自相似性和分形维数在风场分析中的应用

Application of Wind Speed Self-similarity and Fractal Dimension in Wind Field Analysis

通过探究风速时间序列的自相似性和分形维数,将分形学运用到湍流风场分析中,从风速时间序列的局部与整体关系和风速时间序列的分形维数2个角度解决选用湍流风谱模型时存在的盲目性问题.选用某一风场风速时间序列,基于Kaimal、Von Karman、SMOOTH和NWTCUP湍流风谱模型得到风速时间序列,采用Hurst值验证风速时间序列的自相似性,用计盒维数法计算风速时间序列的分形维数.结果表明:不同的湍流风谱模型具有不同的分形维数,湍流风谱模型可定量描述;风速时间序列内部波动不是随机的,是有自相似性的长程相关过程;分形维数与参考风速有关.

The fractal theory was applied to turbulent wind field analysis by studying the self-similarity and fractal dimension of the wind speed time sequence, so as to overcome the blindness in selecting the turbu- lent wind spectrum model from the following two aspects： the local-global relations and the fractal dimen- sion of the wind speed time sequence. Taking the wind speed time sequence of a wind field as the sample data, different wind speed time sequence curves were obtained respectively with Kaimal, Von Karman, SMOOTH and NWTCUP turbulent wind spectrum model, and its self-similarity was then verified with Hurst exponents while the fractal dimension was calculated using box counting method. Results show that different turbulent wind spectrum models have different fractal dimensions, which can be described in a quantitative way; the internal fluctuation of wind speed time sequence is not random, but a long-term cor- related process with self-similarity; the fractal dimension is related to the reference wind speed.