﻿ 新信息优先原理下非等间距GM(1, 1)模型优化研究
 控制与决策  2019, Vol. 34 Issue (10): 2221-2228 0

### 引用本文 [复制中英文]

[复制中文]
XI Lei, DING Song, XU Ning, XIONG Ping-ping. Research on optimization of non-equidistant GM(1, 1) model based on the principle of new information priority[J]. Control and Decision, 2019, 34(10): 2221-2228. DOI: 10.13195/j.kzyjc.2018.0163.
[复制英文]

### 文章历史

1. 南京航空航天大学 经济与管理学院，南京 211106;
2. 安徽科技学院 管理学院，安徽 滁州 233100;
3. 浙江财经大学 经济学院，浙江 杭州 310018;
4. 南京审计大学 管理科学与工程学院，南京 211815;
5. 南京信息工程大学 数学学院，南京 210044

Research on optimization of non-equidistant GM(1, 1) model based on the principle of new information priority
XI Lei 1,2, DING Song 3, XU Ning 4, XIONG Ping-ping 5
1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
2. College of Management, Anhui Science and Technology University, Chuzhou 233100, China;
3. School of Economics, Zhejiang University of Finance & Economics, Hangzhou 310018, China;
4. College of Management Science and Engineering, Nanjing Audit University, Nanjing 211815, China;
5. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Abstract: Aiming at the non-equidistant problems, an optimized non-equidistant GM(1, 1) model is designed based on the principle of new information priority. After analyzing the defects of previous optimized initial conditions, a new initial condition is designed by using the weighted sum of each component in 1-AGO sequence based on the principle of the new information priority. In order to show the modified effects of the new data points, the weight of each component in this newly proposed initial condition is calculated based on its value. Under the premise of minimizing the square sum of the relative error between the original series and the forecasting sequences, the solution to the newly generating parameter is presented. To verify the effectiveness of the novel model, two cases of increasing and decreasing sequences are conductd. The experimental results show that the optimized model can make full use of the new information, so as to achieve better forecasts than the previous modified models.
Keywords: new information priority    non-equidistant GM(1, 1) model    initial condition    optimization
0 引言

1 新信息优先原理下非等间距GM(1, 1)优化模型构建 1.1 非等间距GM(1, 1)模型建模机理

1) 若C为任意常数, 则白化方程的时间响应函数表达式为

 (1)

2) 在初始条件x(1)(t)|t = 1=x(1)(k1)下, i=2, 3, ..., n时的时间响应函数和还原值分别为

 (2)
 (3)

2) 取初始条件x(1)(t)|t=1=x(1)(k1), 将其代入式(1), 则求得

1.2 非等间距GM(1, 1)模型现有初始条件优化方法及缺陷分析

1) 邓聚龙[1]提出的以x(0)(1)为初始条件, 该模型的时间响应函数和还原值如式(2)和(3)所示.该方法没有充分利用新信息, 并且x(0)(1)没有经过累加生成变换弱化随机性, 因而预测效果不太理想.

2) 罗佑新[14]提出的以x(1)(t)|t=1=x(1)(kn)为初始条件的模型, 其时间响应函数和还原值分别为

 (4)
 (5)

3) 熊萍萍等[15]提出的以x(1)(t)|t=ψ = α1x(1)(k1) +α2x(1)(k2)+...+αnx(1)(kn)为初始条件的模型.其中:ψ为时间参数, α1+α2+...+αn=1, αi=, i=1, 2, ... n.其时间响应函数和还原值分别为

 (6)
 (7)

1.3 新信息优先原理下非等间距GM(1, 1)模型初始条件优化

 (8)

 (9)

 (10)
 (11)

 (12)

2) 将结论1)代入, 从而可得

1.4 NEGM(1, 1, ρ)模型中时间参数ρ的求解

X(0) = {x(0)(k1), x(0)(k2), ..., x(0)(kn)}和={(k1), (k2), ..., (kn)}分别为原始序列和预测序列, 建立无约束优化问题

 (13)

 (14)
2 实例分析

1) 建立NEGM(1, 1, x(1)(k1))模型, 可得时间响应函数为

 (15)

2) 建立NEGM(1, 1, x(1)(kn))模型, 可得时间响应函数为

 (16)

3) 建立IVWA-NEGM(1, 1)模型, 通过对序数序列计算, 各分量权重为

 (17)

 (18)

4) 建立NEGM(1, 1, ρ)模型, 可得a=-0.00104, b=10.76857, 根据式(9)可以计算得到1-AGO序列对应的权重为

 (19)

 (20)

1) 建立NEGM(1, 1, x(1)(k1))模型, 可得时间响应函数为

 (21)

2) 建立NEGM(1, 1, x(1)(kn))模型, 可得时间响应函数为

 (22)

3) 建立IVWA-NEGM(1, 1)模型, 通过对序数序列计算, 各分量权重为

 (23)

 (24)

4) 建立NEGM(1, 1, ρ)模型, 可得a=0.001588, b=1.778031, 根据式(9)可以计算得到1-AGO序列对应的权重为

 (25)

 (26)

3 结论

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