非线性优化GM(1,N)模型及其应用研究

Nonlinear optimization method of gray GM(1,N) model and application

GM(1,N)模型在因素一次累加弱化系统指标间波动性和灰性的基础上,建立了各因素线性关系的灰色模型,但其强制性的线性假设以及不够完善的求解方法致使其实际运用较少。为解决这类问题,文章提出了两个非线性优化的GM(1,N)模型——非线性GM(1,N,x(10))和GM(1,N,x(11))模型,即在GM(1,N)白化方程的基础上建立因素间非线性关系,并通过BP网络拟合,最终得出拟合结果和预测值。进一步证明了两种非线性GM(1,N)模型均属于GM(1,N)的派生形式,并提出了运用非线性优化GM(1,N)模型进行指标预测的具体方法。最后通过一个实例进一步表明该模型的可行性与优化性。

The GM（1,N） model in the grey system constructs the linear correlation between various factors,based on the 1-AGO that eliminated certain grey character.But it has not obtained the actual utilization for the compulsory linear hypothesis and the insufficient consummation solution method.So that the nonlinear optimization GM（1,N） model including GM（1,N,x（0）1） and GM（1,N,x（1）1） model are put out for these reasons.The new GM（1,N） model＇s nonlinear relation is built in the GM（1,N） white equation,and then is resolved by BP neural network.It is proved that two nonlinear new GM（1,N） are just produced from the old GM（1,N） model,and the whole forecast technique was given based on these new models.At last,the new models＇ merit is represented by using it to forecast the energy consumption of our country.