# A Deep-Learning-Based Fault Diagnosis Method of Industrial Bearings Using Multi-Source Information
## 2 Bearing Fault Diagnosis Method Based on Knowledge Reasoning
### Decision Conflict Resolution Method Based on Sensitive Differences of Multi-Model Fault
#### 3.2.2 Multi-Local Model Conflict Resolution under the Condition of Balanced Fault Sensitivity
Taking the evidence \(E_{1}\) as an example, when a high degree of conflict occurs, the bearing data sample \(X\) corresponding to the evidence \(E_{1}\) is:  
\[X=(x_{1},x_{2},x_{3},\ldots,x_{p}), \tag{28}\]  
where \(p\) is the sequence length of the bearing samples. The standard samples \(Y\) of each fault category corresponding to the evidence \(E_{1}\) are expressed as follows:  
\[Y_{1} =(y_{11}.y_{21},y_{31},\ldots,y_{p1}).\] \[Y_{2} =(y_{12}.y_{22},y_{32},\ldots,y_{p2}).\] \[Y_{3} =(y_{13}.y_{23},y_{33},\ldots,y_{p3}). \tag{29}\] \[\ldots\] \[Y_{n} =(y_{1n}.y_{2n},y_{3n},\ldots,y_{pn}).\](2) Calculate the gray correlation degree between the conflict samples and each fault standard sample. Taking the calculation of the gray correlation degree between the conflict sample \(X\) and the standard sample \(Y_{1}\) of the fault type 1 as an example, the gray correlation coefficient is:  
\[\epsilon_{1}=\frac{\Delta_{min}+\mu\Delta_{max}}{|x_{p}-y_{p1}|+\mu\Delta_{max}}. \tag{30}\]  
\[\Delta_{min}=min|x_{d}-y_{e1}|,d=1,2,3,\ldots,p\text{ and }e=1,2,3,\ldots,p. \tag{31}\]  
\[\Delta_{max}=max|x_{r}-y_{s1}|,r=1,2,3,\ldots,p\text{ and }s=1,2,3,\ldots,p. \tag{32}\]  
where \(\mu\) is the resolution coefficient, which is used to weaken the distortion caused by the maximum absolute difference in the analysis process to show the difference of the gray correlation coefficient more objectively, and its value is determined in advance according to expert experience, \(\mu\in(0,1)\). The average correlation \(r_{1}\) between the conflict sample \(X\) and the standard sample \(Y_{1}\) is:  
\[X=(x_{1},x_{2},x_{3},\ldots,x_{p}), \tag{28}\]0  
Similarly, the average degree of correlation between the conflict sample \(X\) and the standard sample \(Y_{n}\) of other fault types can be obtained by repeating the above calculation process. (3) Sort all the average correlation degrees corresponding to the evidence \(E_{1}\) in ascending (or descending) order and take the average correlation degree with the largest value as the optimal average correlation degree of this evidence. Similarly, the optimal average correlation degree of other evidence bodies also can be calculated. (4) After normalizing the optimal average correlation degree of all evidence bodies, the trust distribution coefficient \(f_{i}\) corresponding to each conflicting evidence can be obtained. Afterward, the basic probability assignment under the joint action of different evidence can be obtained through the following formula:  
\[X=(x_{1},x_{2},x_{3},\ldots,x_{p}), \tag{28}\]1  
where \(m\) represents the basic probability assignment corresponding to evidence \(i\) after the weighted average, and \(r_{i}\) is the local diagnosis result corresponding to evidence \(i\) when the multi-local model decision conflicts. (5) Finally, fusion is carried out according to the fusion rules of evidence theory, so as to obtain the final fusion diagnosis result.