Efficient Data-Driven Off-Design Constraint Modeling for Practical Aerodynamic Shape Optimization

Abstract

Off-design constraints are essential in practical aerodynamic shape optimization. Physics-based data-driven modeling has shown to be a feasible way to formulate generalizable off-design constraints. However, two issues hinder the adoption of this approach: inadequate physical mechanism studies and the requirement of massive training data. To address these issues, we propose a feature-oriented data-driven model to learn fundamental physical mechanisms from high-dimensional data. This is achieved by finding low-dimensional latent space relevant to the investigated off-design performance. Then, we customize the constraint model based on the learned physical mechanisms, improving generalizability without relying on prior knowledge. We also propose a Bayesian-optimization-based sampling method to adjust the training data distribution, prioritizing samples with good aerodynamic performance. This uneven sampling strategy improves data efficiency by ensuring accuracy when approaching optimal aerodynamic shapes. The effectiveness of the proposed methods is shown in a low-Reynolds-number airfoil design optimization case and a transonic airfoil design optimization case. We obtain generalizable data-driven off-design aerodynamic models with no prior physical studies, and we reduce the training data volume by 95% compared with a conventional data-driven approach. This work lays the technical foundation for sample-efficient and generalizable data-driven modeling of off-design aerodynamic constraints.