Surrogate models are often used to reduce the cost of design optimization problems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by surrogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality constraints. The proposed algorithm-super efficient global optimization coupled with mixture of experts (SEGOMOE)can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained problems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization.
The application of gradient-based optimization to wing design could potentially reveal revolutionary new wing concepts. Giving the optimizer the freedom to discover novel wing designs may increase the likelihood of multimodality in the design space. To address this issue, we investigate the existence and possible sources of multimodality in the aerodynamic shape optimization of a rectangular wing. Our test case, specified by the ADODG Case 6, has a high dimensionality design space and a large degree of flexibility within that design space. We study several subproblems of this benchmark test case and analyze the multimodality introduced by each set of variables. We find evidence of multimodality with both inviscid and viscous analysis. In the full case we find that optimization with inviscid analysis yields multiple non-intuitive local minima. Adding consideration of viscous effects does not remove the multimodality, but allows the multiple local minima to be explained with physical reasoning. Additionally, we find that the shape of the optimized wing is highly dependent on the interplay between induced and viscous drag, providing more incentive to consider viscous effects in the analysis. The best result found by the optimizer reduces the total drag of the baseline wing by 22%.Many of the applications of MDO to aircraft design have been targeted at optimizing specific configurations or features. In one of the first demonstrations of numerical optimization in wing design, Hicks and Henne [4] modified the design of a swept wing with airfoil shape and twist variables to reduce wave drag and increase L/D. Jameson et al. [5] optimized a wide-body wing and wing-fuselage configuration and recovered a shock-free surface. Several studies have investigated the optimization of winglets [6][7][8]. Martins et al. [9] accomplished a CFD-based aerostructural optimization of a supersonic business jet. More recently, a number of studies have been published on the high-fidelity design optimization of the Common Research Model (CRM) benchmark wing [10][11][12][13]. Application of MDO to future aircraft concepts like the blended wing-body [14] and D8 [15] has also been a fruitful area of research.These results have strengthened the credibility of MDO and its applicability to practical aircraft design problems. However, these studies focused on the refinement of existing technologies, or making good aircraft better. There are sound reasons for starting an optimization problem from a design that already employs state-of-the-art knowledge and techniques. In high-fidelity aerostructural optimizations for example, starting the optimization with a poor initial design can prevent the optimizer from finding a feasible solution. However, in the long term, we want to make MDO robust enough that it can be used to explore the full design space and discover novel designs. Ideally we would be able to start an optimization from a sphere and recover an airplane that would be optimally suited to its mission requirements. Gagnon and Zingg [16] tes...
The application of gradient-based optimization to wing design could potentially reveal revolutionary new wing concepts. Giving the optimizer the freedom to discover novel wing designs may increase the likelihood of multimodality in the design space. To address this issue, we investigate the existence and possible sources of multimodality in the aerodynamic shape optimization of a rectangular wing. Our test case, specified by the ADODG Case 6, has a high dimensionality design space and a large degree of flexibility within that design space. We study several subproblems of this benchmark test case and analyze the multimodality introduced by each set of variables. We find evidence of multimodality with both inviscid and viscous analysis. In the full case we find that optimization with inviscid analysis yields multiple non-intuitive local minima. Adding consideration of viscous effects does not remove the multimodality, but allows the multiple local minima to be explained with physical reasoning. Additionally, we find that the shape of the optimized wing is highly dependent on the interplay between induced and viscous drag, providing more incentive to consider viscous effects in the analysis. The best result found by the optimizer reduces the total drag of the baseline wing by 22%. Nomenclature b span c chord C D drag coefficient C L lift coefficient M Mach number Re Reynolds number S planform area t thickness V volume α angle of attack γ twist
Gradient-based optimization with high-fidelity aerodynamic modeling is used to analyze and improve the design of a 100 passenger regional jet. The full configuration of the jet, including wing, body, tail, pylon, and nacelle components, is considered in this optimization. Overset meshing is used to allow component independence in the meshing scheme and in the geometry parametrization. We analyze the tradeoffs between wing shape, altitude, and engine size and consider the impact of adding constraints such as climb rate, takeoff field length, and buffet onset margin. The final optimized design achieves a 2% improvement over the baseline while satisfying these constraints.
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