# Contact Fatigue State Identification of Specim Based on Heterogeneous Data and Evidence Theory
## 3 Contact Fatigue State Identification
### Contact Fatigue State Identification of Specim
#### 3.4.3 State Identification Results and Analysis  
The vibration signals and the contact surface images of the specimen collected by the testing machine are divided into three states of A (normal), B (medium) and C (failure). Thus, the identification framework of D-S evidence theory is set as {A, B, C}. In the following, a group of vibration and image data collected during the same failure period is taken as an example to illustrate the contact fatigue state identification process of the specimen, as shown in Table 11.  
1 The evidence bodies m\({}_{1}\) and m\({}_{2}\) obtained by the SDP image of the vibration signal through the VGG16 and ResNet neural network models are respectively as follows:  
\[m_{1}:m_{1}(A)=0.005,m_{1}(B)=0.0260,m_{1}(C)=0.969\] \[m_{2}:m_{2}(A)=0.005,m_{2}(B)=0.013,m_{2}(C)=0.982\]  
2 The maximum damage area of the contact surface image obtained by image processing is misidentified as 1.65 mm\({}^{2}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Specimen** \\ **Status** \\ \end{tabular} & \begin{tabular}{c} **Vibration Signal** \\ **Original Vibration Signal** \\ \end{tabular} & \begin{tabular}{c} **SDP Image** \\ **SDP Image** \\ \end{tabular} & \
\begin{tabular}{c} **Image Signal** \\ **Visual Recognition of** \\ **Maximum Damage** \\ **Region** \\ \end{tabular} &
\begin{tabular}{c} **Quantification of** \\ **Area Values/mm\({}^{2}\)** \\ \end{tabular} \\ \hline \hline \end{tabular} Note: In the acquisition of vibration signals, the horizontal axis represents the sampling point and the vertical axis represents the signal value corresponding to the sampling point.  
\end{table} 
Table 10: \(Cont.\) \begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Vibration Signal** \\ **Original Vibration Signal** \\ \end{tabular} & \begin{tabular}{c} **SDP Image** \\ **SDP Image** \\ \end{tabular} & \begin{tabular}{c} **Image Signal** \\ **Visual Recognition of** \\ **Maximum Damage** \\ **Region** \\ \end{tabular} & \begin{tabular}{c} **Quantification of** \\ **Area Values/mm\({}^{2}\)** \\ \end{tabular} \\ \hline \hline \begin{tabular}{c} **Recognition** \\ **status** \\ \end{tabular} & \begin{tabular}{c} **Damaged** \\ **Damaged** \\ \end{tabular} & \
\begin{tabular}{c} **Damaged** \\ **Damaged** \\ \end{tabular} &
\begin{tabular}{c} **Damaged** \\ **Medium** \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Contact fatigue damage of a specimen and the recognition results. The damage area data of the specimen obtained in the previous test are shown in Table 12. It can be seen that the damage area identified by machine vision technology in the normal, medium and failure state fluctuates in [0, 0.1511 mm\({}^{2}\)], [0.334932 mm\({}^{2}\), 2.38746 mm\({}^{2}\)] and [3.59476 mm\({}^{2}\), 8.29375 mm\({}^{2}\)], respectively. On this basis, the normal distribution functions of the three states A, B and C in the identification framework constructed by comprehensively considering the median damage area and the coverage rate of all damage areas are:  
\(X_{A}\sim N\big{(}0,0.1^{2}\big{)}\)  
\(X_{B}\sim N\big{(}2,2.9075^{2}\big{)}\)  
\(X_{C}\sim N\big{(}4.9,1.5^{2}\big{)}\)  
The respective function distributions are shown in Figure 11. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen Status** & **Image Number** & **Damage Area/mm\({}^{2}\)** & **Median** \\ \hline \multirow{8}{*}{Normal} & 1 & 0 (min) & \\  & 2 & 0 & \\  & 3 & 0.1511 (max) & \\  & **:** & **:** & 0 \\  & 148 & 0.0894 & \\  & 149 & 0.0560 & \\  & 150 & 0.0273 & \\ \hline \multirow{8}{*}{Medium} & 1 & 1.58652 & \\  & 2 & 0.361148 (min) & \\  & 3 & 2.1244 & \\  & **:** & **:** & 1.21317 \\  & 148 & 2.38746 (max) & \\  & 149 & 0.334932 & \\  & 150 & 1.57748 & \\ \hline \multirow{8}{*}{Failure} & 1 & 8.29375 (max) & \\  & 2 & 3.59476 (min) & \\ \cline{1-1}  & 3 & 3.96178 & \\ \cline{1-1}  & **:** & **:** & 4.10303 \\ \cline{1-1}  & 6 & 4.327 & \\ \cline{1-1}  & 7 & 3.71363 & \\ \cline{1-1}  & 8 & 4.24428 & \\ \hline \hline \end{tabular}
\end{table}