A novel structural adaptive discrete grey Euler model and its application in clean energy production and consumption

With the increasing energy demand, accurate forecasting of energy production and consumption has become critically important for strategic planning in energy systems. To address the limitations of traditional forecasting models in adapting to the sparsity, nonlinearity, and volatility characteristics of clean energy data, this study proposes a structurally adaptive grey Euler model SDHGEM(1,1) based on the Hausdorff fractional-order cumulative generation operator. By incorporating nonlinear dynamic structural terms and periodic fluctuation components into the grey Euler model framework, and synchronously optimizing model parameters through a differential evolution algorithm, the model demonstrates dynamic adaptability to complex energy system features. Theoretical derivations establish parameter perturbation boundary conditions, while a robustness verification framework is constructed through Monte Carlo simulations combined with probability density analysis. Empirical studies employing three typical energy datasets - hydropower generation, nuclear power production, and natural gas consumption - reveal through comparative experiments that the SDHGEM(1,1) model outperforms eight benchmark models, achieving mean absolute percentage errors (MAPE) of 1.3929 %, 4.8783 %, and 1.91966 % respectively. These results demonstrate the model's enhanced predictive capability and adaptability, establishing it as an effective solution for forecasting energy data.