# A Deep-Learning-Based Fault Diagnosis Method of Industrial Bearings Using Multi-Source Information
## 4 Performance Evaluation
### Experimental Settings and Performance Metrics  
The local fault diagnosis model used in the experiments mainly includes a noise reduction encoder, a Bi-LSTM overlay layer with an activation function of tanh, an attention mechanism layer, a fully connected layer with an activation function of Tanh, and an activation function of SoftMax classification layer. Among them, the noise reduction encoder first adds Gaussian noise with a mean value of 0 and a variance of 0.15 to the original signal and then obtains a reconstructed signal through encoding and decoding, then outputs it to the first Bi-LSTM layer. The output of the LSTM forward layer and reverse layer in the first Bi-LSTM layer is used as the input of the second Bi-LSTM forward layer and reverse layer, and the two Bi-LSTM layers jointly complete the feature extraction of the bearing data. Then the extracted features are input into the attention mechanism layer, and the attention weight coefficient is calculated. Finally, the weight coefficient is combined with the vector to obtain the final feature expression. The fully connected layer accepts the output feature vector of the attention mechanism layer. After realizing the feature space conversion of the bearing feature, the classification layer realizes the output of the predicted target state category. The number of Bi-LSTM units is 64, and the number of neurons in the fully connected layer is 32. In addition, a dropout operation with a parameter of 0.25 is set in the fully connected layer, which only takes effect during the training process to prevent the network from memorizing or overfitting the training data. The batch size is set to 64, the learning rate is adjust dynamically. Specifically, Adam optimization algorithm with learning rate adaptive function is used. The optimization algorithm is derived from adaptive moment estimation, which is different from the traditional stochastic gradient descent. The optimization algorithm adaptively corrects the first-order moment and second-order moment estimates of different parameter gradients through the loss function and the bias correction mechanism built into the algorithm. The learning rate of each iteration has a relatively definite range after bias correction, which may ensure the stability of related parameters. The initial learning rate of the multi-local model is set to 0.001. For the typical multi-category classification problem of industrial motor bearing fault diagnosis, commonly used performance evaluation indicators include Accuracy (\(ACC\)), Precision, Recall (\(P\)), and F1-Score (F1). \(ACC\) indicates the proportion of all data samples that are correctly classified, which can be expressed as follows:  
\[ACC=\frac{TP+TN}{TP+TN+FP+FN}, \tag{35}\]  
where \(TP\) represents the number of positive samples that are correctly identified, \(FN\) represents the number of positive samples that are falsely detected as negative samples, \(TN\) \begin{table}
\begin{tabular}{c c} \hline
**Bearing Operating States** & **Normal, Inner Ring Fault, Outer Ring Fault** \\ \hline The speed and the load of the motor & Fixed to 1500 rpm and 0 hp \\ The condition of the motor & Constantly changing among normal, inner ring fault, and \\  & outer ring fault. \\ Data Status Distribution & Equalization \\ The equipment for collecting vibration and & VAL-DC29 and VAL-SC25. \\ current datasets & \\ The ratio of the numbers of training and test samples & 7:3 \\ The numbers of training and test samples & 1680 and 720 \\ The number of sampling data in one sample & The number of sampling points for one revolution of the \\  & bearing, i.e., 512 sampling points \\ \hline \end{tabular}
\end{table} 
Table 2: Details related to data collection. represents the number of negative samples that are correctly recognized, and \(FP\) represents the number of negative samples that are falsely detected as positive samples.