Wind speed and power forecasting using Bayesian optimized machine learning models in Gabal Al-Zayt, Egypt

Results and analysis of WSP models

The effectiveness of ML models for WSP and WPP is evaluated over a range of time horizons (10 M, 30 M, 6 H, 24 H, and 36 H). In this study, a comprehensive dataset is initially formulated and divided into two parts: 80% for training and 20% for testing. This division allows for training the models on a substantial portion of the data while still being rigorously tested on an independent dataset to ensure their ge lizability. Bayesian optimization is used for hyperparameter tuning in an iterative and data-driven way based on fivefold cross-validation to further improve the prediction accuracy of ML models. By continually assessing each model’s performance on the testing dataset, this approach not only helps to determine the best set of parameters for each model but also reduces the risk of overfitting. Tables 2 and 3 list the ideal hyperparameters that yield the best results for each ML model. These hyperparameters, which have a substantial impact on the models’ predictive ability, include fit_intercept, kernel, n_estimators, max_depth, and many more. Adjusting these hyperparameters allows for utilizing the entire capability of each model to produce higher performance in wind speed and power predictions at various time intervals.

Table 4 offers a thorough assessment of the effectiveness of several ML models in forecasting VSTWSP (10 M). This evaluation aids in understanding if a model performs well in one metric at the expense of another, which is crucial information for model selection. The MAPE for the MLR model is 46.006%, the MSE is modest at 7.081, the EV is quite low at 0.172, the R is moderate at 0.416, and the CCC is low at 0.304. With a lower MAPE of 36.321%, a lower MSE of 4.318, a noticeably higher EV of 0.498, a higher R of 0.717, and a significantly higher CCC of 0.624, SVM exhibits improved prediction accuracy. However, the ET model has a higher MSE of 8.236 and a comparatively larger MAPE of 52.223%. It reports worse predictive accuracy as evidenced by a lower EV of 0.033, R of 0.395, and CCC of 0.034. With a MAPE of 46.899% and a comparable MSE of 6.450, RF offers performance equivalent to MLR. Besides, it has a modest predictive ability with an EV, R, and CCC of 0.242, 0.574, and 0.295 respectively. With a MAPE of 46.474%, an MSE of 6.982, an EV of 0.179, an R of 0.423, and a CCC of 0.310, DT exhibits outcomes similar to RF. BDT stands out, showing great prediction accuracy with a strikingly low MAPE of 12.741%, a very low MSE of 0.978, a high EV of 0.886, an extraordinarily high CCC of 0.936, and a high R of 0.942. GB has strong predictive performance with a MAPE of 28.380%, MSE of 2.800, EV of 0.671, R of 0.819, and CCC of 0.800. LGBM shows the best predictive ability with the lowest MAPE and MSE values of 12.274% and 0.953 as well as exceptionally high EV of 0.888, R of 0.943, and CCC of 0.939. XGBoost performs quite well in terms of prediction with an EV of 0.867, a MAPE of 14.709%, an MSE of 1.136, an R of 0.931, and a CCC of 0.927. AdaBoost has an EV of 0.480, a MAPE of 34.965%, an MSE of 4.400, an R of 0.699, and a CCC of 0.618, showing a decent but not exceptional level of prediction accuracy. In conclusion, the LGBM, BDT, and XGBoost stand out as good performers, whereas the ET, MLR, and DT models exhibit somewhat lower prediction accuracy.

To facilitate a more comprehensive understanding of the findings, multiple graphs are plotted to showcase different perspectives on the effectiveness of VSTWSP models. These visual representations provide useful information for selecting the best model based on its unique features and performance requirements. A visual illustration of the effectiveness of multiple ML models for the 10-min VSTWSP is provided in Fig. 3.

The beeswarm plot provides a detailed distribution of each model’s performance along the y-axis, visually representing the spread and dispersion of predictive accuracy. Models that closely mimic the actual data distribution indicate stronger performance, while greater deviations suggest lower accuracy. The scatter matrix, on the other hand, enables a deeper examination of the relationships and trade-offs among the developed models. By analyzing agreement levels and potential biases, this visualization offers valuable insights into model correlations. Additionally, the diagonal boxplots in the scatter matrix help identify variations in central tendencies and outliers, offering a more nuanced perspective on model performance.

