Multi-Objective Hull-Form Optimization of a Slender Submersible Surface Vehicle for Resistance and Vertical-Plane Maneuvering Stability

Submersible surface vehicles (SSVs) must balance resistance in surface and fully submerged navigation while maintaining vertical-plane stability. This study develops a multi-objective hull-form optimization framework for a slender SSV using four free-form deformation (FFD) variables and 20 CFD design samples. Six low-order surrogate models predict surface and submerged resistance coefficients, displacement ratios, and two components of the vertical-plane stability criterion, Cv and Cvh. The combined criterion, Cstab=−(Cv+Cvh), is derived from the linearized heave–pitch equations using hydrodynamic derivatives obtained from CFD. The two components are modeled separately to examine their responses to hull-form variations. Model performance is evaluated using leave-one-out cross-validation (LOOCV), an independent baseline check, and high-fidelity recalculations. The three objective models achieve Q2 values of 0.9396, 0.9767, and 0.9818, respectively. Sensitivity analysis is conducted over a ±10% displacement-variation domain and a narrower ±1% feasible domain. Within the latter, stern vertical deformation accounts for 61.6% of surface-resistance variance, while the grouped longitudinal variables account for 81.7% of submerged-resistance variance. Five constrained NSGA-II runs yield 567 surrogate-predicted non-dominated designs. The selected compromise predicts reductions of 1.25% and 0.24% in surface and submerged resistance, respectively. Independent recalculation instead shows a 4.74% surface-resistance reduction, a 6.20% submerged-resistance increase, and a 2.60% increase in submerged displacement, exceeding the 1% limit. The stability-index prediction error is 6.53%. These results reveal mode-dependent geometric effects and highlight the need for further high-fidelity validation of the selected design.