Abstract: According to the non-equidistance of observation data and the deficiency of NGM$(1,1,k)$ model, a modeling approach for the grey action quantity with non-equidistant NGM$(1,1,k)$ model is established in this paper. A new model's background value optimization method is proposed based on the principle of numerical integration by using non-equidistance Simpson numerical integration formula. Then the desirability function is construsted by the minimizing the square sum of relative error between the raw sequence and the simulative sequence, which is used to determine the optimal constant value in the time response function. Moreover, a complete improved algorithm for non-equidistance NGM$(1,1,k)$ model is proposed. Finally, the efficiency and applicability of the proposed optimization model are demonstrated by two examples. The results show that the optimal model is able to significantly improve the simulation and prediction accuracy.

Key words: non-equidistant sequence, NGM$(1,1,k)$ model, background value, the time res-ponse function