General strategies for modeling joint probability density function of wind speed, wind direction and wind attack angle

Abstract

The joint probability density function (JPDF) of the wind field parameters is essential for wind load analysis or energy assessment, but one key parameter of the wind attack angle is often excluded in current studies. Three different methodologies are proposed, aiming to estimate the JPDF of wind speed, wind direction and wind attack angle. Strategy I consists of the vine approach with the modified binary Bernstein copula adopted for nonparametric estimation. The modified ternary Bernstein copula is recommended to estimate the ternary copula directly in Strategy II. In strategy III, the Offset Elliptical Normal mixture model is extended to evaluate the three-dimensional case, where the wind vector is resolved into three orthogonal components. A typical mountainous bridge site with strongly inhomogeneous wind characteristics is selected to inspect the performance of these strategies. Satisfactory results are given by all these strategies in which the strategy II has better goodness-of-fit. Strategy I is slightly less reliable in estimating the dependencies of higher tree variables while avoids the time-consuming nonparametric estimation of three-dimensional copula. The strategy III is based on the physical model and performs better in the conditional probability estimation when the number of samples is small.