## 3 Experiments and Results  
The experimental data of rolling bearings are derived from the Bearing Data Center of Case Western Reserve University. The bearing is made by Svenska Kullager-Fabriken Company(SKF), and motor power is 2 horse power(HP). The local fault of the bearing is a single point manufactured by electro-discharge machining (EDM). The specific experimental process is shown in Figure 2.  
The fault types of experimental data of a vibration signal can be divided into three types: ball fault (B), inner ring fault (IF), and outer ring fault (OF). There is also a set of normal signals (N). The fault diameter is 0.1778 mm, and the sampling frequency is 12 kHz. Fifty sets of data samples are taken for each type, and the sample length is 2048. Taking one vibration signal x (t) as an example, the signal is decomposed into several IMF components, as shown in Figure 3. Calculate the permutation entropy (PE) of each IMF component to obtain the permutation entropy eigenvectors of each signal type. Since the number of components obtained by the decomposition of each sample signal is generally more than three, the obtained permutation entropy eigenvector is a high-dimensional vector. For the sake of visualization and clustering analysis, it is necessary to reduce the high-dimension of the feature vectors into three dimensions by using the linear discriminate analysis (LDA) algorithm. So, four sets of permutation entropy eigenvectors (including the eigenvectors of a normal bearing signal) are obtained, each of which has a dimension of \(3\times 50\). The mean values are shown in Table 1.  
Figure 1: The flow chart of the fault classification method. Figure 3: The intrinsic mode function(IMF) components of the vibration signals. Figure 2: The data experiment process. The clustering centers of data are shown in Table 3. The clustering centers of the four signal types are V1-V4 in turn. Figure 6 shows the average Hamming approach degree of each sample set. The Hamming approach degree of Group 1 relative to V1 is 0.9442, close to 1, and larger than that of the other three groups. Therefore, Group 1 belongs to V1. Similarly, Group 2 belongs to V2, Group 3 belongs to V3, and Group 4 belongs to V4. Therefore, this proposed method has good performance in the fault diagnosis of rolling bearings. In order to further verify the superiority of EEMD over EMD and modified ensemble empirical mode decomposition (MEEMD) [42], the four groups of signals were decomposed by EMD and  
Figure 5: The GG clustering contour for permutation entropy. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Signal Type**} & \multicolumn{3}{c}{**The Clustering Centers**} \\ \cline{2-4}  & **x** & **y** & **z** \\ \hline N (V1) & 0.1427 & 0.1877 & 0.4770 \\ BF (V2) & 0.5793 & 0.8349 & 0.3453 \\ IF (V3) & 0.9385 & 0.0984 & 0.3699 \\ OF (V4) & 0.7372 & 0.5023 & 0.7214 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The clustering centers of the four types of signals. Figure 6: Average Hamming approach degree of each sample set. MEEMD respectively, and then GG clustering analysis was carried out. The results are shown in Table 4 and Figure 7.  
From Figures 5 and 7, we can draw the following conclusions. (1) The clustering centers of four types of data vary over different signal decomposition methods, and there is an aliasing phenomenon with decomposition based on EMD and MEEMD. (2) The compactness of GG clustering results with EEMD is better than that of EMD and MEEMD. According to Table 4, the index PC of the cluster analysis with EEMD is 1.0000, which is larger than EMD (0.9927) and MEEMD (0.9783). The index CE and XB with EMD and EEMD is NaN (a number approaching zero in MATLAB). It means that they are close to zero. However, the index CE and XB with MEEMD is 0.0383 and 2.5300 respectively, which is larger than EMD and EEMD. According to the three indicators above, we can see that clustering based on EEMD has better performance.