# A Neural Network Model for Decision-Making with Application in Sewage Sludge Management
## 4 Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Target** & **ME** & **MAD** & **MSE** & **MAE** & **MAPE (\%)** \\ \hline \(\text{Th}_{\text{i}}\) & 0.143 & 0.286 & 0.429 & 0.286 & 13.69 \\ \hline \(\text{Sb}_{\text{i}}\) & 0.071 & 0.357 & 0.357 & 0.357 & 17.26 \\ \hline \(\text{D}\text{w}_{\text{i}}\) & 0.214 & 0.214 & 0.214 & 0.214 & 9.52 \\ \hline Co & \(-\)0.071 & 0.214 & 0.214 & 0.214 & 17.86 \\ \hline \(\text{Td}\) & 0.071 & 0.214 & 0.214 & 0.214 & 14.29 \\ \hline \(\text{D}\text{p}_{\text{i}}\) & 0.357 & 0.500 & 0.643 & 0.500 & 16.67 \\ \hline Average & 0.131 & 0.298 & 0.345 & 0.298 & 14.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of the errors evaluated adopting the ANN on 20 cases identified by considering out-of-sample data. Figure 6: Comparison between predicted values (**a**) of output parameters (\(r_{1}\), \(r_{2}\), \(r_{3}\)) and actual values (**b**) of same parameters, evaluated in case of spreading \(r_{6}=0\) (not-dewatered sludge on agricultural land) and \(r_{4}=r_{5}=0\). At the end of the elaboration process, the ANN model suggests a suitable alternative for each phase of SSTS (Figure 8). The ANN model suggests the following phases: dissolved air flotation (Phase 1), lime stabilization (Phase 2), filter press dewatering (Phase 3), no composting (Phase 4), no thermal drying (Phase 5), and finally, spreading of dewatered sludge on agriculture land for disposal (Phase 6). In the second case, the SS treatment referred to a big plant (PC of 120E3 PE) with a single line's configuration, and providing an activated sludge as a secondary treatment to ANN model is required. Consistent with this case, the ANN model leads to different outputs. For this scenario, the ANN model suggests a gravity thickening, a stabilization by anaerobic digestion, a filter press dewatering, thermal drying, and incineration. This output is consistent with the results; indeed, anaerobic digestion and incineration, ensuring high energy recovery, are suggested. Among the theoretical possible alternatives given by different combinations of the \(r_{i}\)-elements, the ANN model has been tested on 20 feasible scenarios, considering a set of input variables that stress the ANN model, evaluating cases very different from each other. It is noted that, generally, for PC values included in the range of Class #1, the ANN model suggests carrying out thickening in sedimentation, stabilization, and disposal by spreading of not-dewatered SS on agricultural land. These suggestions are consistent with the WWTP dimensions considered where high investment costs are not recommended. Therefore, a stabilization treatment is suggested to ensure the SS's safe handling and disposal from an economic perspective. Generally, for PC included in the range of Classes #2 and #3, the ANN model suggests a thickening treatment in dedicated systems, followed by stabilization treatment, dewatering through natural systems, composting (in most cases), and disposal of dewatered SS in agricultural land. In these cases, the mechanical  
Figure 8: Screenshot of the VBA output query interfaced with the ANN model. Figure 7: Screenshot of the VBA input query interfaced with the ANN model. dewatering systems or anaerobic digestion systems are excluded by the ANN model, since they are considered not recommendable by experts. For PC included in the range of Class #4, stabilization by anaerobic digestion, if applicable, is recommended. Indeed, if, on the one hand, the anaerobic digestion treatment ensures high-performance in energy recovery, then, on the other hand, the investment and the running cost are very high. Finally, for PC included in the range of Class #5, the ANN model, in most cases, led to the adoption of dewatering treatment, followed by thermal drying and incineration.