Nature has always inspired scientists and engineers to understand the underlying mechanism leading to optimal design in bio-inspired dynamics. 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 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. 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：自然界始终启迪科学家与工程师，以揭示生物启发动力学中实现最优设计的潜在机制。本研究提出一个计算框架，通过结合"形态学变形"与贝叶斯优化策略来优化波状游动模式。采用形态学变形方法，将五种基准生物启发游动模式进行变形，构建探索性设计空间，以表达游动形态。优化目标在于寻找最优游动形态、波长及波动频率，以最大化推进效率。优化后的游动模式相较于参考的鳗鲡式与鲹科式游动，在推进效率上展现出显著提升。性能最优的优化案例在广泛运动学条件下，峰值效率达49-57%，较参考的鳗鲡式与鲹科式游动整体提升16-35%。性能提升归因于有利的表面应力分布及增强的能量回收机制。详细的力分解表明，最优游动体在身体前部与后部区域最小化阻力并最大化有效功贡献。空间与时间上的功分解揭示了输入能量与回收能量的战略性再分配，从而在降低单位推进力能耗的同时提升性能。这些发现表明，基于变形的参数化设计在代理辅助优化引导下，为发现高效节能的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生物启发运动学领域具有重要启示。