The analysis of Fig. 3 reveals that LGBM, BDT, and XGBoost continually stand out as the top performers, as evidenced by the same clusters in the beeswarm plot and noteworthy correlation patterns in the scatter matrix. In contrast, the beeswarm plot’s deviation from the actual model and the scatter matrix’s poorer correlations show that the ET and DT models have considerably lower predictive accuracy.

Online Appendix B presents the line plot, scatter plot with error histogram, residual plot, and quantile–quantile (Q–Q) plot of Bayesian optimized models. The line plot depicts the agreement level between actual and predicted outputs. Predicted vs actual values are also displayed as a scatter plot with an error histogram, which illustrates the distribution of prediction errors. This plot aids in evaluating the correlation between predicted and actual results as well as the dispersion of forecast errors. The difference between the actual and predicted values, or residuals, is shown against a reference line in the residual plot. This plot supports the evaluation of the linearity and homoscedasticity (constant variance) of errors. The quantiles of the actual and anticipated value distributions are compared using a Q–Q plot, which is employed to evaluate the residuals’ normality.

It is clear from examining these plots that actual values and the predictions of the LGBM model are closely aligned. Additionally, the points in this model are more closely centered around the diagonal line, suggesting few outliers and accurate predictions. More concentrated error distributions are observable around zero in the error histogram, but there is a rightward-pointing error tail. The residuals are closely dispersed around the reference line in the residual plot, while the reference line and the points in the Q–Q plot are in alignment. In many statistical methods, it is suggested that the residuals conform to a normal distribution, and a robust alignment in the Q–Q plot suggests that they adhere to this characteristic. Overall, the figures show that the LGBM model is a good predictor of the VSTWSP outcomes. The remaining models can be interpreted similarly.

By investigating scatter plots and residual plots, BDT and XGBoost provide closely clustered points and homoscedastic residuals, which demonstrate accurate forecasts and reliable performance. In the Q–Q plot, these models show high alignment with the reference line, indicating that the residuals of these models have a normal distribution. Furthermore, there is a quite good alignment between actual and forecasted values for GB, AdaBoost, and SVM. Their residuals have wider distributions but are generally homoscedastic and normal. In contrast, more dispersion from actual values is shown in ET, RF, DT, and MLR, indicating worse forecast accuracy. These models exhibit non-normal residual distributions and heteroscedastic residuals with variable error spreads, suggesting less consistent performance and possible problems with certain data points.

Table 5 depicts the ML results based on several prediction horizons (30 min, 6 h, 24 h, and 36 h) ahead of WSP. These outcomes demonstrate the models’ performance in terms of MAPE, MSE, EV, R, and CCC. For the 30-min prediction horizon, XGBoost has substantially reduced MAPE and MSE, enhancing its predictive accuracy in comparison to other models. Its EV value is much higher at a value of 0.988, indicating that it accounts for a greater share of the variance in the data. Additionally, CCC and R values of 0.994 show a high level of agreement and a strong linear relationship with the actual data. On the other hand, ET, RF, and DT models have larger MAPE and MSE, suggesting less accurate predictions, with their errors almost surpassing other models. Significantly outperforming these models are the BDT and LGBM models, with MAPE improvements varying from 85 to 91%. These models consistently show higher values for EV, R, and CCC, highlighting their propensity to capture a bigger proportion of the variation in the data, preserve robust linear relationships, and demonstrate a better degree of agreement with the actual data.

Similar trends continue when the forecast horizon is increased to six hours. In comparison to the other models, BDT performs better with reduced MAPE and MSE and improved EV, R, and CCC metrics, demonstrating their reliable prediction accuracy. However, ET, MLR, and DT models continue to be less accurate, with their MAPE and MSE errors being around 12–13 and 29–52 times higher than those of the BDT model. Additionally, the EV, R, and CCC values of these models remain lower, suggesting less accuracy in identifying data patterns. Notably, XGBoost (MAPE = 4.581%, MSE = 0.222, EV = 0.964, R = 0.982, and CCC = 0.981) and RF (MAPE = 9.878%, MSE = 0.687, EV = 0.887, R = 0.946, and CCC = 0.935) models outperform the above-mentioned models. They consistently outperform these models in terms of prediction accuracy, which is supported by their satisfactory performance metrics.

