GM1,1模型的特性与优化研究

Key words :
Grey system; GM (1,1) model ; GM (1,1) power model ; characteristic; optimization; forcast.
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GM (1,1) 模型的特性与优化研究
图表清单
图 1.1 图 3.1 图 4.1 表 1.1 表 2.1 表 2.2 表 3.1 表 3.2 表 3.3 续表 3.3 表 3.4 续表 3.4 表 3.5 表 3.6 表 3.7 表 3.8 表 4.1 表 4.2 表 4.3 表 4.4 本文的技术路线.....................................................................................8 传统的背景值误差来源.......................................................................31 某疏港公路历年交通量.......................................................................42 中国学术期刊网非经典预测方面的学术文章（1994.1—2007.11） .2 两种模型的模拟预测值与实际值的比较(例 1).................................23 两种模型的模拟预测值与实际值的比较(例 2).................................24 三种 GM (1,1) 模型的模拟误差比较 ....................................................29 三种 GM (1,1) 模型的预测误差比较 ....................................................29 三种 GM (1,1) 模型的模拟误差 ............................................................34 三种 GM (1,1) 模型的模拟误差 ............................................................35 三种 GM (1,1) 模型的预测误差 ............................................................35 三种 GM (1,1) 模型的预测误差 ............................................................36 1997-2004 年江苏省财政科技投入（亿元） ....................................36 三种模型的模拟预测值与实际值的比较（亿元）...........................37 三种模型对财政科技投入的模拟误差...............................................37 三种模型对财政科技投入的预测相对误差（%） ...........................37 某疏港公路历年交通量.......................................................................41 两种模型的模拟预测值与实际值的比较...........................................42 南京市 1997-2002 年水路货运量 .......................................................48 两种模型的模拟预测值与实际值的比较...........................................49
response sequence of whiterization equation of GM (1,1) . Thereby it creates the optimum time response sequence of whiterization equation for GM (1,1) while primary information is well utilized. 4． Based on the geometrical sense of the background value of the GM (1,1) model, this paper synthesizes the 1-accumulated sequence with function with non-homogeneous exponential law and introduce a new method for modeling the background value and a more reasonable equation for computing computing the background value . With these new ideas, it successfully enhances the optimized stimulation model and the accuracy of forecast. It’s interesting to note that it still maintain a high accuracy when the absolute value of development coefficient is relatively large. 5． Based on the analysis of existing problems of the grey Verhulst model and the Nhomakorabeaii
南京航空航天大学硕士学位论文
forms of Whitenization differential equation, this paper uses trapezoid formula to whiten the grey derivative item and educe a new grey Verhulst model, causing a better uniformity of parameters between the difference equation and differential equation in the grey model. 6． Based on the basic principle of information overlaping in the grey system, this paper educes the estimate arithmetic of parameter α in GM (1,1) power model. Accordingly how different values of parameter α influence the character of model solution is discussed. Simultaneously it supplements the theorem of the solution to whitenization differential equation and presents new methods to optimize the model solution, which further broadens the implementation of the GM (1,1) Power Model.
关键词：灰色系统， GM (1,1) 模型， GM (1,1) 幂模型，特性，优化，预测
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GM (1,1) 模型的特性与优化研究
ABSTRACT
This thesis takes GM (1,1) model as the main, the core of which consists of three parts, namely characteristics of GM (1,1) model, optimization of GM (1,1) model and GM (1,1) Power Model. In each part, relevant models are implemented to further improve the theoretical system of GM and expand the implementation fields of the GM forecast theories and methods. The contents include the following aspects: 1．In this paper, some preliminary researches on the morbidity problem of GM has been done. Results from a series of mathematical deduction, with the implementation of eigenvalue estimation theorems from matrix theory, show that the morbidity problem could only exist in GM (1,1) when the first item of original sequence is unequal to zero while other items are equal to zero approximatively. Accordingly, there's no practical meaning to predict by this kind of sequence. 2．Analyzing the relations between the stability of GM (1,1) and the development coefficient −a , taking into account the reality of the nonlinear system, this paper introduces nonlinear item into Unbiased model GM (1,1) and then deduce its logistic expression. Based on the expression, the steady state, periodic state and chaotic characteristics of Unbiased model GM (1,1) are analyzed. Finally, the superiority of Unbiased model GM (1,1) are well explained with chaos theory. 3．With the aim of sequence minimizing the errors of simulation value of original data and the sequence, this paper finds the constant number c in the time