More accurate and reliable wind speed forecasting results can provide an effective assessment of wind energy resources and improve the efficiency of wind energy utilization. Therefore, this paper is devoted to constructing accurate wind speed forecasting models and quantitatively analyzing the models by using interpretable analysis. Firstly, a multivariate wind speed forecasting model (PMI-CMOGSA-RELM) is proposed based on machine learning methods and a clustering-based multi-objective gravity search algorithm (CMOGSA). Among them, wavelet packet decomposition (WPD) is used for noise reduction, candidate input feature pool and partial mutual information (PMI) are used for feature selection, and CMOGSA is used to optimize the final combined weights. Secondly, a new evaluation metric, Absolute Error Coverage Probability (AECP), is proposed to better evaluate forecasting accuracy. Then, post-hoc attribution analysis methods and visualization tools are used to analyze the forecasting model interpretability to help us better analyze the robustness and reliability of the forecasted results. Finally, this paper validates and evaluates the proposed model with two data sets of different resolutions. The experimental results not only prove the rationality of the AECP evaluation criteria, but also demonstrate that the proposed model has smaller errors, higher estimation accuracy, and is easier to understand.