The patterns in model performance persist for the 24-h and 36-h forecast horizons. In comparison to the other models, XGBoost continues to perform better with MAPE = 2.663%, MSE = 0.044, EV = 0.994, R = 0.997, and CCC = 0.997 for 24-h and MAPE = 4.943%, MSE = 0.137, EV = 0.985, R = 0.992, and CCC = 0.992 for 36-h ahead prediction of wind speed. These evaluation metrics demonstrate the robust outperformance of this model in identifying data patterns. On the other side, ET and MLR models are associated with higher values of MAPE and MSE and lower values of EV, R, and CCC metrics. At the same time, BDT and LGBM models keep improving significantly in comparison to ET and MLR models, with MAPE and MSE reduction ranging from 83 to 90% and 97 to 99%, respectively. These findings highlight the large improvements of XGBoost and BDT models in prediction accuracy across all time frames.

For visual representations of the developed models, the beeswarm graphic and the scatter matrix are plotted in Figs. 4 and 5 to examine the clustering and alignment of points along the diagonal. These charts show how each model performs and how its relationships change for various prediction horizons. Figure 4 illustrates the beeswarm plot for 30 min, 6 h, 24 h, and 36 h ahead of WSP. The distribution of model predictions for the 30-min prediction horizon is shown in the first plot. It demonstrates that XGBoost performs better than other models by displaying how closely its predictions cluster with the actual values. The performance of the developed models is displayed in the second plot when the forecast horizon is extended to six hours. It visually illustrates how BDT has enhanced performance by making more accurate forecasts. A visual comparison of model performance across long prediction horizons is provided by the third and fourth plots. As seen by the near forecasts to the actual values, XGBoost is still the better option for these timeframes.

Scatter matrices are useful for evaluating the relationships between multiple variables. For the 30-min prediction horizon, this plot can be used to support the XGBoost’s strong linear relationship (R = 0.994) with the actual data. It is therefore expected to see tight clusters along the diagonal line of scatter plots for XGBoost, indicating strong correlations with the actual data. Similar to the previous scatter matrix, the second matrix can help visualize the relationships between predictions and actual values when the prediction horizon is extended to 6 h. It is aligned with the assertion that the BDT model outperforms others, as evidenced by a strong linear relationship for this model. Finally, the last two scatter matrices reveal strong linear relationships or high R values of 0.997 and 0.992 for predicting 24 h and 36 h ahead using the XGBoost model.

Results and analysis of WPP models

A comprehensive overview of the findings from multiple ML models for VSTWPP (10 M) can be seen in Table 6. Notably, compared to MLR and SVM, the ET, RF, DT, BDT, GB, LGBM, and XGBoost models show reduced MAPE and MSE, suggesting greater prediction accuracy. These models exhibit high CCC with the actual data, preserve robust linear connections (R), and capture a sizeable percentage of the data variation. On the other hand, MLR and SVM models have larger MAPE (8135.878% and 6365.662%) and MSE (1579536.189 and 220440.296), suggesting less accurate predictions. MLR has a good degree of EV and R, but its CCC is relatively low (i.e., 0.262), indicating poor accuracy in identifying data patterns. With lower EV and R values than MLR, SVM still exhibits considerable prediction accuracy while decreasing MAPE and MSE.

Online Appendix C provides the ML outcomes for WPP. The outcomes produced by different ML models when applied to VSTWPP (10 M) are visually represented by the beeswarm plot and scatter matrix in Fig. C1. These visual representations offer a comprehensive overview of the results produced by the developed models, supporting the performance evaluation metrics highlighted in the textual analysis (Table 6). Notably, output patterns for the LGBM, BDT, GB, and XGBoost models can be seen in the beeswarm plot, supporting the finding that these models have higher predictive accuracy. Furthermore, the scatter matrix illustrates that the points are closely clustered around the diagonal line, indicating the alignment of predictions with the actual values and low error values. Besides, the boxplots for these models are compact, suggesting a narrow spread of the residuals and affirming accurate predictions. In summary, the scatter plot with diagonal boxplot provides insights into the correlations between various outputs, reinforcing the idea that these models not only achieve reduced error metrics but also exhibit strong linear relationships (R) and a high degree of agreement (CCC) with the actual data.

