## 3 Experiments and Results
Therefore, the feature extraction method based on EEMD is better than EMD and MEEMD in fault analysis and diagnosis using GG clustering. In order to further verify the superiority of permutation entropy (PE) over sample entropy (SE) and fuzzy entropy (FE), the four groups of signals were decomposed by EEMD. Then, we calculated sample entropy and fuzzy entropy, respectively. GG clustering analysis was carried out. The results are shown in Table 5 and Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Types of Entropy**} & \multicolumn{3}{c}{**Clustering Index**} \\ \cline{2-4}  & **PC** & **CE** & **XB** \\ \hline EMD & 0.9927 & NaN & NaN \\ EEMD & 1.0000 & NaN & NaN \\ MEEMD & 0.9783 & 0.0383 & 2.5300 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: GG clustering index using permutation entropy. CE: classification entropy, EMD: empirical mode decomposition, EEMD: ensemble empirical mode decomposition, MEEMD: modified ensemble empirical mode decomposition, PC: partition coefficients, XB: [PERSON]’s index. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Types of Entropy**} & \multicolumn{3}{c}{**The Clustering Centers**} \\ \cline{2-4}  & **PC** & **CE** & **XB** \\ \hline Sample Entropy (SE) & 1.0000 & \(1.4336\times 10^{-5}\) & 2.4584 \\ Permutation Entropy (PE) & 1.0000 & NaN & NaN \\ Fuzzy Entropy (FE) & 0.9467 & 0.0931 & 2.3381 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: GG clustering index based on ensemble empirical mode decomposition (EEMD). Figure 7: (**a**) The GG clustering contour for EMD. (**b**) The GG clustering contour for MEEMD. From Figures 5 and 8, we can draw the following conclusions. (1) The clustering centers of four types of data vary adopting different entropies. (2) The compactness of GG clustering results with permutation entropy is better than that of sample entropy and fuzzy entropy. According to Table 5, the index PC of the cluster analysis with permutation entropy and sample entropy is 1.0000, which is larger than that of fuzzy entropy (0.9467). The index CE and XB with permutation entropy is NaN. It means that they are close to zero. However, the index CE and XB with sample entropy and fuzzy entropy are non-zero, which is larger than permutation entropy. According to the three indicators above, we can see that clustering based on permutation entropy has the better performance. Again, to verify the superiority of the GG clustering method compared with FCM and GK, we decomposed the original signal by EEMD and calculated its permutation entropy, and then performed FCM clustering and GK clustering analysis. The results are shown in Table 6 and Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Types of Entropy**} & \multicolumn{3}{c}{**The Clustering Centers**} \\ \cline{2-4}  & **PC** & **CE** & **XB** \\ \hline FCM & 0.8434 & 0.3460 & 9.5330 \\ GK & 0.6392 & 0.6674 & 2.8304 \\ GG & 1.0000 & NaN & NaN \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The fuzzy c-means (FCM), Gustafson–Kessel (GK), and GG clustering index for signals. Figure 8: (**a**) The GG clustering contour for SE. (**b**) The GG clustering contour for FE. Figure 9: (**a**) The FCM clustering contour for PE. (**b**) The GK clustering contour for PE. According to Table 6, the index PC of GG clustering is 1.0000, which is larger than FCM clustering (0.8434) and GK clustering (0.6392). The index CE and XB of GG clustering is NaN. It means that they are close to zero. However, the index CE values of FCM clustering and GK clustering are 0.3460 and 0.6674 respectively, which are larger than that of GG clustering. The index XB of FCM clustering and GK clustering is 9.5330 and 2.8304 respectively, which is larger than GG clustering. That is, GG clustering has better performance than FCM clustering and GK clustering. As can be seen from Figure 9, the clustering centers of GK clustering and FCM clustering are similar, which shows that different clustering methods have less influence on the clustering centers.