Optimization of a biomimetic flapping-wing airfoil based on a surrogate model and weighted-sum with diversity-preserving elitist selection

Biomimetic flapping devices show unique advantages to enhance the hydrodynamic performance of small channels in plain river networks. To further improve the hydrodynamic performance of such systems, this study proposes an optimization framework that combines a Gradient Boosting Regression (GBR) surrogate with a weighted-sum, diversity-preserving elitist selection strategy. First, the National Advisory Committee for Aeronautics 0012 airfoil (zero camber, 12% thickness ratio) is parameterized using the class-shape transformation method, and a set of design samples is generated via Latin hypercube sampling. Each sample's propulsive efficiency and pumping efficiency are then evaluated by computational fluid dynamics (CFD) under statistically steady (cycle-averaged) conditions. The GBR models serve as surrogates for the two objectives, such as after min–max normalization, an equal-weight weighted-sum forms a composite score and candidates are chosen using diversity-preserving elitist selection. During optimization, a backfilling (infill retraining) mechanism incrementally updates the surrogate with the newly obtained CFD data to improve predictive accuracy and to reduce the computational cost. Finally, the optimized airfoil is compared with the baseline using ANSYS Fluent. Two-dimensional simulations show that propulsive efficiency increases from 11.39% to 27.39% and pumping efficiency increases from 7.5% to 14.63%. The proposed method provides both theoretical support and engineering guidance for biomimetic flapping applications and offers a feasible technical solution to the weak-hydrodynamics problem in small river channels.