Data-driven aerodynamic shape design with distributionally robust optimization approaches

Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019

For the modern design of more realistic aerodynamic shapes, disturbances caused by uncertain operating conditions must be conveniently considered, since they can affect significantly the performance of the designed systems. In this situation, the concept of robust design in conjunction with optimization tools is strongly recommended, since the interest is to maximize the performance and its robustness, simultaneously. Clearly, the great number of exact evaluations normally required to compute the robustness makes the robust optimization in aerodynamics computationally prohibitive, particularly when direct methods are chosen. To overcome this drawback, inverse methods appear as an interesting option, provided a robust aerodynamic loading can be furnished previously at low computational costs. However, few works have been dedicated to this subject in the open literature, which motivates the present study. The focus is to apply the robustness concept to optimize the velocity (or pressure) distributions for airfoil inverse designs, using a boundary layer method to predict the aerodynamic coefficients prior to the knowledge of the final airfoil shape. Here, the velocity distribution is parameterized using B-spline polygons with a set of control points, where the design variables are the ordinates of these points in the parameterization. The resulting robust multiobjective optimization problem involves the performance of the airfoil as a first objective function and its robustness introduced as additional objective to be optimized simultaneously. To illustrate the usefulness of the proposed robust design method, an example of drag minimization for an isolated airfoil is addressed and the aerodynamic coefficients for the optimal airfoils are compared with the corresponding obtained by experiments from the open literature.

Archives of Computational Methods in Engineering, 2014

This article focuses on the formulation, validation and application of the continuous adjoint method for turbulent flows in aero/hydrodynamic optimization. Though discrete adjoint has been extensively used in the past to compute objective function gradients with respect to (w.r.t.) the design variables under turbulent flow conditions, the development of the continuous adjoint variant for these flows is not widespread in the literature, hindering, to an extend, the computation of exact sensitivity derivatives. The article initially presents a general formulation of the continuous adjoint method for incompressible flows, under the commonly used assumption of "frozen turbulence". Then, the necessary addenda are presented in order to deal with the differentiation of both low-and high-Reynolds (with wall functions) number turbulence models; the latter requires the introduction of the so-called "adjoint wall functions". An approach to dealing with distance variations is also presented. The developed methods are initially validated in 2D cases and then applied to industrial shape and topology optimization problems, originating from the automotive and hydraulic turbomachinery industries.

2009

1 CIMNE – UPC, International Center for Numerical Methods in engineering, Technical University of Catalonia, Barcelona, Spain. jpons@cimne.upc.edu 2 CIMNE – UPC, International Center for Numerical Methods in engineering, Technical University of Catalonia, Barcelona, ...

1999

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity CFD, geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles, and pylons. (Author)

Computing Systems in Engineering, 1992

2010

A computationally efficient methodology for transonic airfoil design optimization is presented. Our approach exploits a corrected physics-based low-fidelity surrogate that replaces, in the optimization process, an accurate but computationally expensive highfidelity airfoil model. Correction of the low-fidelity model is achieved by aligning its corresponding airfoil surface pressure distributions with that of the high-fidelity model using a shape-preserving response prediction technique. The presented method is applied to airfoil lift maximization in two-dimensional inviscid transonic flow, subject to constraints on shock induced pressure drag and airfoil cross-sectional area. More than a 90% reduction in high-fidelity function calls is achieved when compared to direct highfidelity model optimization.

Computational Mathematics Driven by Industrial …, 2000

This paper reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations and inviscid optimization of complex configurations.

AIAA Journal, 2004

A gradient-based Newton-Krylov algorithm is presented for the aerodynamic shape optimization of single-and multi-element airfoil configurations. The flow is governed by the compressible Navier-Stokes equations in conjunction with a one-equation transport turbulence model. The preconditioned generalized minimal residual method is applied to solve the discrete-adjoint equation, which leads to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. The new algorithm is evaluated for several design examples, including the lift enhancement of a takeoff configuration and a lift-constrained drag minimization at multiple transonic operating points. Furthermore, the new algorithm is used to compute a Pareto front based on competing objectives, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an efficient approach for addressing the issues of complex aerodynamic design.

AIAA Journal, 2013

Large scale three dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended wing-body aircraft. The actual optimization is conducted in a one-shot fashion where the tangential Laplace-operator is used as a Hessian approximation, thereby also preserving the regularity of the shape.

Numerical Methods in engineering (CIMNE), c/Gran Capità s/n 08034 Barcelona, Spain 3 Director, International Center for Numerical Methods in engineering (CIMNE), c/Gran Capità s/n 08034 Barcelona, Spain Abstract. Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and use multi-point criteria to look for robust solutions. From the computational point of view, the application to coupled problems, like fluid-structure interaction, can be extremely expensive. This work proposes a coupling between stochastic analysis techniques and evolutionary optimization algorithms for the definition of a stochastic robust optimization procedure. This procedure has been applied to the optimisation of an aero-elastic coupled problem. Latin Hypercube sampling techniques have been used for the generation of random values, which surrogate uncertain behaviour of input variables. Optimization indi...