Abstract: The nonlinear grey Bernoulli model is a powerful grey forecasting model for analyzing nonlinear small sample sequences, which receives a considerable amount of interest in recent years. However, the inconsistency between its grey basic form used for linear parameters estimation and its grey differential equation used for time response function may cause large errors in some real applications. Thus this paper designs a nonlinear discrete grey Bernoulli model with time power term, abbreviated as NDGBM(1,1, ta), to improve the model accuracy. The expressions of the time response function and the linear system parameters are derived with the linearized form of the NGBM(1,1, ta) model. The structural parameters of the new discrete model are searched by the whale optimization algorithm. Further, according to historical data of gross regional product of Shifang city and Mianzhu city in Sichuan province, different type of continuous and discrete grey forecasting models are built, and the future values of selected cities are calculated.

Key words: Nonlinear discrete grey Bernoulli model, Linearized form, Consistency, Whale optimization algorithm, Gross regional product