The effectiveness of several WPP models is shown in Table 7 for prediction horizons of 30 min, 6 h, 24 h, and 36 h. This table offers insightful information about the models’ propensity for predicting wind power generation at various time periods. At the 30-min prediction horizon, BDT, LGBM, and XGBoost have the highest predictive accuracy followed by AdaBoost, whereas SVM, DT, ET, and MLR have lower predictive accuracy.

At the 6-h prediction horizon, BDT yields a remarkably low MAPE of 0.277%, a low MSE of 17.439, and an outstanding EV, R, and CCC of 1.000, demonstrating its exceptional predictive accuracy. With minimal error metrics and outstanding performance metrics (EV, R, and CCC = 0.999), LGBM and XGBoost models also perform well. However, ET and MLR models yield fewer accurate forecasts as they are associated with lower EV, R, and CCC values and greater MAPE and MSE values.

At the 24-h prediction horizon, LGBM has remarkable predictive accuracy, with a minimal MAPE and MSE of 1.342% and 323.531. It reaches perfect values for EV, R, and CCC, demonstrating an excellent capacity to capture data variance, maintain stable linear relationships, and attain total agreement with the actual data. GB, XGBoost, and AdaBoost also perform well with near-perfect performance metrics (EV, R, and CCC at 0.999), demonstrating their effectiveness in wind power forecasting. However, it is difficult for ET, RF, and MLR to retain strong linear correlations, agreement with the real data, and capture a large percentage of the variation in the data.

The BDT stands out as a top performer at the 36-h prediction horizon, attaining the lowest MAPE (0.888%), lowest MSE (1.529), and perfect EV, R, and CCC (1.000). The LGBM, XGBoost, and GB models work well while exhibiting minimal error metrics and remarkable performance metrics (EV, R, and CCC at 1.000). On the other hand, SVM and MLR exhibit poor accurate predictions with larger MAPE and MSE values. Their lower EV, R, and CCC values further illustrate the difficulties in identifying data patterns and maintaining robust linear correlations and agreement with the actual data.

The beeswarm graphic and the scatter matrix are presented in Figs. C2–C3 to visually illustrate the developed models over a range of prediction horizons. The beeswarm plot for 30 min, 6 h, 24 h, and 36 h ahead of WPP is shown in Fig. C2. The first graphic displays the distribution of model predictions for the 30-min prediction horizon. It illustrates how well BDT’s predictions resemble the actual values, proving its outperformance to other models. When the prediction horizon is extended to six hours, the performance of the assessed models is shown in the second plot. This plot graphically displays how BDT has improved performance by producing more precise forecasts. A visual comparison of model performance across long prediction horizons is provided by the third and fourth plots. As seen by the close forecasts to the actual values, LGBM and BDT yield the best outcomes for these timeframes.

Scatter matrices (Fig. C3) are useful for evaluating the relationships between multiple variables. For the 30-min prediction horizon, this plot can be used to support the BDT’s strong linear relationship (R = 1.000) with the actual data. It is therefore expected to see tight clusters along the diagonal line of scatter plots for BDT, indicating strong correlations with the actual data. Similar to the previous scatter matrix, the second matrix can help visualize the relationships between predictions and actual values when the prediction horizon is extended to 6 h. It is aligned with the assertion that the BDT model outperforms others, as evidenced by a strong linear relationship for this model. Finally, the last two scatter matrices reveal strong linear relationships or high R values of 1.000 for predicting 24 h and 36 h ahead using the LGBM and BDT models.

Computational memory usage of ML models

The memory usage for WSP using ML models across various prediction horizons is shown in Fig. 6a. It is essential to comprehend these memory needs when selecting a suitable model for WSP. This evaluation signifies the trade-offs between memory usage and prediction accuracy, enabling more informed model selection. Notably, MLR uses memory most effectively, using just 361.629 MB for the 10-min prediction horizon. The memory usage of the GB and XGBoost is significantly greater at 489.715 MB and 493.805 MB, respectively. As the forecast horizon gets longer, there exist variations with respect to the memory usage trends. While some models, like MLR, maintain a comparatively consistent memory usage, certain other models including BDT exhibit variances in memory usage.

