Simulation of wind velocities on long span structures: A novel stochastic wave based model

Abstract

A methodology is presented for efficient and accurate modeling of correlated wind velocities along long span structures at a virtually infinite number of points. Currently, the standard approach is to model wind velocities as discrete components of a multivariate stochastic vector process, characterized by a Cross-Spectral Density Matrix. To simulate sample realizations of the vector process, the Spectral Representation Method is one of the most commonly used, which involves a Cholesky decomposition of the Cross-Spectral Density Matrix. However, it is a well-known issue that as the length of the structure, and consequently the size of the vector process, increases, this Cholesky decomposition breaks down numerically. Alternatively, this paper introduces the use of the frequency–wavenumber spectrum to model the wind velocities as a stochastic “wave”, continuous in both space and time. This allows the wind velocities to be modeled at a virtually infinite number of points along the length of the structure. In this paper, the relationship between the Cross Spectral Density Matrix and the frequency–wavenumber spectrum is first examined. The frequency–wavenumber spectrum is then derived for wind velocities. Numerical examples are carried out demonstrating that the simulated wave samples exhibit the desired spectral and coherence characteristics. The efficiency of this method, specifically through the use of the Fast Fourier Transform, is also demonstrated.