The Non-equidistance GM(1,1) Model Improvement And Application

The grey system theory is an uncertain system in which the research objects are "poor information", "small sample", it has a great advantage on the research of small amount of information and uncertainty problems. The GM model is the core content of grey system and many scholars have done a lot of researches about it,the equidistance GM (1,1) model of GM model is modeling based on equidistance sequence distance, the requirements of data sequence are more stringent,so the more widely applied non-equidistance GM (1,1)model has more advantage in the practical problem. Therefore, it is necessary to improve the simulation and forecast accuracy of the non-equidistance GM (1,1) model.This paper used the accumulation method to identify the parameters of non-equidistance GM (1,1) model, and then to improve the initial condition and background values which have a great influence of the non-equidistance model. Using the minimum error variance criterion to determine the augmented variables when improving the initial condition, meanwhile put forward and proved the effective interval of initial values optimization; Secondly, in order to make the background values have more effectiveness when they vary with the fluctuation of original sequences, add variables in the background value. Finally, the simulation example 1 proved that improving the background value, the simulation and prediction accuracy of the new information accumulation non-equidistance GM (1,1) model had been improved, proved that after improving the initial conditions and background values,the simulation and prediction accuracy of the new information accumulated non-equidistance GM (1,1) model had been improved further, the correctness of the effective range which proposed in this paper of the initial value optimization.Simulation examples 2 proved that double improved model proposed in this paper had universality, further proved the accuracy and efficiency.