高阶残差修正GM(1,1)区间预测模型及其应用  

Higher-Order Residual Error Corrected GM(1,1) Interval Prediction Model and Its Application

作　　者：张磊[1] 孙长青[2] ZHANG Lei SUN Chang-qing(The No. 66021^st Troop of PLA, Tianjin 301900, China School of Mechanical and Engineering, Shengyang Institute of Engineering, Shengyang 110136, China)

机构地区：[1]中国人民解放军66021部队 [2]沈阳工程学院机械学院

出　　处：《兵器装备工程学报》2017年第2期177-181,共5页Journal of Ordnance Equipment Engineering

基　　金：国家自然科学基金资助项目(51371173)

摘　　要：提出了一种Markov高阶残差修正GM(1,1)区间模型,在GM(1,1)模型的基础上对拟合数据残差项的绝对值运用Markov模型进行数据拟合,通过将残差项叠加的方式逼近数据真实值。根据残差项的正负状态构建了预测区间,并通过数值模拟论证了预测区间的适用范围与合理性,运用Markov模型对预测区间进行了修正和改进,给出了Markov高阶残差预测区间的表达式。分析结果表明,模型弱化了灰色发展系数的取值条件,并且计算修正残差的阶数越高,预测区间结果可靠性越高,避免了根据概率大小选择预测结果所产生的预测风险,提高了预测结果的可靠性。The interval prediction GM （1, 1 ） with Markov higher order residual error correction was proposed. Based on prediction results of GM （ 1, 1 ） , the absolute residual error was calculated by markov, and the true value was approximated by superposition of residual error items, the prediction interval was constructed, and the suitable range and rationality of model were discussed. Finally the Markov model was used to improve the prediction interval model and the equation was given and discussed. The model softens the restrict range of development coefficients; and the higher order residual error correction is used, the less mean relative error is obtained, and the more reliable the prediction result is. The prediction risk caused by which prediction result is selected according to its state probability is avoided; and the reliability of prediction is imoroved.

关 键 词：GM(1 1)模型 残差修正 MARKOV模型 需求预测 

分 类 号：TJ01[兵器科学与技术—兵器发射理论与技术] N941.5[自然科学总论—系统科学]