Aerodynamic Shape Optimization by Considering Geometrical Imperfections Using Polynomial Chaos Expansion and Evolutionary Algorithms

Abstract

Uncertainties, in the form of either non-predictable shape imperfections (manufacturing) or flow conditions which are not absolutely fixed (environmental) are involved in all aerodynamic shape optimization problems. In this paper, a workflow for performing aerodynamic shape optimization under uncertainties, by taking manufacturing uncertainties into account is proposed. The uncertainty quantification (UQ) for the objective function is carried out based on the non-intrusive Polynomial Chaos Expansion (niPCE) method which relies upon the CFD software as a blackbox tool. PCE is combined with an evolutionary algorithm optimization platform. CAD-free techniques are used to control the shape and simultaneously generate shape imperfections; next to this, a morphing/smoothing tool adapts the CFD mesh to any new shape. In the cases presented in this paper, all CFD evaluations are performed in the OpenFOAM environment.

Development and assessment of an intrusive polynomial chaos expansion‐based continuous adjoint method for shape optimization under uncertainties

“…Once the statistical moments of the QoI are computed by the UQ software, a suitable objective function is formulated and the optimization problem under uncertainties is defined, Section 2. Though evolutionary algorithms have been used to solve problems in the presence of uncertainties, [21][22][23] the high number of required evaluations (compared to gradient-based approaches) combined with the relatively high UQ evaluation cost of each candidate solution is a deterrent factor. If gradient-based optimization is used instead, the gradient of the objective function w.r.t.…”