## 3 Results and Discussion
### Derivation of Mean Velocity using GMDH  
GMDH is used in the present research to present an equation for predicting the relative velocity in the branch channel (\(V\)*) in an intake. The independent parameters influencing the prediction of the dependent variable, \(V\)*, include the ratio of the branch channel width to the main channel (\(W_{r}\)), diversion angle with the longitudinal direction of the main channel (\(\theta\)), and the longitudinal coordinates in the intake channel (\(y\)*) which are introduced as below:  
\[V^{*}=f(W_{r},\theta,y^{*}) \tag{17}\]  
The data obtained from the numerical simulation by CFX need to be divided into two groups of training and testing to predict V* therefore we could examine the flexibility of the model for different data. Therefore, 30% of data (180 data) are CROSS-VALIDATION selected from amongst the 600 existing data and the rest 70% (420 data) are utilized to train the model. Figure 7 shows the evolved  
Figure 6: Verification graphs between the outcomes of the CFX model and the [PERSON] and his colleagues’ experimental model in \(y\)* = -2.00.  
structure of generalized GMDH neural network for modeling the relative velocity in the branch channel. Moreover, the equations obtained through using GMDH for modeling V* are presented as below:  
\[Y_{1}=0.0719+0.234\theta+0.0281y^{*}-0.0206\theta^{2}+0.0175{y^{*}}^{2}+0.0347 \theta\times y^{*} \tag{18}\]  
\[Y_{2}=0.178+0.242W_{r}+0.0279y^{*}-0.122{W_{r}}^{2}+0.0175{y^{*}}^{2}+0.0405W_{r }\times y^{*} \tag{19}\]  
\[Y_{3}=0.0314+0.162W_{r}+0.166\theta-0.122{W_{r}}^{2}-0.0205\theta^{2}+0.0284W_{ r}\times\theta \tag{20}\]  
\[Y_{4}=-0.142-0.549\theta+4.43Y_{1}-0.466\theta^{2}-19.865{Y_{1}}^{2}+6.173 \theta\times Y_{1} \tag{21}\]  
\[Y_{5}=0.2822-1.6592{Y_{2}}-0.4352{Y_{3}}+1.593{Y_{2}}^{2}-0.579{Y_{3}}^{2}+6.9 17Y_{2}\times Y_{3} \tag{22}\]  
\[V^{*}=0.011-1.772Y_{4}+2.666Y_{5}+22.136{Y_{4}}^{2}+13.628{Y_{5}}^{2}-35.634Y_ {4}\times Y_{5} \tag{23}\]  
Figure 8 indicates the performance of the model presented by using GMDH for the purposes of predicting the mean velocity for different angles including the 30-, 60-, and 90-degree angles. The predictions made at \(\theta=30\) is almost very well consistent with the values obtained from CFX in most of the points. In points where the values estimated by the GMDH are different from the target values (the values obtained from CFX), the predictions do not follow a particular pattern and both overestimate and underestimate the values of these differences are however not significant with regard to the Figure 7. The relative velocities obtained in this angle have mostly values smaller than 0.2 m/s. As \(\theta\) increases, the values of the relative velocities also decrease in accordance with the Figure. In such a manner that at \(\theta=60\), the relative velocity is smaller than 0.3 m/s and at \(\theta=90\) it is lesser than 0.4 m/s. As \(\theta\) increases the accuracy of the predictions relatively decreases; however, it could not be specified at which exact angle it performs best; therefore, the accuracy of the predictions are examined quantitatively through using Table 1 and Figure 8. In the values (\(\theta=30\)-, 60-, and 90-degree, samples 25-45), eddy and rotational currents are more and the direction of flow velocity changes, and the measurement error is more likely in these values. Therefore, the results presented by ANSYS-CFX numerical software and GMDH method in areas where secondary currents and vortices are more intense, have more differences and higher error rates. Figure 6:0 Evolved structure of generalized group method of data handling (GMDH) neural network for modeling and prediction of mean velocity. Table 2 shows the results obtained from the model presented for the purposes of forecasting the mean velocity through the use of different statistical indexes for different width ratios at 30-, 60-, and 90-degree angles.