基于风速时间序列分形与传统插值对比研究

The Contrastive Study of Fractal and Traditional Interpolation based on Wind Speed Time Series

风速时间序列具有波动强烈、数学上处处连续、处处不可导特征,为解决风速时间序列的插值问题及提高其精度,采用数学分形学理论的分形插值方法,基于Kaimal和NWTCUP湍流风谱模型进行风场模拟。从得到的风速时间序列中随机抽取数据作为初始点,将分形插值方法与三次样条和Hermite传统插值方法进行对比。结果表明：分形插值方法不仅具有保持原始风速时间序列所具有的本质和内在联系,如自相似性、长程相关性和标度不变性等非线性动力学系统特征信息,而且比三次样条和Hermite传统插值方法更适合剧烈震荡的风速时间序列的插值。

Wind speed time series has the characteristics of strong temporal fluctuation and continuity but non-differentiability in mathematics. In order to solve the interpolation problem of wind speed time series and improve its accuracy, a fractal interpolation method based on mathematical fractal theory is proposed. The wind speed time series is obtained based on Kaimal and NWTCUP turbulence modeling. With the randomly selected time series data as the initial points, the proposed fractal interpolation method is com- pared with the cubic spline and Hermite traditional interpolation methods. The results show that the fractal interpolation method not only has the intrinsic correlations of the original wind speed time series, such as self-similarity,long-range correlation and scale invariance, but also is more suitable for the interpolation of the wind speed time series with violent shocks, compared to the cubic spline and Hermite traditional inter- polation methods.