# A Neural Network Model for Decision-Making with Application in Sewage Sludge Management
## 3 Materials and Methods
Similarly, this parameter allows us to consider the different chemical-physical characteristics of the primary and secondary sludge mixed and separated, thus allowing us to identify the most suitable treatment. In Table 7 are shown the typology and the range evaluated for each parameter. The ANN model output parameter consists of providing for each phase (i.e., Thi, Sbi, Dwi, Co, Td, and Dpi) the most effective strategy in economic terms. The output of the ANN model consists in an array \"\(R\)\" (Equation (1)), including six variables (\(r_{i}\)) defined in Equations (2)-(7). \[R=\{r_{1},r_{2},r_{3},r_{4},r_{5},r_{6}\} \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Phase** & **Treatment** & **Strengths** & **Limitations** \\ \hline Phase 6 & \multirow{2}{*}{\begin{tabular}{c} Spreading of not dewatered \\ sludge on agricultural land (Dp1) \\ \end{tabular} } & Low investment costs. & \multirow{2}{*}{High transport and storage costs.} \\  & & Material recovery. & \\ \cline{3-3} \multirow{2}{*}{\begin{tabular}{c} Disposal \\ (Dp1) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} Spreading of dewatered sludge \\ on agricultural land (Dp2) \\ \end{tabular} } & Low transport and storage costs. & \multirow{2}{*}{High investment costs.} \\  & & Material recovery. & \\ \cline{3-3} \multirow{2}{*}{\begin{tabular}{c} Incineration (Dp3) \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} Almost complete elimination of water. \\ Almost complete stabilization. \\ Suitable also for the treatment of \\ fresh sludge. \\ Energy recovery. \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} Very high investment and \\ management costs. \\ Very hard management. \\ Need to strongly dewater the \\ sludge before treating it. \\ Need to manage fumes. \\ \end{tabular} } \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Strengths and limitations of all considered alternatives to carry out the disposal treatments of the modeled SSTS. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Parameter** & **Unit of Measurement** & **Range** & **Typology** \\ \hline \multirow{4}{*}{PC} & & \#1: [0, 5E3] & \multirow{4}{*}{Class} \\  & & \#2: [5E3, 10E3] & \\ \cline{3-3} \multirow{2}{*}{PC} & (PE) & \#3: [10E3, 20E3] & \\ \cline{3-3} \multirow{2}{*}{\begin{tabular}{c} St \\ \end{tabular} } & & \#4: [20E3, 100E3] & \\ \cline{3-3} \multirow{2}{*}{\
\begin{tabular}{c} CSp \\ \end{tabular} } & (\#) &
\begin{tabular}{c} 0: chemical treatment \\ 1: activated sludge \\ \end{tabular} & Binary \\ \hline \hline \end{tabular}
\end{table} 
Table 7: List of the input parameters of the ANN model. where we have the following:  
\[r_{1}:\{Th_{1},Th_{2},Th_{3},Th_{4}\} \tag{2}\]  
\[r_{2}:\{0,Sb_{1},Sb_{2},Sb_{3},Sb_{4}\} \tag{3}\]  
\[r_{3}:\{0,Dw_{1},Dw_{2},Dw_{3},Dw_{4}\} \tag{4}\]  
\[r_{4}:\{0,1\} \tag{5}\]  
\[r_{5}:\{0,1\} \tag{6}\]  
\[r_{6}:\{Dp_{1},Dp_{2},Dp_{3}\} \tag{7}\]  
Each variable of the R-array represents a suitable alternative to adopt for each phase of the SSTS. The value \"zero\", in the case of \(r_{2}\) and \(r_{3}\), means that one or both treatments (i.e., stabilization and dewatering, respectively) could be not needed. The ANN was adopted to support the model to provide, given a set of input parameters, the suitable alternative for each treatment step (output). A framework of the ANN model developed is provided in Figure 4. A sample of 300 data composed of input and output parameters was collected for the ANN design. The sample includes scientific researches and full-case studies, where, for each work conducted, the most effective strategy was suggested to manage the SS. In other words, the sample collects a set of input-output couples that \"teach\" the ANN how to reproduce, given a specific input set, the correct output. The sample adopted for the ANN training was extracted from the literature, validated, and integrated with other cases (around 10% of the sample size) collected by considering the experts' opinion.