UQ sensitivity analysis and robust design optimization of a supersonic natural laminar flow wing-body

Abstract

The robust design optimization of a natural laminar flow wing for a supersonic business jet is the objective of the reported research work. In particular, 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 approach within the EU funded SUPERTRAC Project. This configuration was firstly analyzed to identify the main dependencies, and interactions of the parameters that describe the uncertainty sources in the robust design problem, and in a second step, a robust design optimization algorithm was used to obtain an optimal solution less sensible to geometrical perturbation with respect to the baseline. The optimization algorithm is an evolutionary one and its principal requirement is the resilience to noise in the objective function values. The objective function that defines the goal of the optimization 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. The initial part of the optimization task is based on VaR risk function computed using a very coarse sample set. In a second step, the CVaR function, computed over a finer sample is used to further improve the results. The confidence intervals of VaR and CVaR estimations 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 techniques.