Aiming at the shortcoming that the classical FGM(1,1) model regards the gray action quantity as a fixed constant, the DGM(1,1) model is used to dynamically simulate and predict the gray action quantity, so that the gray action quantity can change dynamically with time. On this basis, a new FGM(1,1,b) model with dynamic gray quantity change with time is proposed, and the total primary energy consumption in the Middle East is taken as a numerical example for simulation prediction. The results

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... that the prediction accuracy of the dynamic FGM(1,1,b) model proposed in this paper is higher than that of the classical FGM(1,1) model, and the practicability and effectiveness of the FGM(1,1,b) model are verified. At the same time, it also provides relevant theoretical basis for the study of world energy development.