分形插值在风速时间序列中的应用

针对风电场风速数据中大量连续缺失数据的插值问题，提出了一种基于自适应变异粒子群优化（PSO）的分形插值算法。首先，在粒子群优化算法中引入变异因子，增强粒子的多样性，提高算法搜索精度；其次，通过自适应变异粒子群优化算法来得到分形插值算法中垂直比例因子参数的最佳取值；最后，对两组不同趋势和变化特征的数据集进行分形插值计算分析，并把所提算法与Lagrange插值和三次样条插值方法进行对比。结果表明：分形插值不仅可以保持风速曲线的整体波动特性和局部特征，而且比传统插值方法的精度更高；在基于Dataset A的实验中，分形插值的均方根误差（RMSE）分别比Lagrange插值和三次样条插值减小了66.52%和58.57%；在基于Dataset B的实验中，分形插值的RMSE分别比Lagrange插值和三次样条插值减小了76.72%和67.33%。证明分形插值更适合连续缺失且波动强烈的风速时间序列的插值。

Application of fractal interpolation in wind speed time series

A fractal interpolation algorithm based on adaptive mutation Particle Swarm Optimization (PSO) was proposed aiming at the interpolation problem of a large number of continuous missing data in wind speed data of wind farms. First, the mutation factor was introduced into the particle swarm optimization algorithm to enhance the diversity of particles and the search accuracy of the algorithm. Second, the optimal value of the vertical scaling factor in the fractal interpolation algorithm was obtained by the adaptive mutation particle swarm optimization algorithm. Finally, two datasets with different trends and change characteristics were analyzed by fractal interpolation, and the proposed algorithm was compared with Lagrange interpolation and cubic spline interpolation. The results show that fractal interpolation is not only able to maintain the overall fluctuation characteristics and local characteristics of wind speed curve, but also is more accurate than the traditional interpolation methods. In the experiment based on Dataset A, the Root Mean Square Error (RMSE) of fractal interpolation was reduced by 66.52% and 58.57% respectively compared with those of Lagrange interpolation and cubic spline interpolation. In the experiment based on Dataset B, the RMSE of fractal interpolation was decreased by 76.72% and 67.33% respectively compared with those of Lagrange interpolation and cubic spline interpolation. It is verified that fractal interpolation is more suitable for the interpolation of wind speed time series with strong fluctuation and continuous missing data.