A two-stage deep learning-based hybrid model for daily energy consumption forecasting with variational mode decomposition and wavelet thresholding denoising

Global energy demand keeps rising amid economic expansion and population growth. Although renewables like wind and solar have grown fast, fossil fuels (especially petroleum) remain central to the global energy mix, underpinning industry, households, policy, and stability. This article presents an improved hybrid forecasting framework, denoted as the VMD-WTD-GRU model with mode-specific denoising, for daily average petroleum consumption, which adopts a two-stage decomposition-targeted denoising strategy. The framework combines the models of variational mode decomposition, wavelet threshold denoising, and the gated recurrent unit networks for petroleum energy forecasting, where different models are designed for time-series data decomposition, noise elimination, sub-series forecasting, and integration, respectively. In general, the proposed hybrid model has achieved excellent predictive performance on multiple evaluation indicators when compared with several candidate models, especially demonstrating that the mode-specific denoising strategy can effectively reduce noise interference while preserving useful trend information in low-frequency components. Such a framework can be easily implemented to forecast petroleum consumption in real application scenarios.