具自忆性的改进灰色Verhulst模型研究及应用

An Improved Grey Verhulst Model Possessing Self-memory Ability and Its Application

传统灰色Verhulst模型对于饱和发展状态的S型过程有较好的预测精度,但对于具有随机波动特征的S型过程预测效果并不理想。针对以上问题,为了提高预测精度,本文在传统灰色Verhulst模型及动力系统自忆性原理的基础上,构建了一类改进的灰色Verhulst自忆性模型,新模型充分利用了历史观测数据、克服了传统灰色Verhulst模型无法描述波动特征的局限性。通过实例分析,表明所构建模型能够充分体现S型过程中的随机波动特征,具有理想的拟合预测效果。

The traditional grey Verhulst model for sigmoid process with saturation condition has good prediction accuracy, but the prediction effect is unsatisfactory for sigmoid process with random fluctuation.In order to solve this problem and improve the prediction accuracy,the grey Verhulst self-memory model is established based on traditional grey Verhulst model and self-memory principle of dynamical system.The newly-established model can recollect the historical data adequately and overcome the limitation of traditional grey Verhulst model,which can not describe the characteristic of fluctuation.Example analysis shows that the newly-established model can reflect the random fluctuant feature of sigmoid process and possess satisfactory simulation and prediction effect.