GM(1,1)幂模型求解方法及其解的性质

根据灰色系统信息覆盖的基本原理,给出了GM(1,1)幂模型中参数α的估计方法.讨论了α的不同取值对模型解的影响,对其白化微分方程解的定理进行了补充,并给出了白化微分方程解的优化方法.结果表明,所提出的建模方法更能适应于一类具有饱和状态或发展变化受众多因素影响的波动原始序列,在0<α<1且a>0和α>1且a<0两种情形下,GM(1,1)幂模型与灰色Verhulst模型具有相同的极限性质,但模拟预测精度高于灰色Verhulst模型.

Solution of GM(1,1)power model and its properties

Based on the basic principle of information overlap in the grey system,this paper educes the estimate arithmetic of parameter α in GM(1,1) power model.The influence of various values of parameter α on the character of model solution is discussed.Simultaneously the paper renews the theorem of the solution to whitenization differential equation and presents two methods to optimize the model solution.The result shows that the modeling method proposed here is more suitable for fluctuating sequences that has a saturated condition or whose development is affected by multitudinous factors.When 0<α<1 and a>0 or α>1 and a<0,two models,GM(1,1) power model and grey Verhulst model,have the same limit properties but the GM(1,1) power model has superiority over the Verhulst model in the aspects of applicable scope and forecast precision.