## 2 Materials and Methods
### Topology of ANNs  
Process modeling requires the complete identification of the significant process variables whose values must be obtained experimentally. However, the model development and the experimental estimation of the variables are challenging in many conditions and become very difficult as the process complexity (non-linearity) increases. Thus, ANN modeling has attracted researchers' attention as a powerful promising alternative option, but it needs computational effort (Kal  
Some statistical parameters, including correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), and mean bias error (MBE) were used to evaluate the proposed ANN model. Their equations are presented below [27; 28].  
\[\text{Correlation coefficient}\left(\text{R}\right)=\frac{\sum_{i=1}^{n} \bigl{(}Y_{exp,i}-\overline{Y_{exp,i}}\bigr{)}\bigl{(}Y_{est,i}-\overline{Y_{ est,i}}\bigr{)}}{\sqrt{\sum_{i=1}^{n}\bigl{(}Y_{exp,i}-\overline{Y_{exp,i}} \bigr{)}^{2}\sum_{m=1}^{n}\bigl{(}Y_{est,i}-\overline{Y_{est,i}}\bigr{)}^{2}}} \tag{1}\]  
\[\text{Root mean square error}\left(\text{RMSE}\right)=\sqrt{\frac{1}{N}\,\sum \bigl{(}\left(Y_{\text{est}}-Y_{\text{exp}}\right)^{2}} \tag{2}\]  
\[\text{Mean absolute error}\left(\text{MAE}\right)=\frac{1}{N}\sum \bigl{|}Y_{est}-Y_{\text{exp}}\bigr{|} \tag{3}\]  
\[\text{Mean bias error}\left(\text{MBE}\right)=\frac{1}{N}\sum \bigl{(}Y_{est}-Y_{\text{exp}}\bigr{)} \tag{4}\]  
where \(Y_{exp}\) is the experimental value of the weight left percent, \(Y_{est}\) is the ANN-estimated value of the weight left percent;; and \(\overline{Y}\) is the average value of weight left percent.  
In addition, sensitivity analysis was performed using Pearson correlation (Equation (5)) to investigate the uncertainties associated with relationships between input and output parameters.  
\[\text{Pearson correlation coefficient}\left(\text{r}_{XY}\right)=\frac{ \sum_{i=1}^{n}\bigl{(}X_{i}-\overline{X}\bigr{)}\bigl{(}Y_{i}-\overline{Y} \bigr{)}}{\sqrt{\sum_{i=1}^{n}\bigl{(}X_{i}-\overline{X}\bigr{)}^{2}\,\,\sum _{m=1}^{n}\bigl{(}Y_{i}-\overline{Y}\bigr{)}^{2}}} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Plastic**} & \multicolumn{6}{c}{**Proximate Analysis, wt \%**} & \multicolumn{6}{c}{**Ultimate Analysis, wt \%**} \\ \cline{2-9}  & **Moisture** & **Volatile** & **Ash** & **C** & **H** & **N** & **S** \\ \hline PS & 0.235 & 99.590 & 0.175 & 90.47 & 9.43 & 0.00 & 0.08 \\ PP & 0.076 & 99.630 & 0.294 & 85.00 & 14.73 & 0.04 & 0.23 \\ LDPE & 0.199 & 99.653 & 0.148 & 83.00 & 16.75 & 0.00 & 0.25 \\ HDPE & 0.405 & 99.377 & 0.218 & 82.77 & 16.92 & 0.00 & 0.29 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Proximate and ultimate analysis of different waste plastics.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test No.**} & \multicolumn{6}{c}{**Weight Fractions**} \\ \cline{2-5}  & **PP** & **PS** & **HDPE** & **LDPE** \\ \hline
1 & 0 & 0.7 & 0.3 & 0 \\
2 & 0.3 & 0.7 & 0 & 0 \\
3 & 0 & 0.7 & 0 & 0.3 \\
4 & 0 & 0.3 & 0 & 0.7 \\
5 & 0.3 & 0 & 0 & 0.7 \\
6 & 0 & 0 & 0.3 & 0.7 \\
7 & 0 & 0 & 0.7 & 0.3 \\
8 & 0.3 & 0 & 0.7 & 0 \\
9 & 0 & 0.3 & 0.7 & 0 \\
10 & 0.7 & 0 & 0 & 0.3 \\
11 & 0.7 & 0 & 0.3 & 0 \\
12 & 0.7 & 0.3 & 0 & 0 \\
13 & 0.333 & 0.333 & 0.333 & 0 \\
14 & 0 & 0.484 & 0.325 & 0.192 \\
15 & 0.167 & 0.484 where \(X\) and \(Y\) are input and output parameters, respectively, and \(\overline{X}\) and \(\overline{Y}\) are their mean values, respectively.