## 5 Modelling Based on EPR Method
### Evaluating the Model Performance  
In Tables 5-10, the performance parameters of the models for training, testing, and total data are presented. The basis for calculating these parameters was the relations mentioned in Section 3. As is evident, all the models performed desirably in predicting the collapse settlement and coefficient of stress release. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **COD** & **AVG** & **RMSE** & **SSE** & \(\boldsymbol{R^{2}}\) \\ \hline Secant hyperbolic & 0.9728 & 0.111 & 0.014 & 0.015 & 0.9732 \\ Tangent hyperbolic & 0.9733 & 0.142 & 0.016 & 0.021 & 0.9634 \\ Natural logarithm & 0.9667 & 0.134 & 0.02 & 0.019 & 0.9668 \\ Exponential & 0.9746 & 0.101 & 0.013 & 0.014 & 0.9759 \\ Sinusoidal & 0.9374 & 0.204 & 0.018 & 0.036 & 0.938 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Precision and performance of the models for \(\mathrm{\Delta H}\) prediction (testing data). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **COD** & **AVG** & **RMSE** & **SSE** & \(\boldsymbol{R^{2}}\) \\ \hline Secant hyperbolic & 0.9812 & 0.025 & 0.01 & 0.0002 & 0.9812 \\ Tangent hyperbolic & 0.9781 & 0.03 & 0.011 & 0.0002 & 0.9781 \\ Natural logarithm & 0.9706 & 0.036 & 0.014 & 0.0003 & 0.9706 \\ Exponential & 0.9833 & 0.012 & 0.01 & 0.0002 & 0.9833 \\ Sinusus & 0.9687 & 0.015 & 0.013 & 0.0004 & 0.9694 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Precision and performance of the models for \(\mathrm{\Delta H}\) prediction (all data). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **COD** & **AVG** & **RMSE** & **SSE** & \(\boldsymbol{R^{2}}\) \\ \hline Secant hyperbolic & 0.9812 & 0.025 & 0.01 & 0.0002 & 0.9812 \\ Tangent hyperbolic & 0.9781 & 0.03 & 0.011 & 0.0002 & 0.9781 \\ Natural logarithm & 0.9706 & 0.036 & 0.014 & 0.0003 & 0.9706 \\ Exponential & 0.9833 & 0.012 & 0.01 & 0.0002 & 0.9833 \\ Sinusus & 0.9687 & 0.015 & 0.013 & 0.0004 & 0.9694 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Precision and performance of models for CSR prediction (training data). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **COD** & **AVG** & **RMSE** & **SSE** & \(\boldsymbol{R^{2}}\) \\ \hline Secant hyperbolic & 0.9812 & 0.025 & 0.01 & 0.0002 & 0.9803 \\ Tangent hyperbolic & 0.9722 & 0.028 & 0.016 & 0.0002 & 0.9733 \\ Natural logarithm & 0.9593 & 0.035 & 0.02 & 0.0004 & 0.9607 \\ Exponential & 0.9817 & 0.022 & 0.013 & 0.0001 & 0.982 \\ Sinusus & 0.9655 & 0.027 & 0.018 & 0.0003 & 0.9663 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Precision and performance of models for CSR prediction (all data). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **COD** & **AVG** & **RMSE** & **SSE** & \(\boldsymbol{R^{2}}\) \\ \hline Secant hyperbolic & 0.9812 & 0.025 & 0.015 & 0.0003 & 0.9811 \\ Tangent hyperbolic & 0.978 & 0.03 & 0.017 & 0.0003 & 0.9769 \\ Natural logarithm & 0.9709 & 0.036 & 0.019 & 0.0004 & 0.9682 \\ Exponential & 0.9832 & 0.025 & 0.014 & 0.0002 & 0.9833 \\ Sinusoidal & 0.9685 & 0.034 & 0.019 & 0.0004 & 0.9687 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Precision and performance of models for CSR prediction (testing data). Figures 9-13 show the ability of each of the developed models by comparing the measured and predicted coefficients of stress release based on the training and testing data. Similarly, the error range of 20% is shown. It can be clearly seen that the R\({}^{2}\) values for training and testing data were 0.9833 and 0.9820, respectively, and the RMSE values were 0.010 and 0.013, respectively, which in turn indicate the suitable precision of the model. Figure 8: Comparing the results of the predicted and measured collapse settlement based on the sinusoidal function. (**a**) Training data, (**b**) Testing data. Figure 6: Comparing the results of the predicted and measured collapse settlement based on the natural logarithm. (**a**) Training data, (**b**) Testing data.