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《地球科学与环境学报》[ISSN:1672-6561/CN:61-1423/P]

卷:

第34卷

期数:

2012年第04期

页码:

102-106

栏目:

工程地质

出版日期:

2012-12-20

文章信息/Info

Title:

Improvement of GM(1,1)Model and Its Application on Deformation Prediction

作者:

彭正明¹; 王腾军²; 曹冬冬²; 徐秋艳³

1.甘肃省水利水电勘测设计研究院,甘肃 兰州 730000; 2.长安大学 地质工程与测绘学院, 陕西 西安 710054; 3.陕西省煤田地质局,陕西 西安 710054

Author(s):

PENG Zheng-ming¹;  WANG Teng-jun²;  CAO Dong-dong²;  XU Qiu-yan³

1. Gansu Institute of Investigation Design and Research of Water Resources and Hydropower, Lanzhou 730000, Gansu, China; 2. School of Geological Engineering and Surveying, Chang'an University,Xi'an 710054, Shaanxi, China; 3. Shaanxi Bureau of Coal Geological Exploration, Xi'an 710054, Shaanxi, China

关键词:

灰色模型;  GM(1; 1)模型;  灰色多重修正模型;  积分优化;  二次拟合优化;  残差改化;  变形预测

Keywords:

grey model;  GM(1; 1)Model;  grey multiple correction model;  integral optimization;  quadratic fitting optimization;  residual error modification;  deformation prediction

分类号:

P694

DOI:

-

文献标志码:

-

摘要:

为了提高GM(1,1)模型预测精度,采用积分优化、二次拟合优化以及残差改化方法,分步对GM(1,1)模型进行改进,建立灰色多重修正模型。具体改进步骤为:首先,利用积分优化方法对背景值进行纠正,减小模型误差并提高预测精度; 接着,对模型参数(发展系数和灰作用量)进行二次拟合优化,使参数更加接近理论真值; 然后,根据预测结果进行适当的残差改化,提高模型整体的预测精度; 最后,建立根据GM(1,1)模型改进的灰色多重修正模型。以重庆南川地区甄子岩崩塌为例,建立灰色多重修正模型对危岩裂缝累计位移值进行模拟和预测,并与GM(1,1)模型进行对比。精度检验结果表明:灰色多重修正模型后验差比值(0.082 39)明显好于GM(1,1)模型(0.192 67),平均相对残差比(0.073 9)更远好于GM(1,1)模型(0.259 6),表明灰色多重修正模型在预测精度上有较大提高,可靠性更好。

Abstract:

In order to improve the precision of prediction, GM(1,1)Model was modified by the means of integral optimization, quadratic fitting optimization and residual error modification methods step by step, and grey multiple correction model(GMCM)was built. The steps of modification included that background value was corrected by the means of integral optimization in order to reduce the error and improve the precision of prediction firstly; secondly, the parameters including developing coefficient and grey action were optimized by the means of quadratic fitting in order to make the parameters closer to the theoretical value; thirdly, residual error modification was properly done according to the prediction results in order to improve the whole precision of prediction; finally, GMCM, which was modified based on GM(1,1)Model, was built. Collapse of Zengzi Rock in Nanchuan of Chongqing was taken as an example, GMCM was built to simulate and predict the accumulated displacement of crag crack and was compared with GM(1,1)Model. The results of accuracy test showed that posterior error ratio of GMCM(0.082 39)was better than that of GM(1,1)Model(0.192 67), and average relative residual error ratio of GMCM(0.073 9)was better than that of GM(1,1)Model(0.259 6), so that the precision of prediction and reliability of GMCM were improved significantly.

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相似文献/References:

备注/Memo

备注/Memo:

收稿日期:2012-09-04
基金项目:国家自然科学基金项目(40972181)
作者简介:彭正明(1964-),男,甘肃兰州人,高级工程师,E-mail:sdefy_pzm@163.com。

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更新日期/Last Update: 2012-12-20