## 4 Conclusions  
This study introduced a new global static sensitivity assessment and optimization method. The Nanhu railway embankment in Hunan Province, China, was used to test this method's efficacy and accuracy. This study was validated using field data from the year 2020, specifically focusing on the failure that occurred in the section of the K1430 + 110 of the Beijing-Guangzhou railway embankment. However, the authors are currently investigating the long-term coupled impacts of water level fluctuations and environmental factors within the watershed. The results of this study's findings on the hydromechanical properties of the railway slope between two lakes and its process optimization possibilities are as follows:  
* The investigation showed a substantial link between the embankment slope seepage line and lakes water level fluctuations. The Plackett-Burman design was used to independently study the parameters that significantly affect the railway slope's total static stability factor under rising and falling water levels. Key parameters, such as angle of internal friction (\(\phi\)), soil density (\(\rho_{s}\)), and cohesion (\(c\)), significantly impact the slope stability during a rise in water level. However, \(k_{s}\), \(H\), \(u\), \(v\), and \(E\) were less significant. During falling water levels, \(\phi\), \(c\), \(H\), and \(\rho_{s}\) were more important but in a different sequence. * The BBD-RSM and ANN studies used 3D surface and profiler diagrams to find factor-response relationships. These diagrams accurately predicted the components needed to fulfil goals. The predicted results were supported by ANOVA models. The study found some notable second-order interactions. RWL interactions were \(c\)\(x\)\(\rho_{s}\), \(\phi\)\(x\)\(\rho_{s}\), and \(\rho_{s}\)\({}^{2}\), and the FWL interactions were \(H\)\(x\)\(c\) and \(c\)\(x\)\(\rho_{s}\). We also found that RWL was more consistent at higher unit weights and FWL was more stable at lower unit weights. RWL's finest factor combinations are (14.11, 37.4, and 1711.9), and FWL's are (14.175, 37.4, 15.529, and 1713.24)
* The research found that BBD-RSM and ANN were effective for evaluating RWL and FWL stability coefficients. All input variables affected the coefficients, but angle of internal friction had the greatest impact, followed by soil density and then cohesion for the RWL. The angle of internal friction had the greatest impact on FWL, followed by cohesion, water level, and soil density. Compared to ANN-based models, RSM-based models performed slightly better during RWL, with comparable R\({}^{2}\) values but fewer prediction errors (\(RMSE\) and \(MRE\)). Compared to RSM-based models, the RSM model produced R\({}^{2}\) values of 0.99(99) and 0.99 with MREs of 0.01 and 0.24 under both RWL and FWL conditions, respectively. However, for ANN, respectively, they produced R\({}^{2}\) values of 0.99(99) and 0.99(98), with MRE values of 0.02 and 0.21, indicating that ANN-based models performed slightly better during FWL, with higher R\({}^{2}\) values and reduced prediction errors (MRE). Coupled analysis with RSM and ANN models \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Resposes** & **R\({}^{2}\)** & & **MRE** & & **RMSE** & \\ \hline  & **RSM** & **ANN** & **RSM** & **ANN** & **RSM** & **ANN** \\ \hline RWL & 0.99(99) & 0.99(99) & 0.01(04) & 0.17(84) & 0.00(03) & 0.00(84) \\ FWL & 0.99(25) & 0.99(97) & 0.23(90) & 0.21(15) & 0.00(05) & 0.00(54) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical performance rating index. improved accuracy, efficiency, iteration needs, trial durations, and cost-effectiveness for both experimental and numerical processes. B.U.A. : Methodology, software, writing--original draft; L.X. : Conceptualization, Funding acquisition, writing--review and editing; A.-A.D.B. : Writing--validation, review, and editing. B.R. and R.M.K. : Visualization and editing. N.I. : Visualization and editing. A.A.: writing--review and editing; A.S. and R.M.K. : writing--review and editing; R.M.K.