Optimized Fish Locomotion using Design-by-Morphing and Bayesian Optimization

TL;DR

This work addresses efficient undulatory propulsion by integrating design-by-morphing (DbM) with MixedMOBO Bayesian optimization to explore a six-dimensional design space (four morphing weights plus frequency and wavelength) for a fish-like NACA-0012 foil. The swimming profile is formed as a linear combination of five baseline shapes, enabling a rich design space, and evaluated via high-fidelity 2D CFD with an ALE-based fluid–structure interaction framework. The optimization yields a best-profile efficiency of 82.4%, with two additional high-performing profiles that outpace traditional anguilliform and carangiform gaits through strategic distribution of input work and energy recovery, as well as coherent wake structures. The results demonstrate that morphing-based design, when guided by surrogate-assisted BO, can discover high-performance, energy-efficient swimming gaits with direct relevance to autonomous underwater propulsion and bio-inspired locomotion. Key insights include enhanced anterior/posterior force distribution, energy recapture during certain phases, and robust 3D wake consistency, underscoring the practical potential of DbM–BO for propulsion system design.

Abstract

This study presents a computational framework for optimizing undulatory swimming profiles using a combination of design-by-morphing and Bayesian optimization strategies. The body deformation is expressed as a linear combination of five baseline bio-inspired profiles, including two unconventional shapes to enhance diversity in the design space. The optimization objective is to maximize propulsive efficiency over a wide range of frequency-wavelength combinations. The Arbitrary Lagrangian--Eulerian formulation is employed to simulate the unsteady flow around two-dimensional undulating swimmers. The optimized profile achieves a significantly improved efficiency of 82.4\%, while the second- and third-best profiles achieve efficiencies of 51.8\% and 42.8\%, respectively, outperforming the benchmark anguilliform and carangiform profiles by leveraging advantageous surface stress distributions and effective energy recovery mechanisms. A detailed force decomposition reveals that the optimal swimmer minimizes resistive drag and maximizes constructive work contributions, particularly in the anterior and posterior body regions. Spatial and temporal work decomposition indicates a strategic redistribution of input and recovered energy, enhancing performance while reducing energetic cost. The wake topology associated with the optimized swimmer exhibits organized and coherent vortex structures, reflecting superior fluid-structure interaction characteristics compared to conventional profiles. These findings demonstrate that morphing-based parametric design, when guided by surrogate-assisted optimization, offers a powerful framework for discovering energetically efficient swimming gaits, with significant implications for the design of autonomous underwater propulsion systems and the broader field of bio-inspired locomotion.

Figures (19)

• Figure 1: Optimization framework combining Design-by-Morphing, CFD simulation, and Bayesian Optimization to maximize propulsive efficiency.
• Figure 2: (a) Swimming amplitudes and (b) kinematic description of the NACA-0012 airfoil for five baseline shapes.
• Figure 3: A schematic representation of the DbM strategy
• Figure 4: (a) An 'O'-type body fitted orthogonal grid between the airfoil and circular outer domain of radius $25L$ and (b) A schematic of the two-dimensional layout of the domain for the self-propulsion body.
• Figure 5: Benchmarks for MixMOBO for four test functions.