Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model

TANG Limin

doi:10.13203/j.whugis20130012

Volume 39 Issue 9

Sep. 2014

Turn off MathJax

Article Contents

Abstract

References

Geomatics and Information Science of Wuhan University > 2014 > 39(9): 1038-1042. > DOI: 10.13203/j.whugis20130012

TANG Limin. Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1038-1042. DOI: 10.13203/j.whugis20130012

Citation:

TANG Limin. Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1038-1042. DOI: 10.13203/j.whugis20130012

Citation:

TANG Limin. Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1038-1042. DOI: 10.13203/j.whugis20130012

PDF (218 KB)

Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model

TANG Limin^1,2

¹Key Laboratory of Road Structure & Material of Ministry of Communications,Changsha 410004,China;²School of Traffic and Transportation Engineering,Changsha University of Science& Technology,Changsha 410004,China

Funds: The National Natural Science Foundation of China,No.41174001;China Postdoctoral Science Foundation,No.2013M531776;Hunan Provincial Natural Science Foundation of China,No.14JJ3090;Open Fund of Key Laboratory of Road Structureand Material of Ministry of Transport(Changsha University of Science & Technology),No.kfj100209.

More Information

Author Bio:
TANG Limin,lecturer,postdoctoral,specializes in ill-posed problems and nonlinear inversion and deformation monitoringetc.
Received Date: April 08, 2013
Revised Date: September 04, 2014
Published Date: September 04, 2014

Graphical Abstract

Abstract

Abstract

Objective Ill-posed problems exist in the gray system GM(1,1)model.Seriously ill-posed informationmatrices will occur in larger original measured data values.Reasons which cause ill-posed informationmatrices in GM(1,1)modesl are analysized in detail.A method to adjust the measurement unit of theoriginal measured data values to reduce the conditional number of information matrices is put forward.Based on GM(1,1)model theory,we show that an adjustment to the measured data units of measure-ment does not affect the model relative residuals,average residuals,or prediction accuracy.Numericalexperiments and analysis demonstrate that this method of adjusting the measurement unit algorithmfor a GM(1,1)model is easy to implement,simple,accurate,and widely applicable.
- GM(1,1)model,
- ill-posed problem,
- information matrices,
- measurement unit

FullText(HTML)

References (1)

References

[1]

Deng Julong.Grey Theory Basis[M].Wuhan:Huazhong University of Science and TechnologyPress,2002(邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002)[2] Zheng Zhaoning,Wu Yuying,Bao Hanling.TheMorbidity Problem in GM Model[J].Chinese Jour-nal of Management Science,2001,9(5):38-44(郑照宁,武玉英,包涵龄.GM模型的病态性问题[J].中国管理科学,2001,9(5):38-44)[3] Wang Zhongwen,Zhang Hongbo,Liu Dianguo.Creating Ill-Conditioned Matrix in GM(1,N)andImprove Method by Principal Component[J].Jour-nal of Jilin Teachers Institute of Engineering andTechnology,2005,21(6):9-11(王忠文,张洪波,刘1041武汉大学学报 · 信息科学版2014年9月殿国.GM(1,N)模型的病态矩阵的产生及主成分估计改进法 [J].吉林工程技术师范学院学报,2005,21(6):9-11)[4] Dang Yaoguo,Wang Zhengxin,Liu Sifeng.Re-search on Morbidity Problem of AccumulatingMethod for GM(2,1)Model[J].Systems Engineer-ing Theory and Practices,2008,(1):156-160(党耀国,王正新,刘思峰.灰色模型的病态问题研究[J].系统工程理论与实践,2008,(1):156-160)[5] Cui Jie,Dang Yaoguo,Liu Sifeng.Study on Morbid-ity of NGM(1;1;k)Model Based on Conditions ofMatrix[J].Control and Decision,2010,25(7):1050-1054(崔杰,党耀国,刘思峰.基于矩阵条件数的NGM(1;1;k)模型病态性研究[J].控制与决策,2010,25(7):1050-1054)[6] Wu Zhengpeng,Li Bo,Zhang Youping,et al.Studyon the Morbidity Problem in Grey Model[J].Jour-nal of Communication University of China(Scienceand Technology),2011,18(4):31-34(吴正鹏,李波,张友萍,等.GM(1,1)模型的病态问题研究[J].中国传媒大学学报自然科学版,2011,18(4):31-34)[7] Liu Shengbao,Zhang Gongrang,Mao Xuemin,et al.Research on Reverse Accumulating GM(2,1)Modeland Its Morbidity Problem[J].Journal of HefeiUniversity of Technology,2011,34(4):603-608(刘圣保,张公让,毛雪岷,等.反向累积法GM(2,1)模型及其病态性研究[J].合肥工业大学学报(自然科学版),2011,34(4):603-608)[8] Tang Limin.Research on the Ill-Posed and SolvingMethods of Nonlinear Least Squares Problem[J].Acta Geodaetica et Cartographica Sinica,2012,41(4):630(唐利民.非线性最小二乘问题的不适定性及算法研究[J].测绘学报,2012,41(4):630)[9] Yang Heping,Zhan Wentao,Zhao Wenjian,et al.Rapid Determination Method of CBR Indices for Ex-pansive Soil Filler Based on GM(1,1)Model[J].Journal of Highway and Transportation Researchand Development,2012,29(9):1-7(杨和平,湛文涛,赵文建,等.基于GM(1,1)模型的膨胀土填料CBR指标快速确定方法[J].公路交通科技,2012,29(9):1-7)

