## 2 Material and Methods
### Support Vector Regression (SVR)  
One of the most effective approaches for handling regression complications is SVM, which is a supervised technique [28]. The formation and optimization approach of SVM varies according to the nature of inputs, and \(\varepsilon\)-SVR is the regression form of SVM. The principal objective of SVR is to acquire a hypothesis whose entire errors of regression forecast are situated within a predetermined threshold, \(\varepsilon\). The next aim of the learned function is that this function possesses an excellent achievable generalization capability. This aim is purposely attempted in order that a flat model can be established. The following equations enact the aforementioned aims, forming a typical convex quadratic optimization problem with linear constraints set. The above goals are met by the following equations, which, along with the set of linear constraints, make a typical curved quadratic optimization problem.  
\[minimze\ \frac{1}{2}\|\omega\|^{2}+c\sum_{i=1}^{k}(\theta_{i}+\theta_{i}^{*}) \tag{2}\]  
\[subject\ to\left\{\begin{aligned} b_{i}-\langle\omega,a_{i}+c \rangle\leq\vartheta_{i}+\varepsilon,\ \forall n\\ \langle\omega,a_{i}+c\rangle-b_{i}\leq\ \vartheta_{i}^{*}+ \varepsilon,\forall n\\ \vartheta_{i},\ \vartheta_{i}^{*}\geq 0,\forall n\end{aligned}\right. \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Site** & **RQD (\%)** & **Height of Bench (m)** \\ \hline Masai & 60–84 & 15–20 \\ Pasir Gudang & 67–89 & 13–25 \\ Pengerang & 70–91 & 10–23 \\ Ulu Tiram & 65–88 & 10–15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Some additional measurements in blasting sites.  
where, for training points \((a_{i},b_{i})\),..., \((an,bn)\), \(k\) denotes the number of data samples, the vectors of \(a_{i}\) denote values of input, and \(b_{i}\) implies the corresponding output value for \(a_{i}\). The upper and lower errors of training are represented by \(\mathbf{\vartheta}_{i}\) and \(\mathbf{\vartheta}_{i}^{*}\), respectively. The errors are indifferent to a particular margin defined by \(\varepsilon\); afterwards, the cost function will be added by penalties. The normal vector is denoted by \(\mathbf{\omega}\). The regularization parameter (\(c>0\)) regulates the balance of the pair of goals enacted in the above equations. The authors employed Lagrange multipliers to ascertain the SVR's optimization problem expressed by the above equations. Some alterations were performed following that the Lagrangian is calculated until the next equation is obtained:  
\[f(a,\beta_{i},\beta_{i}^{*})=\sum_{i=1}^{n}(\beta_{i}-\beta_{i}^{*})l(a,a_{i})-c \tag{4}\]  
The equation obtained above is based on theories of optimality constraints, the kernel method, and Lagrange multipliers. While four renowned kernels, including sigmoid, polynomial, linear, and RBF, are available, this study employed RBF. This kernel was intentionally picked due to its computational capability. Typically, this kernel outperforms others [28]. RBF is extremely nonlinear, including possessing some inputs and an unlimited-dimensional space of mapping [29]. The RBF kernel is displayed in the following equation:  
\[L\big{(}a_{i},a_{j}\big{)}=e^{-\gamma(\|a_{i}-a_{j}\|^{2})} \tag{5}\]  
where \(\gamma\in\mathbb{R}\), \(\gamma>0\) describes the expanse of the radial basis kernel function.  
Figure 1 displays the structure of SVR based on Equation (3). This structure admits the requirements of Karush-Kuhn-Tucker for resolving a quadratic optimization query. The values of \((\beta_{i}\)-\(\beta_{i}^{*})\) were used to obtain the decision function. It is worth mentioning that these values were non-null support vectors. One of the most vital steps to develop a profoundly accurate and stable prediction model is to optimize the pair of SVR's hyper-parameters, including C and \(\gamma\). Adopting optimization methods for ascertaining these parameters' optimal conditions is considered in recent studies.