## 3 Results and Discussion  
Representative distributions of normalized drilling data samples composed of 4900 data points obtained for concrete, concrete, granite, and granite are presented in Figure 5(a1,b1,c1,d1), respectively. The corresponding lithofacies image-type data structures composed of \(70\times 70=4900\) pixels are, respectively, presented in Figure 5(a2,b2,c2,d2). Details regarding the features of the data samples presented in Figure 5 are listed in Table 1. As can be seen from Figure 5, both the normalized drilling data and the lithofacies images of the concrete and granite samples exhibit strong visual similarities that are difficult for human viewers to distinguish. In contrast, DANNs have demonstrated excellent performance at detecting subtle differences between the features of the samples and distinguishing them accordingly. Figure 5: Representative distributions of normalized drilling data samples composed of 4900 data points: (**a1**) concrete; (**b1**) concrete; (**c1**) granite; (**d1**) granite. Corresponding lithofacies image-type data structures composed of \(70\times 70=4900\) pixels: (**a2**) concrete; (**b2**) concrete; (**c2**) granite; (**d2**) granite. The loss function values obtained according to Equation (3) are plotted with respect to the number of training iterations in Figure 6 for different learning rates with a 14,700-8-3-1 network structure composed of four layers, including an input layer with 14,700 nodes, two hidden layers with eight and three nodes, respectively, and one node in the output layer. As can be seen, the learning rate has a profound effect on the rate at which the loss function value decreases to zero, which is indicative of the neural network having learned the significant sample features reflecting the lithofacies types of the materials. Details regarding the loss values obtained under different learning rates are listed in Table 2. Considering the key factors of time and stability, a learning rate of \(\alpha\) = 0.0020 and 20,000 iterations were selected for the model training process in all subsequent experiments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Lithofacies** & **State** & **Scatter Plot** & **Lithofacies** \\
**Number** & **Classification** & & & **Image** \\ \hline
5 & Concrete & Cutting & Figure 5(a1) & Figure 5(a2) \\
13 & Concrete & Friction & Figure 5(b1) & Figure 5(b2) \\
23 & Granite & Cutting & Figure 5(c1) & Figure 5(c2) \\
31 & Granite & Friction & Figure 5(d1) & Figure 5(d2) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Features of data samples presented in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Learning Rate** & \begin{tabular}{c} **Loss at 20,000** \\ **Iterations** \\ \end{tabular} & \
\begin{tabular}{c} **Iterations When** \\ **Loss = 0.05** \\ \end{tabular} &
\begin{tabular}{c} **Training Time (s)** \\ \end{tabular} \\ \hline
0.0100 & 0.312837 & — & 36.260358 \\
0.0060 & 0.002251 & 2718 & 37.891610 \\
0.0040 & 0.000908 & 2331 & 36.654807 \\
0.0020 & 0.002735 & 4792 & 36.648935 \\
0.0010 & 0.009985 & 8653 & 42.522422 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Loss values obtained under different learning rates. Figure 6: Loss function values (Equation (3)) plotted with respect to the number of training iterations for different learning rates. The effect of network structure on the loss function value is presented in Figure 7, where the abbreviations uniformly follow the 14,700-8-3-1 example discussed above. Details regarding the loss values obtained under different network structures are listed in Table 3. The results demonstrate that the 14,700-8-3-1 network structure provides a relatively ideal learning condition because the training time cost is approximately half that of the most complex model with very nearly the same effectiveness, as indicated by the final loss value obtained after 20,000 iterations.