[1]	DU Yan, NING Lize, XIE Mowen, BAI Yunfei, LI Heng, JIA Beining. A Prediction Model of Landslide Displacement in Reservoir Area Considering Time Lag Effect[J]. Geomatics and Information Science of Wuhan University, 2024, 49(8): 1347-1355. DOI: 10.13203/j.whugis20220133
[2]	XIAO Ruya, HE Xiufeng. Deformation Monitoring of Reservoirs and Dams Using Time-Series InSAR[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1334-1341. DOI: 10.13203/j.whugis20170327
[3]	ZHANG Yan, LV Pinji, LIU Jia. Impact of the Yangtze River Three Gorges Reservoir on Fault Activity[J]. Geomatics and Information Science of Wuhan University, 2017, 42(10): 1497-1500. DOI: 10.13203/j.whugis20140983
[4]	HUANG Shengxiang, LUO Li. Stability Analysis and Results of the Landslide MonitoringDatum in the Three Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2014, 39(3): 367-372. DOI: 10.13203/j.whugis20120019
[5]	WU Xueling, REN Fu, NIU Ruiqing. Spatial Intelligent Prediction of Landslide Hazard Based on Multi-source Data in Three Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2013, 38(8): 963-968.
[6]	HU Teng, DU Ruilin, ZHANG Zhenhua, WU Yue. Simulation and Mechanism Analysis on Crustal Vertically Deformation in Three Gorges Reservoir Area Under the Condition of Reservoir Impoundment[J]. Geomatics and Information Science of Wuhan University, 2010, 35(1): 33-36.
[7]	WU Tao, YAN Huiwu, TANG Guigang. Prediction on Time Series Analysis of Water Quality in Yangtze Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2006, 31(6): 500-502.
[8]	DU Ruilin, QIAO Xuejun, YANG Shaomin, WANG Qi. Results of the Crustal Deformation by GPS Survey and Horizontal Strain Rate Fields in the Three Gorges Area[J]. Geomatics and Information Science of Wuhan University, 2004, 29(9): 768-771.
[9]	SHI Dong, CHEN Jun, ZHU Qing. Oil-Gas Reservoir Evaluation Based on GIS[J]. Geomatics and Information Science of Wuhan University, 2004, 29(7): 592-596.
[10]	JIANG Fuzhen. Role of Gravimetry in Monitoring the Crustal Deformation of Three Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2003, 28(6): 679-682.

Cited By

Cited by

Periodical cited type(6)

1.	李惠民，彭紫薇，李相如. 气候变化下干旱对大别山区植被的影响研究. 治淮. 2024(12): 44-46 .
2.	谢萍，张双喜，金涛勇，韦瑜，蔡剑锋，许晨. 武汉市GRACE水储量变化与气象干旱关联趋势分析. 排灌机械工程学报. 2023(06): 624-629 .
3.	胡艳茹，梁丽娇，何立平，许文锋，刘正学，兰波. 三峡水库蓄水前后库区及周边区域降水变化及其影响因素. 地理研究. 2023(07): 1921-1940 .
4.	肖家豪，张双喜，韦瑜，蔡剑锋，洪敏. 基于GPS垂向位移测定云南地区陆地水储量及其对累积降雨的响应机制. 测绘通报. 2022(01): 61-65 .
5.	咬登魁，段功豪. 基于季节性SARIMA模型的武汉市长序列降雨量趋势分析与预测. 地下水. 2022(02): 166-168 .
6.	谢萍，张双喜，周吕，李庆隆，肖家豪，蔡剑锋. 武汉市中心城区地表形变与洪涝灾害防治新策略. 武汉大学学报(信息科学版). 2021(07): 1015-1024 .

Other cited types(7)

Get Citation

PDF

XML

Article views (1509) PDF downloads (560) Cited by(13)

Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model

Abstract

References

Related Articles

Cited by

Periodical cited type(6)

Other cited types(7)

Catalog

Related

Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model

Abstract

References

Related Articles

Cited by

Periodical cited type(6)

Other cited types(7)

Catalog

Related

Export File

Citation

Format

Content