Aerodynamic Design via Control Theory

Jameson, Antony

doi:10.1007/978-3-642-83733-3_14

Cited by 421 publications

(567 citation statements)

References 23 publications

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“…Consequently the choice of shape parameterisation method can have a significant impact on the effectiveness and efficiency of the overall procedure [3]. Many different methods have been used within an aerodynamic optimisation framework, from standard geometric curve definitions such as B-Splines [4] or NURBS [5] to aerospace-specific methods such as CST [6,7], Hicks-Henne bump functions [8,9] or PARSEC [9,10] to Free-Form Deformation [11,12,13,14], proper orthogonal decomposition [2,15,16] or the discrete method [17]. A whole variety of options are available, however all are subject to the 'curse of dimensionality'.…”

Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Department of Aerospace Engineering, University of BristolThis work presents a shape parameterisation method based on multi-resolutional subdivision curves and investigates its application to aerodynamic optimisation. Subdivision curves are defined as the limit curve of a recursive application of a subdivision rule, which provides an intrinsically hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This is used to construct a progressive aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then periodically increased in resolution through the optimisation. This brings the benefits of a low dimensional design space (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the progressive refinement technique is tested on a variety of optimisation problems. For each problem a range of 'static' (non-progressive) subdivision schemes (equivalent to cubic B-splines) are also used as a control group. For all the optimisation cases the progressive schemes perform comparably or better than the static methods, often providing a significant computational advantage, and in many cases allowing a solution to be found when the static method would otherwise finish prematurely in a local optimum.

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Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

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show abstract

“…We will refer to this method as the Adjoint Continuation Method (ACM). The idea is to develop a variant of a shooting method [29,30] in which a nonlinear functional of the initial condition is minimized using adjoint-based optimal control methods [31][32][33] to obtain a solution of the boundary value problem. Key challenges in adapting this method to the system in Eq.…”

Section: The Adjoint Continuation Methods (Acm)mentioning

confidence: 99%

Continuation of periodic solutions in the waveguide array mode-locked laser

Williams

Wilkening

Shlizerman

et al. 2011

Physica D: Nonlinear Phenomena

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We apply the adjoint continuation method to construct highly-accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.

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“…In general, methods that use the gradient information are more efficient than those methods that do not use the gradient information [20]. Because the gradient formula (16) depends on both the primal and the adjoint states, we need to evaluate both states by numerically solving (3) and (14) to compute the gradient. The pseudoalgorithm to solve the optimization problem (6) using the gradient information is as follows:…”

Section: Algorithmmentioning

confidence: 99%

“…The adjoint-based method for PDE-constrained optimization problems requires more careful analysis than ODE-constrained optimization problems because the solution of the PDEs does not always have enough differentiability and regularity to guarantee the existence of a well-defined gradient. Furthermore, the differentiability and regularity of the solution highly depend on the type of the PDE: therefore, the method has been customized to several types of PDEs and used in relevant applications [1,16,14,3,13,30].…”

Section: Introductionmentioning

confidence: 99%

Regularization-based identification for level set equations

Yang

Tomlin

2013

52nd IEEE Conference on Decision and Control

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An optimization-based method for identifying the speed profile of a moving surface from image data is studied. If the dynamic surface motion is modeled by a level set equation, the identification problem can be formulated as an optimization problem constrained with the level set equation whose (viscosity) solution, in general, has kinks. The non-differentiable solution prevents us from having a bounded gradient of the cost function of the optimization problem. To overcome this difficulty, we develop a novel identification approach using a regularized level set equation. The regularization guarantees the differentiability of the cost function and the boundedness of the gradient. Using numerical optimization techniques with the adjoint-based gradient, we solve the identification problem. We perform a numerical test to validate that the solution of an optimization problem with a regularized level set equation converges to the solution of the same optimization problem with an unregularized level set equation as the regularization factor tends to zero. The performance and usefulness of the method are demonstrated by a biological example in which we estimate the forces (per density) of actin and myosin in cell polarization.

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Aerodynamic Design via Control Theory

Cited by 421 publications

References 23 publications

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Continuation of periodic solutions in the waveguide array mode-locked laser

Regularization-based identification for level set equations

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