## 3 Experiments and Analysis
### Experiment 1: Case Western Reserve University (CWRU) Bearing Dataset
#### 3.1.3 Scale Factor Selection and Feature Extraction Analysis  
In the PE feature extraction process, as described in Section 2.3, \(m\) was selected as 5, and \(t\) was set as 1. Moreover, the range of scale factor \(\lambda\) also plays an important role in feature extraction performance. The maximum scale factor 20 is selected for analysis, and the MPE curves of four types of samples are obtained as shown in Figure 10. It can be seen that the MPE values increase first and then decrease with the increase of scale factor. At the same time, when scale factor is greater than 10, the trend of the MPE curves of different types tend to converge, which indicates that the complexity of different vibration signals tends to decrease at the same rate. This means that when the scale factor is greater than 10, it has little significance for PE to describe the complexity of the signal. As such, the scale factor was selected as 10.  
Figure 11 shows the MPE of the raw vibration signals in the four health conditions. The PE of the vibration signals with different health conditions has similar fluctuation intervals, and the intensity of fluctuation is also similar. Simultaneously, there are overlaps and intersections in the PE fluctuation range. Figures 12 and 13 show the MPE of IMF1 and IMF3 for the four health conditions, respectively. The fluctuation intensity in IMF1 and IMF3 both vary greatly compared with that shown in Figure 11, and the MPE of IMF3 varies more than that of IMF1. In other words, the MPE features of IMF3 are more separable than those of IMF1 and those of the raw signal. However, the fluctuation intervals of PE still overlap. Therefore, it is not easy to directly distinguish faults with MPE parameters.  
Figure 11: MPE of the raw vibration signals for four health conditions.  
Figure 10: Multiscale permutation entropy (MPE) of bearing signals for four health conditions with different scale factor.  
As the raw signal contains a great deal of useful information, the MPE of the raw signal was considered and fused with the IMF permutation entropy to enrich the information of the extracted feature vector. According to the training samples (N, ORF, BF, and IRF), the MPE of the selected IMFs and the raw signals were extracted. The MPE of the raw signal was recorded as MPE\(i\), which is a 10-dimensional vector. The MPE of the first five-order IMFs was recorded as MPE\(j\). Therefore, the final feature vector \(V\) is obtained as follows:  
\[V=\left\{MPE_{i},MPE_{j1},MPE_{j2},MPE_{j3},MPE_{j4},MPE_{j5}\right\} \tag{16}\]  
The dimension of the feature vector \(V\) is 60. Through the above feature extraction method, the obtained feature vector considers the correlation of the IMFs and the raw signals themselves. It also takes advantage of MPE to characterize weak fault signals, which is beneficial in terms of establishing more abundant and comprehensive feature extraction. According to the above method, the feature vectors of all experimental samples were extracted. The MPE feature vector was then used as for input in the SSDAE network for training and testing.