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.

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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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