## 3 Results and Discussion
### Model Performance  
The performance of the RBFNN and MLPNN as a function of the RMSE, SEE, and R\({}^{2}\) is summarized in Table 3. The RBFNN displayed great potential in predicting the biohydrogen production from waste glycerol. As shown in Figure 4a, the actual values depicted as \"1\" are consistent with the predicted values by RBFNN-1 depicted as \"2\". On the contrary, poorer performance in the prediction of the biohydrogen from waste glycerol using the RBFNN-2 is observed in Figure 4b. Moreover, the superior performance of the RBFNN-1 model over the RBFNN-2 model can be further ascertained from the R\({}^{2}\) and RMSE values of 0.903 and 53.31, respectively, obtained for the RBFNN-1 model. This implied that RBFNN-1 had a robust prediction with fewer errors compared to RBFNN-2, which had R\({}^{2}\) and RMSE values of 0.419 and 301.55, respectively. A better performance of RBFNN-1 compared with RBFNN-2 could be attributed to the use of a standardized identity activation function compared to the non-standardized activation function used in RBFNN-2. The use of a standardized identity activation function has been reported to improve the performance of RBFNN [30]. The use of standardized identity as an activation function in the outer layer helps to prevent diminishing gradient problems and improve the computation performance of the RBFNN-1 model [31]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **Range** & **Minimum** & **Maximum** & **Mean** & **Standard Deviation** & **Variance** \\ \hline Waste glycerol (g/L) & 36.58 & 0.23 & 36.81 & 21.39 & 7.43 & 55.27 \\ Urea (g/L) & 0.20 & 0.05 & 0.25 & 0.15 & 0.05 & 0.00 \\ Endo-nutrient (mL/L) & 0.40 & 0.00 & 0.40 & 0.19 & 0.10 & 0.01 \\ Na2 HPO4 (g/L) & 8.00 & 0.00 & 8.00 & 3.93 & 1.89 & 3.57 \\ HP (mL H2/L) & 1489.19 & 117.46 & 1606.65 & 582.98 & 493.17 & 243,213.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics for input and targeted variables. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **RMSE** & **SSE-Training** & **SSE-Testing** & **R\({}^{2}\)** \\ \hline RBFNN-1 & 53.31 & 1.253 & 0.024 & 0.903 \\ RBFNN-2 & 212.25 & 3.082 & 0.017 & 0.736 \\ MLPNN-1 & 21.48 & 1.083 & 0.021 & 0.920 \\ MLPNN-2 & 51.99 & 4.052 & 0.000 & 0.433 \\ MLPNN-3 & 12.66 & 0.034 & 0.010 & 0.969 \\ MLPNN-4 & 88.14 & 0.567 & 0.074 & 0.954 \\ MLPNN-5 & 59.26 & 0.358 & 0.038 & 0.939 \\ MLPNN-6 & 29.63 & 0.028 & 0.018 & 0.957 \\ MLPNN-7 & 258.12 & 0.250 & 0.207 & 0.965 \\ MLPNN-8 & 9.91 & 0.027 & 0.003 & 0.978 \\ MLPNN-9 & 38.43 & 0.317 & 0.076 & 0.934 \\ MLPNN-10 & 43.72 & 0.493 & 0.198 & 0.948 \\ MLPNN-11 & 16.20 & 0.111 & 0.006 & 0.977 \\ MLPNN-12 & 15.09 & 0.035 & 0.019 & 0.959 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of performance analysis for the models. The performance of the MLPNNs with various configurations based on the hidden and outer layer activation functions optimized using a scaled conjugate gradient algorithm is depicted in Figure 5. It can be seen that all the MLPNN configurations optimized using the scaled conjugate gradient algorithms were robust in their predictive modeling of the interconnectivity between the input variables and the targeted output (biohydrogen production), with the exception of MLPNN-2. The actual volume of biohydrogen produced per liter of waste glycerol in Figure 5a,c-e was consistent with the values predicted by the MLPNN-1, MLPNN-3, MLPNN-4, and MLPNN-5, respectively. This implied that the combination of a hyperbolic tangent as the activation function for the hidden layer and identity as the activation function for the outer layer resulted in a robust performance in predicting biohydrogen production. This can be further ascertained from a high R\({}^{2}\) value of 0.920 and a low RMSE value of 21.48. Minimal errors were obtained from training and testing the MLPNN-1 with the experimental data.