## 5 Conclusions and Recommendations  
Based on the stability analysis of the skid-and-mud-return line conducted in this study, the following conclusions and recommendations can be drawn:  
(1) Among these factors on the stability of the skid-and-mud-return line, drilling vessel motion plays a dominant role. In normal operating conditions, the stability of the skid-and-mud-return line meets the requirements for drilling and production operations. However, in extreme operating conditions, the effect on the stability of the skid-and-mud-return line is significant. Therefore, it is necessary to avoid the occurrence of extreme operating conditions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Wind Recurrence Period** & **Wind Direction Angle** & **Sea Recurrence Period** & **Water Flow Attack Angle** & **Voltage** & **Rotational Speed (RFM)** \\ \hline
1 year & 0\({}^{\circ}\) & 1 year & 0\({}^{\circ}\) & 60\%Un & 0 \\
5 years & 45\({}^{\circ}\) & 5 years & 45\({}^{\circ}\) & 80\%Un & 300 \\
10 years & 90\({}^{\circ}\) & 10 years & 90\({}^{\circ}\) & 90\%Un & 600 \\
25 years & 135\({}^{\circ}\) & 25 years & 135\({}^{\circ}\) & 100\%Un & 900 \\  & 180\({}^{\circ}\) & & 180\({}^{\circ}\) & 110\%Un & 1200 \\  & & & & 1500 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Table of parameter levels.  
Figure 12: (**a**) Comparison of prediction results for the training set: mse = 0.0064949 and R\({}^{2}\) = 0.97927. (**b**) Comparison of the prediction results for the testing set: mse = 0.019341 and R\({}^{2}\) = 0.93767.  
(2) Due to the dominant effect of drilling vessel action induced by sea wind and sea current flow on the stability of the mud return pipeline, it is crucial to monitor the wind direction and sea current direction when the recurrence interval is large. Adjusting the vessel's orientation based on the wind direction and sea current flow can change the attack angle and reduce the load on the drilling vessel by sea wind and sea current flow. The safety of drilling, production, and operations can be ensured.  
(3) According to the weight analysis carried out using the SVR-DSWA algorithm, the relative effect weight on the stability of the skid-and-mud-return line from the highest to the lowest are wind condition recurrence interval, sea condition recurrence interval, wind direction angle, water flow attack angle, voltage, and rotational speed. Both wind condition recurrence interval and sea condition recurrence interval are equal in weight, ranking the highest and accounting for 23.29%, respectively.  
A key research direction in the future is the mechanical state monitoring and dynamic analysis of mud upstream and return circulating pipelines. Subsequent research will be compared with other research to obtain environmental and process parameter data suitable for efficient drilling in RMR.  
Conceptualization, G.H. and R.Q.; data curation, H.C. and B.X.; formal analysis, L.W. and J.W.; methodology, C.L. and J.W.; project administration, G.H. and R.Q.; software, G.Y.; writing--original draft, R.Q., C.L. and Q.L. All authors have read and agreed to the published version of the manuscript.  
This research is funded by the National Key Research and Development Program of China (2021 YFC2800802; 2021 YFC2800803), the Hi-tech Ship Project of Ministry of Industry and Information Technology (CJ05N20), the Marine Economy Development Foundation of Guangdong Province (GDNRC [2022]44), and Technical Support for Stimulation and Testing of Gas Hydrate Reservoirs.  
The authors declare no conflict of interest.