Memory usage for estimating wind power using several ML models and across prediction horizons is shown in Fig. 6b. MLR and BDT models exhibit more efficient memory usage at the 10-min prediction horizon; MLR uses around 359.055 MB while BDT uses about 362.543 MB. As the prediction horizon is extended to 30 min, memory use for SVM and ET marginally increases with SVM consuming 398.379 MB and ET using 405.930 MB. In the meanwhile, MLR exhibits consistent trends of memory usage and keeps memory consumption fairly constant. GB demonstrates a significant reduction in memory usage (i.e., 364.586 MB) for the 6-h projection horizon. On the other hand, DT exhibits an increase in memory usage to 417.766 MB. XGBoost and AdaBoost show greater memory consumption than the other models with memory usage values of 440.125 MB and 475.840 MB at the 24-h and 36-h prediction horizons, respectively.

Computational time comparison of ML models

The execution time for predicting wind speed using different ML models is shown in Fig. 7a. It is crucial to comprehend these variances in execution timeframes when choosing the best ML model and setting up the system for wind speed forecasting tasks. This evaluation allows for choosing a model by highlighting the trade-offs between prediction speed and model accuracy. AdaBoost is the quickest model for the 10-min prediction horizon, completing predictions in just 0.781 s, which makes it stand out with incredibly short execution times. However, SVM exhibits a very long execution time when the prediction horizon increases, particularly at 30 min and 6 h, where it takes 73.439 and 67.98 s, respectively, to complete predictions. Moreover, LGBM is one of the fastest for the 6-h timeframe, finishing predictions in 19.234 s. BDT takes the longest time to finish predictions for the 24-h and 36-h prediction horizons, with execution durations ranging from 202.840 to 246.652 s. Nevertheless, despite a modest increase in execution time, AdaBoost continues to be the quickest model for all prediction horizons.

The execution time for predicting wind power using different ML models across different prediction horizons is shown in Fig. 7b. AdaBoost comes out as the quickest model at the 10-min prediction horizon, with an execution time of just 1.016 s. On the other hand, SVM has one of the slowest execution times (i.e., 93.363 s) for this timeframe. SVM continues to have noticeably long execution times, requiring 96.973 s to finish predictions when the prediction horizon is extended to 30 min. On the other hand, AdaBoost continues to run the quickest model, showcasing the advantages of its effectiveness even when the prediction horizon grows. Execution speeds differ amongst models for the 6-h prediction horizon, with LGBM being one of the quickest, finishing predictions in 25.898 s. On the other hand, BDT and ET have longer execution times, being slow for this timeframe. BDT and RF take the longest to finish predictions at the 24-h and 36-h prediction horizons, with execution durations ranging from 171.825 to 258.135 s. Contrarily, despite a modest increase in execution time, AdaBoost continues to be the quickest model.

Comparison and discussion

The 10 created models are evaluated using MAPE, MSE, EV, R, and CCC, as shown in Tables 8 and 9. Evaluating the constructed ML models’ efficacy, advantages, and disadvantages is the aim. Table 8 summarizes the efficacy of the established machine learning models for WSP at different time scales. While the ET, RF, and MLR models produce the most erroneous forecasts across all time scales, the XGBoost and BDT models perform exceptionally well for various periods.

Table 9 summarizes how the established ML models performed for predicting wind power at various time frames. BDT, LGBM, and XGBoost models have excellent performance for different time scales, whereas the RF and AdaBoost models have exhibited good performance. Nevertheless, these models’ applicability is contingent upon the particular period of the wind power prediction task. Meanwhile, AdaBoost and RF perform well and consistently as well, making them valuable alternatives for various predicting horizons. It is therefore crucial to select the model that best fits the unique prediction requirements for the specified time scale.

