## 4 Denoising and Prediction of Optical Fiber Monitoring Signals Based on EEMD-DE-SVD and DBO-LSTM-BP
### Accuracy Evaluation Metrics  
According to the model prediction results, the denoising prediction model's output strain curve is closely aligned with the original curve and shows minimal deviation from the actual values. To evaluate the accuracy of the prediction model, four common error metrics are used: Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the Linear Regression Correlation Coefficient (R\({}^{2}\)). The calculation formulas are shown in Equations (14)-(17). Among them, smaller values for MAE, MSE, and RMSE are better, while R\({}^{2}\) values range from 0 to 1, with values closer to 1 indicating better curve fitting. The metric values reflect how well the prediction curve fits the actual curve and indicate the prediction accuracy, where \(y_{i}\) represents the original data and \(\hat{y}_{i}\) represents the fitted data.  
\[MAE=\frac{1}{n}\sum_{i=1}^{n}|y_{i}  
Figure 13 shows the comparison between predicted and actual monitoring values at different advancement distances of the working face. When the working face advanced to approximately 1360.5 m, a small peak in strain at monitoring point 9, close to the 22,208 working face mining side, was observed. At this point, the MAE, MSE, RMSE, and R\({}^{2}\) were 6.93, 55.31, 7.44, and 0.89, respectively. The MAE, MSE, and RMSE values were relatively small, and the R\({}^{2}\) value of 0.89 was close to 1, indicating an accuracy of approximately 88%.  
When the working face advanced to 1382.5 m, entering the stage of passing the residual inclined coal pillar, the strain trend prediction curves for the seven monitoring points had R\({}^{2}\) values around 0.95, with an accuracy of about 95%.  
When the working face advanced to 1436.5 m, entering the stage of retreating from the residual inclined coal pillar, the strain curves showed an increasing trend. However, the deformation of the coal pillar in this area was relatively small and remained in a stable range. The actual strain curve and the predicted curve had minimal deviation, with the R\({}^{2}\) values for the strain trend prediction curves around 0.96, indicating an accuracy of about 96%.  
When the working face advanced to 1440 m, despite being in the retreat stage, it was still on the edge of the residual inclined coal pillar influence zone. At this stage, the R\({}^{2}\) values for the strain trend prediction curves were around 0.99, with an accuracy of approximately 99%.  
The predicted strain trend results for the coal pillar section ranged between 88% and 99%, confirming the feasibility and accuracy of the EEMD-DE-SVD-DBO-LSTM-BP denoising prediction model for forecasting the optical fiber strain monitoring data of the underlying coal pillar section when passing through the residual inclined coal pillar. This model can achieve a certain degree of the advanced prediction of coal pillar deformation strain.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Monitoring Point** & **MAE** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline
4 & 0.56 & 0.98 & 0.42 & 0.99 \\
5 & 1.52 & 0.33 & 0.54 & 0.98 \\
6 & 0.24 & 0.62 & 0.35 & 0.99 \\
7 & 0.81 & 1.42 & 0.63 & 0.98 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluation index of strain prediction result of No.5 hole of coal pillar in 5-1# section.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Monitoring Point** & **MAE** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline
1 & 0.29 & 0.13 & 0.36 & 0.94 \\
2 & 1.19 & 1.75 & 1.32 & 0.95 \\
4 & 0.53 & 0.40 & 2.63 & 0.93 \\
5 & 1.20 & 1.96 & 1.40 & 0.95 \\
6 & 1.16 & 1.86 & 1.36 & 0.92 \\
8 & 1.01 & 1.63 & 1.22 & 0.95