A novel structural adaptive Caputo fractional order derivative multivariate grey model and its application in China's energy production and consumption prediction

With the deepening of economic globalization and the intensification of global warming, all countries are faced with the challenges of low-carbon transition and continuous growth of energy demand. Therefore, precise forecasting of future energy development patterns is critical for our government to optimize its energy structure. Based on this, by introducing Caputo fractional order derivative, power exponential term, linear correction term, and stochastic perturbation term, a novel structural adaptive nonlinear multivariate grey prediction model constructed using Caputo fractional order derivatives is presented. To increase the adaptability of the model, the Grey Wolf Optimization (GWO) technique is used to optimize the model's adaptive parameters. To evaluate the model's validity, seven current grey prediction models are compared to the CFNGMC(p, n) model using three real-world examples of electricity production, energy processing and conversion efficiency, and energy consumption per capita. Experimental findings suggest that the CFNGMC(p, n) is highly predictive and adaptable. Furthermore, Monte Carlo simulation and probability density analysis are used to evaluate the robustness of the CFNGMC(p, n), further confirming its superiority. It demonstrates that the proposed model is an effective way to anticipate energy data in China.