# A Machine Learning Method for Modeling Wind Farm Fatigue Load
## 4 Case Study
### GP Prediction Results
#### 4.3.2 Three-Turbine Case  
Figures 11 and 12 show the BREM and BRFM sample data on normalized damage equivalent loads in three turbines. For this case, the wind speed, turbulence intensity, and direction are 9 m/s, 5%, and 0 degrees. The axis scales of the four subplots are the same. The obtained fatigue load is normalized for visual expression by dividing a fixed value. The obtained fatigue load is normalized for visual expression by dividing a fixed value. The fixed values, in this case, take the fatigue load of the first turbine under the yaw offset [0, 0, 0]. **Remark 1**. : _The first-row turbine's damage equivalent load in blade root edgewise moment is less affected by yaw misalignment, while the second- and third-row turbines are more affected by yaw misalignment._  
As shown in Figure 11, the normalized BREM-DELs of WT1 remain essentially constant, which proves that the BREM-DELs in the first row of turbines are less affected by yaw misalignment. In contrast, the yaw misalignment affects the BREM-DELs of the second and third rows of turbines because the BREM-DELs curves of WT2 and WT3 vary with yaw angles. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**DEL**} & \multirow{2}{*}{**Precursor**} & **TI** & **LUT** & **GP** & **Improvement** \\  & & **/\%** & \(RMSE\)/\%** & \(RMSE\)/\% & \(RMSE\)/\% \\ \hline \multirow{3}{*}{BREM} & P1 & 5\% & 48.88 & 9.21 & 39.67 \\  & P2 & 10\% & 36.88 & 10.36 & 26.52 \\ \cline{1-1}  & P3 & 15\% & 18.09 & 1.51 & 16.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(RMSE\) error of blade root flapwise moment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**DEL**} & \multirow{2}{*}{**Precursor**} & **Wind Speed** & **LUT** & **GP** & **Improvement** \\  & & **m/s** & \(RMSE\)/\% & \(RMSE\)/\% & \(RMSE\)/\% \\ \hline \multirow{3}{*}{BREM} & P1 & 5 & 22.69 & 5.45 & 17.24 \\  & P4 & 7 & 35.58 & 9.53 & 26.05 \\ \cline{1-1}  & P7 & 9 & 50.09 & 15.19 & 34.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(RMSE\) error of blade root edgewise moment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**DEL**} & \multirow{2}{*}{**Precursor**} & **Wind Speed** & **LUT** & **GP** & **Improvement** \\  & & **m/s** & \(RMSE\)/\% & \(RMSE\)/\% & \(RMSE\)/\% \\ \hline \multirow{3}{*}{BREM} & P1 & 5 & 48.88 & 9.21 & 39.67 \\  & P4 & 7 & 164.16 & 43.13 & 121.03 \\ \cline{1-1}  & P7 & 9 & 370.03 & 99.20 & 274.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: \(RMSE\) error of blade root flapwise moment. **Remark 2**. : _The damage equivalent load in blade root flapwise moment is affected in all turbines._  
As shown in Figure 12, the normalized BRFM-DELs of WT1 stay constant when the yaw angle of WT2 changes. However, this changes with the yaw angle of WT1. Regarding WT2 and WT3, the normalized BRFM-DELs vary with WT1 and WT2 yaw angles. Although all three turbines are affected by yaw misalignment, the influencing factors differ. Specifically, the fatigue load of WT1 is affected by its yaw deflection. In addition, WT2 is affected by WT1 wake and its yaw deflection. WT3, on the other hand, is affected by the mixed wake of WT1 and WT2 since the yaw angle of WT3 is zero. Figure 13 displays the max-min range (defined in Equation (8)) of normalized fatigue load. Figure 13a is blade root edgewise moment, and Figure 13b is blade root flapwise moment. In Figure 13a, the max-min range of WT1 is 2%, meaning the first row of turbines is almost unaffected by its yaw misalignment. On the other hand, the max-min range of WT2 and WT3 is 32% and 33% when the yaw misalignment is active. From Figure 13b, all turbines' blade root flapwise moments are affected by the yaw misalignment. The max-min ranges of WT1, WT2, and WT3 are 38%, 100%, and 75%, respectively. Thus, the above results confirmed the observations from Figures 11 and 12 (Remarks 1 and 2). Figure 11: Blade root edgewise moment samples of normalized damage equivalent load under 9 m/s wind speed and 5% turbulence intensity.