Yonatan A. Tesfahunegn

Aerodynamic Design Optimization: Physics-Based Surrogate Approaches for Airfoil and Wing Design

The aerodynamic optimization community has recently started an effort to develop benchmark problems suitable for exercising aerodynamic optimization methods in a constrained design space. In the first round, four problems have been developed, two involving two-dimensional airfoils and the other two three-dimensional wings. In this paper, we address the two-dimensional problems which involve optimization of the NACA 0012 in inviscid transonic flow, as well as optimization of the RAE 2822 in viscous transonic flow. We solve the problems using a computationally efficient physics-based surrogate approach exploiting space mapping. Our results indicate that by shifting the computational burden to fast low-fidelity models, significant performance improvements can be achieved at the cost of a few evaluations of the expensive computational fluid dynamic models. In our approach, a commercial package FLUENT is used as the high-fidelity fluid flow solver with a hyperbolic C-mesh, whereas the versatile viscous-inviscid solver MSES is utilized as the low-fidelity model. The PARSEC parameterization method is used to describe the airfoil shapes with up to 10 design variables.

Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flo...

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.

Application of Direct and Surrogate-Based Optimization to Two-Dimensional Benchmark Aerodynamic Problems: A Comparative Study

This paper presents the results of applying direct and surrogate-based optimization (SBO) algorithms to two-dimensional aerodynamic benchmark problems, both involving transonic flow, one invisvid and the other viscous. The direct optimization methods used in this study are the adjoint-based FUN3D and Stanford University Unstructured solvers. The SBO algorithms include the SurroOpt framework, which exploits approximation-based models, the multi-level optimization (MLO) algorithm, which relies on physics-based models, as well as the adjoint-enhanced MLO algorithm. The results demonstrate that direct optimization and the approximation-based methods are able to yield designs that are comparable to those obtained with high-dimensional shape parameterization methods. Physics-based SBO shows a rapid design improvement at a low computational cost compared to the direct and the approximation-based SBO techniques, which indicates that—for certain problems—derivative-free methods may be competitive to adjoint-based algorithms when embedded in surrogate-assisted frameworks. On the other hand, global search approaches, while more expensive, exhibit the potential to produce the best quality results.

Surrogate-Based Airfoil Design with Multi-Level Optimization and Adjoint Sensitivity

Robust and computationally efficient airfoil shape optimization algorithm is presented. Our technique enhances a recently introduced multi-level optimization (MLO) algorithm with adjoint sensitivity. Adjoint-enhanced MLO exploits a set of computational fluid dynamics (CFD) models of increasing discretization density that are sequentially optimized with the optimal design of the “coarser” model being the initial design for the “finer” one. Transition between the models of different fidelities is governed by suitably selected termination criteria, more relaxed at the initial stages, and stricter towards the end of the optimization process. Exploitation of variable-fidelity models allows for taking larger steps in the design space at a lower CPU cost, leading to an improved efficiency when compared to gradient-based direct optimization of the high-fidelity model with adjoints as demonstrated by several test cases of transonic airfoils. In particular, the results show that up to a 43% reduction in the optimization cost can be achieved with MLO when compared with the direct approach.

Multi-Fidelity Aerodynamic Shape Optimization Using Manifold Mapping

A computationally efficient optimization algorithm for aerodynamic design is presented. In our approach, direct optimization of a computationally expensive model is replaced by an iterative updating and re-optimization of a fast physics-based replacement model, following the surrogate-based optimization paradigm. The surrogate is constructed using a low-fidelity model which is corrected using manifold mapping (MM) to become a reliable representation of the high-fidelity one during the optimization process. MM exploits the high-fidelity simulation data accumulated in the course of the optimization run gradually improving the generalization capability of the surrogate. The version of MM utilized here does not require gradient information. The method is applied to lift-constrained airfoil drag minimization in two-dimensional inviscid and viscous transonic flows. MM yielded optimized shapes, with 8 B-spline design variables, that are comparable to the shapes obtained by direct optimization algorithms equipped with adjoint sensitivities and trust regions. In the inviscid benchmark case, MM needed less than 150 equivalent high-fidelity model evaluations (only flow solutions), or approximately 460 minutes on a HPC with 32 processors, whereas the direct algorithm needed 391 high-fidelity model evaluations (flow and adjoint), or approximately 4,494 minutes on the same HPC. For the viscous case, MM yields 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.

