Aerodynamic Shape Optimization Under Flow Uncertainties Using Non-Intrusive Polynomial Chaos and Evolutionary Algorithms

Abstract

Abstract. The existence of uncertainties, associated with the operating conditions or manufacturing imperfections, occur quite often in aerodynamic optimization problems. In this paper, a workflow for shape optimization in the presence of environmental uncertain flow conditions, varying stochastically around an average value with an a-priori known standard deviation, is presented. To do so, the Uncertainty Quantification (UQ) for the objective function needs to be carried out. This is based on the non-intrusive Polynomial Chaos Expansion (niPCE) method [1], which allows for a controllable number of calls to the CFD tool used to evaluate each candidate solution, compared to other sampling methods such as Monte-Carlo. Within the proposed workflow, PCE is combined with the optimization platform EASY (Evolutionary Algorithms SYstem) [2], which undertakes the optimization task. The overall process is fully automated. The shape under consideration is parameterized using CAD-free approaches, such as Radial Basis Function techniques or the combined use of two cages and the corresponding Harmonic Coordinates, which are responsible only for surface deformations whereas, as it will be explained below, other morphing/smoothing [3] tool undertakes the adaptation of the CFD mesh to the updated boundaries at each optimization cycle. The PCE method selects the points (Gaussian nodes) in the design space to be evaluated and the computed performance metrics are integrated with weights indicated by the Gauss integration rules, in order to compute the mean value and standard deviation of the objective function of the flow problem under uncertainties. The aforementioned tools are applied in two problems, in which OpenFOAM is the CFD evaluation software.