分数阶累加多变量灰色模型FMGM(1,n)及应用

Multivariable grey model FMGM(1,n) with fractional order accumulation and its application

在分析单变量分数阶累加生成和累减生成的基础上,推导多变量分数阶累加生成的计算公式,建立多变量分数阶累加灰色模型FMGM(1,n),给出基于最小二乘法估计模型参数。以分数阶数为设计变量,以最小平均相对误差为目标函数,建立优化模型,以Matlab为平台编写优化求解程序。多变量分数阶累加灰色模型FMGM(1,n)模型是单变量的FGM(1,1)模型在多变量情况下的自然推广,旨在反映各变量间相互制约、相互促进的关系。最后给出了算例,算例表明本文所建模型的适应性、有效性。

After analyzing the fractional order AGO and IAGO of single variable,formula of multivariable fractional order AGO was deduced;the multivariable grey model FMGM(1,n)with fractional order accumulation was established;the model parameter estimation based on least square method was derived.By taking fractional order and minimum average relative error as design variable and object function,the optimal model was established and the solution program based in Matlab was written.As natural promotion of single variable model FGM(1,1),multivariable grey model FMGM(1,n)with fractional order accumulation reflected the interaction of variables.At last,the numerical example was given to indicate correctness and effectiveness of the model.