# 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
#### 3.1.2 Bearing Timing Data Cleaning Based on Denoising Autoencoder  
The data directly collected from the sensors of industrial motor bearings is extremely nonlinear, and the noise pollution brought by the operating environment to the bearing sample data makes it difficult to dig out the deep relationship in the data information during the fault diagnosis process. In response to the above problems, this section introduces the noise reduction autoencoder to perform preliminary cleaning on the bearing current and vibration signals of industrial motors. The denoising autoencoder first performs a certain degree of noise processing on the original data and then inputs the noised data into the encoder and decoder. The encoder eliminates the influence of noise according to the statistical characteristics of the data, while the decoder restores the detailed information and finally generates the reconstructed data. The specific structure of the noise reduction autoencoder is shown in Figure 2. Compared with traditional denoising methods, denoising autoencoders have more powerful functions of data representation, removing noise, and preventing overfitting. The most important thing is that the noise reduction self-encoder does not destroy the timing of the original industrial motor bearing data while eliminating noise. Therefore, the local diagnosis model based on Bi-LSTM and the attention mechanism  
Figure 1: Structure diagram of multi-local fault diagnosis model based on Bi-LSTM.  
can maximize the deep-level relationship of time series in the data information, effectively improving the generality and robustness of the model.  
In the denoising autoencoder network, Gaussian noise processing is first performed on the original current data set \(C\) and vibration data set \(V\) to reconstruct the bearing sample data disturbed by noise. and obtain the input layer data \(C_{s}\) and \(V_{s}\) of the noise reduction autoencoder, which can be expressed as follows:  
\[C_{s}=C+\alpha,\alpha\in(0,\delta^{2}). \tag{1}\]  
\[C_{s}|C\sim N(C,\delta^{2},I). \tag{2}\]  
\[V_{s}=V+\beta,\beta\in(0,\delta^{2}). \tag{3}\]  
\[V_{s}|V\sim N(V,\delta^{2},I). \tag{4}\]  
Afterward, the input layer data \(C_{s}\) and \(V_{s}\) are input into the autoencoder, and after being processed by the encoder \(f_{D}\), the characteristic expressions \(h_{c}\) and \(h_{v}\) are obtained as:  
\[h_{c}=f_{D}(C_{s})=s(W_{D}\cdot C_{s}+b), \tag{5}\]  
\[h_{v}=f_{D}(V_{s})=s(W_{D}\cdot V_{s}+b), \tag{6}\]  
where \(s\) is the encoder activation function, \(W_{D}\) is the weight matrix, and \(b\) is the bias. Finally, the decoder \(g\) maps the feature expressions \(h_{c}\) and \(h_{v}\) to the output layer to obtain the reconstructed data \(C_{j}\) and \(V_{j}\) without noise, the expressions are as follows:  
\[C_{j}=g(h_{c})=o(Z\cdot h_{c}+d). \tag{7}\]  
Figure 2: Denoising autoencoder network structure.  
\[V_{j}=g(h_{v})=o(Z\cdot h_{v}+d). \tag{8}\]  
where \(o\) is the decoder activation function, \(Z\) is the weight matrix, and \(d\) is the bias.