改进的GM(1,1)幂模型的构建与应用

Construction and Application of Improved GM(1,1)Power Mode

在构建GM(1,1)幂模型中,经常利用一阶非齐次线性方程的常数变易法求得GM(1,1)幂模型白化方程的解,再利用白化方程,在灰色系统信息覆盖原理下经过离散化处理推导出参数γ的计算公式,并利用最小二乘法求解参数a,b.但是在求解过程中由于离散化的处理,造成了时间响应预测函数精度的下降。为了弥补精度下降的缺陷,对于预测模型利用PSO算法进行了系数修正.案例对比研究发现,传统的GM(1,1)预测效果最差,改进的GM(1,1)幂模型预测效果最好.

In the construction of GM(1,1) power model, the solution of whitening equation of GM(1,1) power model is often obtained by constant variation method of first-order non-homogeneous linear equation. Then, by using whitening equation, the calculation formula of parameters is deduced by discretization under the principle of information coverage of grey system, and the parameters are solved by least square method. In order to compensate for the defect of decreasing precision, the PSO algorithm is used to modify the coefficients of the prediction model. A case stu d y shows that the traditional GM (1,1) model has the worst prediction effect and the improved GM (1,1) power model has the best prediction effect.