GM(1，1)模型背景值构造的不同方法与应用

doi:10.12068/j.issn.1005-3026.2017.06.022

东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (6): 869-873.DOI: 10.12068/j.issn.1005-3026.2017.06.022

GM(1，1)模型背景值构造的不同方法与应用

彭振斌¹，张闯¹，彭文祥¹，王继武²

(1. 中南大学地球科学与信息物理学院，湖南长沙410083； 2. 北京城建道桥建设集团有限公司，北京100124)

收稿日期:2016-03-21 修回日期:2016-03-21 出版日期:2017-06-15 发布日期:2017-06-11
通讯作者: 彭振斌
作者简介:彭振斌(1952-)，男，湖南宁乡人，中南大学教授，博士生导师.
基金资助:
国家自然科学基金资助项目(50878212)；中央高校基本科研业务费专项资金资助项目(2016zzts435).

Different Structure Methods and Application of Background Value in GM(1，1) Model

PENG Zhen-bin¹， ZHANG Chuang¹， PENG Wen-xiang¹， WANG Ji-wu²

1. School of Geosciences and Info-Physics， Central South University， Changsha 410083； 2. Beijing Urban Construction and Bridge Engineering Co. Ltd， Beijing 100124.

Received:2016-03-21 Revised:2016-03-21 Online:2017-06-15 Published:2017-06-11
Contact: ZHANG Chuang
About author:-
Supported by:
-

摘要/Abstract

摘要： GM(1，1)模型的误差主要来源于背景值和初始值，因此提出3种不同的背景值构造方法分别为:把背景值的固定权改为变权构造背景值的方法、将数据序列抽象为指数函数构造背景值的方法、将数据序列抽象为非齐次指数函数构造背景值的方法，并以X(n)为初始值和新陈代谢方法来建立GM(1，1)模型.通过工程实例检验这3种不同背景值构造方法建立的GM(1，1)模型的预测精度.计算结果表明，将数据序列抽象为非齐次指数函数构造背景值建立的模型预测精度较高，可为类似工程提供参考.

关键词: GM(1, 1)模型, 背景值, 新陈代谢方法, 预测精度

Abstract: The error of GM (1，1) model is mainly from the background value and the initial value， thus the paper puts forward three different construction methods of background value， viz. the method of changing fixed right of background value to the variable right， the method of abstracting the data sequence as index function to construct background value， the method of abstracting the data sequence non homogeneous exponential function to construct background value. And the prediction accuracy of the three methods for background value were compared by setting up GM (1， 1) model with the initial value of X (n). Because the prediction accuracy of future development model for GM (1，1) model is weak， we use metabolism way to establish GM (1， 1) model and continuously optimize and update the model to avoid the large error. The prediction accuracy of GM(1，1) model from the three different construction methods of background value was compared with the engineering examples. The results show that the method of abstracting data sequence as non homogeneous exponential function has a higher prediction precision， and it can provide reference for similar projects.

Key words: GM(1, 1) model, background value, metabolic method, prediction precision

中图分类号:

TU433

彭振斌，张闯，彭文祥，王继武. GM(1，1)模型背景值构造的不同方法与应用[J]. 东北大学学报:自然科学版, 2017, 38(6): 869-873.

PENG Zhen-bin， ZHANG Chuang， PENG Wen-xiang， WANG Ji-wu. Different Structure Methods and Application of Background Value in GM(1，1) Model[J]. Journal of Northeastern University:Natural Science, 2017, 38(6): 869-873.

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GM(1，1)模型背景值构造的不同方法与应用

Different Structure Methods and Application of Background Value in GM(1，1) Model

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