Single- and Multipoint Aerodynamic Shape Optimization Using Multifidelity Models and Manifold Mapping

Nagawkar, Jethro; Ren, Jie; Leifsson, Leifur; Kozieł, Sławomir

doi:10.2514/1.c035297

Cited by 18 publications

(8 citation statements)

References 45 publications

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“…Most aerodynamic design optimization methods using surrogate models rely on an iterative model refinement [440]. Such surrogate-based optimization strategies have shown to be effective in various aerodynamic shape optimization applications including single-point design [441,442], multipoint design [328,443], massively multipoint design [100], multi-objective design [93,444,445], inverse design [168,446], and robust design [313,[447][448][449]. Optimization using these methods is generally composed of two phases.…”

Section: Surrogate-based Optimizationmentioning

confidence: 99%

Machine Learning in Aerodynamic Shape Optimization

Li¹,

Martins²

2022

Preprint

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Large volumes of experimental and simulation aerodynamic data have been rapidly advancing aerodynamic shape optimization (ASO) via machine learning (ML), whose effectiveness has been growing thanks to continued developments in deep learning. In this review, we first introduce the state of the art and the unsolved challenges in ASO. Next, we present a description of ML fundamentals and detail the ML algorithms that have succeeded in ASO. Then we review ML applications contributing to ASO from three fundamental perspectives: compact geometric design space, fast aerodynamic analysis, and efficient optimization architecture. In addition to providing a comprehensive summary of the research, we comment on the practicality and effectiveness of the developed methods. We show how cutting-edge ML approaches can benefit ASO and address challenging demands like interactive design optimization. However, practical large-scale design optimizations remain a challenge due to the costly ML training expense. A deep coupling of ML model construction with ASO prior experience and knowledge, such as taking physics into account, is recommended to train ML models effectively.

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Section: Surrogate-based Optimizationmentioning

confidence: 99%

Machine Learning in Aerodynamic Shape Optimization

Li¹,

Martins²

2022

Preprint

Self Cite

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“…These polynomial approaches that are mathematically interpretable were widely used to parameterize airfoils. However, there have been some frontier studies which show that curves or surfaces of an airfoil exist in manifold space [14,15]. Hence, existing polynomial approaches can only capture features from Euclidean space, and some latent features (e.g., geometric-features from manifold space) are omitted.…”

Section: Related Workmentioning

confidence: 99%

“…Manifold theory has been applied to the optimization of modern complex airfoil geometry structures with manifold mapping method [8], [9]. Du et al applied manifold mapping to align the high-fidelity mode and the low-fidelity model to obtain the optimal target based on the performance distribution (i.e., Mach number and pressure coefficient) in inverse design [10].…”

mentioning

confidence: 99%

An airfoil geometric-feature extraction and discrepant data fusion learning method

Xiang

Zhang

et al. 2022

Preprint

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The perception of geometric-features of airfoils is the basis in aerodynamic area for performance prediction, parameterization, aircraft inverse design, etc. There are three approaches to percept the geometric shape of airfoils, namely manual design of airfoil geometry parameters, polynomial definition and deep learning. The first two methods directly define geometric-features or polynomials of airfoil curves, but the number of extracted features is limited. Deep learning algorithms can extract a large number of potential features (called latent features). However, the features extracted by deep learning lack explicit geometrical meaning. Motivated by the advantages of polynomial definition and deep learning, we propose a geometric-feature extraction method (named Bézier-based feature extraction, BFE) for airfoils, which consists of two parts: manifold metric feature extraction and geometric-feature fusion encoder (GF encoder). Manifold metric feature extraction, with the help of the Bézier curve, captures manifold metrics (a sort of geometric-features) from tangent space of airfoil curves, and the GF-encoder combines airfoil coordinate data and manifold metrics together to form novel fused geometric-features. To validate the feasibility of the fused geometric-features, two experiments based on the public UIUC airfoil dataset are conducted. Experiment I is used to extract manifold metrics of airfoils and export the fused geometric-features. Experiment II, based on the Multi-task learning (MTL), is used to fuse the discrepant data (i.e., the fused geometric-features and the flight conditions) to predict the aerodynamic performance of airfoils. The results show that the BFE can generate more smooth and realistic airfoils than Auto-Encoder, and the fused geometric-features extracted by BFE can be used to reduce the prediction errors of C L and C D .

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“…These polynomial approaches that are mathematically interpretable were widely used to parameterize airfoils. However, there have been some frontier studies which show that curves or surfaces of an airfoil exist in manifold space [13,14]. Hence, existing polynomial approaches can only capture features from Euclidean space, some latent features e.g.…”

Section: Related Workmentioning

confidence: 99%

A Geometry-Based Deep Learning Feature Extraction Scheme for Airfoils

Xiang¹,

Hu²,

Zhang³

et al. 2021

Preprint

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The perception of geometry-features of airfoils is the basis in aerodynamic area for performance prediction, parameterization, aircraft inverse design, etc. There are three approaches to percept the geometric shape of an airfoil, namely manual design of airfoil geometry parameter, polynomial definition and deep learning. The first two methods can directly extract geometry-features of airfoils or polynomial equations of airfoil curves, but the number of features extracted is limited. While deep learning algorithms can extract a large number of potential features (called latent features), however, the features extracted by deep learning are lacking of explicit geometrical meaning. Motivated by the advantages of polynomial definition and deep learning, we propose a geometry-based deep learning feature extraction scheme (named Bézier-based feature extraction, BFE) for airfoils, which consists of two parts: manifold metric feature extraction and geometry-feature fusion encoder (GF encoder). Manifold metric feature extraction, with the help of the Bézier curve, captures features from tangent space of airfoil curves, and GF encoder combines airfoil coordinate data and manifold metrics together to form a novel feature representation. A public UIUC airfoil dataset is used to verify the proposed BFE. Compared with classic Auto-Encoder, the mean square error (MSE) of BFE is reduced by 17.97% ~29.14%.

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Single- and Multipoint Aerodynamic Shape Optimization Using Multifidelity Models and Manifold Mapping

Cited by 18 publications

References 45 publications

Machine Learning in Aerodynamic Shape Optimization

Machine Learning in Aerodynamic Shape Optimization

An airfoil geometric-feature extraction and discrepant data fusion learning method

A Geometry-Based Deep Learning Feature Extraction Scheme for Airfoils

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