Multi-fidelity Surrogate Assisted Design Optimisation of an Airfoil under Uncertainty Using Far-Field Drag Approximation

Abstract

Uncertainty-based optimisation techniques provide optimal airfoil designs that are less vulnerable to the presence of uncertainty in the operational conditions (i.e., Mach number, angle-of-attack, etc.) at which an airfoil is functioning. These uncertainty-based techniques typically require numerous function evaluations to accurately calculate the statistical measure of the quantity of interest. To render the computational burden down, the design optimisation of the airfoil is performed by a multi-fidelity surrogate-based technique. The high-fidelity aerodynamic performance is calculated with a compressible RANS solver using a fine grid. At the low-fidelity level a coarser grid is used. To obtain accurate drag predictions despite the lower grid resolution the so-called far-field drag approximation is employed.

Inverse design under uncertainty with surrogate models

“…From a design optimisation perspective the required number of FEM evaluations necessary to straddle and home in on some design parameter optimum can be limiting due to computational expense and model complexity, and so introduction of surrogate models is becoming more prevalent, particularly in cases where there are multiple parameters being optimised, high fidelity models are needed, and if there are stochastic parameters [1] [2]. In [3] an example of surrogate model assisted optimisation under uncertainty can be found where a Gaussian process regression surrogate, trained on a low fidelity FEM model, is introduced into the workflow to optimise the drag coefficient of an airfoil given some uncertainty on the in flight angle of attack, and successfully reduces the expense of evaluating high fidelity FEM models in the process. However, the optimisation process is iterative and an unknown number of evaluations are needed before convergence is reached.…”

“…For the purpose of demonstrating the framework used here, the shear force (F ) at the root of the wing is targeted, and the L/D is calculated relative to a fixed baseline α when the aircraft is cruising. This problem contains more complexity than [3] in that there are more stochastic parameters, the aerodynamic model is coupled with the structural model, and optimisation of the important parameters is based on two quantities of interest (F and L/D).…”