摘要
GM(1,1)幂模型是灰色Verhulst模型的推广.在灰色Verhulst模型和等间隔GM(1,1)幂模型基础上提出了非等间隔GM(1,1)幂模型,并对模型进行求解.同时讨论了GM(1,1)幂模型曲线形状和幂指数以及发展系数之间的关系,研究了非等间隔GM(1,1)幂模型的参数空间.将平均相对误差看成幂指数的函数,根据序列形状判断幂指数的范围,利用粒子群算法求解幂指数,克服了灰色Verhulst模型的缺陷.最后实例表明:GM(1,1)幂模型建模精度高于灰色Verhulst模型,该方法具有重要的理论意义.
GM（1,1） power model generalizes the grey Verhulst model.Based on the grey Verhulst model and the equidistance GM（1,1） power model,this paper puts forward the non-equidistance GM（1,1） power model and solves the model.In this paper,the relations of the model＇s curve and power＇s exponent, development coefficient are analyzed.At the same time the paper studies the non-equidistance GM（1, 1） power model＇s parameter space.The average relative error is seen as a function of power＇s exponent. The numeric area of power＇s exponent can been got according to the shape of sequences of raw data.The particle swarm optimization（PSO） algorithm is used to solve the power＇s exponent.Then the defects of the grey Verhulst model are overcame.Finally the example shows that the precision of the GM（1,1） power model is higher than the grey Verhulst model.So the method is feasible and effective and has important theory significance.
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2010年第3期490-495,共6页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(70471019)
