基于等维新息的GM(2,1)递推预测模型
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摘要
针对GM(2,1)白化方程的解影响其预测精度的问题,提出了一种新的预测模型——等维新息GM(2,1)递推预测模型。该模型通过其灰色微分方程推导出GM(2,1)递推预测模型的表达式,避免了对二阶白化方程进行求解,同时解决了差分方程与微分方程之间因转换而产生误差的问题,并结合等维新息的思想更新GM(2,1)递推预测模型的参数。最后通过实例验证了所提等维新息GM(2,1)递推预测模型的有效性和实用性。
Aiming at the problem that the solution of GM(2,1) whitening equation affects its prediction accuracy, a new prediction model dubbed GM(2,1) recursive prediction model of equal dimension new information was proposed. The model was deduced from the grey differential equation of GM(2,1) mode, which could avoid solving the second-order whitening equation, solve the problem that the errors between equations and differential equations for conversion, and update the model parameters combining the idea of equal dimension and new information. Both the simulation and analysis of the example demonstrate that the proposed method is more effective and practical.
Aiming at the problem that the solution of GM(2,1) whitening equation affects its prediction accuracy, a new prediction model dubbed GM(2,1) recursive prediction model of equal dimension new information was proposed. The model was deduced from the grey differential equation of GM(2,1) mode, which could avoid solving the second-order whitening equation, solve the problem that the errors between equations and differential equations for conversion, and update the model parameters combining the idea of equal dimension and new information. Both the simulation and analysis of the example demonstrate that the proposed method is more effective and practical.
引文
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[2]曾柯方.几种灰预测模型的参数辨识与优化方法研究[D].南充:西华师范大学,2015.ZENG K F.Identifying parameters and optimization method research of several grey prediction models[D].Nanchong:China West Normal University,2015.
[3]李玲玲,单锐,崔红芳.改进GM(2,1)模型的MATLAB实现及其应用[J].数学的实践与认识,2011,41(20):179-183.LI L L,SHAN R,CUI H F.The application of the improved GM(2,1)grey model using MATLAB[J].Mathematics in Practice&Theory,2011,41(20):179-183.
[4]XU N,DANG Y G.An optimized grey GM(2,1)model and forecasting of highway subgrade settlement[J].Mathematical Problems in Engineering,2015(1):1-6.
[5]牛思先,陈鹏宇,苏玉刚.基于加权组合和最小二乘法改进的GM(2,1)模型[J].统计与决策,2010(22):28-30.NIU S X,CHEN P Y,SU Y G.Improvement of GM(2,1)model based on weighted combination and least squares method[J].Statistics and Decision,2010(22):28-30.
[6]刘虹,张岐山.基于微粒群算法的GM(2,1,λ,ρ)优化模型[J].系统工程理论与实践,2008,28(10):96-101.LIU H,ZHANG Q S.GM(2,1,λ,ρ)based on particle swarm optimization[J].Journal of Systems Science and Information,2008,28(10):96-101.
[7]刘丽桑,彭侠夫,周结华.两种改进的GM(2,1)模型及其在船舶横摇预报中的应用[J].厦门大学学报(自然科学版),2011,50(3):515-519.LIU L S,PENG X F,ZHOU J H.Two improved model of GM(2,1)and its application in ship rolling forecast[J].Journal of Xiamen University(Natural Science),2011,50(3):515-519.
[8]卢懿.灰色预测模型的研究及其应用[D].杭州:浙江理工大学,2014.LU Y.The research and application of grey forecast model[D].Hangzhou:Zhejiang Sci-tech University,2014.
[9]ZHANG H,YANG Y.Application of equal dimension and new information gray prediction model in power load forecasting[C]//2010 2nd International Conference on Signal Processing Systems(ICSPS),July 5-7,2010,Dalian,China.New Jersey:IEEE Press,2010:196-200.
[10]ZHANG Q,CHEN R.Application of metabolic GM(1,1)model in financial repression approach to the financing difficulty of the small and medium-sized enterprises[J].Grey Systems,2014,4(2):311-320.