Variable-fidelity CFD models and co-Kriging for expedited multi-objective aerodynamic design optimization

Purpose Strategies for accelerated multi-objective optimization of aerodynamic surfaces are investigated, including the possibility of exploiting surrogate modeling techniques for computational fluid dynamic (CFD)-driven design speedup of such surfaces. The purpose of this paper is to reduce the overall optimization time. Design/methodology/approach An algorithmic framework is described that is composed of: a search space reduction, fast surrogate models constructed using variable-fidelity CFD models and co-Kriging, and Pareto front refinement. Numerical case studies are provided demonstrating the feasibility of solving real-world problems involving multi-objective optimization of transonic airfoil shapes and accurate CFD simulation models of such surfaces. Findings It is possible, through appropriate combination of surrogate modeling techniques and variable-fidelity models, to identify a set of alternative designs representing the best possible trade-offs between conflicting design objectives in a realistic time frame corresponding to a few dozen of high-fidelity CFD simulations of the respective surfaces. Originality/value The proposed aerodynamic design optimization algorithmic framework is novel and holistic. It proved useful for fast design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search space, which is extremely challenging when using conventional methods due to the excessive computational cost.

Shape Optimization of Trawl-doors Using Variable-fidelity Models and Space Mapping

Trawl-doors have a large influence on the fuel consumption of fishing vessels. Design and optimization of trawl-doors using computational models are key factors in minimizing the fuel consumption. This paper presents an efficient optimization algorithm for the design of trawl-door shapes using computational fluid dynamic models. The approach is iterative and uses variable-fidelity models and space mapping. The algorithm is applied to the design of a multi-element trawl-door, involving four design variables controlling the angle of attack and the slat position and orientation. The results demonstrate that a satisfactory design can be obtained at a cost of a few iterations of the algorithm. Compared with direct optimization of the high-fidelity model and local response surface surrogate models, the proposed approach requires 79% less computational time while, at the same time, improving the design significantly (over 12% increase in the lift-to-drag ratio).

Surrogate-based Airfoil Design with Space Mapping and Adjoint Sensitivity

Abstract This paper presents a space mapping algorithm for airfoil shape optimization enhanced with adjoint sensitivities. The surrogate-based algorithm utilizes low-cost derivative information obtained through adjoint sensitivities to improve the space mapping matching between a high-fidelity airfoil model, evaluated through expensive CFD simulations, and its fast surrogate. Here, the airfoil surrogate model is constructed though low-fidelity CFD simulations. As a result, the design process can be performed at a low computational cost in terms of the number of high-fidelity CFD simulations. The adjoint sensitivities are also exploited to speed up the surrogate optimization process. Our method is applied to a constrained drag minimization problem in two-dimensional inviscid transonic flow. The problem is solved for several low-fidelity model termination criteria. The results show that when compared with direct gradient-based optimization with adjoint sensitivities, the proposed approach requires 49-78% less computational cost while still obtaining a comparable airfoil design.

Fast Multi-Objective Aerodynamic Optimization Using Space-Mapping-Corrected Multi-Fidelity Models and Kriging Interpolation

The chapter describes a computationally efficient procedure for multi-objective aerodynamic design optimization with multi-fidelity models, corrected using space mapping, and kriging interpolation. The optimization procedure utilizes a multi-objective evolutionary algorithm to generate an initial Pareto front which is subsequently refined iteratively using local enhancements of the kriging-based surrogate model. The refinements are realized with space mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The method yields—at a low computational cost—a set of designs representing trade-offs between the conflicting objectives. We demonstrate the approach using examples of airfoil design, one in transonic flow and another one in low-speed flow, in low-dimensional design spaces.