# Improved Adversarial Transfer Network for Bearing Fault Diagnosis under Variable Working Conditions
## 5 Discussion
### Data Analysis  
Based on the observations in Tables 4 and 5, the closer the working conditions are, the more similar the distribution of the collected data will be. This paper calculates the MK-MMD and MMD between the data collected under different working conditions to verify the hypothesis. The results are shown in Table 8.  
According to Table 8, it is evident that the more similar the working conditions of the source domain data and the target domain data are, the lower the MK-MMD and MMD between them are. To express the connection between the distribution difference between source and target domain data and the model performance more intuitively, we perform correlation analysis on them according to (14):  
\[\rho_{x,y}=\frac{\text{Cov}(X,Y)}{\sqrt{D(X)D(Y)}}=\frac{E(XY)-E(X)E(Y)}{\sqrt {E(X^{2})-E^{2}(X)}\sqrt{E(Y^{2})-E^{2}(Y)}} \tag{14}\]  
The correlation coefficient between the MK-MMD of dual-rotor tasks and their transfer learning accuracy is defined as \(\rho_{1}\); the correlation coefficient between the MMD of dual-rotor tasks and their transfer learning accuracy is defined as \(\rho_{2}\); the correlation coefficient between the MK-MMD of CWRU tasks and their transfer learning accuracy is defined as \(\rho_{3}\); the correlation coefficient between the MMD of CWRU tasks and their transfer learning  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Task** & **MK-MMD** & **MMD** & **Mean Acc** \\ \hline D0\(\leftrightarrow\)D1 & 0.438 & 0.122 & 91.79 \\ D0\(\leftrightarrow\)D2 & 1.085 & 0.312 & 90.03 \\ D0\(\leftrightarrow\)D3 & 1.782 & 0.511 & 75.74 \\ D1\(\leftrightarrow\)D2 & 0.316 & 0.087 & 97.01 \\ D1\(\leftrightarrow\)D3 & 1.175 & 0.253 & 82.15 \\ D2\(\leftrightarrow\)D3 & 0.321 & 0.084 & 96.23 \\ R0\(\leftrightarrow\)R1 & 0.061 & 0.011 & 98.58 \\ R0\(\leftrightarrow\)R2 & 0.072 & 0.010 & 96.23 \\ R0\(\leftrightarrow\)R3 & 0.071 & 0.014 & 93.16 \\ R1\(\leftrightarrow\)R2 & 0.052 & 0.008 & 99.80 \\ R1\(\leftrightarrow\)R3 & 0.065 & 0.013 & 98.69 \\ R2\(\leftrightarrow\)R3 & 0.054 & 0.012 & 100 \\ O0\(\leftrightarrow\)O1 & 0.854 & 0.198 & 68.03 \\ O0\(\leftrightarrow\)O2 & 0.927 & 0.209 & 68.01 \\ O0\(\leftrightarrow\)O3 & 0.833 & 0.194 & 76.62 \\ O1\(\leftrightarrow\)O2 & 0.207 & 0.045 & 87.58 \\ O1\(\leftrightarrow\)O3 & 0.029 & 0.006 & 89.61 \\ O2\(\leftrightarrow\)O3 & 0.021 & 0.004 & 96.82 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The distribution connections of different domains.  
accuracy is defined as \(\rho_{4}\); the correlation coefficient between the MK-MMD of Ottawa dataset tasks and their transfer learning accuracy is defined as \(\rho_{5}\); the correlation coefficient between the MMD of Ottawa dataset tasks and their transfer learning accuracy is defined as \(\rho_{6}\). According to (11), it can be calculated that \(\rho_{1}=-0.9523\), \(\rho_{2}=-0.9044\), \(\rho_{3}=-0.8456\), \(\rho_{4}=-0.5045\), \(\rho_{5}=-0.9574\) and \(\rho_{6}=-0.9549\).  
It is obvious that there exists a strong negative correlation. Therefore, it can be summarized that the more similar the working conditions of the source domain data and the target domain data are, the lower the MK-MMD and MMD between them are, and the better the transfer learning results will be.