摘要
GM(1,1)拟合的原始序列为非负齐次指数函数,对任何呈指数变化的序列x(k),可采用x^(0)(k)=x(k)—M或x^(0)(k)=M—x(k)将其转换为非负齐次指数函数变化。GM(1,1)建模的背景值生成Z^(1)=xx^(1)(k)+(1—α)x^(1)(k+1),应满足α=1/α—1/(e^0—1)。当|α|较小时,α非常接近0.5,但当|α|较大时,α偏离0.5值较大,这是在|α|较大时GM(1,1)传统建模方法失效的原因。文中基于建模机理与应用条件的分析,提出了改进的计算方法。
The original time-series fitted by GM(1, 1) are non-negative exponetial functions x^((0))= be^(αt)(b>0). Any exponetial function x^((0))=be^(αt)+c can be changed into a function x_1^((0))=b^1e_ ^(-αt)(b'>0) by x_1^((0))(k)=x^((0))(k)-M or x_1^((0))(k)=M-x^((0))(k). There is a relation α=(L/α)-(1/e~α-1) for Z^((1))(k+1)=αx^((1))(k)+(1-α)x^((1))(k+1). The relation shows that if |α| is close to 0, x is very close to 0.5, but if |α| is great α is significantly deviated from 0.5, which explains why the now—used computing method of GM(1, l) is invalid if |a| is great. On the basis of the mechanism and prereguisites for GM(1, 1), the author puts forward its revised methods.
出处
《江苏农学院学报》
CSCD
1993年第4期19-24,共6页
Jiangsu Agricultural Research
关键词
预测
灰色系统
建模机理
Forecasting
Modeling+Mechanism
Exponetial function/Grey system
GM(1, 1)
