The stability of the power grid and the operational security of the power system depend on the precise prediction of wind speed. In consideration of the nonlinear and non-stationary characteristics of wind speed in different seasons, this paper employs the weight of wind resource index calculated by triangular fuzzy analytic hierarchy process (TF-AHP), criteria importance through inter-criteria correlation (CRITIC), and entropy weight method (EWM) to improve gray correlation analysis (GRA) and obtain the gray correlation degree of each season. In addition, a wind speed prediction model is provided that includes single-layer and two-layer weighting and is based on both deep and shallow machine learning models. At first, we establish each quarter's wind resource characteristics at typical monthly intervals of 10min, 30min, 60min, and 120min. The GRA's TF-AHP-CRITIC-EWM, enhanced with subjective and objective weights, is used to assess the available wind resources in each season and to compute the forecasted combination of wind speed for each season. As the final prediction results, the prediction values of each layer model are evaluated independently. For the intervals with considerable errors, we apply wavelet denoising and replacement combination. The simulation findings show that the proposed combined model surpasses earlier benchmark models in terms of goodness of fit, prediction accuracy, and generalizability.