## 4 Discussion  
Fault diagnosis is a basic problem in reliability analysis. Since a rolling bearing fault has nonlinearity and nonstationary characteristics, it is difficult to identify the fault category. A rolling bearing clustering fault diagnosis method based on ensemble empirical mode decomposition (EEMD), permutation entropy (PE), linear discriminant analysis (LDA), and the Gath-Geva (GG) clustering algorithm is proposed. The data experiments have shown the good fault diagnosis performance of the proposed method.  
When diagnosing bearing faults, based on the data results before and after the dimensionality reduction, we can see that the difference in entropy of different fault categories is significantly improved by reducing the dimensions, which can help to distinguish different fault signals. Therefore, dimension reduction is necessary in the process of fault diagnosis. With the exception of dimensionality reduction, three other steps need to be passed when diagnosing bearing faults. For each step, three feasible methods can be selected so that there is a total of 27 combinations. According to the clustering figures above, we can intuitively see that the proposed combination method has better cluster compactness than the other combinations. The distinction between each type of fault is obvious, and there is no aliasing. It indicates that the method has better discrimination, which will help to accurately determine the type of failure in actual applications and improve the accuracy of fault diagnosis.  
In order to get a more comprehensive understanding of the fault diagnosis effect of each method combination, we calculate the clustering index of each combination and obtain the results shown in Figure 10. From the figure, we can clearly see that the clustering index PC is highly volatile. This shows that compared with the CE and XB clustering indicators, the PC indicator is better able to show the advantages and disadvantages of each combination. From Figure 10, we can clearly see that Method 15 (EEMD + PE + GG) performs the best overall, which proves that our proposed fault diagnosis method is the best among all the possible combinations. At the same time, we can also see that Method 12 (EMD + PE + GG) is also very good. The clustering indexes of Method 12 and Method 15 are very close. Although Method 15 is slightly better, calculating EEMD takes more time than calculating EMD. In actual bearing fault diagnosis, we can select each of them as bearing fault diagnosis according to specific needs.  
Based on the data experiments above, we can conclude that our proposed fault diagnosis method has a satisfactory fault diagnosis effect. However, in practical engineering problems, especially in the non-bearing fault signal fault diagnosis, the best method proposed in this article cannot be applied blindly, and the fault diagnosis method should be selected according to the characteristics of the actual engineering itself. For example, if the signal diagnosed is less noisy and the signal is relatively stable, it may be more appropriate to use EMD or EEMD. We should also adopt the fuzzy entropy or sample entropy and then perform FCM clustering. Conversely, if the signal is noisy and extremely unstable, MEEMD may have better results than EMD and EEMD. At the same time, performing GG cluster analysis and calculating permutation entropy may be the proper way to obtain satisfactory fault diagnosis results.