Posterior robust optimization for design update based on measurements

Abstract

A Bayesian unified framework is proposed for data-informed robust design optimization. Models of uncertainties postulated in conventional robust design optimization are treated as prior uncertainties in a Bayesian context. Measurements collected for one or more components of the system to be designed are used by standard Bayesian inference tools to update uncertainties at component level and quantify these uncertainties by posterior PDFs. For the data-informed model parameters, approximations of uncertainty models by Gaussian posterior PDFs, arising from the use of Bayesian central limit theorem, are particularly suited for certain methods used for robust design optimization, such as first-order or Taylor expansion techniques or sparse grid methods required to estimate the multi-dimensional integrals that arise in the robust objective functions. The posterior robust design optimization framework is demonstrated by applying it to the optimization of the aerodynamic shape of an airfoil under data-informed turbulence model uncertainties estimated from measurements on simplified flows such as flow over a flat plate, and prior uncertainties postulated for the Mach and angle of attack.