Multi-objective optimization of transonic airfoils using variable-fidelity models, co-kriging surrogates, and design space reduction

Amrit, Anand
Major Professor
Leifur Leifsson
Committee Member
Journal Title
Journal ISSN
Volume Title
Research Projects
Organizational Units
Aerospace Engineering
Organizational Unit
Journal Issue
Aerospace Engineering

Computationally efficient constrained multi-objective design optimization of transonic airfoils is considered. The proposed methodology focuses on fixed-lift design aimed at finding the best possible trade-offs between the conflicting objectives. The algorithm exploits the surrogate-based optimization principle, variable-fidelity computational fluid dynamics (CFD) models, as well as auxiliary approximation surrogates (here, using kriging). The kriging models constructed within a reduced design space. The optimization process has three major stages: (i) design space reduction which involves the identification of the extreme points of the Pareto front through single-objective optimization, (ii) construction of the kriging model and an initial Pareto front generation using multi-objective evolutionary algorithm, and (iii) Pareto front refinement using co-kriging models. For the sake of computational efficiency, stages (i) and (ii) are realized at the level of low-fidelity CFD models. The proposed algorithm is applied to the multi-objective optimization of a transonic airfoil at a Mach number of 0.734 and a fixed lift coefficient of 0.824. The shape is parameterized with eight B-spline control points. The fluid flow is taken to be inviscid. The high-fidelity model solves the compressible Euler equations. The low-fidelity model is the same as the high-fidelity one, but with a coarser description and is much faster to execute. With the proposed approach, the entire Pareto front of the drag coefficient and the pitching moment coefficient is obtained using 100 low-fidelity samples and 3 high-fidelity model samples. This cost is not only considerably lower (up to two orders of magnitude) than the cost of direct high-fidelity mode optimization using metaheuristics without design space reduction, but, more importantly, renders multi-objective optimization of transonic airfoil shapes computationally tractable, even at the level of accurate CFD models.