Anand Amrit

Application of Multifidelity Optimization Techniques to Benchmark Aerodynamic Design Problems

Two-dimensional benchmark cases involving lift-constrained drag minimization in inviscid and viscous transonic flows are solved using derivative-free multi-fidelity optimization algorithms (space mapping and manifold mapping) and are compared with direct gradient-based optimization algorithms using adjoint sensitivities and trust regions. With 8 B-spline design variables, the multi-fidelity algorithms yield optimized shapes comparable to the shapes obtained by the direct algorithms but at a fraction of the cost. In particular for the inviscid case, the multi-fidelity algorithms needed less than 150 equivalent high-fidelity model evaluations (only flow solutions) taking approximately 460 minutes on a HPC with 32 processors, whereas the direct algorithm needed 391 high-fidelity model evaluations (flow and adjoint) taking approximately 4,494 minutes on the same HPC. For the viscous case, the multi-fidelity algorithms yield an optimized shape using less than 125 equivalent high-fidelity evaluations taking approximately 17.4 hours on the HPC. The direct algorithm was unsuccessful in optimizing the baseline shape in this case. A simple variation of surrogate-based optimization, the sequential approximate optimization (SAO), is utilized to optimize the twist distribution of a rectangular unswept wing in inviscid flow. Using 3 Bspline design variables, the SAO algorithm is able to obtain an optimized design with a nearelliptic section lift distribution. The total optimization cost is 22 high-fidelity model evaluations or approximately 42.5 hours on a HPC with 32 processors.

Design strategies for multi-objective optimization of aerodynamic surfaces

Purpose This paper aims to investigates several design strategies to solve multi-objective aerodynamic optimization problems using high-fidelity simulations. The purpose is to find strategies which reduce the overall optimization time while still maintaining accuracy at the high-fidelity level. Design/methodology/approach Design strategies are proposed that use an algorithmic framework composed of search space reduction, fast surrogate models constructed using a combination of physics-based surrogates and kriging and global refinement of the Pareto front with co-kriging. The strategies either search the full or reduced design space with a low-fidelity model or a physics-based surrogate. Findings Numerical investigations of airfoil shapes in two-dimensional transonic flow are used to characterize and compare the strategies. The results show that searching a reduced design space produces the same Pareto front as when searching the full space. Moreover, as the reduced space is two orders of magnitude smaller (volume-wise), the number of required samples to setup the surrogates can be reduced by an order of magnitude. Consequently, the computational time is reduced from over three days to less than half a day. Originality/value The proposed design strategies are novel and holistic. The strategies render multi-objective design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces computationally tractable.

Rapid Multi-Objective Aerodynamic Design Using Co-Kriging and Space Mapping

In this paper, a procedure for computationally feasible multi-objective design optimization of aerodynamic surfaces is presented. Our approach exploits multi-fidelity aerodynamics models as well as a multi-objective evolutionary algorithm (MOEA). For the sake of cost reduction, the initial Pareto front is obtained by optimizing a fast kriging surrogate model using MOEA. The surrogate is constructed from sampled low-fidelity model which is pre-conditioned using high-fidelity model data and space mapping. The surrogate is then iteratively refined by enhancing it using high-fidelity model data points sampled along the Pareto set using co-kriging. The process is continued until the Pareto front representation produced by the surrogate aligns with the high-fidelity verification samples. The proposed method allows us to obtain—at a low computational cost—a set of aerodynamic geometries representing trade-offs between the figures of merit. Our approach is illustrated on the design of airfoil shapes in transonic flow at constant lift and obtaining the Pareto front for the drag and pitching moment coefficients.