Development of Efficient UQ and RO Methods

Focusing on the uncertainties in aeronautical components, this work introduces polynomial chaos as a means to assess performance output influenced by these uncertainties. It addresses the curse-of-dimensionality by employing a reduced basis approach, utilizing simulations to derive output covariance in stochastic space. The methodology is applied to both a 2D airfoil and a 3D transonic compressor, incorporating robust, gradient-based shape optimization techniques. An adjoint methodology is utilized to efficiently calculate gradients, crucial for optimizing designs with numerous variables.