摘要
针对GM(1,1)幂模型对于小样本振荡序列对含突变信息无能为力的问题,提出了基于小波变换的小样本振荡序列灰色预测模型.首先,针对原始数据序列建立GM(1,1)幂模型描述其总体趋势特征;然后,利用小波变换提取GM(1,1)幂模型残差序列所包含的有用信号和随机噪声,并结合GM(1,1)幂模型构成新的时间相应函数;最后,以与原始平均误差最小为原则确定小波变换的小波基和分解层次并对小波进行重构GM(1,1)幂模型残差序列,并结合原始GM(1,1)幂模型对随机振荡序列进行预测.算例中通过对城市用水量的拟合及预测结果表明:应用基于傅立叶变换的GM(1,1)幂振荡序列模型和基于分数阶离散GM(1,1)幂模型研究了振荡序列模型平均误差分别为3.22%和5.66%,而本文的方法平均误差为1.11%.算例研究表明,此方法能够快速高效的解决GM(1,1)幂模型对小样本有突变趋势振荡序列的预测问题.
To solve the problem that GM(1,1)power model is powerless for small sample oscillation sequence to contain mutation information,a grey prediction model of small sample oscillation sequence based on wavelet transform is proposed.Firstly,the GM(1,1)power model is established to describe the general trend characteristics of the original data sequence;then,the useful signals and random noises contained in the residual sequence of GM(1,1)power model are extracted by wavelet transform,and a new time-dependent function is constructed by combining the GM(1,1)power model;finally,the wavelet basis and decomposition level of the wavelet transform are determined based on the principle of minimizing the original average error.The residual sequence of GM(1,1)power model is reconstructed by wave,and the random oscillation sequence is predicted by combining the original GM(1,1)power model.The fitting and prediction results of urban water consumption in the example show that the GM(1,1)power oscillation sequence model based on Fourier transform and the fractional order discrete GM(1,1)power model are used to study the average of the oscillation sequence model.The errors are 3.22%and 5.66%,respectively,while the average error of the method in this paper is 1.11%.Case studies show that this method can quickly and efficiently solve the prediction problem of GM(1,1)power model for small samples with sudden trend oscillation sequence.
作者
张娜
雷明
ZHANG Na;LEI Ming(Guanghua School of Management,Peking University,Beijing 100871,China;School of economics and management,Shihezi University,Shihezi 832000,China)
出处
《数学的实践与认识》
北大核心
2020年第9期28-35,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(41801119):整体性治理视阈下深度贫困地区精准脱贫多元主体协同机制研究
国家语委重点资助项目(ZDI135-67):少数民族地区推普的精准扶贫效应及完善路径研究
中国博士后科学基金第63批面上项目(2018M631220):整体性治理视阈下我国精准扶贫多元主体协同机制研究
石河子大学高层次人才科研启动资金专项(RCSX201754):精准扶贫过程中的脱贫机制研究。
关键词
小波变换
随机振荡序列
突变信息
GM(1
1)幂模型
萤火虫算法
wavelet transform
random oscillation sequence
mutation information
GM(1,1)power model
firefly algorithm
