# Study on the \"Two-Zone\" Heights in Lower Slice Mining Under Thick Al Alluvium and Thin Bedrock
## 4 Height Prediction of 'Two Zones' of Overlying Strata in Lower-Layer Working Face
### Height Prediction of Water-Conducting Fracture Zone Based on BP Neural Network  
Many factors affect the prediction of the water-conducting fracture zone, which are complex and nonlinear. The BP neural network is a multi-layer grid learning algorithm based on multi-layer neurons. It is characterized by high adaptability, fault tolerance, and nonlinearity. The BP neural network is composed of an input layer, output layer, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Two Zones’** & **Lithology** & **Formula** & **Computation/m** \\ \hline \multirow{2}{*}{Falling zone \(H_{k}\)} & Medium-hard & / & \(H_{k}=\frac{100\sqrt{\Sigma}\cdot M}{\Sigma\cdot M+15}\pm 2.2\) & 11.24–15.65 \\  & Soft weak & / & \(H_{k}=\frac{100\sqrt{\Sigma}\cdot M}{6\Sigma\cdot M+32}\pm 1.5\) & 7.74–10.74 \\  & Medium-hard & Formula one: & \(H_{ll}=\frac{100\sqrt{\Sigma}\cdot M}{15\cdot M+36}\pm 5.6\) & 41.58–52.78 \\  & Formula two: & \(H_{ll}=20\sqrt{\Sigma}\cdot M+10\) & 62.65 \\  & Soft weak & Formula one: & \(H_{ll}=\frac{100\sqrt{\Sigma}\cdot M}{3\Sigma\cdot M+5.0}\pm 4.0\) & 22.17–30.17 \\  & Formula two: & \(H_{ll}=10\sqrt{\Sigma}\cdot M+5\) & 31.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculation height of ‘two zones’ based on the ‘three-underground mining norm’ [23]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Two Zones’** & **Lithology** & **Formula** & **Computation/m** \\ \hline \multirow{2}{*}{Falling zone \(H_{k}\)} & Medium-hard & \(H_{k}=(3\sim 4)\sum M\) & 20.79–27.72 \\  & Soft weak & \(H_{k}=(1\sim 2)\sum M\) & 6.93–13.86 \\  & Medium-hard & \(H_{ll}=\frac{100\sqrt{\Sigma}\cdot M}{3\pi\cdot 38}+5.1\) & 71.73 \\  & \multirow{2}{*}{Soft weak} & \(H_{ll}=\frac{100\sqrt{\Sigma}\cdot M}{5\cdot M+5.2}+5.1\) & 50.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The calculation height of ‘two zones’ based on the ‘exploration specification’ [24]. hidden layer. The signal forward calculation in the BP neural network is achieved through three different layers of functions. The error between the expected output and the actual output of the neuron is corrected using error backpropagation. The prediction goal is ultimately reached when the global error approaches the minimum value. According to the principles of BP neural network modeling, the height of the typical water-conducting fracture zone in China was determined based on the measured data [25]. The measured data from 100 mine working faces were selected as the learning and training samples for the BP neural network. The first 80 sets of data were used to create the neural network training model. The other 20 sets of data represent neural network test models, and the measured data for each working face are presented in Table 3.  
Since the dimensions and orders of magnitude of each input parameter are different, the input parameters must be dimensionless during neural network training [26]. The extreme value method is applied to standardize the mining thickness, mining depth, coal seam dip angle, dip length, and hard rock ratio coefficient of the sample set working face to remove the impact of dimension. The equation used is as follows:  
\[X_{n}=\frac{2(x_{n}-x_{\text{min}})}{x_{\text{max}}-x_{\text{min}}}-1 \tag{8}\]  
In the formula, \(X_{n}\) represents the normalized sample data, \(x_{n}\) stands for the measured data, \(x_{min}\) denotes the minimum value of the measured data, and \(x_{max}\) indicates the maximum value of the measured data. The mining thickness, mining depth, coal seam dip angle, dip length, and hard rock ratio coefficient of the processed working face are used as input parameters in the model for training. The results are shown in Figure 8, and the optimal network structure is obtained at the 17 th round.