Simulation of wind velocity time histories on long span structures modeled as non-Gaussian stochastic waves

Abstract

A methodology is proposed for efficient and accurate modeling and simulation of correlated non-Gaussian wind velocity time histories along long-span structures at an arbitrarily large number of points. Currently, the most common approach is to model wind velocities as discrete components of a stochastic vector process, characterized by a Cross-Spectral Density Matrix (CSDM). To generate sample functions of the vector process, the Spectral Representation Method is one of the most commonly used, involving a Cholesky decomposition of the CSDM. However, it is a well-documented problem that as the length of the structure – and consequently the size of the vector process – increases, this Cholesky decomposition breaks down numerically. This paper extends a methodology introduced by the second and fourth authors to model wind velocities as a Gaussian stochastic wave (continuous in both space and time) by considering the stochastic wave to be non-Gaussian. The non-Gaussian wave is characterized by its frequency–wavenumber (FK) spectrum and marginal probability density function (PDF). This allows the non-Gaussian wind velocities to be modeled at a virtually infinite number of points along the length of the structure. The compatibility of the FK spectrum and marginal PDF according to translation process theory is secured using an extension of the Iterative Translation Approximation Method introduced by the second and third authors, where the underlying Gaussian FK spectrum is upgraded iteratively using the directly computed (through translation process theory) non-Gaussian FK spectrum. After a small number of computationally extremely efficient iterations, the underlying Gaussian FK spectrum is established and generation of non-Gaussian sample functions of the stochastic wave is straightforward without the need of iterations. Numerical examples are provided demonstrating that the simulated non-Gaussian wave samples exhibit the desired spectral and marginal PDF characteristics.