灰色增量──微分动态模型与中间变量辨识方法及其应用

本文对灰色GM(1, 1)、GM(2, 1)建模方法作了扩展和改进, 重新构造累加生成模式。利用多级增量序列首先进行回归建模, 引入中间变量并对其辨识和模拟, 使原始时间序列中隐含的有序性、规律性及灰色信息不断白化。灰色增量--微分动态模型具有系统开放性, 模型结构的包容量和信息量十分丰富, 为自然、社会经济等复杂系统建模、控制、预测提供了有效方法, 并消除了灰色GM(1, 1)、GM(2, 1)模型的局限性及不足之处；对全国总人口序列采用柯布--道格拉斯函数模型进行增量序列拟合建模, 在中间变量层次中揭示出周期性变化规律, 拟合效果极显着, 平均误差率1.21%, 最大误差率2.73%, 拟合精度极高。

Method of Identification and Application of Grey Increment Differential Dynamic Model and Intermediate Variables

The method of model-constructing of GM(1,1) and GM(2,1) has been extended and improved and new accumulat ed growth model has been constructed in this paper. Introducing the intermediate variables, the regression model has built with the help of multi-step increment sequency.The grey-increment model has advantages over the models of GM(1,1),GM(2,1) in model-building control and forecasting. Increment sequency im-itated modeiling of total population in China has been finished by using the model of Cop-Daugglas function. The average error rate is 1.21 percent and the maximum error rate 2.73 percent,the accuracy of imitation is very high.