Rapid aerodynamic shape optimization under uncertainty using a stochastic gradient approach

Abstract A common approach in aerodynamic design is to optimize a performance function—provided some constraints—defined by choice of an model at nominal operating conditions. Practical experience indicates that such deterministic may result considerably sub-optimal designs when the adopted does not lead accurate predictions, or actual conditions differ from those considered design. One address this shortcoming consider average robust design, wherein statistical moments function, given uncertainty and model, optimized. However, number uncertain inputs large function exhibits significant variability, evaluation these require evaluations each optimization iteration, rendering problem significantly expensive. To tackle difficulty, we variant stochastic gradient descent method where approximation objective, constraints, their gradients generated. This done via small forward/adjoint solutions corresponding random selections uncertainties. The methodology applied NACA-0012 airfoil subject condition turbulence uncertainty. With cost only factor larger than methodology, improves for wide range models.