## 3 Bearing Experiment and Feature Extraction Method
### Feature Extraction Method  
According to the bearing experimental conditions, the bearing outer ring is fixed, the speed is 0; the speed of the bearing inner ring is 10,776 deg/s = 29.93 r/s. According to the speed relationship, the speed of the bearing cage is 4271.2 deg/s = 11.87 r/s; the angular speed of the roller is 24,971.8 deg/s = 69.37 r/s. When processing the data, the data points collected by each fault bearing need to be segmented, and the features are extracted from each segment to obtain a trained sample. In order to ensure that each section of the data points can contain a number of complete cycles of the bearing operation, take the cage that has the slowest speed as a benchmark, and ensure the cage can rotate to three laps or more when segmenting the data. By calculating 12 kHz \(\div\) 11.87 r/s = 3033, so that each segment of data needs to contain at least 3033 data points in order to facilitate the calculation, this paper takes 4000 data points per segment. Using this as a standard, each of the four faulty bearings, each of which has 120,000 data points, can be divided into 30 segments, which makes 30 samples. The 240,000 data points collected on the normal bearing, in order to maintain the alignment of the samples, are also segmented to obtain 30 samples by using only the first 120,000 data points. This gives a total of 150 samples in five different fault categories. The statistical features are extracted from the acceleration signal. Equations (1)-(6) are the statistical characteristics of the formula:  
1. Mean The mean represents the mathematical expectation of the signal, as shown in Equation (1): \[\overline{X}=\frac{1}{N}\sum_{i=1}^{N}x_{i}\,,\] (1)
2. Root mean square (RMS) The RMS is a measure of the size of an important indicator of vibration. From the energy point of view, it is to convert the alternating current (AC) component into the equivalent direct current (DC) component, as shown in Equation (2): \[X_{rms}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}x_{i}^{2}}.\] (2)
3. Square root amplitude The physical meaning of the square root amplitude is to reflect the vibration amplitude at a certain frequency, and the expression is as shown in Equation (3): \[X_{r}=\bigg{[}\frac{1}{N}\sum_{i=1}^{N}\sqrt{|x_{i}|}\bigg{]}^{2}.\] (3)
4. Skewness The skewness reflects the asymmetry of the probability density function of the signal distribution with respect to the ordinate, and the larger the skewness value is, the more serious the asymmetry is. This feature calculates the third-order central moment of the sample space, as shown in Equation (4): \[m=\frac{1}{N}\sum_{i=1}^{N}x_{i}^{3}.\] (4)(5) Kurtosis  
The kurtosis is mainly effective in analyzing whether the signal contains a pulse fault. The expression is as shown in Equation (5):  
\[\beta=\frac{1}{N}\sum\
olimits_{i=1}^{N}{\chi_{i}^{4}}. \tag{5}\]  
(6) Standard deviation  
The standard deviation, as a measure of the uncertainty of a sample, reflects the degree of dispersion of the mean of the sample data, as shown in Equation (6):  
\[\sigma=\sqrt{\frac{1}{N}\sum\
olimits_{i=1}^{N}{\left({x_{i}-\overline{X}} \right)^{2}}}. \tag{6}\]  
(7) Absolute mean  
The absolute mean of the signal represents the statistical mathematical expectations of the absolute value, as shown in Equation (7):  
\[\overline{|X|}=\frac{1}{N}\sum\
olimits_{i=1}^{N}{\left|{x_{i}}\right|}. \tag{7}\]  
The above is the dimension of statistical features. In order to ensure the consistency of the sample features, this paper also uses the dimensionless features. The calculation formulas of dimensionless features are shown in Table 1.  
In this paper, the above six dimensionless features are taken, besides an absolute average (dimension features), so a total of seven features are used as the input features of the training samples of the degenerative model.