基于函数arccos(px+q)变换的灰色预测模型研究

借助于函数变换理论和灰色系统建模理论,并结合反余弦函数和线性函数的特点,提出了反余弦函数和线性函数相结合的变换方法并建立了一个改进的GM(1,1)模型.证明了这种变换一方面能提高序列的光滑比并压缩序列的级比;另一方面可以使还原误差减小.具体算例结果表明,经过反余弦函数和线性函数相结合建立的改进GM(1,1)模型的拟合精度优于传统GM(1,1)模型和基于反余弦函数变换的GM(1,1)模型的拟合精度.

Research on Grey Prediction Model Based on arccos(px+q) Transformation

On the basis of the function transformation,Grey system theory and the features of the arccosine and linear functions,a new transformation and a generalized GM (1,1) model are proposed.Then that the new transformation could improve the ratio of smoothness of the original statistical data is proved.And that this new transformation is a stepwise compressible transformation and may decrease the reduction error are also established.Regarding the simulation accuracy of the model,an example is given to illustrate that our generalized GM (1,1) based on the combination of the arcconsine function with linear function is better than the classical GM (1,1) and the GM (1,1) based on the arccosine function.