Table 10 summarizes the developed ten ML algorithms. The strengths, weaknesses, interpretability, missing values handling, accuracy, and complexity of each algorithm are mentioned. For example, XGBoost and LGBM performed exceptionally well due to their ability to handle large datasets with complex patterns efficiently. These models leverage gradient boosting, which sequentially corrects prediction errors by optimizing weak learners, thereby improving accuracy. Additionally, their capability to manage missing data, feature interactions, and non-linearity contributed to their robust performance. BDT exhibited superior results, particularly for short-term and long-term predictions. This is likely due to its strong regularization techniques that prevent overfitting while maintaining high interpretability. RF and AdaBoost, although not as optimal as XGBoost and LGBM, performed consistently well across different time scales. These models are effective in reducing variance by aggregating multiple decision trees; however, their performance was slightly limited in cases with high data variability. ET and DT exhibited lower performance due to their tendency to overfit, particularly in long-term forecasts, where generalization becomes crucial. SVM and MLR, while interpretable, showed limitations in handling non-linearity and complex interactions between meteorological variables, leading to reduced accuracy compared to ensemble-based models.

Feature importance analysis

A feature importance analysis is conducted to determine how each feature (i.e., input factor) affects the model’s output (i.e., WSP and WPP). This analysis examines the effect of eliminating each factor on the predicted output to investigate its relative importance. The LGBM model-based feature significance analysis is shown in Fig. 8. According to the plot, on a 10-min time frame, air pressure has the biggest effect on VSTWSP, followed by humidity. The importance scores for humidity, temperature, and hour are nearly equal. Conversely, the height predictor has little effect on VSTWSP. The wind speed predictor has the biggest effect when taking VSTWPP into account, and this outcome upholds the high correlation between wind power and speed. Furthermore, the WPP is moderately impacted by other factors. The influence of height and month predictors on power generation is rather small.

Similarly, the feature importance analysis is conducted for WSP and WPP using the optimal model at different time scales (30 M, 6 H, 24 H, and 36 H) as shown in Figs. 9 and 10. The analysis in Fig. 9 indicates that the wind-vane, air pressure, and month have the highest impact on predicting wind speed 30 min ahead. Contrarily, height and temperature predictors have a relatively low impact. Pressure, temperature, and humidity are the main predictors, according to an analysis of their effects six hours before WSP. In the meanwhile, the main determinants of 24-h WSP are month, humidity, and windvane. According to the final graphic, the primary predictor for the 36 h before WSP is air pressure. Furthermore, while height has a negligible effect, temperature, month, and humidity all have a big influence. The feature importance analysis reveals that the wind speed predictor has the most influence on various scales ahead, as illustrated in Fig. 10.

Key findings and contributions

1. 1.

   To compare the outcomes and choose the best algorithms for WSP and WPP, a variety of evaluation methods are used. The best models for WSP and WPP at all time scales are shown in Fig. 11.

2. 2.

   The study assesses how well ten machine learning models predict wind power and speed over a range of time periods. The most accurate ones are LGBM, XGBOOST, and BDT.

3. 3.

   Depending on the time scale, ensemble learning models and tree-based models perform better than individual machine learning algorithms. As a result, ensemble learning algorithms may become popular in prediction applications in the future.

4. 4.

   A new case study is addressed in Gabal El-Zayt wind farm (200 MW), Red Sea governorate, Egypt. The biggest publicly available dataset on wind speed and power over various time ranges is presented in this paper.

5. 5.

   Feature importance analysis is conducted to evaluate the impact of the ML model’s predictors.

Therefore, this paper uniquely contributes to wind energy forecasting by addressing critical gaps in existing research, particularly the need for optimized ML models that balance accuracy and computational efficiency across multiple time horizons. While previous studies have explored ML models for WSP and WPP, they often overlook the comparative performance of tree-based ensemble methods such as LGBM, XGBoost, and BDT, especially when optimized using Bayesian techniques. By systematically evaluating ten ML models and leveraging Bayesian optimization to fine-tune hyperparameters, this research enhances both precision and computational efficiency. Additionally, the study introduces a large, publicly available dataset from the Gabal El-Zayt wind farm, providing valuable insights into wind energy forecasting in a real-world setting. The inclusion of feature importance analysis further strengthens the findings by identifying key predictors influencing wind behavior. Through these contributions, this research advances the field by developing a robust, integrated forecasting system that improves wind farm operations, supports grid stability, and demonstrates the growing importance of ensemble learning models for renewable energy applications.