灰色广义Verhulst模型的构建及其应用

一般认为,灰色Verhulst模型(grey verhulst model,简称GVM)适用于具有单峰或饱和S形的序列.然而,在利用GVM建模时,模拟值有时会出现"漂移"现象,使得模型精度变差.针对这一问题,将常数项引入GVM模型,构建了灰色广义Verhulst模型(grey generalized verhulst model,简称GGVM),并在参数的不同分类下,借助灰色建模序列的非负性,完整地给出了灰色广义Verhulst模型的时间响应式及其还原值.将GGVM与GVM模型分别对四个单峰型序列建模,发现GGVM能有效地解决GVM模型模拟值出现的“漂移”现象.在实证部分,利用新模型对江苏省石油与天然气的基础储量进行建模分析,并与GVM模型、数据分组处理算法比较,验证了GGVM在模拟及预测时的优势.

The grey generalized Verhulst model and its application

Generally speaking, the grey Verhulst model (abbreviated as GVM) can be fit to the sequence with single peak feature or saturated S shape. However, when using the GVM for empirical analysis, there sometimes appears drift phenomenon in the simulation values, which leads to reduce the model precision. In order to solve this problem, the constant term is introduced to the GVM model, and the grey generalized Verhulst model (abbreviated as GGVM) is constructed. Then, the time response sequence and the restore values of the GGVM are solved under different kinds of parameters and the non negative of sequence. By four data sets with single peak feature included the total electricity consumption, line loss rate, per capita water resources and mineral price index in China, it is found that GGVM can effectively solve the drift phenomenon in simulation values of GVM model. In empirical part, the new model is used to analyze the basic reserves of petroleum and natural gas in Jiangsu province. Compared with GVM model and group method of data handling algorithm, the advantages of GGVM in simulation and prediction are verified.