# A Deep-Learning-Based Fault Diagnosis Method of Industrial Bearings Using Multi-Source Information
## 2 Bearing Fault Diagnosis Method Based on Knowledge Reasoning
### Construction of Multi-Local Fault Diagnosis Model Based on Bi-LSTM
#### 3.1.4 Multi-Local Model Decision Fusion under Conflict-Free Conditions  
Due to various objective or subjective reasons, the local diagnosis results formed by the multi-part model may be inconsistent, making it difficult to make a further comprehensive diagnosis of the fault conditions of industrial motor bearings. Hence, it is necessary to introduce decision-level information fusion technology that is used as a support to integrate the diagnosis results of multiple local diagnosis models to obtain more comprehensive and accurate fusion diagnosis results. The emergence of decision-level information fusion technology has greatly improved the uncertainty situation in industrial motor bearing fault diagnosis. Bayesian reasoning and evidence theory are typical decision fusion algorithms. Bayesian reasoning is an earlier method used to deal with the uncertainty mentioned above problems, but because the theory itself obeys the principle of additivity, the theory cannot properly deal with the uncertainty problems caused by \"unknown situations\". D-S evidence theory is developed based on Bayesian theory, further improves the description of probability point estimation, redefines the representation method of uncertain information, and specifically uses the form of \"confidence interval estimation\" to describe uncertain information, making the reasoning mechanism more concise, the reasoning process more rigorous, and the uncertainty measurement more flexible. For this reason, we apply the classic D-S evidence theory in multi-source information fusion technology to the fault diagnosis of industrial motor bearings. Specifically, we use the classic D-S evidence theory to fuse two local diagnosis results and take the fusion result as the final fault diagnosis conclusion. The basic process of applying the classic D-S evidence theory for decision fusion is mainly divided into the following steps:  
(1) Construct the identification framework and evidence of the global fusion system for the local diagnosis stage: According to all fault types of industrial motor bearings, an identification framework for decision fusion fault diagnosis is constructed \(\theta=\{A_{1},A_{2},A_{3},\ldots,A_{n}\}\), where \(A_{n}\) represents the \(n\)-th bearing fault type. Afterward, according to the output of the two local diagnostic models based on Bi-LSTM, the evidence based on the recognition framework is constructed as \(\theta=\{E_{1},E_{2}\}\) to determine the corresponding elements of different evidence. (2) Determine the basic probability assignment of each evidence and the reliability interval under the action of a single evidence: In this paper, the basic probability assignment \(\{m_{1}(A_{1}),m_{1}(A_{2}),m_{1}(A_{3}),\ldots,m_{1}(A_{n})\}\) and \(\{m_{2}(A_{1}),m_{2}(A_{2}),m_{2}(A_{3}),\ldots,m_{2}(A_{n})\}\) is constructed while the reliability interval under the action of every single evidence \(\{[Bel_{11},Pl_{11}],[Bel_{12},Pl_{12}],[Bel_{13},Pl_{13}],\ldots,[Bel_{1n},Pl_{ 1n}]\}\) and \(\{[Bel_{21},Pl_{21}],[Bel_{22},Pl_{22}],\)\([Bel_{23},Pl_{23}],\ldots,[Bel_{2n},Pl_{2n}]\}\) is calculated mainly based on the diagnosis results of the multi-local diagnosis model. (3) Determining the basic probability assignment and reliability interval under the joint action of multiple evidence. The composition rule of classical D-S evidence theory can be expressed as:  
\[m(A_{i})=m_{1}(A_{i})\oplus m_{2}(A_{i})=\frac{\sum_{A_{x}\bigcap A_{y}=A_{i}} m_{1}(A_{x})m_{2}(A_{y})}{K}, \tag{21}\]  
where \(\oplus\) is an orthogonal sum operator, and \(K\) is called a normalization constant or conflict coefficient, which indicates the degree of conflict between pieces of evidence. The normalization constant increases with the degree of conflict. Carry out fusion reasoning according to the above D-S evidence theory combination rules, and calculate the basic probability function \(\{m(A_{1}),m(A_{2}),m(A_{3}),\ldots,m(A_{n})\}\) under the joint action of two evidence and reliability interval \([Bel,Pl]\).