基于初值修正的组合灰色Verhulst模型

Combination Grey Verhulst Model Based on Initial Value Modification

对灰色Verhulst模型的拟合精度进行了分析,表明初值的选取对模型精度有重要影响.为提高灰色模型的拟合精度,利用最小二乘原理确定初值中的待定常数,给出了初值修正的灰色Verhulst模型.进一步利用修正模型和传统灰色Verhulst模型建立了组合灰色Verhulst模型,在平均相对误差最小的原则下,利用蚁群算法确定组合权系数.最后通过两个应用实例进行了计算和分析,结果表明,通过初值修正和组合模型能够提高灰色Verhulst模型的拟合精度,便于通过程序实现.

The fit precision of the grey verhulst model is analyzed. It shows that the selection of initial value has an important effect on the model＇s precision. In order to enhance the fit precision of the grey verhulst model, modify initial value grey verhulst model are put forward. The unknown constants in the initial value can be obtained using least square principle. By grey verhulst model and initial value modify model, the combination grey model are established. Under the norm of minimizing the average relative error criterion, the parameters of the combination grey model can be obtained by ant colony algorithm. The application examples show that the fit precision of the initial value modify model and combination grey model can be enhanced through. Moreover, the methods of modification initial value are simple and these methods can be realized by the program conveniently.