This study presents a computational framework for optimizing undulatory swimming profiles using a combination of Design-by-Morphing and Bayesian optimization strategies. The swimming profile are expressed by \textit{morphing} five baseline bio-inspired profiles using Design-by-Morphing to create an exploratory design space. The optimization objective is to find the optimal swimming profile, wavelength and undulation frequency to maximize propulsive efficiency. Arbitrary Lagrangian--Eulerian formulation is employed to simulate the unsteady flow around two-dimensional undulating swimmers. The optimized swimming profiles demonstrate a marked improvement in propulsive efficiency relative to the reference anguilliform and carangiform modes. The best-performing optimized cases achieve peak efficiencies in the range of 49\%--57\% over a broad range of kinematic conditions, representing an overall enhancement of 16\%--35\% compared to reference anguilliform and carangiform modes. The improved performance is attributed to favorable surface stress distributions and enhanced 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 relative to propulsive force. 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.

翻译：本研究提出了一种结合形态设计与贝叶斯优化策略的计算框架，用于优化波动式游动轮廓。游动轮廓通过形态设计方法对五种基线仿生轮廓进行形态变换，从而构建出探索性设计空间。优化目标在于寻找最优的游动轮廓、波长及波动频率，以实现推进效率的最大化。采用任意拉格朗日-欧拉方法模拟二维波动游动体周围的非定常流动。优化后的游动轮廓相较于参考的鳗鲡模式与鲹科模式，在推进效率上展现出显著提升。在广泛的运动学条件下，性能最优的优化案例实现了49\%--57\%的峰值效率范围，较参考的鳗鲡模式与鲹科模式整体提升了16\%--35\%。性能改善归因于有利的表面应力分布与增强的能量回收机制。详细的力分解表明，最优游动体能够最小化阻力并最大化有效做功贡献，尤其在身体前部与后部区域。时空功分解揭示了输入能量与回收能量的策略性重分布，在降低推进力所需能耗的同时提升了运动性能。这些发现表明，基于形态变换的参数化设计在代理辅助优化的引导下，为发掘高能效游动步态提供了强大框架，对自主水下推进系统设计及更广泛的仿生运动领域具有重要启示。