Gradient based empirical cumulative distribution function approximation for robust aerodynamic design

A robust optimization approach based on the use of the conditional value at risk function is presented, together with an application to a robust transonic aerodynamic design problem of the central section of a Blended Wing-Body configuration. The conditional value at risk is estimated using an approach based on the empirical cumulative probability distribution function. The quantities of interest of the risk function are the aerodynamic characteristics of the airfoil, namely lift, drag, and pitching moment coefficients, computed solving the Reynolds-averaged Navier-Stokes equations with the open-source fluid-dynamic solver SU2. Conditional value at risk computation is costly, so techniques and methods for the reduction of the computational cost are introduced. In particular, the empirical cumulative distribution function is approximated with a first-order series expansion using efficiently calculated gradients from SU2 discrete adjoint solver.