## 4 Experiments and Results
### Experimental Results  
The MAAPE-based fault feature extraction method proposed in this paper can extract fault features contained in rolling bearing vibration signals at different scales. In order to highlight the fault characteristics in different time scales of vibration, the scale factor is set as 20 in the experiments of this paper since a too large \(\tau\) will affect the computation efficiency, while a too small \(\tau\) cannot extract enough information [26]. The MAAPE feature values of rolling bearing vibration signal under normal condition is shown in Figure 4. From Figure 4, there are obvious differences in the MAAPE feature values at the different scales. AAPE can describe the amplitude and frequency characteristics of vibration signals at different time scales. The characteristics of vibration signals in different time scales are different, which can highlight the fault characteristics more comprehensively. Figure 5 shows the MAAPE feature values of rolling bearing vibration signal under inner race fault condition with different loads. As shown in Figure 5, although the failure size of the inner race is the same and the trend of AAPE values under different scale factors is basically consistent, there are obvious differences in the MAAPE features of rolling bearing vibration signals under different loads. Under different loads, the MAAPE fault feature extraction method can describe the characteristics of vibration signals. In addition, as shown in Figures 4 and 5, it can be seen that in the case of failure, the MAAPE feature extraction method can effectively describe the characteristics of vibration signals under inner race fault condition, and has obvious separability. MAAPE feature values of rolling bearing vibration signal under different fault conditions with the same loads are shown in Figure 6. It can be seen that under the same load conditions, although the size of faults is the same, the fault feature vectors extracted by MAAPE have obvious differences. Therefore, MAAPE can effectively extract the feature vector of vibration signals of rolling bearings with different fault types, and the difference of feature vectors is obvious. The fault feature extraction method based on MAAPE proposed in this paper has a good effect on fault feature description. Figure 5: MAAPE feature values of rolling bearing vibration signal under inner race fault condition with different loads. (**a**) Inner race fault, 7 mils, with load 0 hp. (**b**) Inner race fault, 7 mils, with load 1 hp. (**c**) Inner race fault, 7 mils, with load 2 hp. (**d**) Inner race fault, 7 mils, with load 3 hp. Figure 7 shows the feature clustering graph of MAAPE with different loads. In this figure, the 3-dimensional data in the 20-dimensional feature vector constitute the clustering graph. It can be seen that the characteristics of different fault types have certain separability in 3-dimensional space. Therefore, the fault feature extraction method based on MAAPE proposed in this paper can effectively describe the fault features of rolling bearings with different fault types. Figure 6: MAAPE feature values of rolling bearing vibration signal under different fault conditions with the same loads. (**a**) Inner race fault, 7 mis, with load 1 hp. (**b**) Outer race fault, 7 mis, with load 1 hp. (**c**) Ball elements fault, 7 mis, with load 1 hp. Figure 7: Feature clustering graph of MAAPE with different loads. (**a**) Load 0 hp. (**b**) Load 1 hp. (**c**) Load 2 hp. (**d**) Load 3 hp. Figure 8 shows that MAAPE feature clustering diagram of each fault severity under different loads. As shown in the figure, the 2-dimensional data in the 20-dimensional feature vector constitute the clustering graph. It can be seen that the fault feature extraction method of MAAPE rolling bearings proposed in this paper has certain feature description effect of fault severity. Fault features extracted under different fault severity have different characteristics which is helpful to identify the fault types and fault severity.