## 2 Methods
### Bb-Ann
To this end, a research program was carried out to predict blast-induced ground vibration in these quarry mines. A total of 80 blasting events were monitored and 80 sets of data were prepared. In this database, several effective parameters affecting the PPV, including burden (\(B\)), spacing (\(S\)), stemming (\(ST\)), powder factor (\(PF\)), maximum weight charge per delay (\(W\)), rock mass rating (\(RMR\)), and distance from the blasting-point (\(D\)) were provided. These parameters were used as the input parameters in the modeling process of the predictive models. Additionally, PPV was used as the output parameter. To measure the PPV values, a MR2002-CE SYSCOM seismograph was installed on the site. This instrument can measure PPV values in the range of 0.001 to 115 mm/s. Also, the values of \(B\), \(S\), \(ST\), \(PF\), and \(W\) were measured by controlling the blast-hole charge. To measure \(D\), GPS (global positioning system) was also used. The ranges of the model inputs and outputs together with some other information are provided in Table 1. Furthermore, the histograms of the input and output parameters are shown in Figure 4. According to this figure, for the B parameter, 23, 20, 19, and 18 data values were varied in the ranges of 0-3.2 m, 3.2-3.5 m, 3.5-3.8 m, and 3.8-4.5 m, respectively. Figure 3: A simple architecture of the extreme learning machine (ELM). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Unit** & **Min** & **Max** & **Mean** \\ \hline \(B\) & M & 2.7 & 4.1 & 3.50 \\ \(S\) & M & 3.4 & 5.3 & 4.37 \\ \(S_{T}\) & M & 1.8 & 3.4 & 2.70 \\ _PF_ & gr/cm\({}^{3}\) & 153 & 213 & 172.24 \\ \(W\) & Kg & 180 & 1450 & 791 \\ _RMR_ & - & 38 & 55 & 45.38 \\ \(D\) & M & 308 & 944 & 563.45 \\ _PPV_ & mm/s & 3.3 & 9.9 & 6.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The ranges of the model inputs and outputs and some other information. Figure 4: Histograms of the input and output parameters. ## 4 Empirical Methods to Predict PPV

In this study, three well-known empirical methods, namely the US Bureau of Mines (USBM, Washington, DC, USA) [39], Indian Standard [40], and Ambraseys-Hendron [41] models, were used to predict PPV. These methods are only related to \(W\) and \(D\) parameters, and are formulated as:

\[PPV=Q\times\left[\frac{D}{\sqrt{W}}\right]^{2} \tag{3}\]

\[PPV=Q\times\left[\frac{W}{D^{\frac{2}{3}}}\right]^{2} \tag{4}\]

\[PPV=Q\times\left[\frac{D}{W^{0.33}}\right]^{2}. \tag{5}\]

Equations (3)-(5) show the USBM, Indian Standard, and Ambraseys-Hendron methods. In these equations, \(Q\) and \(z\) are the site constants, and can be computed using the SPSS software. Using the database and our analysis, Equations (6)-(8) are updated as follows:

\[PPV=0.367\times\left[\frac{D}{\sqrt{W}}\right]^{-0.228} \tag{6}\]

\[PPV=0.447\times\left[\frac{W}{D^{\frac{2}{3}}}\right]^{0.283} \tag{7}\]

\[PPV=0.351\times\left[\frac{D}{W^{0.33}}\right]^{-0.237}. \tag{8}\]

Note that to construct the empirical methods, firstly, the datasets used were normalized, as well as the same AI models. In other words, Equations (6)-(8) are based on normalized datasets. The performance of these empirical methods is evaluated in Section 6. ## 5 Development of BBO-ANN, PSO-ANN, MPMR, and ELM to Predict PPV

The algorithm for the prediction of PPV was developed with the help of MATLAB sub-routines. The structure of the models drew on an input matrix (\(x\)) defined by \(x\) = (B, S, ST, PF, W, RMR, and D) which provided the predictor variables, while PPV induced by blasting was denoted as the target variable (\(y\)). In any modeling process, the most important task is to find the appropriate size of the training data and testing dataset. Therefore, in this research, 70% of the total dataset was randomly selected and used to develop the models and the developed models was tested on the remaining dataset. In other words, 56 and 24 datasets were used to develop and test the models, respectively. Prior to model development, the whole dataset was normalized to the range of zero to one.