基于驱动因素控制的线性时变参数DLDGM(1,N)模型

Construction of Linear Time-varying Parameters DLDGM(1,N) Model Based on Driving Factors Control

针对传统GM(1,N)模型未考虑参数随时间变化的动态特征及未明确驱动因素作用机制的问题,首先引入线性时变参数以及驱动因素控制函数,构建基于驱动因素控制的线性时变参数DLDGM(1,N)模型,论证DGM(1,1)、NDGM(1,1)、TDGM(1,1)、DGM(1,N)、DCDGM(1,N)模型均是该模型在不同参数取值下的特殊形式;然后基于白化信息充分和匮乏的两种情况,给出驱动因素控制参数的识别方法;最后应用所提模型对河南省粮食产量进行预测,验证模型的有效性和实用性。

Aiming at the problem that the dynamic change characteristics of parameters with time is not considered, and the mechanism of driving factors is not clarified in the traditional GM(1,N) model, a linear time-varying parameters discrete GM(1,N) model based on driving factors control is constructed by introducing linear time-varying parameters and driving factor control function, which is abbreviated as DLDGM(1,N) model. The new model has more reasonable modeling process, more stable structure, and the traditional multi-variable model’s defects are eliminated in it. To identify the mechanism of driving factor control parameters, calculation methods based on the two situations of sufficient and lack of whitening information are given. In addition, it is proved that DLDGM(1,N) model is entirely compatible with the single variable grey prediction model GM(1,1), DGM(1,1), NDGM(1,1) and TDGM(1,1), and the multi-variable grey prediction model DGM(1,N) and DCDGM(1,N) by adjusting the parameter values,. Finally, to verify the practicality and effectiveness of DLDGM(1,N) model, the model is used to simulate and predict the grain yield in Henan Province and the sample data is obtained by Henan Statistical Yearbook. The mean relative simulation and prediction percentage errors of DLDGM(1,N) model are 0.49% and 1.23%, in comparison with those of DGM(1,N) model and traditional GM(1,N) model, which are 1.00%, 3.12% and 4.68%, 5.25% respectively. The results show that DLDGM(1,N) model has the best performance in simulation and prediction, which on one hand testifies the effectiveness of improving model’s structure, and on the other hand proves that the model has good practicability in the system with time-varying parameters and complex driving factors mechanism.