# Parametric Analysis Towards the Design of Micro-Scale Wind Turbines: A Machine Learning Approach
## 3 Results and Discussion
### Power Coefficient  
The ML models were trained to fit the training set of the data, which represents 70% of the entries. They are then used to predict the output using the remaining 30% of the features, and the predicted output is compared to the actual output. The quality metrics are calculated for each model and tabulated in order of highest accuracy to the lowest accuracy. Table 2 shows the outputs of the different ML models for the prediction of the power coefficient.  
The ensemble methods have generally shown the best performance for predicting the power coefficient. On the top of them is the random forest regressor which has shown an accuracy of 99.9% in predicting the output. The other quality metrics also show the superiority of ensemble models where the RMSE and MAE show very low values as compared to the mean value of \(\mathrm{C_{p}}\) of 0.367.  
The linear models have entirely failed to predict the output. Despite their very low computational cost, represented in the training time, the highest accuracy of linear models is for the linear regression model, at 17.7%. This value is not reliable for the preliminary design stages of a wind turbine. The different errors are also significant compared to the mean value of \(\mathrm{C_{p}}\).  
The results of neural networks are also not satisfactory, so, deep learning is not worth investigating since it is mostly time-consuming, and the preliminary results have shown that the accuracy is not up to expectations.  
To further show the results of \(\mathrm{C_{P}}\) predictions, the model of the highest accuracy (random forest regressor) is used to plot the predicted output with the actual \(\mathrm{C_{P}}\) values. The residual density distribution is also plotted to show the quality of the model. Figure 7 shows the predicted Vs. actual results, and the residuals distribution.  
The figure shows the very good results of the Random Forest Regressor. The predicted value is almost the same as the actual value for most of the entries. There are very few distinct points where there is a big difference, representing the maximum error of 0.01 offsets from the mean \(\mathrm{C_{P}}\) value of 0.367. The residuals also follow a normal distribution, showing the high quality of this model to predict the power coefficient.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ML Model** & \(\mathbf{R^{2}}\) & **RMSE** & **Max Error** & **MAE** &
\begin{tabular}{c} **Training** \\ **Time (s)** \\ \end{tabular} \\ \hline Random & & & & & \\ Forest & 0.9997 & 0.001 & 0.010 & 0.000 & 0.188 \\ Regression & & & & & \\ Decision Tree & 0.9995 & 0.001 & 0.012 & 0.000 & 0.000 \\ Regression & & & & & \\ Gradient & & & & & \\ Boosting & 0.866 & 0.019 & 0.073 & 0.014 & 0.078 \\ Regression & & & & & \\ Adaptive & & & & & \\ Boosting & 0.625 & 0.031 & 0.089 & 0.024 & 0.125 \\ Regression & & & & & \\ Nonlinear & 0.431 & 0.039 & 0.102 & 0.030 & 0.016 \\ Regression & & & & & \\ Ridge & 0.176 & 0.046 & 0.121 & 0.035 & 0.000 \\ Regression & & & & & \\ Vector & 0.157 & 0.047 & 0.102 & 0.036 & 0.000 \\ Regression & & & & & \\ Neural & 0.112 & 0.048 & 0.147 & 0.038 & 0.188 \\ Network & & & & & \\ Elastic Net & & & & & \\ Regression & & & & & \\ Lasso & & & & & \\ Regression & 0.000 & 0.051 & 0.128 & 0.040 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Machine learning models results for the prediction of power coefficient.