Shape Parameterization and Efficient Optimization Design Method for the Ray-like Underwater Gliders.

To address the challenges of high computational cost and lengthy design cycles in the high-precision optimization of ray-like underwater gliders, this study proposes a high-accuracy, low-cost parametric modeling and optimization method. The proposed framework begins by extracting the characteristic contours of the manta ray and reconstructing the airfoil sections using the Class-Shape Transformation (CST) method, resulting in a flexible parametric geometry capable of smooth deformation. High-fidelity Computational Fluid Dynamics (CFD) simulations are employed to evaluate the hydrodynamic characteristics, and detailed flow field analyses are conducted to identify the most influential geometric features affecting lift and drag performance. On this basis, a Kriging-based sequential optimization framework is developed. The surrogate model is adaptively refined through dynamic infilling of sample points based on combined Mean Squared Prediction (MSP) and Expected Improvement (EI) criteria, thus improving optimization efficiency while maintaining predictive accuracy. Comparative case studies demonstrate that the proposed method achieves a 116% improvement in lift-to-drag ratio and a more uniform flow distribution, confirming its effectiveness in enhancing both design accuracy and computational efficiency. The results indicate that this approach provides a practical and efficient tool for the parametric design and hydrodynamic optimization of bio-inspired underwater vehicles.