# A Neural Network Model for Decision-Making with Application in Sewage Sludge Management
## 4 Results and Discussions  
The developed ANN model was tested on 20 possible scenarios, identified considering out-of-sample data. In other words, no data, already adopted to train, validate, and test the ANN was considered in this phase. The scenarios considered are generated on different combinations of the input values (i.e., PC, St, and Csp), while experts suggested the actual output values (i.e., \(r_{1}\), \(r_{2}\), \(r_{3}\), \(r_{4}\), \(r_{5}\), and \(r_{6}\)). The values assumed from the predicted values of \(r_{1}\) (Th\({}_{i}\)), \(r_{2}\) (Sb\({}_{i}\)) and \(r_{3}\) (Dwi\({}_{i}\)), given \(r_{6}\) = 1 (Dp\({}_{1}\)), excluding compositing and thermal drying treatment (\(r_{4}=r_{5}=0\)), were compared with actual values corresponding to the recommended strategies for SS management. The graphs showed a good consistency of predicted values by ANN, as shown in Figure 6; in most cases, the ANN allows us to identify the same alternatives suggested by \"experts\" for each phase. Figure 5: Architecture of the ANN with one input layer (x\({}_{i}\)) with 3 nodes (i.e., PC, St, and Csp), one hidden layer (h\({}_{i}\)) with 27 nodes, and one output layer (y\({}_{i}\)) with six output nodes (i.e., \(r_{1}\), \(r_{2}\), \(r_{3}\), \(r_{4}\), \(r_{5}\), and \(r_{6}\)) (adapted by [PERSON] et al., “Predicting Root Pressures on a Low-Rise Structure from Freestream Turbulence Using Artificial Neural Networks”). \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristic** & **Value** \\ \hline Dataset (Training, Validation, Testing) & 210-63-27 \\ \hline Architecture (Input/Hidden/Output) & 3-27-6 \\ \hline Structure & RNN \\ \hline Activations & Sigmoid \\ \hline Gradient update rules & Stochastic gradient descent \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Summary of the ANN characteristics. The reliability of the designed ANN was tested on the same dataset, evaluating all output parameters obtained by considering different features. Most representative error parameters (i.e., Mean error (ME), Mean Absolute Deviation (MAD), Means Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE)), showed a good performance of the ANN to predict the target variables (Table 9). In all cases, the error is lower than twenty percent. The trend of ME and MAD showed that the ANN is not affected by systematic errors. Although the MSE and MAE are generally good (the average value is around 0.3), the performance decrees for the \(\text{D}\text{p}_{\text{i}}\) prediction. Probably, the ANN has trouble identifying this value, since, in many cases, the same values of \(\text{D}\text{p}_{\text{i}}\) are given for a different combination of the other features. It is possible to claim that the average errors identified can exclude an overfitting problem. On the contrary, it should be better to evaluate the accuracy of the ANN adapting a Multi-Layer Perceptron (MLP) architecture. If, on the one hand, this could lead to an exponential increase in the running time, then, on the other hand, the performance could be drastically improved. The introduced ANN model was interfaced with a query developed by Microsoft Office Visual Basic for Applications (VBA) version 7.1. Purely by way of example, two numerical cases were tested to validate the tool's effectiveness. The tool, as appears in the screenshots shown below (Figures 7 and 8), is handy, and a user-friendly query was designed. Only the information strictly required to query the ANN is included. In the first case, the ANN model to identify the more efficient SS treatment in a plant with PC of 12E3 PE was questioned, with a single line's configuration and providing a chemical treatment as secondary treatment. The screenshot shown below provides the representation of the input query of the tool (Figure 7).