as a normal stochastic process, then its complete characterization is ensured by the knowledge of the power spectral density (PSD) function. For extended wind exposed structures one has to characterize the velocity at different point locations, then the wind velocity is astochastic time-dependent field, that is, the velocity » at a given point depends on the coordinate of the point in the space (x , x , x ) and on the time t,    then »"»(x , x , x , t). It follows that the stochastic field velocity »(x , x , x , t) is       a so-called one-variate four-dimensional (1-V, 4-D) stochastic field. Readers are referred to the review paper on simulation of astochastic field [1], efficiency and accuracy in simulation of a random field is discussed by Lutes et al. [2].
0167-6105/98/$19.00 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 0 0 8 - 7

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M. Di Paola/J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 91–109

If one is interested to characterize the velocity field only in some points (say n) such as the nodal points ofa structure, by collecting the velocities in the different points » (t), » (t),2, » (t) into a vector, the discretized stochastic field is represented by an  L  n-variate one-dimensional (n-V-1D) stochastic vector process. Then the discretization transforms the 1-V, 4-D stochastic field into an n-V-1D stochastic vector process. Simulation of normal stochastic vector processes can be performedusing two main different approaches. Digital simulation based on superposition of harmonic waves with random phase [3—11]. Digital simulation obtained as output of digital filters exposed to band-limited white noise input. These numerical schemes are commonly referred to auto-regressive (AR) algorithms and auto-regressive moving-average (ARMA) algorithms [8,9, 12—18]. Simulation of non-normal processessuch as wind pressure can be made by using the proper tools of non-normal simulation [19]. These approaches are based on the correlation distorsion method [1] it mainly consists in generating a normal process which is then transformed to the desired non-normal process through a memoryless non-linear transformation. More detailed informations on this subject can be found in Ref. [20]. Local effectsas well as non-stationarity in the measured time history of velocity can be computed by using wavelet functions [21]. This paper represents an overview of the generation of multivariate stationary wind field velocity, which is hopefully of some use to researchers as well as practicioners. Physical aspects connected with the decomposition of the PSD matrix are discussed in detail.

2. Stochastic...