基于粒子群算法的GM(1，1)幂模型及应用

在灰色Verhulst模型的基础上对等间隔和非等间隔GM(1,1)幂模型进行了研究,讨论了模型的求解过程,分析了模型曲线形状与幂指数、发展系数之间的关系。将平均相对误差看成幂指数、发展系数和灰作用量的函数,同时考虑初始条件对建模精度的影响,利用粒子群算法进行参数辨识,克服了灰色Verhulst模型和最小二乘法参数辨识的缺陷。最后实例表明,基于粒子群算法参数辨识的GM(1,1)幂模型建模精度高于灰色Verhulst模型,同时也表明了该方法的有效性和可行性,具有重要的理论意义。

GM(1,1) power model based on Particle Swarm Optimization algorithm

Based on the grey Verhulst model,in this paper the equidistance and non-equidistance GM(1,1) power model is studied.The models' solutions are got.The relations of the model's curve and power's exponent,development coefficient are ana- lyzed.The average relative error is seen as a function of power's exponent,development coefficient and grey action quantity.At the same time the initial condition is considered.The Particle Swarm Optimization (PSO) algorithm is used to solve the models' pa- rameters.Then the defects of the grey Verhulst model and the least square method are overcome.Finally one example shows the precision of the GM(1,1) power model with parameter identification based on PSO is higher than the grey Verhulst model.So the method is feasible,effective and has important theory significance.