# Contact Fatigue State Identification of Specim Based on Heterogeneous Data and Evidence Theory
## 2 Methodology  
### Vibration Signal Visualization Method  
At present, the methods of converting vibration signals into images mainly include the Symmetry Dot Pattern (SDP) method, Gramian Angular Field (GAF) method and Grayscale image (GRI) method [16; 17; 18; 19]. The following uses the bearing public data set from Case Western Reserve University (CWRU) to verify the validity of the above three vibration signal imaging methods applied to state recognition, and to determine the method used in this paper. The rolling bearing test bench of CWRU is shown in Figure 1, which is mainly composed of motor, torque sensor, power tester and electronic controller. During the test, the motor speed is 1720 r/min\(\sim\)1797 r/min, and the test bearing is SKF bearing with single-point damage by Electrical Discharge Machining (EDM) [20]. The data set includes four categories, namely, normal state, inner ring damage, outer ring damage and rolling element damage. The diameters of each type of damage are 0.007\({}^{\prime\prime}\) (0.1778 mm), 0.014\({}^{\prime\prime}\) (0.3556 mm) and 0.021\({}^{\prime\prime}\) (0.5334 mm) [20]. The acceleration sensor is used to collect vibration signals, and the sampling frequency is 12 kHz. In this paper, three types data of drive end rollers with a rotating speed of 1730 r/min, normal and damaged diameters of 0.3556 mm and 0.5334 mm are selected to verify the effectiveness of the vibration signal visualization method in state identification, as shown in Table 1. In each type of state data, 1024 data points are a group, and each type of state data has 1500 groups. In order to visually compare the image transformation effects of SDP method, GAF method and GRI method, the transformed images of vibration signals in different time periods for the same type of damage in the CWRU bearing public data set are shown in Table 2. It should be noted that, in this paper, a set of sample data corresponds to generate an SDP image. The specific steps are as follows: 1 Preprocess the vibration data and convert it to the range of 0-255; 2 Set the conversion parameters to convert the vibration signal to 224 \(\times\) 224 SDP image. The initial angle \(\theta\) = 120\({}^{\circ}\), time interval parameter \(l\) = 5 and the magnification factor \(\zeta\) = 30\({}^{\circ}\) were chosen [22], while the deflection angle was set to 120\({}^{\circ}\) in order to form a trilateral centrosymmetric pattern and to avoid interference phenomena in the information between adjacent images. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Damage Diameter** & **Motor Load** & **Motor Speed** & & \\
**(mm)** & **(w)** & **(r/min)** & **Bearing Number** & **Status Number** \\ \hline
0 & 3 & 1730 & Ball\_0 & 0 \\
0.3556 & 3 & 1730 & Ball\_1 & 1 \\
0.5334 & 3 & 1730 & Ball\_2 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected types of rolling bearing damages. Figure 1: CWRU rolling bearing test bench [21]. 1. Fan end bearings; 2. Motor; 3. Drive end bearing; 4. Torque sensors and encoders; 5. Dynamometers. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image Type and Size** & **Sample Type** & **Data Set Size** & **Epoch** & **Batch\_Size** & **Learning Rate** \\ \hline SDP & Training samples & 1200 & & & \\
224 \(\times\) 224 & Test samples & 300 & & 150 & 32 & 0.001 \\ GAF & Training samples & 1200 & & & \\
64 \(\times\) 64 & Test samples & 300 & & 150 & 32 & 0.001 \\ GRI & Training samples & 1200 & & & \\
32 \(\times\) 32 & Test samples & 300 & & 150 & 32 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Training parameters of VGG16 model. Figure 3: Loss degree change curve of model training set. Figure 2: Accuracy change curve of model training set.