Dimension Reduction for Aerodynamic Design Optimization

Viswanath, Asha; Forrester, Alexander I. J.; Keane, Andy J.

doi:10.2514/1.j050717

Cited by 56 publications

(30 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Evolutionary algorithms (EA) are gradient-free optimization algorithms that mimic the process of biological evolution through mutation, recombination, and reproduction of different designs. Genetic algorithms (GA), a type of EA, is widely used in aerodynamic shape optimization [12,15,20]. Work has also been done to augment GA with the Bees algorithm [21] and adaptive mutation rates [22], resulting in more accurate optimization and/or faster convergence.…”

Section: Evolutionary Algorithmsmentioning

confidence: 99%

“…Previous research has looked into dimensionality reduction (DR) of the original parametric design space (i.e., the space of designs represented by shape parameters such as B-spline control points). This permits faster exploration by capturing only those dimensions that either affect the final design's performance [7][8][9][10][11] or capture major shape variability [12][13][14][15][16]. But these DR models may not accurately capture the true variation that we observed in real-world airfoils, e.g., those in the UIUC airfoils database.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Aerodynamic Design Optimization and Shape Exploration using Generative Adversarial Networks

Chen

Chiu

Fuge

2019

AIAA Scitech 2019 Forum

View full text Add to dashboard Cite

Global optimization of aerodynamic shapes requires a large number of expensive CFD simulations because of the high dimensionality of the design space. One means to combat that problem is to reduce the dimension of the design space-for example, by constructing low dimensional parametric functions (such as PARSEC and others)-and then optimizing over those parameters instead. Such approaches require first a parametric function that compactly describes useful variation in airfoil shape-a non-trivial and error-prone task. In contrast, we propose to use a deep generative model of aerodynamic designs (specifically airfoils) that reduces the dimensionality of the optimization problem by learning from shape variations in the UIUC airfoil database. We show that our data-driven model both (1) learns realistic and compact airfoil shape representations and (2) empirically accelerates optimization convergence by over an order of magnitude.

show abstract

Section: Evolutionary Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Aerodynamic Design Optimization and Shape Exploration using Generative Adversarial Networks

Chen

Chiu

Fuge

2019

AIAA Scitech 2019 Forum

View full text Add to dashboard Cite

show abstract

“…Selecting few variables is a rather natural idea to get back to a moderate search space, as done e.g., in [48], [41], [44] or [5]. Another common strategy of dimension reduction is to construct a mapping from the high-dimensional research space to a smaller one, see e.g., [52], [33] and references therein. Other techniques suppose that the black-box function is only varying along a low dimensional subspace, possibly not aligned with the canonical basis, such as in [10] or [18], using low rank matrix learning.…”

Section: Related Work and The Random Embedding Approachmentioning

confidence: 99%

On the choice of the low-dimensional domain for global optimization via random embeddings

2019

View full text Add to dashboard Cite

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. Specifically, in the case of time consuming black-box functions and when the budget of evaluations is severely limited, global optimization with random embeddings appears as a sound alternative to random search. Yet, in the case of box constraints on the native variables, defining suitable bounds on a low dimensional domain appears to be complex. Indeed, a small search domain does not guarantee to find a solution even under restrictive hypotheses about the function, while a larger one may slow down convergence dramatically. Here we tackle the issue of low-dimensional domain selection based on a detailed study of the properties of the random embedding, giving insight on the aforementioned difficulties. In particular, we describe a minimal low-dimensional set in correspondence with the embedded search space. We additionally show that an alternative equivalent embedding procedure yields simultaneously a simpler definition of the low-dimensional minimal set and better properties in practice. Finally, the performance and robustness gains of the proposed enhancements for Bayesian optimization are illustrated on numerical examples.

show abstract

“…hidden) because they are not known a priori. The notion of using latent variables for DR in aerodynamic shape optimization is nothing new; for example, see the work by Toal et al 14 or Viswanath et al 15 However, additional benefit is possible if gradient information is available. This paper thus describes a new DR method, in which PCA is used with gradient observations to reduce dimensionality at a cost of n = O(p log p), where p is the number of design variables and n is the number of samples required.…”

Section: Introductionmentioning

confidence: 98%

Dimensionality Reduction In Aerodynamic Design Using Principal Component Analysis With Gradient Information

Berguin

Mavris

2014

10th AIAA Multidisciplinary Design Optimization Conference

View full text Add to dashboard Cite

The cost of dimensionality reduction in aerodynamic design applications involving highdimensional design spaces and CFD is often prohibitive. In an attempt to overcome this challenge, a new method for dimensionality reduction is presented that scales as p log(p), where p is the number of design variables. It works by taking advantage of adjoint design methods in order to collect gradient observations, which are then used to compute the covariance matrix of the design variables. Dimensionality is then reduced by using principal component analysis to develop a linear transformation that allows an aerodynamic optimization problem to be re-formulated in a new coordinate system of lower dimensionality. In order to demonstrate it's feasibility, the method is tested on a 2D staggered airfoil problem, intentionally chosen as an abstraction of a more realistic over-wing nacelle integration problem, and shown to exhibit similarities with the latter. Results show that the method outperforms typical screening methods used in aerospace engineering, either in terms of effectiveness, cost or the ability to capture nonlinear effects. Furthermore, the method is found to improve convergence during gradient-based optimization. Overall, results offer strong evidence in support of the proposed method, paving the way for larger analytical efforts such as design space exploration, where dimensionality reduction is unavoidable to cope with the necessity of gradient-free approaches.

show abstract

Dimension Reduction for Aerodynamic Design Optimization

Cited by 56 publications

References 33 publications

Aerodynamic Design Optimization and Shape Exploration using Generative Adversarial Networks

Aerodynamic Design Optimization and Shape Exploration using Generative Adversarial Networks

On the choice of the low-dimensional domain for global optimization via random embeddings

Dimensionality Reduction In Aerodynamic Design Using Principal Component Analysis With Gradient Information

Contact Info

Product

Resources

About