# Application of Machine Learning for Bulbous Bow Optimization Design and Ship Resistance Prediction
## 4 Discussion  
Latin hypercube sampling divides each input dimension into equal intervals and randomly selects a point from each interval. This method ensures a uniform sample distribution within the input space, reducing bias and avoiding the unevenness of traditional random sampling. The results in Table 4 show that Latin hypercube sampling produces sample points with a greater average distance between them. Additionally, the variance in the distances to the nearest neighbors is lower than that of random sampling. This confirms that Latin hypercube sampling better represents the entire input space. This significantly  
Figure 14: Comparison of the residual drag coefficients between the initial and optimized ship models at different speeds corresponding to \(F_{r}\). Figure 15: Comparison of the wave patterns between the initial and optimized ship types. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter Name** & \begin{tabular}{c} **Total** \\ **Resistance** \(R_{t}\) **(N)** \\ \end{tabular} & \begin{tabular}{c} **Total** \\ **Resistance** \\ **Coefficient** \\ \(C_{t}\times\mathbf{10^{3}}\) \\ \end{tabular} & \begin{tabular}{c} **Residual** \\ **Resistance** \\ **Factor** \\ \(C_{r}\times\mathbf{10^{3}}\) \\ \end{tabular} & \begin{tabular}{c} **Drainage** \\ **Volume (m3)** \\ \end{tabular} & \
\begin{tabular}{c} **Wet Surface** \\ **Area (m2)** \\ \end{tabular} &
\begin{tabular}{c} **Effective** \\ **Power on** \\ **Board (kW)** \\ \end{tabular} \\ \hline Initial Ship & 148.029 & 5.575 & 3.75 & 0.369 & 0.743 & 31,517.2 \\ Optimized Ship & 140.704 & 5.177 & 3.356 & 0.371 & 0.7524 & 29,637.4 \\ Optimization (\%) & 4.95 & 7.14 & 10.62 & \(-\)0.65 & \(-\)1.28 & 5.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: CFD validation results. affects the efficiency and accuracy of the subsequent WOA algorithm in identifying the minimum overall ship resistance of the model. The prediction performance results of the three models indicated that the CBR model exhibited the lowest MAE relative to the BP and RBF models on the test set, with a 2.62% reduction in the median for both instances. This signifies that the CBR model exhibits the highest accuracy in forecasting the resistance. The CBR model showed impressive RMSE performance on the test set. It reduced the mean by 1.08% compared to the BP model and the median by 1.78% compared to the RBF model. This highlights the model's stability and improved resilience. The box plots in Figure 10 indicate that the RBF model exhibits the highest stability, whereas the BP model demonstrates greater variability in accuracy but can attain a lower minimum. The CBR model integrates the strengths of both models, resulting in lower accuracy and commendable stability. Furthermore, the \(p\)-values for the CBR model compared to the RBF and BP models are all below 0.05, signifying a statistically significant difference in the MAE and RMSE between the CBR, RBF, and BP models. The CBR model, due to its fast resistance prediction capability, can accurately design the ship's structure based on real-time feedback to achieve optimal performance indicators. For example, the ship needs to consider indicators such as structural strength, propulsion efficiency, and fuel consumption. These indicators are closely related to the ship's resistance. After designing a ship's shape, the designer can use the CBR model to predict the resistance and immediately calculate the response of the above indicators. The ship's shape can then be adjusted in real-time according to the requirements of actual production, without the need for hours of CFD simulations. By using transfer learning to combine the training data of the DTMB5415 hull form with the design data of other hull forms, the CBR model can better transfer knowledge from the experience of one hull form to another, thereby reducing the amount of retraining required. When extending the surrogate model to other ship designs, it is necessary to map and normalize the input variables according to the geometric shape of the new hull form.