## 3 Impact of Yaw Operation on Wind Turbine Blades
### Prediction of the Blade Loads during Yaw Operation
The fitting effect of quadratic regression is shown in Figure 5. The fitting effect difference between the quadratic regression equation and quadratic regression modified equation is not obvious. However, some independent variables appear multicollinearity in the quadratic regression equation, and the modified quadratic regression equation can eliminate the influence of the multicollinearity. Hence, it is reasonable to choose the quadratic regression modified equation as the final expression of the regression equation. As a result, the edgewise moment \(T_{1}\) and flapwise moment \(T_{2}\) are expressed as  
\[\left\{ \begin{array}{l}T_{1}=-126.153-11.5843x_{2}+30.3772x_{3}+38.3866x_{4} -0.3044x_{1}x_{2}\\ +3.5391x_{2}x_{3}+1.4918x_{2}x_{4}-4.3295x_{3}x_{4}-2.09x_{3}^{2}-1.7081x_{4} ^{2}\\ T_{2}=-503.248+86.4759x_{3}+90.5354x_{4}-1.0512x_{1}x_{2}+9.6435x_{2}x_{3}\\ -2.0776x_{2}x_{4}-13.7919x_{3}x_{4}+0.9843x_{2}^{2}-2.7821x_{3}^{2}\end{array} \right. \tag{3}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Variable** & **Estimated Value** & **Standard Error** & \(t\)**Value** & \(P\)**Value** \\ \hline Constant term & \(-\)126.153 & 65.9001 & \(-\)1.9143 & 0.0577 \\ \(x_{2}\) & \(-\)11.5843 & 4.4283 & \(-\)2.6159 & 0.0099 \\ \(x_{3}\) & 30.3772 & 8.3611 & 3.6331 & 0.0004 \\ \(x_{4}\) & 38.3866 & 7.4002 & 5.1871 & 7.71 \(\times 10^{-7}\) \\ \(x_{1}x_{2}\) & \(-\)0.3044 & 0.0957 & \(-\)3.1783 & 0.0018 \\ \(x_{2}x_{3}\) & 3.5391 & 0.2769 & 12.7769 & 6.05 \(\times 10^{-25}\) \\ \(x_{2}x_{4}\) & 1.4918 & 0.3048 & 4.8937 & 2.79 \(\times 10^{-6}\) \\ \(x_{3}x_{4}\) & \(-\)4.3295 & 0.2819 & \(-\)15.3572 & 2.47 \(\times 10^{-31}\) \\ \(x_{2}^{2}\) & \(-\)2.09 & 0.3316 & \(-\)6.3035 & 3.9 \(\times 10^{-9}\) \\ \(x_{4}^{2}\) & \(-\)1.7081 & 0.3615 & \(-\)4.7248 & 5.74 \(\times 10^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Parameter estimates of modified quadratic regression for \(T_{1}\). \begin{table}
\begin{tabular}{c c c c c} \hline
**Variable** & **Estimated Value** & **Standard Error** & \(t\)**Value** & \(P\)**Value** \\ \hline Constant term & \(-\)503.248 & 150.9133 & \(-\)3.3346 & 0.0011 \\ \(x_{3}\) & 86.4759 & 24.1402 & 3.5822 & 0.0004 \\ \(x_{4}\) & 90.53534 & 14.4742 & 6.2549 & 4.89 \(\times 10^{-9}\) \\ \(x_{1}x_{2}\) & \(-\)1.0512 & 0.2755 & \(-\)3.8146 & 0.0002 \\ \(x_{2}x_{3}\) & 9.6435 & 0.7354 & 13.1123 & 7.61 \(\times 10^{-26}\) \\ \(x_{2}x_{4}\) & \(-\)2.0776 & 0.8526 & \(-\)2.4366 & 0.0161 \\ \(x_{3}x_{4}\) & \(-\)13.7919 & 0.8213 & \(-\)16.791 & 7.28 \(\times 10^{-35}\) \\ \(x_{2}^{2}\) & 0.9843 & 0.4941 & 1.9916 & 0.0484 \\ \(x_{3}^{2}\) & \(-\)2.7821 & 0.9659 & \(-\)2.88 & 0.0046 \\ \hline \end{tabular}
\end{table} 
Table 7: Parameter estimates of modified quadratic regression for \(T_{2}\). By using the above analysis method, the loads acting on the blade in both edgewise and flapwise directions can be estimated, i.e.,  
\[\left\{ \begin{array}{l}F_{1}=-5.2047+0.6044x_{1}-0.0536x_{1}x_{3}+0.0525x_{2}x_{ 3}+0.0533x_{2}^{2}-0.0643x_{4}^{2}\\ F_{2}=-12.9322+2.4262x_{3}+2.4704x_{4}-0.0553x_{1}x_{2}+0.0361x_{1}x_{4}+0.3563x _{2}x_{3}\\ -0.0648x_{2}x_{4}-0.4508x_{3}x_{4}+0.0483x_{2}^{2}-0.1005x_{3}^{2}\end{array} \right. \tag{4}\]  
where, \(F_{1}\) is the resultant force acting on the blade in the edgewise direction; \(F_{2}\) is the resultant force acting on the blade in the flapwise direction.