风向风速的联合概率结构建模

Modeling of the joint probabilistic structure of wind direction and speed

风向和风速的联合分布模型是结构工程和风能研究领域的重要参数,但两者的相关性等致使模型建立困难。基于乘法定理导出离散-连续混合联合分布模型,明确各项的物理和数学意义,并指出将风向风速离散-连续混合联合分布模型与2维连续联合分布模型建立联系的可能性。以重庆市日极值风数据为对象,导出风速条件密度变换解,计算出各风向上的数值解,并与经验累积分布函数比较验证数值解的准确性;然后引入混合概率密度函数对数值解进行拟合,建立风速条件概率密度的两分量混合模型,较单一概率分布模型有明显改善;将风速条件概率密度与风向频度函数相联合即可获得风向风速的离散-连续混合联合分布模型。为建立风向风速的2维连续联合分布模型,首先由风向频度函数和风向角概率直方图之间的联系确定风向角的概率直方图,再经拟合给出风向角的混合分布模型;类似地,由曲线拟合亦可获得风速混合模型中各参数与风向角的关系式,从而建立统一的风速条件概率密度模型;将两者结合起来,即为风向风速的2维连续联合分布模型。

The joint probability density function （PDF） of wind direction （WD） and wind speed （WS） is important in both structural engineering and wind energy, but it is difficult to model because of the correlation between WD and WS. Based on multiplication rules in probability theory, a discrete-continuous joint distribution model for WD and WS is derived, and the relation with 2-dimensional continuous joint distribution is pointed out. The transform solution of conditional density function for WS as well as its approximation is derived. Taking the daily extreme wind records in Chongqing city as example, the numerical results of conditional density function for WS in every WDs are obtained, and these results are verified by comparing with empirical cumulative distribution function （CDF）. By introducing the finite mixture distribution, a two-component finite mixture distribution for WS is available, which is more accurate than unimodal distribution. The discrete-continuous joint distribution model can be constructed if the distribution for WS is combined with the frequency function of WD. In order to formulate the 2-dimensional continuous joint distribution for WD and WS, the histogram of WD is determined by the frequency histogram of WD, and the finite mixture distribution of WD is obtained by curve fitting; then a unified conditional density function for WS is formed, where the parameters of two-component finite mixture distribution is a function of the angle of WD; finally, by multiplication, the 2-dimension continuous joint distribution for WD and WS is obtained.