# Predictive Modelling for Blasting-Induced Vibrations from Open-Pit Excavations
## 5 Prediction Results  
### Performance Comparisons of the Six Prediction Models  
The 298 test datasets, which account for 25% of the total datasets obtained, were predicted using the eight predictive analysis methods, ANN, EF-1, EF-2, EF-3, ISEE model, USBM model, MLRA, and MnLRA, described in Chapter 4. First, the PPVs were predicted using the weights and biases matrices of the optimal ANN model. Here, all seven influential factors, VoD, W, SW, VoP, D, K, m were used as input parameters. Second, we used EF-1 which grouped 50 empirical formulas to predict PPVs of the test datasets. Here, each test dataset was predicted by the empirical formula of the site where they were obtained. W and D were used as input parameters. Finally, the test datasets were predicted by EF-2, 3, ISEE model, USBM model, MLRA, and MnLRA expressed as Equations (14)-(19), respectively, using input parameters of each method. In this study, three performance indicators, mean absolute error (MAE), root mean square error (RMSE), and mean absolute percent error (MAPE), were used to analyze prediction results. These performance indicators are listed in Table 6.  
Here, Vmi and Vpi are the i-th measured and predicted values, respectively, and \(n\) is the total number of test datasets. Table 7 summarizes the performances of the eight prediction models on the predicted PPVs. The developed ANN model achieved the lowest MAE of 0.064 cm/s, RMSE of 0.161 cm/s, and MAPE of 23.2%. These results were approximately 30%, 56%, and 11% lower than those from EF-1, which is currently the most commonly used method to predict PPVs when designing blasting patterns for construction. However, the EF-2 deduced the highest MAE of 0.305 cm/s and RMSE of 0.731 cm/s.  
Linear regression analyses were performed with a coefficient of determination known as R\({}^{2}\) to explain the correlation and similarity between the predicted PPVs from the six predictive analysis methods and measured PPVs of the test datasets. The value of R\({}^{2}\) can  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Performance Indicator** & **Equation** \\ \hline MAE & MAE = \(\frac{1}{n}\frac{n}{i}\lvert\mathrm{V}_{\mathrm{mi}}-\mathrm{V}_{\mathrm{pi}}\rvert\) \\ RMSE & RMSE = \(\sqrt{\frac{1}{n}\frac{n}{i}\
abla\left(\mathrm{V}_{\mathrm{mi}}-\mathrm{V}_{ \mathrm{pi}}\right)^{2}}\) \\ MAPE & MAPE = \(\frac{1}{n}\frac{n}{i}\lvert\frac{\mathrm{V}_{\mathrm{m}}-\mathrm{V}_{\mathrm{ g}}}{\mathrm{V}_{\mathrm{m}}}\rvert\times 100\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Equations of performance indicators.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **MAE (cm/s)** & **RMSE (cm/s)** & **MAPE (\%)** \\ \hline ANN & 0.064 & 0.161 & 23.2 \\ EF-1 & 0.092 & 0.370 & 26.1 \\ EF-2 & 0.305 & 0.731 & 146.5 \\ EF-3 & 0.123 & 0.309 & 47.8 \\ ISEE model & 0.244 & 0.601 & 115.7 \\ USBM model & 0.123 & 0.308 & 40.7 \\ MLRA & 0.202 & 0.370 & 175.1 \\ MnLRA & 0.108 & 0.298 & 39.1 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Performances of the six prediction models.  
be found using Equation (20), where \(\rm V_{m}\) and \(\rm V_{p}\) are measured and predicted PPV values, Cov is the covariation between two factors, and Var is the variation of a factor.  
\[\rm R^{2}=\frac{Cov^{2}(V_{m},V_{p})}{Var(V_{m})\times Var(V_{p})} \tag{20}\]  
Each predicted PPV by the six prediction methods is plotted as a small circle in Figure 6a to 6h respectively according to prediction methods. The x and y axes represent the measured and predicted PPV, respectively, in cm/s. There are two lines in each figure. The dashed line is the Measured PPV = Predicted PPV (1:1) line and the solid line is the linear regression line. In the lower right corner of each figure, it shows the equation of the linear regression line and \(\rm R^{2}\). The linear regression line resulting from the ANN shows the best result in terms of similarity to the 1:1 line as shown in Figure 6. The linear regression line resulting from the MLRA displays the greatest distance between the two lines.  
Figure 6: _Cont._