## 2 Materials and Methods
### Modeling with ANN  
While determining the ANN model, the model parameters were changed and the feedforward backpropagation algorithm with the highest prediction success was used. The ANN model was designed by using the traingdx algorithm, and the learngdm function as a learning function, and the tangent sigmoid (tansig) and logistic sigmoid (logsig) activation functions in training datasets.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Days** & **January** & **February** & **March** & **April** & **May** & **June** \\ \hline
1 & 8.05 & 6.  
The performance of the model was calculated with the mean square error (MSE) function. In the designed model, wind speeds are used as input data and the output power of the Enercon E92 turbine as output data. The single-layer model was first used in the network structure, and the number of neurons in the hidden layers was determined as 10, 15, and 20, respectively. After training the network with a single layer and generating predictive values, tests were conducted using two hidden layers as a multilayer model, and the number of neurons in the hidden layers were determined as 10 and 15, 10 and 20, and 15 and 20, respectively. Tests were carried out with the tansig and logsig functions as transfer functions and the number of neurons mentioned above. The model, which is multilayered from the created ANN structure and in which the number of neurons is determined as 10 and 15, is shown in Figure 3.  
The training data were divided into 70% training, 15% validation, and 15% testing with the dividerand function. In the model created, the stopping criterion of \"1000\" iterations, the \"0\" error \(1\times 10^{-5}\) gradient value, and the \"1000\" validation error number were used. The training stopped after reaching 1000 iterations in 1 s. The error performance values of the training, validation, and test data are shown in Figure 4.  
As a result of comparing the actual values and the output values produced by the network to determine the performance of the network, the regression values for all of the training, validation, and test data were close to 1. According to these results, it can be concluded that the output values of the network and the real data are close to each other. Regression curves for all data are shown in Figure 5.  
Figure 4: Validation performance values (MSE) of training, validation, and test data.  
Figure 3: ANN structure with multi-hidden layers.  
After the network is trained and the predicted test values are produced, the predicted values should be compared with the actual data. In Table 5, the performance criteria of the ANN model calculated by the RMSE (root mean squared error), MAPE (mean absolute percentage error), and R\({}^{2}\) methods are given. The equations of performance criteria are as follows:  
\[\text{MAPE}=100/\text{n}\sum{{}_{i}}^{\text{n}}\ (\ |\ y_{\text{i}}-\bar{y}_{ \text{i}}\ |)/y_{\text{i}},\]  
ANN model with 15 and 20 neurons using the Tansig transfer function produced the closest prediction value to the real values.  
Table 5 shows that the mean RMSE values of the ANN models with two hidden layers (33.27) are significantly lower than the mean RMSE values of the ANN models with one hidden layer (51.46). When the mean MAPE values are considered, it is seen that there is no significant difference between the models with one hidden layer and two hidden layers (23.05-21.2). When the average R\({}^{2}\) values are analyzed, it is seen that the average of the two hidden layer models (0.9982) produces slightly better results than the average of the single-hidden layer models (0.99625). When analyzed according to the number of neurons, it is understood that models with 15 neurons give better results than single-hidden layer models by looking at different activation functions. Two hidden layer models, on the other hand, confirm the number of 15 neurons in the first layer, and using 20 neurons in the second hidden layer improved the results.