## 5 Conclusions  
In this paper, an enhanced cross-working condition RUL prediction method via an initial degradation detection-enabled joint transfer metric network is proposed. This method solves the problem of insufficient RUL prediction accuracy due to differences in the distribution of the training and test data. On one hand, a novel DACAEN is built to train reconstruction ability based on healthy samples from a healthy process. The health indicator RAPP is obtained by calculating the discrepancy between the input and reconstruction of trained DACAEN, not only in the input space, but also in the hidden spaces, which is implied for the IDD, and then RUL prediction is triggered at this time. Additionally, a novel joint domain adaptation loss combined with representation subspace distance and variance discrepancy representation is designed to build a JTMN for cross-working condition RUL prediction. JTMN is enacted on the final layer of the mapping regression network to weaken data distribution discrepancies and ultimately obtain cross-domain invariant features. The experimental results from the PHM2012 bearing dataset show that the proposed method leads to superior prediction accuracy and enhanced model generalization capability compared to typical and advanced transfer RUL prediction  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**Target**} & \multirow{2}{*}{**Tests**} & \multicolumn{3}{c}{**VDR + RSD + CNN**} & \multicolumn{3}{c}{**Wasserstein + CNN**} & \multicolumn{3}{c}{**CORAL + CNN**} & \multicolumn{3}{c}{**CCD + CNN**} \\  & & & MAE & RMSE & Score & MAE & RMSE & Score & MAE & RMSE & Score & MAE & RMSE & Score \\ \hline \multirow{6}{*}{\begin{tabular}{c} Bearing \\ 1-2 \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} Bearing \\ 2-1 \\ 3-1 \\ \end{tabular} } & **2-3** & **0.320** & **0.389** & 0.244 & 0.332 & 0.429 & 0.246 & 0.357 & 0.413 & 0.178 & 0.322 & 0.392 & **0.247** \\  & & **2-6** & **0.082** & **0.105** & 0.316 & 0.122 & 0.145 & 0.226 & 0.087 & 0.108 & 0.342 & 0.112 & 0.138 & **0.329** \\  & & **2-7** & 0.241 & 0.302 & 0.282 & 0.354 & 0.428 & 0.236 & 0.240 & 0.305 & 0.338 & **0.192** & **0.256** & **0.414** \\  & & **AVG** & 0.214 & 0.265 & 0.280 & 0.269 & 0.334 & 0.236 & 0.228 & 0.275 & 0.286 & **0.208** & **0.262** & **0.330** \\  & & **3-2** & 0.115 & 0.150 & **0.373** & **0.103** & **0.310** & 0.365 & 0.111 & 0.137 & 0.137 & 0.168 & 0.232 & 0.314 \\  & & **3-3** & **0.082** & **0.103** & **0.477** & 0.141 & 0.166 & 0.282 & 0.133 & 0.164 & 0.342 & 0.149 & 0.199 & 0.321 \\  & & **AVG** & **0.099** & **0.126** & **0.425** & 0.122 & 0.148 & 0.323 & 0.122 & 0.159 & 0.330 & 0.159 & 0.215 & 0.317 \\ \hline \multirow{6}{*}{\
\begin{tabular}{c} Bearing \\ 2-1 \\ 3-1 \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} Bearing \\ **3-2** \\ **4-3** \\ **4-4** \\ **4-5** \\ **4-6** \\  
methods under cross-over operating conditions. Its MSE, RMSE, and Score are improved by 0.047, 0.053, and 0.058, respectively.  
Conceptualization, J.P. and L.Q.; methodology, L.Q.; software, L.Q.; validation, L.Q. and J.P.; formal analysis, L.Q. and T.H.; investigation, J.P.; resources, J.P.; data curation, F.H.; writing--original draft preparation, L.Q.; writing--review and editing, J.P., T.H. and Z.Z.; visualization, L.Q.; supervision, J.P.; project administration, F.H.; funding acquisition, F.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Guangxi Key Research and Development Program Project Grant No. AB24010202.  
Not applicable.  
The **PHM2012** ([[https://www.femto-st.fr/fr](https://www.femto-st.fr/fr)]([https://www.femto-st.fr/fr](https://www.femto-st.fr/fr))) datasets are available in the references.  
The authors declare no conflicts of interest.