期刊文献+

基于傅立叶级数的小样本振荡序列灰色预测方法 被引量:19

Grey forecasting method for small sample oscillating sequences based on Fourier series
原文传递
导出
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.
作者 王正新
出处 《控制与决策》 EI CSCD 北大核心 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)
关键词 灰色系统 小样本振荡序列 傅立叶级数 预测 grey system small sample oscillating sequence; Fourier series; forecasting
  • 相关文献

参考文献16

  • 1邓聚龙.灰预测与灰决策[M]{H}武汉:华中科技大学出版社,2002.
  • 2刘思峰;党耀国;方志耕.灰色系统理论及其应用(Liu S F,Dang Y G,Fang Z G.Grey systems theory and its application[M].Beijing:Science Press,2004.)Grey systems theory and its application[M].Beijing:Science Press,2004.)[M].{H}北京:科学出版社,2004.
  • 3肖新平;宋中民;李峰.灰技术基础及其应用(Xiao X P,Song Z M,Li F.Elements and application of grey technology[M].Beijing:Science Press,2005.)Elements and application of grey technology[M].Beijing:Science Press,2005.)[M].{H}北京:科学出版社,2005.
  • 4Dang Y G,Liu S F. The GM models that x(n)be taken as initial value[J].{H}KYBERNETES,2004,(02):247-255.
  • 5Wang Y N,Chen Z J,Gao Z Q. A generalization of the GM(1,1)direct modeling method with a step by step optimizing grey derivative's whiten values and its applications[J].{H}KYBERNETES,2004,(02):382-389.
  • 6Wei Y,Zhang Y. An essential characteristic of the discrete function transformation to increase the smooth degree of data[J].The J of Grey System,2007,(03):293-300.
  • 7Xie N M,Liu S F. Discrete grey forecasting model and its optimization[J].{H}Applied Mathematical Modeling,2009,(02):1173-1186.
  • 8曾波,刘思峰,孟伟.基于核和面积的离散灰数预测模型[J].控制与决策,2011,26(9):1421-1424. 被引量:10
  • 9Deng J L. Undulating grey model(UGM)GM(1,1∣tan(k-π)p,sin(k-π)p)[J].The J of Grey System,2001,(03):201-205.
  • 10王正新,党耀国,裴玲玲.基于GM(1,1)幂模型的振荡序列建模方法[J].系统工程与电子技术,2011,33(11):2440-2444. 被引量:19

二级参考文献34

共引文献82

同被引文献228

引证文献19

二级引证文献159

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部