## 3 Impact of Yaw Operation on Wind Turbine Blades
### Prediction of the Blade Loads during Yaw Operation
\begin{table}
\begin{tabular}{c c c c c} \hline
**Variable** & **Estimated Value** & **Standard Error** & \(t\)**Value** & \(P\)**Value** \\ \hline Constant term & \(-109.989\) & \(79.7698\) & \(-1.3788\) & \(0.1703\) \\ \(x_{1}\) & \(3.1879\) & \(5.8569\) & \(0.5443\) & \(0.5871\) \\ \(x_{2}\) & \(-18.7357\) & \(8.2338\) & \(-2.2754\) & \(0.0245\) \\ \(x_{3}\) & \(31.5959\) & \(8.6289\) & \(3.6616\) & \(0.0003\) \\ \(x_{4}\) & \(35.5136\) & \(7.7962\) & \(4.5552\) & \(1.2\times 10^{-5}\) \\ \(x_{1}x_{2}\) & \(-0.4873\) & \(0.2298\) & \(-2.1204\) & \(0.0358\) \\ \(x_{1}x_{3}\) & \(-0.1132\) & \(0.213\) & \(-0.5317\) & \(0.5958\) \\ \(x_{1}x_{4}\) & \(0.2654\) & \(0.234\) & \(1.1341\) & \(0.2588\) \\ \(x_{2}x_{3}\) & \(3.5584\) & \(0.2785\) & \(12.7757\) & \(1.16\times 10^{-24}\) \\ \(x_{2}x_{4}\) & \(1.4949\) & \(0.306\) & \(4.8848\) & \(3.01\times 10^{-6}\) \\ \(x_{3}x_{4}\) & \(-4.3281\) & \(0.2836\) & \(-15.2599\) & \(1.11\times 10^{-30}\) \\ \(x_{1}^{2}\) & \(-0.065\) & \(0.204\) & \(-0.3205\) & \(0.749\) \\ \(x_{2}^{2}\) & \(0.4057\) & \(0.3072\) & \(1.3207\) & \(0.1889\) \\ \(x_{3}^{2}\) & \(-2.1032\) & \(0.3329\) & \(-6.3173\) & \(3.97\times 10^{-9}\) \\ \(x_{4}^{3}\) & \(-1.7072\) & \(0.3628\) & \(-4.7052\) & \(6.44\times 10^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter estimates of 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 & \(-539.501\) & \(232.1584\) & \(-2.3238\) & \(0.0216\) \\ \(x_{1}\) & \(5.6244\) & \(17.0458\) & \(0.3299\) & \(0.7419\) \\ \(x_{2}\) & \(6.407\) & \(23.9632\) & \(0.2673\) & \(0.7896\) \\ \(x_{3}\) & \(95.5963\) & \(25.1133\) & \(3.8065\) & \(0.0002\) \\ \(x_{4}\) & \(65.6491\) & \(22.6898\) & \(2.8933\) & \(0.0044\) \\ \(x_{1}x_{2}\) & \(-1.2143\) & \(0.6688\) & \(-1.8154\) & \(0.0717\) \\ \(x_{1}x_{3}\) & \(-0.7268\) & \(0.6199\) & \(-1.1724\) & \(0.2431\) \\ \(x_{1}x_{4}\) & \(1.2093\) & \(0.6811\) & \(1.7755\) & \(0.0781\) \\ \(x_{2}x_{3}\) & \(9.5762\) & \(0.8106\) & \(11.8133\) & \(2.79\times 10^{-22}\) \\ \(x_{2}x_{4}\) & \(-2.1539\) & \(0.8906\) & \(-2.4184\) & \(0.0169\) \\ \(x_{3}x_{4}\) & \(-13.7124\) & \(0.8254\) & \(-16.6117\) & \(7.65\times 10^{-34}\) \\ \(x_{1}^{2}\) & \(-0.1948\) & \(0.5937\) & \(-0.3281\) & \(0.7433\) \\ \(x_{2}^{2}\) & \(0.8518\) & \(0.8942\) & \(0.9525\) & \(0.3425\) \\ \(x_{3}^{2}\) & \(-2.8406\) & \(0.9689\) & \(-2.9316\) & \(0.0039\) \\ \(x_{4}^{2}\) & \(0.8189\) & \(1.056\) & \(0.7755\) & \(0.4394\) \\ \hline \end{tabular}
\end{table} 
Table 5: Parameter estimates of quadratic regression for \(T_{2}\). Because there may be multicollinearity between the independent variables in the quadratic regression equation, the method called stepwise regression analysis is further used to modify the quadratic regression equation. The basic idea of stepwise regression analysis is that independent variables are introduced into the model in turn, and then F-test (F-test is used to test the significance of population regression) and \(t\)-test are carried out after each new variable is introduced. If the new variable causes the original variable to become less significant, the new variable is deleted to ensure that only significant variables are included in the regression equation. This process is repeated until no significant variable enters the regression equation. After modifying the quadratic regression equation, the parameter estimates of modified quadratic regression for \(T_{1}\) and \(T_{2}\) are shown in Tables 6 and 7, respectively. It is worth noting that the P value of the constant term in the modified equation of quadratic regression for \(T_{1}\) is 0.0577, which is a little more than 0.05. The item should have been deleted, but since its \(P\) value is only slightly larger than 0.05, and once deleted, the item would have a greater impact on the \(P\) value of other originally significant variables; hence, this item is retained.