基于自忆性原理的多变量MGM(1,m)耦合系统模型构建及应用

doi:10.16381/j.cnki.issn1003-207x.2015.11.014

中国管理科学 ›› 2015, Vol. 23 ›› Issue (11): 112-118.doi: 10.16381/j.cnki.issn1003-207x.2015.11.014

基于自忆性原理的多变量MGM(1,m)耦合系统模型构建及应用

郭晓君^1,2, 刘思峰^2,3, 杨英杰³

1. 南通大学理学院, 江苏南通 226019;
2. 南京航空航天大学经济与管理学院, 江苏南京 211106;
3. 英国De Montfort大学计算智能研究中心, 莱斯特LE1 9BH

收稿日期:2013-08-09 修回日期:2014-07-23 出版日期:2015-11-20 发布日期:2015-12-01
作者简介:郭晓君(1978-),男(汉族),江苏南通人,南通大学理学院副教授,博士研究生,研究方向:灰色系统理论、系统工程.
基金资助:
欧盟第7研究框架玛丽居里国际人才引进计划Fellow项目(FP7-PIIF-GA-2013-629051);国家自然科学基金资助项目(71271226,71363046,71401051,71503103);国家社会科学基金重点资助项目(12AZD102);江苏省社会科学基金资助项目(14GLC008);南通市科技计划资助项目(HS2013026)

Construction and Application of Multi-variable MGM(1,m) Coupled System Model Based on Self-memory Principle

GUO Xiao-jun^1,2, LIU Si-feng^2,3, YANG Ying-jie³

1. School of Science, Nantong University, Nantong 226019, China;
2. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
3. Centre for Computational Intelligence, De Montfort University, Leicester LE1 9BH, UK

Received:2013-08-09 Revised:2014-07-23 Online:2015-11-20 Published:2015-12-01

摘要/Abstract

摘要： 针对小样本条件下具有相互制约关系的多变量系统,本文提出了一种新颖的多变量MGM(1,m)自忆性耦合系统模型,用来统一描述系统各变量间关系并且提高其建模精度。该模型通过有机耦合动力系统自忆性原理与传统MGM(1,m)模型,综合了两者各自的优势。系统的自忆性方程包含多个时次初始场而不仅是单个时次初始场,从而克服了传统灰色预测模型对初值比较敏感的弱点。对基坑变形预测的实例研究结果表明,所构建模型能够充分利用系统的多个历史时次资料,可以紧密捕捉系统演化趋势,模拟预测精度显著高于传统多变量MGM(1,m)模型。研究结果表明,新模型丰富和完善了灰色预测理论,值得推广应用于其他类似的多变量系统。

关键词: 多变量系统, MGM(1,m)模型, 自忆性原理, 耦合系统, 基坑变形

Abstract: A novel multi-variable MGM(1,m) self-memory coupled system model is presented for use in multi-variable systems with interactional relationship under the condition of small sample size. The proposed model can uniformly describe the relationships among system variables and improve the modeling accuracy. The model combines the advantages of the self-memory principle of dynamic system and traditional MGM(1,m) model through coupling of the above two prediction methods. The weakness of the traditional grey prediction model, i.e., being sensitive to initial value, can be overcome by using multi-time-point initial field instead of only single-time-point initial field in the system's self-memorization equation. As shown in the case study of foundation pit deformation prediction, the novel model can take full advantage of the system's multi-time historical data and accurately predict the system's evolutionary trend. And it prominently possesses higher accuracy of simulation and prediction than the traditional multi-variable MGM(1,m) model. The results show that the proposed model enriches and perfects grey prediction theory, and can be applied to other similar multi-variable engineering systems.

Key words: multi-variable system, MGM(1,m) model, self-memory principle, coupled system, foundation pit deformation

中图分类号:

N941.5

郭晓君, 刘思峰, 杨英杰. 基于自忆性原理的多变量MGM(1,m)耦合系统模型构建及应用[J]. 中国管理科学, 2015, 23(11): 112-118.

GUO Xiao-jun, LIU Si-feng, YANG Ying-jie. Construction and Application of Multi-variable MGM(1,m) Coupled System Model Based on Self-memory Principle[J]. Chinese Journal of Management Science, 2015, 23(11): 112-118.

参考文献

[1] Deng Julong. Control problem of grey system[J]. Systems and Control Letters, 1982, 1(5):288-294.

[2] Liu Sifeng, Lin Yi. Grey systems theory and applications[M]. Berlin:Springer-Verlag, 2010.

[3] 肖新平,毛树华.灰预测与决策方法[M].北京:科学出版社, 2013.

[4] Wu Lifeng, Liu Sifeng, Yao Ligen, et al. The effect of sample size on the grey system model[J]. Applied Mathematical Modelling, 2013, 37(9):6577-6583.

[5] 张岐山.提高灰色GM(1,1)模型精度的微粒群算法[J].中国管理科学, 2007, 15(5):126-129.

[6] 张斌,西桂权.基于背景值和边值修正的GM(1,1)模型优化[J].系统工程理论与实践, 2013, 33(3):682-688.

[7] 刘斌,刘思峰,翟振杰,等. GM(1,1)模型时间响应函数的最优化[J].中国管理科学, 2003, 11(4):54-57.

[8] Wu Lifeng, Liu Sifeng, Yao Ligen, et al. Grey system model with the fractional order accumulation[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(7):1775-1785.

[9] 翟军,盛建明,冯英浚. MGM(1,n)灰色模型及其应用[J].系统工程理论与实践, 1997, 5(5):109-113.

[10] 李小霞,同小军,陈锦云.多因子灰色MGMp(1,n)优化模型[J].系统工程理论与实践, 2003, 4(4):47-51.

[11] 崔立志,刘思峰,吴正朋.基于向量连分式理论的MGM(1,n)模型[J].系统工程, 2008, 26(10):47-51.

[12] 熊萍萍,党耀国,王正新. MGM(1,m)模型背景值的优化[J].控制与决策, 2011, 26(6):806-810, 815.

[13] 熊萍萍,党耀国,朱晖.基于非等间距的多变量MGM(1,m)模型[J].控制与决策, 2011, 26(1):49-53.

[14] 熊萍萍,党耀国,束慧. MGM(1,m)模型的特性研究[J].控制与决策, 2012, 27(3):389-393, 398.

[15] Cao Hongxing. Self-memory equation for atmosphere motion[J]. Science in China (Series B):Chemistry, 1993, 36(7):845-855.

[16] Gu Xiangqian, You Xingtian, Zhu He, et al. Numerical tests of efficiency of the retrospective time integration scheme in the self-memory model[J]. Progress in Natural Science, 2004, 14(9):833-836.

[17] Wang Wei, Su Jingyu, Hou Benwei, et al. Dynamic prediction of building subsidence deformation with data-based mechanistic self-memory model[J]. Chinese Science Bulletin, 2012, 57(26):3430-3435.

[18] 范习辉,张焰.灰色自记忆模型及应用[J].系统工程理论与实践, 2003, 23(8):114-117, 129.

[19] Chen Xiangdong, Xia Jun, Xu Qian. Differential Hydrological Grey Model (DHGM) with self-memory function and its application to flood forecasting[J]. Science in China Series E:Technological Sciences, 2009, 52(4):1039-1049.

[20] 郭晓君,刘思峰,方志耕.基于合成灰数灰度的区间灰数自忆性预测模型[J].系统工程与电子技术, 2014, 36(6):1124-1129.

基于自忆性原理的多变量MGM(1,m)耦合系统模型构建及应用

Construction and Application of Multi-variable MGM(1,m) Coupled System Model Based on Self-memory Principle

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