基于最优RBF核主成分的空间多维风电功率降维及重构

Dimension Reduction and Reconstruction of Multi-dimension Spatial Wind Power Data Based on Optimal RBF Kernel Principal Component Analysis

为应对风电数据多样化、复杂化和精细化带来的"维数灾"问题,文章提出一种基于最优RBF核主成分的非线性降维及重构方法,以准确挖掘空间多维风电数据的本质特征。针对传统核主成分降维方法存在的核参数选择困难问题,文章以原始数据与线性变换构造出的同质数据之间降维误差最小为优化目标,通过交叉验证搜寻最优核参数,并采用k近邻多维尺度分析解决目前非线性降维中原像重构的难题。实际算例结果表明,所提方法在降维结果的可信赖性和连续性方面优于常用线性降维方法。在针对多维风电功率降维结果进行预测和重构可提高预测效率,避免直接预测多维变量带来的"维数灾"问题,且能获得更高的预测精度。

In order to deal with the curse of dimensionality caused by the diversification, complication and elaboration of wind power data, this paper proposes a nonlinear dimension reduction and reconstruction method based on an optimal RBF kernel principal component analysis(ORBF-KPCA). Addressing the difficulty of selecting the kernel parameters in the traditional KPCA method, this paper searches for the optimum to minimize the difference between the dimension reduction results of raw data and homogenous data by means of a cross-validation method. Then a multi-dimensional scale(MDS) technology based on k-nearest neighbors is used for pre-image reconstruction. An actual example shows the proposed method performs better than the common linear dimension reduction methods in reliability and continuity of the results, and it can not only improve the forecasting efficiency to avoid the curse of dimensionality, but also achieve higher prediction accuracy.