## 4 Results
### Imbalanced Fault Diagnosis  
In this section, we make seven training sets and one testing set based on the datasets in Table 1. A total of 100 normal data and only one sample of each fault class are selected. As an extremely limited sample set, named training dataset 1, is used to simulate real S & I failure data scenarios. On this basis, the generator model trained is used to synthesize the sample data and gradually adds to dataset 1 so that the majority class and minority class ratios are 100:1, 25:1, 20:1, 10:1, 2:1, and 1:1, and training sets 2-7 are obtained. The specific details of each dataset are shown in Table 6.  
To test the analytical performance of the proposed method on the S & I dataset, different classification models are used for testing. Datasets 1-7 are used for training and then classifying the testing set. There are a total of seven different classification models, including: Multilayer perceptron MLP with [1024, 128, 64] hidden layer neurons; convolutional neural network structure with output channels [16, 32, 64, 128], for which the specific parameters can be found in [32]; LeNet; ResNet; and AlexNet. For the BiLSTM model in the proposed method, the parameter settings can be found in Section 3. We use three indicators to measure the performance of the model, namely accuracy, F1-score (F1), and the average area under the receiver operating characteristic curve (AUC). The fault diagnosis results of the six trained classification models in the testing dataset are shown in Figure 10. We found that when dataset 1 composed of real data was used for testing, all of the models were affected by unbalanced samples and could not achieve the best diagnosis progress. This is because the number of samples in the dataset was too sparse. The number of samples is only 1, which is not conducive to the model learning the real data distribution law. The synthetic data are added to dataset 1, i.e., datasets 2-7, resulting in a balanced dataset 7. During this process, the diagnostic accuracy of MLP, CNN, ResNet, and LSTM is greatly improved. AlexNet's diagnostic accuracy jumps from 10% to 99.50% from dataset 4, while LeNet only reaches 94.5% and 99.3%, respectively in balanced dataset 7. The following inferences can be drawn:  
* LeNet and AlexNet have the worst performance in processing S & I data. The possible reason for this is that they cannot fit the data distribution of the test set from the S & I data. A diagnostic accuracy of 10% corresponds to the prediction results of the normal data, which indicates that the imbalanced data do indeed affect the prediction results of the model. * The diagnosis accuracy of the MLP, CNN, ResNet, and LSTM models has been greatly improved since dataset 2, which shows that the synthetic fault data promote the training process of the model, and the synthetic data are very similar to the real data. * We found that BiLSTM achieved an accuracy of 97.6% in dataset 2, and the diagnostic accuracy in dataset 2\(-\)dataset 7 was higher than that of the comparison method, which shows that BiLSTM has a strong classification performance for the bearing frequency domain data. Although the effect of CNN and ResNet is also very good, the calculation time of ResNet is too long. Considering the time cost and diagnosis accuracy, BiLSTM is used in this paper to perform fault diagnosis tasks on S & I data.