# Rotational Speed Control Using ANN-Based MPPT for OWC Based on Surface Elevation Measurements
## 4 Results and Discussion
### ANN Training Performance  
With the forward approach-based trial-and-error rule method, numerous structures with different hidden layers and neurons have been tested with our problem. For the training process, the data were divided into 40% for the learning stage, 30% for the testing stage and 30% for the validation stage.  
The results of calculations for determining the ANN model are detailed in Table 2. The results of training show that the best neural model that has been calculated is the MLP 2 \(\times\) 4 \(\times\) 8 \(\times\) 1 with 2 neurons on the input layer (for the wave amplitude and period), 4 neurons on the first hidden layer, 8 neurons on the second hidden layer and 1 neuron on the output layer (for the rotational speed reference). The second best MLP is 2 \(\times\) 4 \(\times\) 4 \(\times\) 1 with 2 neurons on the input layer, 4 neurons on the first hidden layer, 4 neurons on the second hidden layer and 1 neuron on the output layer. These two nets have the best learning, testing and validation qualities moreover, their validation quality is not lower than that of the learning and testing qualities.  
During the simulations, the study case takes into consideration the number of epochs and the smallest MSE. Table 3 shows the validation results obtained of training different network structures applied to the problem of wave characteristics recognition.  
Results of Table 3 indicate that using a network with a single hidden layer provides less accurate results due to the nonlinearity and complexity of the problem. On the other hand, multiple hidden layer networks provide better results. However, when increasing the number of neurons in the hidden layers and the number of epochs the obtained MSE is worsened. This is due to the overlearning effect.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Capture Chamber** & **Wells Turbine** & \multicolumn{2}{c}{**DFIG Generator**} \\ \hline \(w_{c}=4.5\) m & \(n=5\) & \(R_{s}=0.5968\)\(\Omega\) & \(P_{rated}=18.45\) kW \\ \(l_{c}=4.3\) m & \(b=0.21\) m & \(R_{r}=0.6258\)\(\Omega\) & \(V_{rated}=400\) V \\ \(\rho_{a}=1.19\) kg/m\({}^{3}\) & \(l=0.165\) m & \(L_{ss}=0.0003495\) H & \(f_{rated}=50\) Hz \\ \(\rho_{w}=1029\) kg/m\({}^{3}\) & \(r=0.375\) m & \(L_{rr}=0.324\) H & \(p=2\) \\  & \(a=0.4417\) m\({}^{2}\) & \(L_{m}=0.324\) H & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Plant parameters from the NREIDA wave power plant at Mutriku.  
More analysis has been performed on the curves of the training performance of the multiple hidden layer networks with the best MSE labeled as ANN1 and ANN2 for adequate structure selection.  
The training process history of ANN1 (\(2\times 4\times 8\times 1\)) is given by Figure 17 while the one of ANN2 (\(2\times 8\times 4\times 1\)) is given by Figure 18. Both figures indicate that for ANN1 the training process took more epochs to converge to a minimum MSE of \(2.3787\times 10^{-5}\) in 615 epochs however with ANN2 it converged to a smaller MSE of \(1.5633\times 10^{-5}\) in fewer epochs at 200.  
Finally, ANN2's structure has been chosen as ANN rotational speed reference generator to be used in the developed rotational speed control strategy with real measured data.