## 5 Results and Discussion
### Development of Closed-Form AOp ANN-Aided Prediction Equations  
The retrieved network weights and biases of the two optimized ANN models (SMA-ANN and MVO-ANN) are listed in Table 4. The weights and biases were successfully converted into simple and adaptable closed-form explicit equations that can be used to predict AOp generation when planning a blasting round for construction rock excavations. The generated AOp predictor equation for the SMA-ANN model is presented in Equation (24).  
\[AOp_{SMA-ANN}=16.55 tanh\left(\sum_{i=1}^{9}x_{i}+1.4006\right)+68.05 \tag{24}\]  
where \(x_{i}\) (\(i\) = 1, 2 \(\ldots\), 9) are input variables that are mathematically formulated using the weights and \(b1\), as demonstrated in Table 4, and can be derived as shown in Equation (25) below.  
\[x_{1}=-5.2400 tanh(0.9218B-0.20655+2.0207D-2.1869L+0.92177+4.2406 PF+3.4291Q+0.023 3 DIS-2.1843 RMR-1.7374)\] \[x_{2}=-0.6904 tanh(-0.1981B+1.2497S-1.1091D-3.1843L-0.1999T-1.4348 pF-0.4071Q+0.1439 DIS+2.1539 RMR-3.5815)\] \[x_{3}=3.326 tanh(2.9352B-0.5492S-2.0234D-0.2689L+4.7197T+2.0032 PF+0.5673Q+2.1549 DIS-1.7423 RMR+0.5541)\] \[x_{4}=-3.7788 tanh(2.8495B-5.3477S-2.1881D+2.2159L+4.88337T+1.1803 PF-5.0623Q+5.5159 DIS-0.1145 RMR+3.0744)\] \[x_{5}=3.3778 tanh(1.9090B-4.3624S-0.0267D+12.0182L+1.8981T-3.2526 PF-4.5959Q+6.2092 DIS-1.3156 RMR+3.9849) \tag{25}\] \[x_{6}=8.3641 tanh(-1.3518B+1.6233S-0.2834D-2.7341L-1.3456T+0.109 7 PF+0.5537Q-3.7619 DIS+0.3139 RMR-3.8069)\] \[x_{7}=4.0458 tanh(1.7754B-1.8998S-0.0859D+3.5352L+1.8467T+0.4503 OP-7.0705Q+2.9821 DIS+0.5262 RMR-1.5019)\] \[x_{8}=-0.2037 tanh(0.4929B+0.1933S-0.0307D-7.3747L+0.2709T-0.0737 PF-6.3318Q+0.1578 DIS-0.1736 RMR-0.0216)\] \[x_{9}=1.1364 tanh(1.1422B+10.6302S-1.0916D-3.15188L+1.0554T+2.7472 PF-0.9890Q+4.0753 DIS+0.1246 RMR+4.9379)\]  
For the MVO-ANN model, the generated equation is as presented in Equation (26).  
\[AOp_{MVO-ANN}=16.55 tanh\left(\sum_{i=1}^{9}x_{i}+1.3982\right)+68.05 \tag{26}\]  
where \(y_{i}\) (\(i\) = 1, 2 \(\ldots\), 9) are input variables that are mathematically formulated using the weights and \(b1\), as highlighted in Table 4, and can be derived as shown in Equation (27).  
\[y_{1}=0.6818 tanh(3.2593B+7.1832S-2.4079D-0.1395L+3.9862T-5.9387 PF-0.9281Q+3.3369 DIS+4.4127 RMR+3.6026)\] \[y_{2}=4.7120 tanh(-1.6501B-1.1915S-0.1357D-0.1925L-0.9058T-0.1382 PF-1.9574Q-1.0608 DIS+0.8722 RMR+2.7622)\] \[y_{3}=-1.4915 tanh(-1.0329B-0.6646S-0.2764D-3.3653L-1.1693T-2.7454 pF-1.7059Q+2.2366 DIS-0.7899 RMR-1.8593)\] \[y_{4}=-1.7079 tanh(0.1325B-2.7229S+0.7861D+0.7534L-0.5904T+2.8602 PF-2.0336Q-1.0599 DIS-3.9818 RMR+1.4799)\] \[y_{5}=2.8986 tanh(2.1845B-0.1519S+1.0670D-5.641L+1.9426T+0.4679 PF+0.9504Q+3.7224 DIS-0.0898 RR-1.4936) \tag{27}\] \[y_{6}=-1.6146 tanh(0.8432B+2.5071S+0.8191D+0.3777L-0.9472T-2.9196 PF-0.1334Q+4.8667 DIS+6.8268 MR-1.4919)\] \[y_{7}=-2.9749 tanh(-0.0580B+3.71265-0.1745D-3.3070L-0.8605T+0.9504 pF+1.4986Q-3.7591 DIS+0.7592 RMR-2.5205)\] \[y_{8}=0.8277 tanh(-2.9660B-3.64245+3.3059D+0.3393L-2.3650T+9.7145 pF+1.8197Q+0.6470 DIS+1.3214 RMR+3.6159)\] \[y_{9}=-4.7780 tanh(1.008B-2.3431S+0.4299D+1.1599L+0.8472T-0.1035 SPF-1.2063Q+3.82278 DIS-0.0846 RMR+3.5629)\]  
When applying the proposed ANN-aided mathematical equations for predicting the AOp in construction rock excavation blasting, it is pertinent to note that the parameters \(x_{1}\)-\(x_{9}\) and \(y_{1}\)-\(y_{9}\) are in a normalized form and must be denormalized back to the original values after the calculation.