A novel structure adaptive fractional derivative grey model and its application in energy consumption prediction

The importance of energy in modern life is self-evident. Forecasting future energy consumption can help governments and businesses formulate reasonable energy supply and demand policies to ensure energy security and economic development. To this end, a novel adaptive fractional grey model with fractional derivative was established. Firstly, a novel fractional cumulative operator is proposed that operates in a fractional-order domain and has the potential to alternate between giving priority to new or old information. This method facilitates the effective utilization of data when working with a limited number of samples. Secondly, the model's adaptability and flexibility were improved through the introduction of a nonlinear term in the whitening equation; and the fractional derivative was introduced into the whitening equation to solve the problem of poor adaptability of existing integer-order derivative to nonlinearity and volatility. To enhance the model’s performance, the study utilized the Grey Wolf Optimization (GWO) algorithm to optimize the model parameters. Furthermore, the robustness of the proposed model was verified using Monte Carlo simulations and probability density analysis; and the experimental results indicated that the proposed model exhibits better robustness. Finally, three actual cases of China’s total energy consumption, total crude oil consumption and domestic heat consumption are predicted.