A Novel Nonlinear Different Fractional Discrete Grey Multivariate Model and Its Application in Energy Consumption

With global energy demand escalating and climate change posing unprecedented challenges, accurate forecasting of regional energy consumption has emerged as a cornerstone for national energy planning and sustainable development strategies. This study develops a novel nonlinear different fractional discrete grey multivariate model (NDFDGM(ri,N)). This model improves the shortcomings of the conventional GM(1,N) in handling nonlinear relationships and variable differences by introducing different fractional order accumulation and nonlinear logarithmic conditioning terms. In addition, the Firefly Algorithm (FA) was utilized to optimize the model’s hyperparameters, significantly enhancing the prediction accuracy. Through empirical analysis of energy consumption data in China’s eastern, central and western regions and across the country, it has been confirmed that the NDFDGM model outperforms others during both the simulation and forecasting phases, and its predicted MAPE values are, respectively, 1.4585%, 1.4496%, 2.0673% and significantly lower than that of compared models. The findings indicate that this model can effectively capture the complex characteristics of energy consumption, and its prediction results offer a solid scientific foundation for guiding energy strategies and shaping policy decisions. Finally, this paper conducts extrapolation and predictive analysis using the NDFDGM(ri,N) to explore the development trends of energy consumption in the whole country in the coming three years and puts forward energy policy suggestions for different regions to promote the optimization and sustainable development of the energy structure.