## 3 Results  
In order to establish the ANN, a data set must be provided. As mentioned previously, these data set were obtained through the CFD model. A total of 125 cases were analyzed using different values of the aspect ratio, overlap, and twist angle. Particularly, five values of the aspect ratio were employed: 1, 3, 5, 7, and 9; five values of the overlap/chord length ratio: 0, 0.05, 0.1, 0.15, and 0.2; and five values of the twist angle: 0\({}^{\circ}\), 60\({}^{\circ}\), 120\({}^{\circ}\), 180\({}^{\circ}\), and 240\({}^{\circ}\). These ranges were chosen according to proposed values in the literature. Taking into account these values of the aspect ratio, overlap/chord length ratio, and twist angle, a total of 5 \(\times\) 5 \(\times\) 5 = 125 cases were analyzed. These cases are graphically represented in Figure 12.  
Figure 11: Data fitting performance; (**a**) appropriate fitting; (**b**) underfitting; (**c**) overfitting. Figure 10: Structure of the ANN employed for the present analysis. Once these 125 data were obtained through CFD, they will be employed to set the ANN and analyze a considerably higher amount of data. In order to minimize the domination of any parameter, data standardization was realized. This standardization or normalization process eliminates the dimensions and scales the data in a range, usually from 0 to 1, Equation (6). \[x_{n}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{6}\]  
where \(x_{n}\) is the normalized value, \(x_{max}\) is the maximum x value, and \(x_{min}\) is the minimum x value. Once normalized, these 125 cases analyzed through CFD were employed as samples to train, validate, and test the network. Particularly, 89 samples, randomly selected, were used to train the network, 18 to validate it, and 18 to test it. Figure 14 shows the performance separated into three sets: training, validation, and test. Moreover, all data are also provided. The accuracy is evaluated on the basis of the prediction errors from the verification data. Equation (7) is used to compute the correlation coefficient R. The global R-value is too close to the optimum value R = 1. The closer to R = 1, the more accurate the ANN is. Graphically, Figure 16 shows that the fitting of the four images is practically diagonal, thus providing an excellent data fitting. It can be seen that the curves of the four images are basically on the diagonal, which indicates an appropriate data fitting, i.e., an accurate prediction of the maximum power coefficient. \[R=\sqrt{1-\frac{\sum\limits_{i=1}^{m}\left[(t_{i}-\sigma_{i})^{2}\right]}{ \sum\limits_{i=1}^{m}\sigma_{i}^{2}}} \tag{7}\]  
where t is the target value, o the output, and m the number of samples. As mentioned previously, this ANN was employed to analyze a much higher quantity of cases than 125. Particularly, 81 values of the aspect ratio were employed: 1, 1.1, 1.2,... 9;81 values of the overlap/chord length ratio: 0, 0.0025, 0.005,... 0.2; and 121 values of the twist angle: 0\({}^{\circ}\), 2\({}^{\circ}\), 4\({}^{\circ}\),... 240\({}^{\circ}\). Taking into account these values of the aspect ratio, overlap/chord length, and twist angle, a total of 81 \(\times\) 81 \(\times\) 121 = 793,881 cases were analyzed. The most appropriate solution obtained by the ANN is shown in Table 2. It can be seen that the optimum solution corresponds to AR = 7.5, O/C = 0.1125, and TA = 112\({}^{\circ}\), providing a maximum power coefficient of 0.3263. Regarding the aspect ratio, high values increment the power coefficient, but excessive values reduce the positive effect that the endplates promote on the performance (reducing escaping of air). Regarding the overlap, it is positive since it allows the flowing of air from the advancing to the returning blade,  
Figure 15: Maximum power coefficient against AR and TA. O/C = 0.  
incrementing the power. Nevertheless, excessive overlaps lead to a high reduction in the air on the advancing blade, which reduces the power. Regarding the twist angle, the optimum value also improves the aerodynamics of the turbine.