Accelerating Dimensionality Reduction in Wave-Resistance Problems through Geometric Operators

TL;DR

The paper tackles the high computational cost of sensitivity analysis in wave-resistance design by introducing geometry-based surrogates that connect hull geometry to the physics QoI $C_w$ via high-order geometric moments and slender-body theory. It develops two operators—the Shape Signature Vector (SSV) and the Slender Body Operator ${\cal G}(n)$—and uses Sobol global sensitivity analysis with Dynamic Propagation Sampling to compare their fidelity against the physics-based $C_w$ and to assess computational efficiency. Analytically, closed forms for the modified Wigley hull’s geometric moments are derived, enabling rapid evaluation of the geometry-based descriptors; empirically, ${\cal G}(15)$ achieves 100% similarity to $C_w$ in capturing sensitivity and does so with orders of magnitude lower cost than the full physics solver, outperforming SSV-based surrogates. The approach offers a practical pathway to accelerate dimensionality reduction and design-space exploration in hull optimisation, with potential extensions to richer parametric modellers and broader geometries.

Abstract

Reducing the dimensionality and uncertainty of design spaces is a key prerequisite for shape optimisation in computationally intensive fluid problems. However, running these analyses at an offline stage itself poses a computationally demanding task. In this work, we propose a unique framework for the inexpensive implementation of sensitivity analyses for reducing the dimensionality of the design space in wave-resistance problems. At the heart of our approach is the formulation of a geometric operator that leverages, via high-order geometric moments, the underlying connection between geometry and physics, specifically the wave-resistance coefficient ($C_w$), of ships using the slender body theory based on the well-known Vossers' integral. The resulting geometric operator is computationally inexpensive yet physics-informed and can act as a geometry-based surrogate to drive parametric sensitivities. To analytically demonstrate the capability of the proposed approach, we use a well-known benchmark geometry, namely, the modified Wigley hull. Its simple analytical formulation allows for closed expressions of the geometric operators and exploration of computational domains that would otherwise be inaccessible. In this context, the proposed geometric operator outperforms existing similar approaches by achieving 100% similarity with $C_w$ at a fraction of the computational cost.

Figures (26)

• Figure 1: Illustration of the application of the geometric operator ${\cal G}$. It's important to note that ${\cal G}$ is not employed in the optimisation step; rather, its use is confined to identifying the most sensitive parameters for dimension reduction. This enables an expedited physics-based optimisation process.
• Figure 2: Diagrammatic representation of the methodology for identifying a suitable geometric operator ${\cal G}$ compatible with a physics-based quantity ${\cal P}$ across a set of parametric modellers ${{\cal D}_1, {\cal D}_2, \ldots}$.
• Figure 3: Effect of $c_1$ parameter on the modified Wigley hull. In this top-view figure, each curve is the deck-line corresponding to $c_1=\{0.0,\ 0.25,\ 0.5,\ 0.75,\ 1.0\}$ with all other parameters fixed at $\{L = 1,\ B = 0.0996,\ T = 0.13775,\ c_2=0,\ c_3=0\}$.
• Figure 4: Renders of the modeller instances depicted in Figure \ref{['fig:c1']}. Specifically, from left to right, each hull corresponds to $c_1=\{0.0,\ 0.25,\ 0.5,\ 0.75,\ 1.0\}$ with all other parameters fixed at $\{L = 1,\ B = 0.0996,\ T = 0.13775,\ c_2=0,\ c_3=0\}$.
• Figure 5: Effect of $c_2$ parameter on the modified Wigley hull. In this top-view figure, each curve is the deck-line corresponding to $c_2=\{0.0,\ 0.25,\ 0.5,\ 0.75,\ 1.0\}$ with all other parameters fixed at $\{L = 1,\ B = 0.0996,\ T = 0.13775,\ c_1=0,\ c_3=0\}$.