Robust Design of a Supersonic Natural Laminar Flow Wing-Body

Abstract

The robust design of a natural laminar flow wingbody for a supersonic business jet is here described. The pursued goal is to obtain a wing shape whose performance is influenced as least as possible by geometrical uncertainties. The starting point is a supersonic business jet wing-body that was already optimized for natural laminar flow using a deterministic objective function formulation. The definition of the optimization goal is based on special risk functions, namely Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), that are widely used in financial engineering community and that offer interesting advantages with respect to more classical approaches based on expectation or variance risk functions. VaR and CVaR are used in conjunction with two different stochastic optimization algorithms, namely the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and the Surrogate-based Local Optimization (SBLO). These risk functions are computed using a very coarse sample set and their confidence intervals are computed using the bootstrap computational statistics technique. The results illustrate the feasibility of such a robust optimization approach for the application to industrial class robust design optimization problems in aerospace.