Evaluating the Risk of Local Optima in Aerodynamic Shape Optimization

Streuber, Gregg M.; Zingg, David W.

doi:10.2514/1.j059826

Cited by 13 publications

(4 citation statements)

References 33 publications

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“…In this study, the sequential quadratic programming (SQP) optimization algorithm is employed as the gradient-based optimizer. The SQP algorithm, chosen for its high efficiency and ability to handle large-scale design variables and function constraints [54,55], is a prominent gradient optimizer widely employed in current practices and has found extensive application in various engineering problems [56][57][58]. The fundamental concept revolves around transforming constrained nonlinear optimization problems into subproblems of quadratic programming at each iteration.…”

Section: Gradient-based Optimization Algorithmmentioning

confidence: 99%

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Qiao

et al. 2023

Aerospace

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Currently, the aviation industry is facing an oil and energy crisis and is contributing much more greenhouse gas emissions to the environment. Aircraft design approaches, such as aerodynamic shape optimization, new configuration concepts, and active control technology, have been the primary and effective means of achieving goals concerning fuel burn, noise, and emissions. For now, the design problems of relaxed static stability (RSS, an active control technique) and truss-braced wing (TBW) configurations with high-fidelity aerodynamic shape optimization methods have been investigated widely to promote aerodynamic performance. Nevertheless, they are studied almost always separately, and the combination of exploration and refined design is rarely presented. Therefore, the purposes of this work are to evaluate the benefits of RSS on a full TBW wing–body–tail configuration under various flight conditions and the effects on multi-components and to further explore the potential and analyze the aerodynamic features with the combination of shape optimization and RSS. To address these issues, on the one hand, a range of seven static stability margins are adopted to evaluate its effects with a high-fidelity Reynolds-averaged Navier–Stokes solver. On the other hand, seven cases of drag minimization multipoint aerodynamic design optimization are performed, which are with 600 shape variables and 13 twist variables, subject to lift coefficient, trim, and thickness constraints. The results indicate that with RSS only, the initial configuration has a 2.39% drag reduction under cruise conditions and a 3.01% and a 5.24% drag reduction under two off-design conditions. Additionally, the effects on the multi-components are observed and analyzed. Moreover, all of the optimized configurations with RSS have 2.13%, 2.42%, and 2.12% drag reductions under cruise conditions, drag divergence conditions, and near-buffet-onset conditions, respectively. The most promising optimized configuration has a lift-to-drag ratio of 24.48 with an aerodynamic efficiency of 17.14. The evaluations with a series of off-design points also present high-level aerodynamic efficiency.

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Section: Gradient-based Optimization Algorithmmentioning

confidence: 99%

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Qiao

et al. 2023

Aerospace

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“…These articles have focused on MLPs as their DL framework and have specifically employed a gradient-enhanced version of such networks. While such methods have shown good accuracy, they have been explicitly developed for gradient-based optimization algorithms, which may not be adequate in many cases [8,48]. Another set of data-driven ROMs employed recently was based on proper orthogonal decomposition (POD) bases [55] and hyper-reduction based on POD modes [30].…”

Section: Uniqueness Of the Proposed Reduced-order Modeling Approachmentioning

confidence: 99%

“…[12,27,17]. These studies have completely relied on a gradient-based search algorithm, which can very frequently converge to local optima for a non-convex, multi-objective shape optimization problem, especially when there are many design parameters [8,48]. However, employing expensive metaheuristic algorithms that can convergence to the global optima remain largely non-tractable with high-fidelity solvers.…”

Section: Introductionmentioning

confidence: 99%

Deep convolutional neural network for shape optimization using level-set approach

Mallik¹,

Farvolden²,

Jelovica³

et al. 2022

Preprint

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This article presents a reduced-order modeling methodology via deep convolutional neural networks (CNNs) for shape optimization applications. The CNN provides a nonlinear mapping between the shapes and their associated attributes while conserving the equivariance of these attributes to the shape translations. To implicitly represent complex shapes via a CNN-applicable Cartesian structured grid, a level-set method is employed. The CNN-based reduced-order model (ROM) is constructed in a completely data-driven manner thus well suited for non-intrusive applications. We demonstrate our ROM-based shape optimization framework on a gradient-based three-dimensional shape optimization problem to minimize the induced drag of a wing in low-fidelity potential flow. We show a good agreement between ROM-based optimal aerodynamic coefficients and their counterparts obtained via a potential flow solver. The predicted behavior of the optimized shape is consistent with theoretical predictions. We also present the learning mechanism of the deep CNN model in a physically interpretable manner. The CNN-ROM-based shape optimization algorithm exhibits significant computational efficiency compared to the full-order model-based online optimization applications. The proposed algorithm promises to develop a tractable DL-ROM driven framework for shape optimization and adaptive morphing structures.

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“…The overall goal of this work is to make high-fidelity global multi-disciplinary optimization of wings a reality, and the use of a compact aerofoil decomposition for the design variables is a pillar to this goal. Whilst fixed planform optimization of rigid aerodynamic wings is generally considered to be unimodal (Yu et al 2018), introducing planform changes along with sectional changes introduces clear multimodality (Poole et al 2018b;Streuber and Zingg 2021). Furthermore, similar behaviour is also likely to be seen in aeroelastic wing optimization so there is a clear need to consider how global methods could be introduced into high-fidelity wing optimization.…”

Section: Introductionmentioning

confidence: 99%

Efficient aeroelastic wing optimization through a compact aerofoil decomposition approach

Poole

Allen

Rendall

2022

Struct Multidisc Optim

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Efficient optimization of an aeroelastic wing is presented through multi-disciplinary analysis using low-dimensional modal design variables. Much work in wing optimization has concentrated on high-fidelity surface control, therefore utilising often hundreds of design variables. However, whilst fine surface control can be useful, problems can arise such as large disparities in design variable values when planform variables are introduced, slow convergence speeds, and lack of compatibility with global algorithms. Therefore, the focus of this paper is to filter the design space of this problem to reduce the dimensionality and complexity of the problem. Orthogonal geometric design variables are derived in the geometric space via singular value decomposition. Orthogonality of design variables leads to a well-conditioned design space and ensures effective optimizer convergence. These variables are applied in a sectional fashion for fixed planform drag minimization of a flexible transonic wing, using a gradient-based optimizer. Shock-free solutions are demonstrated when optimizing a rigid wing, indicating suitability of the aerofoil modes for sectional-based wing optimization. However, it is shown that these wings have poor performance when subsequently deformed under flight loads, hence optimisation including full aeroelastic performance is performed. Encouragingly, shock-free solutions are again computed. Loading is shifted outboard, leading to increased tip deflection. Monotonic improvement in the objective function (drag) with increase in dimensionality is also proven. Furthermore, applying these sectional deformation modes globally across the wing with only 10 design variable leads to a 28% drag reduction, which is within 7 drag counts of when the modes are applied locally through 82 design variables. This therefore opens the possibility of introducing global optimization algorithms to high-fidelity aeroelastic wing optimization.

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Evaluating the Risk of Local Optima in Aerodynamic Shape Optimization

Cited by 13 publications

References 33 publications

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Deep convolutional neural network for shape optimization using level-set approach

Efficient aeroelastic wing optimization through a compact aerofoil decomposition approach

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