## 4 Simulation and Analysis
### Comparison with the Literature  
To demonstrate the superiority of the proposed cutting pattern recognition method through the cutting sound based on FCM-FGOA, some related research were taken was compared. According to the relevant literature, \(\gamma\)-ray concentration detection in [2], vibration analysis in [5], original FCM, FCM optimized by PSO in [23], FCM optimized ACO in [24] and FCM optimized by the combination of PSO and GA (FCM-PSGOA) in [47] were selected as the typical solutions to compare with the proposed FCM-FGOA. The first two approaches adopted the \(\gamma\)-ray concentration of the cutting walls and the vibration of shearer as source signal, respectively. A cutting sound signal was used in the subsequent four methods. Three-hundred training samples were organized to obtain the centers of each cutting pattern, and 100 testing points were introduced for verification. It is necessary to point out that \(\gamma\)-ray concentration and vibration must be detected through contact measurement, which resulted in detectors that were difficult to install and easily damaged during the experiment. The convergence time of the clustering process and the recognition accuracy of the testing samples were listed in Table 4. In order to decrease the accidental error during the experiment, each method was performed ten times, respectively. The average convergence time and recognition rate were presented in the table. It could be seen that sound-based recognition system performed better than other signal sources, and that clustering centers updated by intelligent algorithms had obvious advantages compared to the original FCM. The reason lies in the fact that the original FCM is easily trapped into local extrema, and the iteration solution based on gradient descent algorithm is time-consuming. Moreover, FCM optimized by hybrid optimization algorithms had efficient calculation and high recognition accuracy compared with that of single solutions. The FGOA had overall consideration on the convergence speed and the diversity of population. In summary, the proposed cutting pattern recognition method through cutting sound based on FCM-FGOA had the best comprehensive performance in the comparison.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Compared Methods** & **Convergence Time (s)** & **Recognition Accuracy** \\ \hline \(\gamma\)-ray detection & 32.776031 & 44\% \\ Vibration analysis & 18.764410 & 57\% \\ FCM 1  & 17.007964 & 64\% \\ PSO-FCM 2  & 3.896237 & 82\% \\ ACO-FCM 3  & 5.674583 & 79\% \\ PSGOA-FCM 4  & 6.963550 & 92\% \\ The proposed method & 4.433216 & 95\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of some related methods.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Genetic Proportion** & **Fitness Value** & **Convergence Time (s)** \\ \hline
0 & 0.509624 & 2.173550 \\
0.1 & 0.600524 & 2.960945 \\
0.2 & 0.421024 & 3.581077 \\
0.3 & 0.643496 & 4.433216 \\
0.4 & 0.643496 & 5.698395 \\
0.5 & 0.643496 & 9.298510 \\
0.6 & 0.643496 & 8.314697 \\
0.7 & 0.643496 & 10.441968 \\
0.8 & 0.643496 & 17.276850 \\
0.9 & 0.643496 & 15.218627 \\
1.0 & 0.643496 & 21.970014 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Fitness value and the corresponding convergence time at different \(P_{g}\).