## 3 Results and Discussion
### Pattern Analysis for APA Using Machine Learning  
In order to review the applicability of the aerodynamic imbalance APA region and IPC determined in Section 3.3, a pattern analysis using the artificial neural network-one of the machine learning techniques-was performed. Here, we used the commercial code Matlab [19]. This study employed the scaled conjugate gradient back propagation (SCGBP) algorithm suitable for pattern recognition among back propagation algorithms among the ANN techniques [20]. The ANN structure consists of the input, hidden, and output layers, as shown in Figure 13; the input layer has three input vectors. Additionally, the number of neurons used in the hidden layer were 10 to 40, due the convergence of results and unnecessary learning time, and the transfer function was obtained by tangent sigmoid function in Equation (7). The transfer function of the output layer used the sigmoid function shown in Equation (8), and the output of the neuron y was expressed as a result value from 0 to 1, as shown in Equation (9).  
\[\overset{\rightarrow}{f}_{1}=\frac{2}{\left(1+e^{-2\gamma_{j}}\right)}-1 \tag{7}\]  
\[\overset{\rightarrow}{f}_{2}=\frac{1}{1+e^{-\gamma_{a}}} \tag{8}\]  
\[y=\overset{\rightarrow}{f}_{2}\left(v_{j}\overset{\rightarrow}{f}_{1}\left(w_ {ij}\overset{\rightarrow}{a}_{i}+\overset{\rightarrow}{b}_{j}\right)+\overset{ \rightarrow}{b}_{o}\right) \tag{9}\]  
Figure 13: Simple ANN model.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**a3 (Blade 3)** & \multicolumn{6}{c}{**a1 (Blade 1), a2 (Blade 2)**} \\ \hline  & 11 m/s & 14 m/s & 17 m/s & 20 m/s & 22 m/s & 24 m/s \\
4\({}^{\circ}\) & 2\({}^{\circ}\)-6\({}^{\circ}\) & & & & & \\
6\({}^{\circ}\  
For pattern analysis, we generalized the target value of 1 for the APA region, and the target value of 0 for the non-allowable pitch angle. There were a total of 4096 data for each wind speed, and they were randomly classified into 70% training data, 15% validation data, and 15% test data. Next, pattern analysis was performed.  
Figure 14 shows the confusion matrix that represents the values that resulted from the ANN training with the \(M_{a}\) at the hub at a wind speed of 20 m/s. First, the training confusion matrix in the upper left corner was examined. We considered values where the target and prediction values matched to be true values. For the true values, 2826 (98.5%) of 0 and 33 (1.2%) of 1, respectively, matched-that is, a total of 2859 (99.7%) matched. Hence, these results were identified as having a 99.7% success rate. Combining this with the results of the validation confusion matrix (100%) and the test confusion matrix (99.7%), the success rate of all confusion matrix was 99.7%. Table 6 shows the success rates of all confusion matrix for each wind speed, and the appropriate number of neurons to obtain them. The success rate may change slightly depending on the number of neurons and hidden layers.  
Figures 7-12 show the prediction results (red asterisk) obtained through the above ANN pattern analysis, and the APA region analysis results (blue circle) for each wind speed based on the resultant moment. From these figures, the APA prediction results by ANN very well match the APA analysis results by ultimate loads analysis. This shows that the APA pattern analysis using ANN can implement the meta models for each wind speed. Furthermore, it is expected that this procedure can be used to make the basic design data of IPC strategy.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Steady Wind Speed**} & \multicolumn{2}{c}{**Moment**} \\
**(m/s)** & **Success Rate (\%)** & **Neuron Number** \\ \hline \hline \multirow{4}{*}{Stationaryhub} & 11 & 99.5 & 10 \\  & 14 & 99.4 & 10 \\ \cline{1-1}  & 17 & 99.8 & 10 \\ \cline{1-1}  & 20 & 99.7 & 10 \\ \cline{1-1}  & 22 & 100 & 20 \\ \cline{1-1}  & 24 & 99.8 & 10 \\ \cline{1-1}  & Average & 99.7 & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: All confusion matrix for success rate.  
Figure 14: Confusion matrix for success rate (\(M_{a}\), 20 m/s).