基于傅立叶级数的小样本振荡序列灰色预测方法  

Grey forecasting method for small sample oscillating sequences based on Fourier series

作　　者：王正新[1] 

机构地区：[1]浙江财经大学经济与国际贸易学院,杭州310018

出　　处：《控制与决策》2014年第2期270-274,共5页Control and Decision

基　　金：国家自然科学基金项目(71101132;71271086);中国博士后科学基金项目(2013M540448)

摘　　要：针对现有灰色模型不能适用于小样本振荡序列预测的问题,提出了基于傅立叶级数的小样本振荡序列灰色预测方法.首先对原始序列建立GM(1,1)幂模型以描述系统行为的总体趋势;然后利用傅立叶级数提取模型的残差序列所包含的周期性振荡规律,并以二者之和构成新的时间响应函数;最后以平均误差最小化为目标,建立非线性优化模型求解最优参数.应用实例表明,该方法能够有效地提高灰色模型对小样本振荡序列的预测精度.For the problem that the existing grey models are not applicable to forecast small sample oscillating sequences, a grey forecasting method for these sequences based on Fourier series is proposed. Firstly, a GM（1,1） power model of the original sequence is built to describe the behavior of the system overall trend. Then, Fourier series is used to extract of the periodic oscillation law contained in the residual sequence, thus a new time response function is formed by adding the two parts. Finally, the average error is minimized as the goal to establish the nonlinear optimization model for solving the optimal parameters. Numerical simulation and application examples show that simulation and forecasting accuracy are effectively enhanced.

关 键 词：灰色系统 小样本振荡序列 傅立叶级数 预测 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]