## 4 Experiment Study
### Results and Discussion for RUL Prediction
#### 4.3.2 Results and Discussion of Cross-Working Condition RUL Prediction
Secondly, VDR has been proved to be an improvement of MMD, and this paper uses it as a new metric instead of MMD to verify and compare its effect on RUL prediction performance. Finally, RSD was added to form joint domain adaptation loss as the main method to implement RUL prediction. Their comparative results are listed in Table 6.  
The results in Table 6 show that the RUL prediction effect of these methods gradually becomes better with the upgrade of modules. Compared with the traditional method, the proposed method shows improvement by 0.047, 0.053, and 0.058 of the MSE, RMSE, and Score. Due to a lack of understanding of the information of the target domain, the big difference in data distribution leads to poor prediction effect when using the deep learning prediction model directly. In order to make the model have the ability of cross-domain prediction, adding the traditional distance measure MMD to build the transfer learning model can achieve better prediction effect than baseline. VDR overcame the poor discrepancy representation of MMD's mean statistic in an RKHS space. Therefore, this paper uses VDR as a new metric instead of MMD to achieve better results in most RUL prediction tasks. Nonetheless, VDR lacks the representation ability of feature manifold distribution. To effectively enhance the model's learning of cross-domain invariant features, RSD is further combined with VDR to design joint domain adaptation loss to enhance  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Source** \\ **Domain** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Target** \\ **Domain** \\ \end{tabular}  } & \multirow{2}{*}{**Tests**} & \multicolumn{2}{c}{**VDR + RSD + CNN**} & \multicolumn{4}{c}{**VDR + CNN**} & \multicolumn{4}{c}{**MMD + CNN**} & \multicolumn{4}{c}{**CNN**} \\  & & & **MAE** & **RMSE** & **Score** & **MAE** & **RMSE** & **Score** & **MAE** & **RMSE** & **Score** & **MAE** & **RMSE** & **Score** \\ \hline \multirow{4}{*}{ \begin{tabular}{c} Bearing 1-2 \\ \end{tabular}  } & \multirow{4}{*}{Bearing 2-1} & **2-3** & **0.320** & **0.389** & **0.244** & 0.332 & 0.426 & 0.277 & 0.345 & 0.413 & 0.229 & 0.430 & 0.509 & 0.140 \\  & & **2-6** & **0.082** & **0.105** & 0.316 & 0.115 & 0.132 & 0.354 & 0.088 & 0.115 & 0.347 & 0.121 & 0.156 & **0.384** \\  & & **2-7** & **0.241** & **0.302** & **0.282** & 0.274 & 0.385 & 0.454 & 0.323 & 0.359 & 0.209 & 0.322 & 0.372 & 0.210 \\  & & **AVG** & **0.214** & **0.265** & **0.280** & 0.241 & 0.314 & 0.362 & 0.250 & 0.294 & 0.262 & 0.291 & 0.346 & 0.245 \\  & & **3-2** & 0.115 & 0.150 & **0.373** & **0.081** & **0.105** & **0.375** & 0.111 & 0.312 & 0.159 & 0.183 & 0.173 \\  & & **3-3** & **0.082** & **0.103** & **0.477** & 0.141 & 0.173 & 0.341 & 0.134 & 0.163 & 0.304 & 0.111 & 0.145 & 0.304 \\  & & **AVG** & **0.099** & **0.126** & **0.425** & 0.111 & 0.139 & 0.358 & 0.123 & 0.147 & 0.308 & 0.135 & 0.164 & 0.238 \\ \hline \multirow{4}{*}{\ \begin{tabular}{c} Bearing 2-1 \\ \end{tabular}  } & \multirow{4}{*}{Bearing 3-1} & **1-4** & **0.103** & **0.128** & **0.320** & 0.137 & 0.166 & 0.186 & 0.115 & 0.140 & 0.245 & 0.134 & 0.173 & 0.275 \\  & & **1-5** & **0.145** & **0.175** & 0.318 & 0.161 & 0.196 & 0.297 & 0.184 & 0.211 & 0.270 & 0.161 & 0.202 & **0.321** \\  & & **1-7** & 0.110 & 0.136 & 0.291 & 0.108 & 0.131 & 0.299 & **0.088** & **0.108** & **0.348** & 0.133 & 0.171 & 0.272 \\  & & **AVG** & **0.119** & **0.146** & **0.310** & 0.135 & 0.165 & 0.261 & 0.129 & 0.153 & 0.288 & 0.143 & 0.182 & 0.289 \\  & & **3-2** & **0.106** & **0.137** & 0.250 & 0.117 & **0.137** & **0.278** & 0.164 & 0.197 & 0.218 & 0.163 & 0.199 & 0.234 \\  & & **3-3** & **0.126** & **0.148** & **0.343** & 0.147 & 0.170 & 0.262 & 0.132 & 0.159 & 0.211 & 0.154 & 0.196 & 0.230 \\  & & **AVG** & **0.116** & **0.143** & **0.297** & 0.132 & 0.153 & 0.270 & 0.148 & 0.178 & 0.214 & 0.158 & 0.198 & 0.232 \\ \hline \multirow{4}{*}{ \begin{tabular}{c} Bearing 3-1 \\ \end{tabular}