# Research on a Coal Seam Gas Content Prediction Method Based on an Improved Extreme Learning Machine
## 2 Development of Prediction Models for Coal Seam Gas Content
### Parameter Optimization and Testing of the Model  
The parameter initialization process involves utilizing the fitness function of the GASA algorithm, which is the MSE between the predicted and actual values, to optimize the initial \begin{table}
\begin{tabular}{c c c c c c c c} \hline Factors Influencing & \(X_{1}\) & \(X_{2}\) & \(X_{3}\) & \(X_{4}\) & \(X_{5}\) & \(X_{6}\) & \(X_{7}\) & \(X_{8}\) \\ \hline \(r_{e}\) & 0.6698 & 0.5623 & 0.2908 & 0.3176 & 0.5024 & 0.6117 & 0.5102 & 0.5785 \\ \hline \end{tabular}
\end{table} 
Table 4: The results of grey correlation analysis. parameters of the three gas content prediction models. To circumvent the potential issue of stochastic errors that may arise in random search algorithms, the GASA was employed to optimize the parameters of each model for 100 iterations. Figure 13 depicts the average evaluation function values during the parameter optimization process. As observed in the figure, the target requirement was not met within 800 iterations while optimizing BPNN parameters using GASA. Hence, the threshold and weight corresponding to the minimum fitness value were selected as the optimal initial parameters and assigned to the BPNN model to complete the parameter initialization process. As the SVM and KELM models underwent initial optimization of kernel parameters and penalty factors, optimal initial parameters were discovered by the two models in the 673 rd and 487 th iterations, respectively. Once these parameters were decoded and assigned values, the initialization process was complete. The results depicted in Figure 13 reveal that the optimization speed and quality of the SVM and KELM parameters with GASA were markedly superior to those of the BPNN, which has a larger number of parameters to optimize. After initializing each model with optimal initial parameter values, we trained the final models separately using the data collected in Table 3. To evaluate the predictive performance of the GASA-BPNN, GASA-SVM, and GASA-KELM models for gas content prediction, we performed 10-fold cross-validation ten times under identical conditions. In each iteration, the training set and test set were input into the model for 100 iterations of training and prediction. The prediction results for the ten test sets in the 10-fold cross-validation are presented in Table 5. As observed from Table 5, the variance of the average relative error and the total average relative error for the coabled methane prediction by the GASA-SVM and GASA-KELM models in each of the ten test sets is lower than that of the GASA-BPNN model. This suggests that the accuracy and stability of the SVM and KELM models for methane content prediction are superior to those of the GASA-BPNN model. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \(\mathbf{A_{1}}\) & \(\mathbf{A_{2}}\) & \(\mathbf{A_{3}}\) & \(\mathbf{A_{4}}\) & \(\mathbf{A_{5}}\) & \(\mathbf{A_{6}}\) & \(\mathbf{A_{7}}\) & \(\mathbf{A_{8}}\) & \(\mathbf{A_{9}}\) & \(\mathbf{A_{10}}\) & **Average/\%** & **Variance** \\ \hline BPNN & 19.46 & 12.59 & 16.6 & 7.53 & 15.32 & 17.9 & 17.82 & 12.06 & 20.89 & 17.21 & 15.738 & 3.99 \\ SVM & 13.81 & 15.3 & 8.74 & 15.11 & 18.29 & 13.76 & 10.03 & 15.58 & 14.71 & 13.15 & 13.848 & 2.76 \\ KELM & 12.46 & 7.92 & 10.07 & 8.14 & 9.24 & 11.44 & 13.78 & 9.16 & 8.35 & 8.09 & 9.865 & 2.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ten-fold cross-validation of the prediction results. Figure 13: Average mean square error convergence curves. In the final stage of the study, 12 sets of samples were designated as validation sets, and the three models were utilized to predict the gas content of these samples. The predictive performance of the 12 validation samples, which were included in the test set of all 10 simulated tests, was analyzed, and the prediction outcomes of the three models were compared.