# Application of Machine Learning for Bulbous Bow Optimization Design and Ship Resistance Prediction
## 4 Discussion
Normalizing the design parameters ensures that the surrogate model has good generalizability across different hull forms. The optimized bulbous bow extends outward along the centerline on both sides, transforming from a U-shape to a V-shape. Although the width is augmented, the bulbous bow appears flatter overall, facilitating a reduction in the wave resistance. The length of the bulbous bow is significantly increased, resulting in a longer inlet section below the waterline in the ship design, which may increase the friction resistance. However, this elongation also contributes to a decrease in the wave resistance, ultimately leading to a reduction in the total resistance, as wave resistance predominates in high-speed navigation. The optimized bulbous bow features an upturned tip, exhibiting a more pronounced slope alteration, whereas the bulbous bow of the original model remained predominantly at the level with minimal slope variation. The optimized bulbous bow design resulted in a 4.95% reduction in total resistance, a 7.14% reduction in the total resistance coefficient, and a 5.96% decrease in the effective power of the actual ship. Ref. [35] applied a gradient-based local optimization method to optimize the total resistance coefficient of the KCS ship, achieving a 1.8% improvement, which translated to a 3.1% reduction in effective power. In comparison, the method presented in this paper shows a significant improvement in the field of ship resistance prediction. The residual resistance coefficient of the optimized bulbous bow is inferior to that of the initial ship model across various speeds, and the disparity is negligible when \(F_{r}\) is below 0.3. The speed of the ship was low when \(F_{r}\) was minimal, resulting in the friction resistance being predominant. Conversely, when \(F_{r}\) is substantial, and the speed of the ship increases, the wave resistance becomes the primary factor, highlighting the effectiveness of the bulbous bow in reducing the resistance at this stage. Wave resistance typically increases linearly with velocity. The bulbous bow significantly reduces wave resistance, and changes in its shape have little effect on resistance at low speeds. The residual resistance coefficient curve indicates that the turning point for the DTMB5415 ship type occurs between \(F_{r}=0.2\sim 0.3\). The bulbous bow of the lowest resistance ship type may have adverse effects when \(F_{r}<0.2\), as friction resistance predominates. The free-surface wave pattern diagrams indicate that the bow peak of the optimized vessel is marginally displaced forward, with the apex of the peak exhibiting a tendency to contract inward. The change is due to the optimized vessel's elongated, flatter V-shaped bulbous bow. This design reduces the area from the bow tip to the peak of the wave, leading to a decrease in wave resistance around the vessel. The remainder of the area is consistent with the initial model; hence, the free-surface wave elevation of the optimized model remains largely unaltered following the second wave crest. According to the results shown in Figure 12, the improved WOA algorithm exhibits the fastest convergence rate. The parameter \(\epsilon\) helps the algorithm maintain a balance between model development and exploration processes, which enables the algorithm to converge quickly and find the global optimal solution in a short period of time. Simultaneously, the spiral update mechanism of the WOA algorithm allows for a progressive concentration on superior solutions within the search space, enhancing the convergence rate. The ABC method has the slowest convergence rate, owing to its reliance on extensive random searches facilitated by the exchange and transfer of information among various persons. The improved WOA algorithm has fewer core control parameters, including only population count, maximum iterations, and convergence factor. This reduces complexity and improves the efficiency of the search process.