Generation of spatially correlated wind histories

Turbulent wind is a natural and therefore random phenomenon. The analysis of flexible structures
subjected to turbulent wind requires, in a finite element approach, the resolution of a system of
stochastic differential equations. It is supposed that the characteristics of the structure are perfectly known; thus the stochastic aspect of the problem comes from the random loading only. As the turbulent wind is most commonly characterized by its frequency content, the resolution of this equation is generally performed in the frequency domain. All governing equations must therefore be linear. If this can be reasonably supposed for the structure, this hypothesis is not mathematically justified for the wind loading.
When the non linear behaviour of any part of the structure has to be accounted for, the resolution
in the frequency domain is not valid anymore. It is then necessary to compute, with a step-by-step
dynamic analysis, the response of the structure to a series of generated wind histories. In a finite
element approach, this is for example achieved thanks to Newmark’s or Wilson’s methods.
Averaging across the ensemble of the computed time-varying responses allows then to recover
statistical results that a stochastic analysis would provide. This analysis method is known as a stochastic Monte Carlo simulation.
After having emphasised the need to represent correctly the coherence between wind pressures at
different points of the structure, this paper will present a method for generating a set of correlated
wind histories that must be used in a finite element analysis. Finally an example of application of
the presented method will prove its efficiency.