# 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

Table 12: Damage area statistics table. Figure 11: Distribution diagram of normal function of three states. Therefore, the normal probability density values corresponding to the three states when the damage area in the identification frame is 1.65 mm\({}^{2}\) are:  
\[f_{A}(1.65)=\frac{1}{0.05\sqrt{2\pi}}e^{-\frac{(x-0)^{2}}{2\times 0.05^{2}}}=2.68 \times 10^{-236}\]  
\[f_{B}(1.65)=\frac{1}{2.905\sqrt{2\pi}}e^{-\frac{(x-2)^{2}}{2\times 2905^{2}}}=0.1363\]  
\[f_{C}(1.65)=\frac{1}{1.5\sqrt{2\pi}}e^{-\frac{(x-4)^{2}}{2\times 1.5^{2}}}=0.254\]  
The basic probability assignments corresponding to various states in the recognition framework are:  
\[m(i)=f_{i}(x)/\sum_{i=1}^{n}f_{i}(x) \tag{4}\]  
where \(x\) is the damage area; \(f_{i}(x)\) is the normal probability density value corresponding to the \(i\)-th state in the identification frame; \(n\) is the number of states in the identification frame. Therefore, the evidence bodies m\({}_{3}\) is:  
\[m_{3}:m_{3}(A)=0.001,m_{3}(B)=0.843,m_{3}(C)=0.156\]  
3 Using the Dempster combination rule of the D-S evidence theory, the decision-level fusion of the evidence bodies m\({}_{1}\), m\({}_{2}\) and m\({}_{3}\) can be obtained:  
\[m(A)=0.000,m(B)=0.0008,m(C)=0.9992\]  
Therefore, it is determined that the state identification result of the specimen corresponding to this set of data is \"failure\". According to the above method, the contact fatigue state identification of the specimen is carried out for three states of normal, medium and failure with 100 validation set data respectively. The results are shown in Table 13.  
From an individual case analysis, it can be seen that: 1 When the real state of the specimen is \"0\", although the samples numbered 98, 99 and 100 are wrong to identify the state of the specimen based on the image signal, the state can be correctly identified by the vibration and image information fusion method in this paper. 2 When the real state of the sample is \"1\", although the state identification of the specimen based on the vibration signal of the sample numbered 3 is wrong, and based on the vibration signal VGG16 model of the sample numbered 98 is also wrong, the state can still be correctly identified by the vibration and image information fusion method in this paper. 3 When the real state of the sample is \"2\", although the state identification of the specimen based on the vibration signal ResNet model of the sample numbered 99 is wrong, the state can also be correctly identified by the vibration and image information fusion method in this paper. It is clear that the fusion of vibration and image data can achieve information complementation and can more accurately identify the contact fatigue state of the specimen. From the overall analysis, it can be seen that: 1 For the state identification of the specimen based on vibration signal, the accuracy of VGG16 model is 95.33%, while the accuracy of ResNet model is 91.00%; 2 The state identification of the specimen based on the image signal has an accuracy rate of 93.33%; 3 Based on the multi-source information fusion method proposed in this paper, the accuracy of state identification reaches 98.67%, which is 3.34%, 7.67% and 5.34% higher than that of VGG16 model, ResNet model and image signal identification, respectively. Therefore, in terms of the contact fatigue state identification of the specimen, whether from an individual case or an overall analysis, the method in this paper can more accurately identify the state of the specimen than the method based on a single vibration or image information source. The validity of the method proposed in this paper is further verified by the ROC curve (Receiver Operating Characteristic Curve). The ROC curve takes each detection result as a possible recognition threshold, calculates the corresponding True Positive Rate (TPR) and False Positive Rate (FPR) as follows, and the curve drawn with FPR as the abscissa and TPR as the ordinate [33]. The ideal state should be TPR = 1, FPR = 0, that is, the (0,1) point in the figure.