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。
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（l,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（l,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.
出处
《中国管理科学》
CSSCI
北大核心
2015年第11期112-118,共7页
Chinese Journal of Management Science
基金
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)
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
multi-variable system
MGM（1
m） model
self-memory principle
coupled system
foundation pit deformation
