## 2 Methodology
### Exploratory Data Analysis  
The three datasets were analyzed collectively to observe the relationships among the features and the outputs. The original datasets contained 192,001 entries for each turbulence class. The pitch control was only activated when the generator speed exceeded the rated value of 12.1 rpm. Other than that, the blade pitch angle was set to zero. To examine the pitch angle as a key feature in the ML models, the values of zero pitch angle were eliminated from the datasets, resulting in a reduction in the entries of all datasets to 107,918, 110,186, and 113,712 entries for turbulence classes A, B, and C, respectively. After reducing the datasets, they were all concatenated into one large dataset with 331,816 entries for data analysis. The correlation between features and outputs was calculated using the Pearson correlation method to check for a linear relationship among them. The formula used to calculate the Pearson correlation is shown in Equation (2) [29]. Figure 3 shows the Pearson correlation between the features and the outputs  
\[r=\frac{n\sum xy-\sum x\sum y}{\sqrt{\left[n\sum x^{2}-\left(\sum x\right)^{2 }\right]\left[n\sum y^{2}-\left(\sum y\right)^{2}\right]}} \tag{2}\]  
where \(r\) is the correlation coefficient and \(x\) and \(y\) are the independent and dependent variables, respectively. This formula estimates the correlation between each pair of variables, whether between the input features to check for multicollinearity or between the input features and the desired outputs to check for linear relationships. A key observation from the figure is that the flapwise outputs depend inversely on the downwind velocity and the blade pitch angle. As the downwind velocity increases, the rotational speed of the rotor increases, resulting in a centrifugal force that reduces the blade deflections and forces in the flapwise direction. Blade pitch angle also reduces the force component normal to the rotor plane on the blade after it has been rotated, reducing the flapwise outputs. In the edgewise direction, the blade azimuth angle plays a significant role in the output value, which is expected since it affects the direction of gravitational loads to be in favor of or against the deflections and shear loads on the blade. Another key observation is the high correlation between the rotor and generator speeds with a value of 0.98. To avoid multicollinearity, one of the two values should be removed. The generator speed was chosen to be removed since it has a slightly lower correlation with the outputs. Pearson correlations could not capture the nonlinear relationship between the features and the outputs. [PERSON] and [PERSON] Tau's correlations did not capture the relationships either. However, further exploration of the data has shown a non-linear relationship that cannot be shown using correlations. For instance, the yaw misalignment angle with the lowest correlation amongst the control parameters when plotted against the outputshas shown a dependence between their values. Figure 4 shows the effect of the yaw misalignment angle on the outputs. Figure 4 shows the direct relationships between the yaw deflection angle and the four desired outputs. The scatter plot containing 331,816 points may be unclear to show a direct relationship between the mentioned variables. However, the scattering of the points all over the graph shows that there is a dependency between the yaw deflection and the outputs. This is emphasized by the histograms on the upper and right spines which also show a direct relationship with the flapwise direction outputs and an inverse relationship with the edgewise outputs. Noting the signs of the values, the peaks in the variables' distribution show an increase in the values of the flapwise outputs with the increase in the yaw deflection, whether in the positive or negative senses. They also show that the outputs in the edgewise direction increase when the yaw deflection angle decreases and vice versa.