Bayesian Transfer Learning-Based Aerodynamic Robust Optimization of Ultrahigh-Lift Turbine Blades

Geometric deviations can significantly degrade the aerodynamic performance of ultrahigh-lift (UHL) low-pressure turbine (LPT) blades. Conventional uncertainty quantification and robust optimization require extensive computational fluid dynamics (CFD) evaluations and are seldom practical. For efficient analysis and optimization based on limited data, we propose a Bayesian framework that integrates priors and external knowledge, as well as uncertainty modeling, to evaluate and enhance the aerodynamic robustness of UHL LPT blades. The Bayesian neural network (BNN) surrogate predicts deviation-induced performance variations while simultaneously quantifies its own predictive uncertainty, providing interpretability and facilitating transfer learning. Further, by integrating Bayesian inference and active learning, the active transfer learning scheme utilizes regularization from pretrained posterior information and adaptively selects high-value samples, lowering the BNN's training cost by 80%-90% relative to training from scratch. Building on this efficient surrogate model, a biobjective Bayesian optimization approach balances aerodynamic robustness against blade area reduction. By leveraging external knowledge from low-cost nominal optimization and sensitivity analysis, this optimization method further halves the cost and yields a diverse Pareto front. When applied to the reference T106D-EIZ profile, the method increases the loading margin by 20%, lowers sensitivity to geometric deviations, and decreases blade area by 14.8%, demonstrating significantly enhanced robustness. Strategies to mitigate the detrimental effects of ultrahigh loading and geometric deviations are consistent: the key is to mitigate excessive adverse pressure gradients and improve the flow conditions in sensitive regions, thereby enhancing resistance to high loading and random perturbations. This Bayesian framework can be deployed to other turbomachinery blades with modest retraining, providing a data-efficient route for aerodynamic robust design in turbomachinery.