To optimize hydrogen refueling stations (HRS), which are reliant on renewable energy sources such as solar and wind, it is imperative to have precise predictions of wind speed and direct normal irradiance (DNI). Nevertheless, conventional forecasting techniques frequently fail to account for the intricacies of renewable energy generation. To address this issue, this study presents a novel hybrid model that integrates Multivariate Empirical Mode Decomposition (MEMD) with Improved Artificial Rabbit Optimization (IARO) and Bidirectional Gated Recurrent Unit (BiGRU) to improve the predictions of wind speed and DNI. The model is compared to conventional forecasting methods and demonstrates substantial improvements, with coefficient of determination (R2) values of 0.991, 0.989, 0.982, and 0.980 for DNI prediction and R2 values of 0.955, 0.941, 0.950, and 0.969 for wind speed prediction across spring, summer, autumn, and winter, respectively. Additionally, this investigation includes an economic assessment of an HRS powered by renewable energy in Zhangjiakou, China. The system has a Levelized Cost of Hydrogen (LCOH) of 6.79 $/kg and a Net Present Cost (NPC) of 904,629 $ over 25 years. These findings underscore the system's cost-effectiveness and competitiveness. The MEMD-IARO-BiGRU model ensures that energy production is by demand by optimizing hydrogen production and enhancing system efficiency by integrating precise energy forecasts. This study illustrates the potential of sophisticated forecasting models to improve the sustainability and dependability of clean energy technologies, decrease operational expenses, and decrease the LCOH. Consequently, it facilitates the transition to HRSs that are powered by renewable energy sources and are more efficient.