组合GM(1,1)幂模型及其应用

Combination GM(1,1) Power Model and Its Application

GM(1,1)幂模型是灰色Verhulst模型的推广.由于初始条件选取影响GM(1,1)幂模型的精度,将平均相对误差函数分别看成是幂指数、发展系数、灰作用量的函数,利用蚁群算法进行参数辨识,从而建立多个单项GM(1,1)幂模型.利用这些单项模型建立了线性组合GM(1,1)幂模型,组合权系数利用最大相对误差最小化原则采用粒子群算法确定.实例表明,组合GM(1,1)幂模型的建模精度高于传统GM(1,1)幂模型,同时也说明方法是有效的和可行的,具有重要的理论意义.

GM（1,1） power model generalizes the grey Verhulst model. Since the initial conditions affect the accuracy of the model, the average relative error function is seen as functions of power exponent, development coefficient and grey action. The ant colony algorithm is used to solve the models parameters based on the average relative error function minimization. And then the GM（1,1） power models are established, according to these GM（1,1） power models, the combination GM（1,1） power model is present, and the combination weights are determined using the maximum relative error minimization and particle swarm optimization algorithm. Then the effect of initial condition is overcome. Finally one example shows the precision of the combination GM（1,1） power model is higher than the GM（1,1） power model. So this method is feasible, effective and has important theory significance.