基于优化组合核和 Morlet 小波核的 LSSVM脉动风速预测方法

摘要

Kernel functions,which are the important components of support vector machines (SVM),directly affect the results of prediction models.In accordance to the Mercer theorem,a Morlet wavelet kernel rendering the advantages of localization,multi-level and mufti-resolution was developed.The representative radial basis function (RBF) kernel and polynomial (Poly)kernel functions were taken into consideration to construct a linear combination kernel function with both local and global properties,so as to form prediction models with superior learning ability and perfect generalization capability given by the RBF kernel and Poly kernel functions respectively.Further,the particle swarm optimization (PSO)algorithm was used to optimize the penalty parameter,kernel parameters and the weight and scale factor.Then,a PSO-LSSVMmodel using the Morlet wavelet kernel and combination kernel was developed.By resorting to the proposed prediction models,the time histories of fluctuating wind velocity were forecasted.By comparing the predicting performance evaluation indices,it is found that the PSO-LSSVM model with the Morlet wavelet kernel and combination kernel functions renders more accurate results than the common single kernel (such as Poly and RBF)based PSO-LSSVMmodels.%核函数是支持向量机的重要组成部分，直接影响预测模型的结果。根据 Mercer 定理，推导出了 Morlet 小波核函数，使其具有局部化、多层次、多分辨的优点。选择具有代表性的径向基（RBF）核函数和多项式（Poly）核函数构建出局部性和全局性相结合的线性组合核函数，使得预测模型保留 RBF 核函数所赋予的优越学习能力以及 Poly 核函数所拥有的强泛化能力；进一步，使用粒子群优化（PSO）算法，对惩罚参数、核参数、权重、尺度因子进行寻优，分别建立了基于Morlet 小波核和组合核的 PSO-LSSVM模型；使用建立的预测模型，对脉动风速进行了预测。通过比较预测性能评价指标，发现基于 Morlet 小波核和组合核 PSO-LSSVM的预测精度优于常用的单核 PSO-LSSVM模型。