## 4 Experimental Analysis and Verification
### Test 1  
The purpose of this experiment was to test the performance of the ITCA-DBN model for a fault diagnosis under variable working conditions. There were a total of six tasks of cross-working condition fault diagnoses in this experiment, which were A \(\rightarrow\) B, A \(\rightarrow\) C, A \(\rightarrow\) D, B \(\rightarrow\) C, B \(\rightarrow\) D, and C \(\rightarrow\) D. We took all the samples from the source domain dataset as the training set, randomly selected 50 samples from each state type in the target domain as the validation set, and then randomly selected 120 samples from each state type in the target domain as the testing set for the target domain. To verify the effectiveness of the proposed method, it was compared with the different methods: DBN, IG-CWT-CNN [31], TF-MDA [32], ICPW-HPF-CNN [33], ML [34], JDA [35], TCA-DBN [36], DSAN [18], and S-Alexnet [37]. The structure of the DBN was [80; 40; 40; 20], and the learning rate was 0.05. The structure of the DBN in the TCA-DBN model was [50; 30; 20], and the learning rate is 0.01. The structure of the DBN in the method proposed was [50; 30; 20], with a learning rate of 0.01, SRPLC-K-means preserves the top 80% of the samples. Based on multiple preliminary experiments, \(u=1/16\) and \(\lambda=1/5\) were ultimately selected. The fault diagnosis results of six cross-working condition tasks using the different methods are shown in Table 3 and Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline
**Name** & **Definition** & **Name** & **Definition** \\ \hline Average & \(\overline{x}=\frac{1}{N}\sum_{i=1}^{N}x_{i}\) & Standard deviation & \(S=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_{i}-\overline{x})^{2}}\) \\ Margin index & \(C_{e}=\frac{x_{\text{rms}}}{\overline{x}}\) & Skewness index & \(C_{w}=\frac{1}{N}\sum_{i=1}^{N}(\frac{|x_{i}-\overline{x})}{x_{\text{rms}}}^{3}\) \\ Root mean square & \(x_{rms}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}x_{i}^{2}}\) & Kurtosis index & \(C_{q}=\frac{1}{N}\sum_{i=1}^{N}(\frac{|x_{i}|-\overline{x})}{x_{\text{rms}}})^{4}\) \\ Pulse index & \(C_{f}=\frac{x_{f}}{\overline{x}}\) & Waveform entropy & \(C_{q}=\frac{1}{N}\sum_{i=1}^{N}x_{i}\log x_{i}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Expressions of the time domain features. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Methods** & \(\mathbf{A}\rightarrow\mathbf{B}\) & \(\mathbf{A}\rightarrow\mathbf{C}\) & \(\mathbf{A}\rightarrow\mathbf{D}\) & \(\mathbf{B}\rightarrow\mathbf{C}\) & \(\mathbf{B}\rightarrow\mathbf{D}\) & \(\mathbf{C}\rightarrow\mathbf{D}\) & **Average Accuracy** \\ \hline DBN & 83.333 & 84.375 & 86.25 & 85.208 & 84.583 & 84.167 & 84.653 \\ S-Alexnet & 85.417 & 83.958 & 83.542 & 87.292 & 85.625 & 86.458 & 85.382 \\ IG-CWT-CNN & 82.917 & 81.458 & 80.833 & 83.958 & 82.5 & 84.167 & 82.639 \\ TF-MDA & 85.833 & 85.208 & 83.542 & 86.875 & 86.667 & 87.927 & 86.009 \\ ICPW-HPF & 80.209 & 81.0417 & 79.583 & 82.917 & 78.333 & 82.083 & 80.694 \\ ML & 72.927 & 71.875 & 71.25 & 74.167 & 72.5 & 75.417 & 73.023 \\ JDA & 89.583 & 90.417 & 87.917 & 90.208 & 88.333 & 91.458 & 89.653 \\ TCA-DBN & 94.792 & 96.25 & 96.875 & 95.625 & 94.167 & 94.583 & 95.382 \\ DSAN & 98.958 & 99.167 & 98.958 & 98.542 & 96.875 & 99.792 & 98.715 \\ ITCA-DBN & 100 & 99.792 & 99.167 & 99.167 & 99.375 & 99.167 & 99.445 \\ \hline \end{tabular}
\end{table} 
Table 3: Cross-working conditions fault diagnoses results using different methods. As shown in Table 3 and Figure 6, the average accuracy of DBN, S-Alexnet, IG-CWT-CNN, TF-MDA, ICPW-HPF-CNN, ML, JDA, TCA-DBN, DSAN, and ITCA-DBN were 84.653%, 85.382%, 82.639%, 86.009%, 80.649%, 73.023%, 85.382%, 89.653%, 98.582%, 98.715%, and 99.445%, respectively. Due to the DBN, IG-CWT-CNN, TF-MDA, ICPW-HPF-CNN, ML, and S-Alexnet, without considering the discrepancies in the data distribution under different working conditions, the fault diagnosis effect was poor.