# Parametric Analysis Towards the Design of Micro-Scale Wind Turbines: A Machine Learning Approach
## 3 Results and Discussion
### Rotor Torque  
Finally, the models are trained to predict the rotor torque. This value, together with the rotational speed of the rotor, gives the output power production. If the rotor's tip/speed ratio is fixed at a certain value, then the rotor's rotational speed is linearly correlated with the wind velocity which is considered as a feature in all models. In Table 5, the results of all the ML models used are shown after fitting each model using the 70% training set and predicting the remaining 30% based only on the input features, leaving the actual output to test the model accuracy. Again, the Random Forest Regressor comes out on top of the different models in predicting the rotor torque. With an accuracy of 98.6%, the model can successfully anticipate the value of torque induced on the rotor, which is later used to calculate the rotor power. Decision Trees come in second place with a difference of only 0.3% less accuracy. However, the training time is significantly lower, which means lower computational cost, especially for extremely large datasets. Both models could be used for predicting the rotor torque depending on the desired goal, whether to decrease the computational cost or increase the accuracy of predictions. It is also notable that Neural Networks give a satisfactory accuracy of 67.6%. Further investigations on deep learning algorithms with hyperparameter tuning by changing the number of layers or activation functions could lead to better results. For the linear models, while the accuracy of predictions is around 64.4%, this accuracy is insufficient for power predictions for a wind turbine despite its extremely low training time. It will give misleading results in the preliminary design stages. So, as a compromise between computational cost and accuracy, a Decision Tree Regressor is the optimal solution. Figure 9: Random Forest Regressor results for tangential force: (**a**) the actual vs. predicted values, and (**b**) residuals distribution. In Figure 10, the Random Forest Regression results for the predicted results are plotted against the actual torque and the density distribution of the residuals. Almost all the predicted values lie on the 45\({}^{\circ}\) line, indicating the high accuracy of predictions. The maximum error is not significant compared to the mean value of the  
Figure 10: Random Forest Regressor results for rotor torque: (**a**) the actual vs. predicted values, and (**b**) residuals distribution. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ML Model** & **R2** & **RMSE** & **Max Error** & **MAE** & **Training Time (s)** \\ \hline Random & & & & & \\ Forest & 0.986 & 0.015 & 0.181 & 0.006 & 0.219 \\ Regression & & & & & \\ Decision Tree & & & & & \\ Regression & 0.983 & 0.016 & 0.220 & 0.004 & 0.000 \\ Gradient & & & & & \\ Boosting & 0.823 & 0.052 & 0.346 & 0.032 & 0.031 \\ Regression & & & & & \\ Nonlinear & & & & & \\ Regression & 0.762 & 0.060 & 0.357 & 0.037 & 0.016 \\ Adaptive & & & & & \\ Boosting & 0.721 & 0.065 & 0.261 & 0.051 & 0.125 \\ Regression & & & & & \\ Neural & 0.676 & 0.070 & 0.418 & 0.046 & 0.125 \\ Network & & & & & \\ Linear & 0.644 & 0.073 & 0.393 & 0.050 & 0.000 \\ Regression & & & & & \\ Elastic Net & & & & & \\ Regression & 0.622 & 0.076 & 0.391 & 0.054 & 0.000 \\ Support & & & & & \\ Vector & 0.612 & 0.077 & 0.318 & 0.063 & 0.172 \\ Regression & & & & & \\ Lasso & & & & & \\ Regression & 0.587 & 0.079 & 0.368 & 0.061 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Machine learning models results for the prediction of rotor torque. rotor torque. The residuals also follow a normal distribution, which is a measure of the model quality. As mentioned earlier, further investigations into deep learning models could give higher accuracy and fewer prediction errors. However, it is anticipated that the computational cost will be significantly larger. Overall, the different prediction models could give very satisfactory results.