A Novel Optimized Grey Model with Quadratic Polynomials Term and its Application

A grey forecasting model NGM(1,1,k2) with quadratic polynomials bt2+ct+d as grey action time is proposed based on the theory of grey system modeling in this paper. It is found that GM(1,1) model, NGM(1,1,k) model, SAIGM model, GM(1,1,k2) model are the special forms of NGM(1,1,k2) with different parameters. Moreover, the characteristics of NGM(1,1,k2) and its effect on the modeling precision are evaluated under the contractive transformation. We further analyze the error of NGM(1,1,k2) model and propose a new model called BNGM(1,1,k2) model, which is obtained by optimizing the background value based on Simpson formula, so as to improve the prediction precision of the model. Three numerical cases show that BNGM(1,1,k2) is significantly superior to the other grey models. Finally, three examples indicate that the practicability of the BNGM(1,1,k2) model is very good.