A novel fractional nonlinear discrete grey model with kernel-markov adaptation for clean energy forecasting

In response to the escalating global environmental pollution crisis and the growing demand for clean energy, accurate prediction and assessment of clean energy production and consumption have become crucial for strategic energy development. This study presents an innovative data-driven adaptive fractional nonlinear discrete grey prediction model, which incorporates the kernel method from support vector machines and integrates enhanced concepts from Markov chains. The proposed model achieves dual advancements: it addresses nonlinear factors at the structural level while effectively capturing temporal dependencies in historical data patterns. Furthermore, we introduce a fractional-order integration generator that extends the grey sequence operator's order to the real domain, thereby significantly enhancing the model's applicability and flexibility. To optimize model parameters, we conducted a comprehensive comparison of optimization algorithms, ultimately implementing the Grey Wolf Optimizer (GWO). The model's performance was rigorously evaluated through comparative analysis with existing high-performing models, employing three case studies: quarterly net photovoltaic electricity generation in U.S. small-scale solar energy systems, quarterly natural gas consumption in the U.S. residential sector, and other renewable energy generation in the United States. Additionally, we employed Monte-Carlo simulation and probability density analysis to assess the model's robustness. The results demonstrate superior stability and predictive accuracy compared to existing models, with the adaptive structure of our proposed model proving particularly effective in generating reliable forecasts. Based on these predictive outcomes, we provide strategic recommendations to decision-makers regarding clean energy production and consumption development.