## 4 Fault Diagnosis Results
### Fault Diagnosis Results  
In this section, fault diagnosis was performed on the experimental data and synthetic data to evaluate the effectiveness of data augmentation. Figure 9 shows the 1D CNN model structure that was used for fault diagnosis, and Table 4 indicates the detailed information of the model. To maintain the uniformity of the research, the same 1D CNN model structure was applied in all instances of fault diagnosis. Considering complex embedded information in the random signal, the model is constructed with several Convuoltional-Maxpooling pairs. To activate the nonlinearities from convolution layers, the ReLU activation function was applied. After extracting features, the dropout layer was added after the dense layer to reduce overfitting due to its complex model structure. For the 1120 signals in the experiment, they were randomly divided into 60%, 20%, and 20% for training, validation, and testing of the model while maintaining the proportion of the data for each class. After generating synthetic signals with the WGAN model, as written in Section 3.2, they were used for training and validation data with the same 1D \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network Layer** & **Output Data Size** & **Parameters** \\ \hline Input Layer & 1875 \(\times\) 1 & 1875 length signal input \\ Conv1D & 1875 \(\times\) 32 & 32 @ 3 \(\times\) 1, stride = 1, activation = ReLU \\ Conv1D & 1875 \(\times\) 32 & 32 @ 3 \(\times\) 1, stride = 1, activation = ReLU \\ Max pooling 1D & 937 \(\times\) 32 & 2 \(\times\) 1, stride = 2, activation = ReLU \\ Conv1D & 937 \(\times\) 64 & 64 @ 3 \(\times\) 1, stride = 1, activation = ReLU \\ Conv1D & 937 \(\times\) 64 & 64 @ 3 \(\times\) 1, stride = 1, activation = ReLU \\ Max pooling 1D & 468 \(\times\) 64 & 2 \(\times\) 1, stride = 2, activation = ReLU \\ Conv1D & 468 \(\times\) 128 & 128 @ 2 \(\times\) 1, stride = 1, activation = ReLU \\ Max pooling 1D & 234 \(\times\) 128 & 2 \(\times\) 1, stride = 2, activation = ReLU \\ Conv1D & 234 \(\times\) 128 & 128 @ 2 \(\times\) 1, stride = 1, activation = ReLU \\ Max pooling 1D & 117 \(\times\) 128 & 2 \(\times\) 1, stride = 2, activation = ReLU \\ Conv1D & 117 \(\times\) 256 & 256 @ 2 \(\times\) 1, stride = 1, activation = ReLU \\ Max pooling 1D & 58 \(\times\) 256 & 2 \(\times\) 1, stride = 2, activation = ReLU \\ Conv1D & 58 \(\times\) 256 & 256 @ 2 \(\times\) 1, stride = 1, activation = ReLU \\ Max pooling 1D & 29 \(\times\) 256 & 2 \(\times\) 1, stride = 2, activation = ReLU \\ Flatten Layer & 1 \(\times\) 7424 & 7424 neurons \\ Input Layer & 1 \(\times\) 7424 & 7424 neurons \\ Dense & 1 \(\times\) 1024 & 1024 neurons \\ Dropout & 1 \(\times\) 1024 & Dropout rate: 0.4 \\ Dense & 1 \(\times\) 512 & 512 neurons \\ Dropout & 1 \(\times\) 512 & Dropout rate: 0.4 \\ Dense & 1 \(\times\) 128 & 128 neurons \\ Dropout & 1 \(\times\) 128 & Dropout rate: 0.4 \\ Dense & 1 \(\times\) 3 & 128 neurons \\ SoftMax & 1 \(\times\) 3 & Classification Layer \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Detailed information of 1D CNN model for the research. Figure 9: Structure of the 1D CNN model for the research. CNN model structure. For each health state, 3000 signals were generated, 9000 in total. Then, synthetic signals were randomly divided into a 60% allocation for training data and a 40% allocation for validation data while maintaining the class proportion. To demonstrate the enhanced fault diagnosis performance, the test dataset for the experimental data case was used for both cases. Because the data were divided randomly, test data may contain some identical data used for data augmentation. However, this fault diagnosis result could bring meaningful conclusions for the solution of the data imbalance problem. The test results are shown in Figure 10. For the experimental data case, because of the severe data imbalance problem, the training process of the 1D CNN model is biased for a healthy state, dropping the fault diagnosis performance of fault states, as shown in Figure 10a.