# Fault Diagnosis of Planetary Gear Train Crack Based on DC-DRSN
## 3 Fault Diagnosis Method Based on DC-DRSN and Verification
### Method Validation
#### 3.2.2 Experimental Results and Discussion  
(1) Comparison of different numbers of residual shrinkage modules  
The signal-to-noise ratio (SNR )s a measure of the comparison between the intensity of a signal and noise and is usually used to evaluate the relative strength of a signal and noise. The formula of SNR is expressed as [28]:  
\[SNR=10\cdot\log_{10}\biggl{(}\frac{P_{signal}}{P_{noise}}\biggr{)}(dB) \tag{11}\]  
where \(P_{signal}\) is the original signal power and \(P_{noise}\) is the power that contains noise in the signal. The higher the SNR value is, the stronger the signal relative to the noise is, which is easier to identify and analyze. In order to test the noise immunity of a different number of RSBUs, the number of RSBUs is adjusted without changing the preprocessing and other layer hyperparameters. Five different SNRs are added to the original vibration signal to compare the effect of the number of RSBUs on diagnostic performance. Figure 5 shows the average of the network after 150 iterations of training and five tests. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Label**} & \multirow{2}{*}{**Vibration Signal**} & \multicolumn{3}{c}{**Image Conversion Method**} \\ \cline{3-5}  & & **STFT** & **WT** & **GASF** & **GST** \\ \hline
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Table 3: Images of vibration signal conversion of the bearing datasets. When the number of RSBUs is one or two, the network depth is insufficient, which limits the expression and learning ability of the model, resulting in the performance of the model not reaching the optimum. When the number of RSBUs is four, the number of model parameters is too large, resulting in network degradation and decreased diagnostic capabilities. When the number of RSBUs is three, the model has the highest diagnostic accuracy, and the accuracy of the test set reaches 99.56% when the signal-to-noise ratio is 4 dB. In order to better simulate the noise in actual operation, taking the signal-to-noise ratio equal to 4 dB as an example, the accuracy curve of the model is shown in Figure 6. The convergence curves of training and testing have achieved a good fitting effect, and the visual classification of the test set in the confusion matrix and T-SNE is shown in Figures 7 and 8. It can be clearly found that the same type of fault has a good aggregation and different types of features can be effectively distinguished. The proposed method can be used to reshape and classify them in the high-dimensional space. Figure 5: The accuracy of test sets at different SNR and RSBUs. Figure 6: Training process of CWRU bearing datasets. (2) Comparison of different image conversion methods  
STFT, WT, GASF and GST are used to convert the two-dimensional image of the vibration signal, and the converted image is used as the input of the upper channel of the DC-DRSN model. The accuracy of fault diagnosis when a 4 dB signal-to-noise ratio noise is added to the original signal is shown in Table 4. It can be seen that the GST-DCDRSN method has the lowest fault diagnosis accuracy of 98.31%. This is due to the high-resolution  
Figure 8: T-SNE visualization. Figure 7: Classification of confusion matrices. characteristics of GST and data redundancy, which allows the model to process irrelevant details that distract from key features. The STFT transform can accurately locate the time point of fault occurrence and track the dynamic changes in the system, with a fault diagnosis accuracy of up to 99.56%, which is 1.25% higher than that of the GST transform. At the same time, it is also proved that the 2D graph transformed by STFT can be used as the input of the channel on the DC-DRSN, which achieves higher diagnostic accuracy.