Data-driven parameterization refinement for the structural optimization of cruise ship hulls

TL;DR

The paper tackles the problem of rapidly optimizing cruise ship hulls in the early design phase under structural and manufacturing constraints. It introduces a data-driven hierarchical reparameterization workflow together with POD-GPR surrogates, Bayesian optimization, and multi-objective genetic algorithms to refine problem formulation and explore trade-offs efficiently. A central contribution is an ILP-based parameterization refinement that splits element groups into subpatches, enabling more expressive design spaces and better mass/yield/buckling performance. Results on a midship section and a full ship demonstrate significant speedups, improved Pareto frontiers, and mass reductions compared with designer baselines, validating the approach for complex, novel hull configurations.

Abstract

In this work, we focus on the early design phase of cruise ship hulls, where the designers are tasked with ensuring the structural resilience of the ship against extreme waves while reducing steel usage and respecting safety and manufacturing constraints. At this stage the geometry of the ship is already finalized and the designer choose the thickness of the primary structural elements, such as decks, bulkheads, and the shell. Reduced order modeling and black-box optimization techniques reduce the use of expensive finite element analysis to only validate the most promising configurations, thanks to the efficient exploration of the domain of decision variables. However, the quality of the final results heavily relies on the problem formulation, and on how the structural elements are assigned to the decision variables. With the increased request for alternative fuels and engine technologies, the designers are often faced with novel configurations and risk producing ill-suited parameterizations. To address this issue, we enhanced a structural optimization pipeline for cruise ships developed in collaboration with Fincantieri S.p.A. with a novel data-driven hierarchical reparameterization procedure, based on the optimization of a series of sub-problems. Moreover, we implemented a multi-objective optimization module to provide the designers with insights into the efficient trade-offs between competing quantities of interest and enhanced the single-objective Bayesian optimization module. The new pipeline is tested on a simplified midship section and a full ship hull, comparing the automated reparameterization to a baseline model provided by the designers. The tests show that the iterative refinement outperforms the baseline, thus streamlining the initial design phase and helping tackle more innovative projects.

Figures (28)

• Figure 1: Optimization pipeline implementing the inner-outer loop approach. The process starts with a coarse parameterization of the model and a random sampling of the parametric space. The inner loop consists of the high-fidelity expensive simulation of the samples, from which ROMs are built in the outer loop. The ROMs are optimized with a multi-objective genetic algorithm and single-objective BO, with infill criteria selecting the most promising configurations for addition to the high-fidelity database. The reparameterization procedure starts when the optimization step is unable to find new candidates. The ROMs are queried in the proximity of the current optimum to collect the structural responses, which are then clustered to generate a finer parameterization of the model, producing a new set of decision variable adapted to the emerging structural behavior. The new decision variables are hierarchically dependent on the previous ones and the high-fidelity database is easily updated. New samples from the larger parametric domain are drawn and the cycle repeats until the stopping criteria are met.
• Figure 2: A full ship model under hogging load condition on the left, and sagging on the right. Displacements are magnified, colors represent the value of the von Mises yielding criterion.
• Figure 3: On the left, position $i^*$ in the low-fidelity Pareto Frontier is selected as maximizer of the infill criterion $\Delta$ evaluated on matrices $\mathbf{C}^\text{LL}$ and $\mathbf{C}^\text{LH}$ using Equation \ref{['eq:mobj_infill_delta']}. The addition of the $i^*$-th sample to the high-fidelity set is simulated with the removal of row (and column) $i^*$ from $\mathbf{C}^\text{LL}$, its addition to $\mathbf{C}^\text{LH}$, followed by the removal of row $i^*$. The next sample is selected using the updated matrices.
• Figure 4: On the left, the GPR prediction with its uncertainty on the top and the acquisition functions at the bottom. On the right, the updated GPR after the addition of the previously selected sample, for each acquisition function.
• Figure 5: The reparameterization procedure on a simplified parameterized section. The section is composed of 6 patches, represented in steps 1, 2, and 3 with different colors corresponding to different thicknesses. In step 1, all patches have the same thickness as selected by the previous optimization. In step 2, different thicknesses are evaluated to obtain the structural responses of each patch. In step 3, the structural responses determine the reparameterization problem, and its optimal solution clusters the patches in two groups. In step 4, the patches are assigned the optimized thicknesses, and two parameterized sections are determined.