A novel robust aerodynamic optimization technique coupled with adjoint solvers and polynomial chaos expansion

• Published in: Chinese journal of aeronautics 2022-10, Vol.35 (10), p.35-55
• Main Authors: Zhang, Wei, Wang, Qiang, Zeng, Fanzhi, Yan, Chao
• Format: Article
• Language: English
• Subjects: Adjoint technique; Polynomial chaos expansion; Robust design; Uncertainty analysis; Uncertainty gradient propagation
• ISSN: 1000-9361
• DOI: 10.1016/j.cja.2022.06.003

Uncertainty is common in the life cycle of an aircraft, and Robust Aerodynamic Optimization (RAO) that considers uncertainty is important in aircraft design. To avoid the curse of dimensionality in surrogate-based optimization, this study proposes an adjoint RAO technique called “R-Opt”. Polynomial Chaos Expansion (PCE) is coupled with the R-Opt technique to quantify uncertainty in the responses of the target (including its mean and standard deviation). Only one process of PCE model construction is required in each iteration, and the gradients of uncertainty can be inferred via chain rules. The proposed method is more efficient than prevalent methods, and avoids the problem of a disagreement over the best PCE basis from among a number of PCE models (especially in case of sparse PCE). It also supports the application of sparse PCE. Two benchmark tests and two airfoil cases were used to verify R-Opt, and the optimal solutions were deemed to be robust. It improved the mean aerodynamic performance and reduced the standard deviation of the target.