## 4 Results and Discussion
### Assessment of Models Performance  
In evaluating the prediction capabilities of the five predictive models presented in the study, the statistical performance outcomes of the testing samples are outlined in Table 11.  
Notionally, a predictive model is said to be accurate if \(R\) and \(R^{2}\) are 1, MSE is 0 and VAF is 100%. In that regard, it can the seen that the GPR with the MSE value of 0.0903 closest to 0, \(R\) values of 0.9985 closest to 1, \(R^{2}\) values of 0.9971 closest to 1 and VAF value of 99.1728% closest to 100% outperformed all the techniques applied in this study. This shows the reliability of the GPR in predicting ground vibration. The MARS performed better than the ELM by having had MSE value of 0.1038 and a VAF value of 98.5469% with the ELM having an MSE value of 0.1381 and a VAF value of 98.2273%. The ELM also performed better than the BPNN with MSE and VAF values of 0.2178 and 98.1919%. It is worth mentioning that the GPR, MARS, ELM and BPNN were superior in predicting ground vibration to the simple MVRA model which had an MSE of 3.2456, \(R\)-value of 0.8310, the \(R^{2}\) value of 0.6906 and VAF value of 66.0603%. Figure 7 depicts the interpretation of the obtained results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Architecture**} & **Number of Hidden** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} \\ \cline{3-6}  & **Neurons** & \(R\) & **MSE** & \(R\) & **MSE** \\ \hline
7-1-1 & 1 & 0.6989 & 5.2395 & 0.8328 & 2.9447 \\
7-2-1 & 2 & 0.7562 & 4.3848 & 0.8797 & 2.3808 \\
7-5-1 & 5 & 0.9371 & 1.2477 & 0.9877 & 0.4775 \\
7-8-1 & 8 & 0.9441 & 1.1130 & 0.9624 & 0.7056 \\
7-10-1 & 10 & 0.9910 & 0.1832 & 0.9948 & 0.1832 \\
7-12-1 & 12 & 0.9958 & 0.0870 & 0.9957 & 0.1384 \\
7-15-1 & 15 & 0.9950 & 0.2181 & 0.9930 & 0.1521 \\
7-18-1 & 18 & 0.9836 & 0.3341 & 0.9914 & 0.1989 \\
7-20-1 & 20 & 0.9848 & 0.3080 & 0.9862 & 0.2530 \\
7-25-1 & 25 & 0.9919 & 0.1656 & 0.9738 & 0.7639 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Training and Testing \(R\) and MSE Results for ELM.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & \(R\) & \(R^{2}\) & **VAF (\%)** \\ \hline GPR & 0.0903 & 0.9985 & 0.9971 & 99.1728 \\ MARS & 0.1038 & 0.9953 & 0.9906 & 98.8692 \\ ELM & 0.1381 & 0.9957 & 0.9915 & 98.5469 \\ BPNN & 0.1714 & 0.9924 & 0.9848 & 98.2273 \\ MVRA & 3.2456 & 0.8310 & 0.6906 & 66.0603 \\ \hline \hline \end{tabular}
\end{table}
Table 11: PPV Prediction Results of Various Models.  
As ground vibration is one of the most unfavorable environmental effects of blasting operations which can cause serious damage to neighboring residences and structures, a precise prediction of its severity is critical to managing and lessening its incidence. The \(R\), \(R^{2}\) and VAF values for the GPR, MARS, BPNN, and ELM may not vary significantly, but any predictive model that delivers the most accurate prediction is of paramount relevance to the blast engineer. Hence the need to develop different models. This study found that the GPR is more accurate in forecasting ground vibration than the MARS, BPNN, ELM and MVRA and that it can be used by blast engineers to predict blast-induced ground vibration.