Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation

Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

doi:10.2514/6.1996-94

Cited by 213 publications

(118 citation statements)

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“…The computational cost of evaluating the partial derivatives of an objective or constraint function is insensitive to the number of design variables, requiring only one flow solution and one adjoint solution. This method becomes the most practical one for the design of complex aerodynamic configurations [56,57] because it can deal with the optimization problems with 100-1000 design variables [58,59] or even more. The drawback of a gradient-based method is that the solution optimality can be sensitive to the initial guesses, and it can become trapped into a local minimum [60].…”

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Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

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A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to ameliorate the "curse of dimensionality". The core idea is to build a series of submodels with much smaller correlation matrices and then sum them up with appropriate weight coefficients, aiming to avoid the prohibitive cost associated with decomposing the large correlation matrix of a gradient-enhanced kriging. A self-contained derivation of the proposed method is presented, and then it is verified by surrogate modeling test cases. The present method is integrated into a surrogatebased optimizer and tested for design optimizations. It is further demonstrated for inverse design of a transonic wing, parameterized with a number of design variables in the range from 36 to 108, using Reynolds-averaged Navier-Stokes flow and adjoint solvers. It is observed that, for the wing design with 36 and 54 variables, the weighted and conventional gradient-enhanced kriging are comparable, and both are much more efficient than kriging without using any gradient. For the wing design with 72 and 108 variables, the cost of training a gradient-enhanced kriging increases rapidly and becomes prohibitive. In contrast, the cost of training a weighted gradient-enhanced kriging is kept in an acceptable level, which makes it more practical for higher-dimensional problems.

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Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

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“…A eficiência dessa metodologia, comprovada por modelos numéricos de previsão do tempo já operacionais [10], tem produzido um formidável crescimento no leque de suas aplicações [2], [12], [4], o que requer uma contínua utilização de resultados teóricos cada vez mais complexos, o que, aliado à rapidez com que esses modelos surgem, dificulta o pleno entendimento de suas bases teóricas. Atenuar esse efeito, é outro dos objetivos deste trabalho.…”

Section: Introductionunclassified

Um Modelo Numérico Determinístico de Previsão no Contexto da Teoria do Controle Ótimo

Silva¹,

Oliveira²,

Morales³

2011

TEMA - Tendências Em Matemática Aplicada E Computacional

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Resumo. Assimilação Variacional de Dados e Equações Adjuntas são dois métodos que, combinados, originam uma metodologia capaz de fornecer uma condição inicial de um sistema em estudo bastante realística e adequada a simulações numéricas, a um custo computacional aceitável e temporal que permite tomadas de decisão mais eficientes no caso de certos acidentes ambientais, quando apenas algumas observações e a dinâmica do sistema são conhecidas. Neste artigo, os fundamentos matemáticos e os procedimentos para se obter o adjunto de um dado programa computacional, uma tarefa fundamental para a aplicação da metodologia, são examinados.Palavras-chave. Assimilação variacional de dados, Método das equações adjuntas. IntroduçãoO estudo dos escoamentos geofísicos, sejam atmosféricos ou oceânicos, vêm revelando, desde a implementação operacional de um modelo numérico de previsão do tempo já na década de 1950, características que dificultam extremamente a simulação computacional desses fenômenos. Os modelos numéricos empregados nas simulações de escoamentos geofísicos são representações, na forma discreta, das leis físicas que os governam, em geral, um sistema evolutivo de equações diferenciais parciais [11]. Portanto, para a simulação numérica da evolução espaço-temporal de um escoamento em estudo, é necessário o conhecimento de sua condição inicial, isto é, a contrapartida numérica do estado ou configuração inicial real do escoamento em estudo.Contudo, a distribuição de uma rede de observações eficiente nos domínios espaciais dos escoamentos geofísicos é sempre dificultada pela própria natureza (tamanho e localização) desses domínios, acarretando uma escassez de informações sobre o fenômeno em estudo capaz de comprometer a qualidade das simulações computacionais [14]. Além disso, esses escoamentos contêm aspectos de difícil representação 1 paulosd@uenf.br. 2 phgoliveira@ibest.com.br. A autora agradece o apoio da CAPES.

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“…In this case, the angle of attack is not controlled by the optimiser, but will change during the optimisation. The computation of the gradients has to be accordingly adapted and following the work of Reuther et al [23], we first consider the variation of the drag and the lift with respect to the shape and the angle of attack:…”

Section: The Metric Termsmentioning

confidence: 99%

Applications of a discrete viscous adjoint method for aerodynamic shape optimisation of 3D configurations

Brézillon

Dwight

2011

CEAS Aeronaut J

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Within the next few years, numerical shape optimisation based on high-fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimisation problems, and the adjoint approach-which allows fast and accurate evaluations of the gradients with respect to the design parameters-is proved to be very efficient to eliminate the shock on aircraft wing in transonic flow. However, few applications were presented so far considering other design problems involving 3D viscous flows. This paper describes how the adjoint approach can also help the designer to efficiently reduce the flow separation onset at wing-fuselage intersection and to optimise the slat and flap positions of a 3D high-lift configuration. On all these cases, the optimisations were successfully performed within a limited number of flow evaluations, emphasising the benefit of the adjoint approach in aircraft shape design.

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Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation

Cited by 213 publications

References 10 publications

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Um Modelo Numérico Determinístico de Previsão no Contexto da Teoria do Controle Ótimo

Applications of a discrete viscous adjoint method for aerodynamic shape optimisation of 3D configurations

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