# Prediction of Blast-Induced Ground Vibration Using an Adaptive Network-Based Fuzzy Inference System
## 7 Numerical Example  
In order to explain the developed ANFIS technique, we have presented a calculation method for predicting the _PPV_ and _FREQUENCY_ caused by tunnel blasting in Pluska-Ponikve [45]. The proposed system ANFISBLAST was applied. In the numerical example, the _PPV_ and _FREQUENCY_ were predicted for a charge of 36 kg and a distance of 63 m. Because the proposed ANFISBLAST system comprises two different ANFIS models, two different model calculations were executed in order to predict the _PPV_ and _FREQUENCY_. The predicted peak particle velocity, calculated by the ANFIS model _PPV_, yielded 5.882 mm/s. The predicted frequency, calculated by the ANFIS model _FREQUENCY_, yielded 63.661 Hz. The premise parameters for this solution are shown in Table 10 and the consequent parameters, the weighted averages of every rule's output, and the definitive output are given in Table 11.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Membership Function**} & \multicolumn{3}{c}{**ANFISBLAST-PPV**} \\  & **Premise Parameters** & \multicolumn{1}{c}{\# **(Q)**} & \multicolumn{1}{c}{\# **(d)**} \\ \hline \(i\) & \(\alpha_{i}^{PPV}\) & \(c_{i}^{PPV}\) & \(\mu\) _(36)_ & \(\mu\) _(63)_ \\ \(A_{1}\) & 7.064 & 37.168 & 0.638 & - \\ \(A_{2}\) & 14.451 & 68.800 & 0.000 & - \\ \(B_{1}\) & 0.870 & 2.031 & - & 0.000 \\ \(B_{2}\) & 0.815 & 4.039 & - & 0.564 \\ \multicolumn{2}{c}{**ANFISBLAST-FREQUENCY**} \\  & **Premise parameters** & \multicolumn{1}{c}{\# **(Q)**} & \multicolumn{1}{c}{\# **(d)**} \\ \(i\) & \(\alpha_{i}^{PPV}\) & \(c_{i}^{PPV}\) & \(\mu\) _(36)_ & \(\mu\) _(63)_ \\ \(A_{1}\) & 65.821 & 25.857 & 0.364 & \\ \(A_{2}\) & 64.280 & 76.438 & 0.000 & \\ \(B_{1}\) & 1.690 & 1.623 & 0.993 \\ \(B_{2}\) & 1.349 & 4.631 & 0.034 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Premise parameters of the Gaussian membership function for the ANFIS models _PPV_ and _FREQUENCY_.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(i\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(\overline{\textbf{u}}_{i}^{PPV}\) & \(PPV_{i}\)=\(\alpha_{i}^{PPV}\)+\(\alpha_{i}^{PPV}\).Q+\(\alpha_{i}^{PPV}\).Q & \(\overline{\textbf{u}}_{i}^{PPV}\).Q \\ \hline \(1\) & 11.6401 & 0.0179 & -0.1016 & 0.000 & 1.000 & 5.882 \\ \(2\) & -3.0130 & 0.3535 & -0.1469 & 0.000 & 0.000 & 0.459 & 0.000 \\ \(i\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(PPV\) (mm/s) & & \(\overline{\textbf{c}}_{i}^{PPV}\) \\ \(i\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(\alpha_{i}^{PPV}\) & \(\overline{\textbf{u}}_{i}^{PPV}\) & \(\overline{\textbf{c}}_{i}^{PPV}\) & \(\overline{\textbf{c}}_{i}^{PPV}\) \\ \(1\) & 2.5956 & -0.0083 & 0.9740 & 0.362 & 1.000 & 63.661 \\ \(2\) & 1351.65 & -28.304 & 1.3909 & 0.000 & 0.000 & 420.342 & 0.000 \\ \multicolumn{2}{c}{\(FREQUENCY\) (Hz)} \\ \hline \hline \end{tabular}
\end{table}
Table 11: Consequent parameters and final outputs for the ANFIS models _PPV_ and _FREQUENCY_.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Measurement No.** & **Measured (mm/s)** & **USBM** & **Ambraseyes-Hendron** & **Langefors–Kihlstorm** & **ANFISBLAST-PPV** \\ \hline \(1\) & 2.2 & 2.67 & 2.82 & 2.13 & 1.66 \\ \(2\) & 7.3 & 4.69 & 4.91 & 3.73 & 5.88 \\ \(3\) & 2.8 & 2.89 & 2.96 & 2.71 & 1.58 \\ \(4\) & 4.9 & 4.49 & 4.58 & 4.12 & 5.18 \\ \(5\) & 5.5 & 5.66 & 5.75 & 5.24 & 6.53 \\ \(6\) & 7.9 & 10.71 & 10.88 & 9.40 & 8.55 \\ \(7\) & 3.7 & 4.00 & 3.99 & 4.12 & 3.94 \\ \(8\) & 7.7 & 5.78 & 5.66 & 6.39 & 6.82 \\ \hline \hline \multicolumn{5}{c}{Statistical parameter} \\  & SSE & 14.27 & 14.50 & 13.32 & 4.67 \\  & R-squared & 0.59 & 0.59 & 0.62 & 0.87 \\  & Adjusted R-squared & 0.53 & 0.52 & 0.56 & 0.84 \\  & RMSE & 1.54 & 1.55 & 1.49 & 0.88 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Measure of performance for the adaptive network-based fuzzy inference system (ANFIS) and conventional predictors.