# Evolutionary Design Optimization of an Alkaline Water Electrolysis Cell for Hydrogen Production
## 2 Physics and Economy of the Alkaline Water Electrolysis Cell
### Artificial Neural Network (ANN)
#### 2.2.2 Sensitivity Analysis of Void Fraction and Ohmic Resistance  
In order to observe the effect of the different parameters on the electrolysis performance, the artificial neural network has been used to predict the void fraction \(\varepsilon\) and the electrolyte ohmic resistance \(R\). Therefore, we performed a fractional factorial design of experiment (DOE). The DOE used is a \"one factor at a time\" (OFAT), referred to the minimal parameter-values curve (red). In all other curves, a single parameter among (T, Y, j, H, and h) changes from min to max value to assess the effect of each one on the void fraction and electrolyte ohmic resistance. Table 3 gives the minimum and maximum values of different parameters in this DOE. The bubble radius \(r\) is set at 25 \(\upmu\)m. Because the ANN \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \(i=0\) & \(i=1\) & \(i=2\) & \(i=3\) \\ \hline \multirow{2}{*}{\(H_{1,j}\)} & \(w_{0,i}\) & 1.3965 & 1.3532 & 1.4242 & 1.4926 \\ \cline{2-6}  & \(c_{0,i}\) & 0.61711 & 0.6445 & 0.5920 & 0.1461 \\ \hline \multirow{4}{*}{\(H_{2,i}\)} & \(w_{1,i}\) & 41.63 & \(-\)0.848 & \(-\)0.444 & – \\ \cline{2-6}  & \(w_{1,(i+3)}\) & \(-\)2.6544 & \(-\)0.837 & 114 & – \\ \cline{2-6}  & \(w_{1,(i+6)}\) & \(-\)1.5778 & \(-\)9.13 & \(-\)0.015 & – \\ \cline{2-6}  & \(w_{1,(i+9)}\) & 0.2068 & \(-\)0.154 & \(-\)0.347 & – \\ \cline{2-6}  & \(c_{1,i}\) & 29.78 & \(-\)13.57 & 81.04 & – \\ \hline \multirow{4}{*}{\(H_{3,i}\)} & \(w_{2,0}\) & \(-\)0.4 & – & – & – \\ \cline{2-6}  & \(w_{2,1}\) & \(-\)0.959 & – & – & – \\ \cline{2-6}  & \(w_{2,2}\) & 12.54 & – & – & – \\ \cline{2-6}  & \(c_{2,0}\) & 19.84 & – & – & – \\ \hline \multirow{2}{*}{\(H_{4,i}\)} & \(w_{3,0}\) & 0.99 & – & – & – \\ \cline{2-6}  & \(c_{3,0}\) & \(-\)2.03 & – & – & – \\ \hline \(H_{5,i}\) & \(w_{4,0}\) & 2.30 & – & – & – \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for Equations (25)–(29). Figure 3: Results of the training of the artificial neural network (ANN), the results of void fraction of the ANN \(\varepsilon_{ANN}\) are compared to the void fraction calculated to \(\varepsilon_{fluent}\). The blue points represent the learning samples and the red points the validation samples. The red line is \(\varepsilon_{fluent}+\ 40\%\) and the blue line \(\varepsilon_{fluent}-40\%\). In Figure 5a, it can be clearly seen that the electrolyte thickness has a great influence on the void fraction. By decreasing the electrolyte thickness \(h\) by few hundred micrometers, the void fraction increases abruptly from 0.1 to 0.6. Therefore, the existence of an optimum is explained. In the Figure 5b, the optimum of electrolyte thickness \(h_{opt}\) can be observed. This optimum mainly depends on the electrode heights \(H_{dec}\) and pressure \(p\). The pressure reduces the radius of the bubble \(r\) and thus diminishes the optimal thickness of the electrolyte. Increasing the electrode height means increasing the injected gas flow so it increases the void fraction and the electrolyte ohmic resistance. In Figure 6a,b, it can be observed that the current density increases the void fraction until 1500 A m\({}^{-2}\) and reached a plateau. The value of the plateau depends on the geometry of the cell especially the ratio electrolyte thickness/electrode height. However, the kinematic viscosity \(v\) seems to play a role also. In Figure 7a,b, the electrode height sensitivity impact on the ohmic resistance and void fraction can be observed. As expected, the electrode height increases the void fraction and thus the ohmic resistance. However, for \(p_{max}\) (30 bar), it seems that electrode height does not impact the void fraction values. This is a surprising result that must be taken with caution. In conclusion, the neural network gives roughly the sensitivity to all parameters even if for some case the results are surprising. Indeed, increasing the pressure must strictly decreases the void fraction and the void fraction should always increase according to electrode height.