Stochastic Gradient Optimization of Transonic Airfoils
Fatma Demet Ulker, Alireza Doostan, Mark Drela · AIAA Scitech 2021 Forum · 2021
View Video Presentation: https://doi.org/10.2514/6.2021-1592.vid Stochastic gradient-based optimization is used to overcome the combinatorial scaling problem of deterministic multi-point optimization over potentially many design parameters. The specific application is transonic airfoil design to minimize the mission fuel burn of a transport aircraft flying over some ranges of the operating (design) parameters, specifically the Mach number, Reynolds number, and lift coefficient. At each optimization descent step, mini-batch samples are used to approximate the objective function and its design gradient over the design variables, which here are Chebyshev-mode geometric design variables and the angle of attack. Robustness of optimal solution to initial seed airfoil and on the chosen operating ranges is examined. Adaptive variation of the Mach range is implemented to address the fact that the appropriate range is not known a priori, and also to suppress problems arising from solution non-convergence at unrealistically high sampled Mach numbers. The transonic airfoil analysis code MSES is used as the flow solver, with flow parameters chosen in each design step by mini-batch random sampling. The stochastic present optimization method improves performance over the multi-dimensional parameter space, and prevents the appearance of irregular geometries frequently seen in single-point or sparse-sampled deterministic airfoil optimization.