Kriging-based shape optimization framework for blended-wing-body underwater glider with NURBS-based parametrization

Zhang, Daiyu; Wang, Zhidong; Ling, Hongjie; Zhu, Xinyao

doi:10.1016/j.oceaneng.2020.108212

Cited by 30 publications

(5 citation statements)

References 24 publications

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“…Bézier curves, B-splines, and NURBS have been frequently employed to produce polynomial coefficients derived from airfoil curves 4,11,12 . Among these, the Bézier curve is considered the most fundamental polynomial.…”

Section: Related Workmentioning

confidence: 99%

A geometry-based deep learning feature extraction method for airfoils

Hu¹,

Zhang²

2023

International Conference on Computer, Artificial Intelligence, and Control Engineering (CAICE 2023)

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The geometry of airfoils, crucial in predicting aerodynamic coefficients, can be perceived by three existing methods: manual definition of geometry parameters, polynomial and deep learning. The first two methods are capable of directly obtaining geometry-features or polynomial coefficients from airfoil coordinates, but they are insufficient to extract latent features. Current deep learning techniques are capable of extracting latent features from only Euclidean space. However, it has been proven that curves of airfoils are exists in Riemannian space. Inspired by deep learning and polynomial (especially the Bézier polynomial) and deep learning, we propose a Geometry-based Feature Extraction method (GFE) to extract airfoil geometry-features from both Euclidean space and Riemannian space. By utilizing Bézier curve, GFE can extract geometry-features (i.e., manifold metrics) of airfoils in Riemannian space. Through an internal auto-encoder, GFE encodes airfoil coordinates and manifold metrics to generate a novel feature representation. The UIUC airfoil dataset is employed to test the feasibility of GFE. Experimental results show that smooth and realistic airfoils can be rebuilt based on the geometry-features extracted by GFE, and the average MSE of rebuilt airfoils is 38.66% lower than those rebuilt by existing auto-encoders.

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Section: Related Workmentioning

confidence: 99%

A geometry-based deep learning feature extraction method for airfoils

Hu¹,

Zhang²

2023

International Conference on Computer, Artificial Intelligence, and Control Engineering (CAICE 2023)

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“…The Bézier curve, B-spline and NURBS are typical polynomials that were used to derive equations of airfoil curves [5], [6], [19], which can be regarded as effective approaches for extracting features of airfoils. Among them, the Bézier curve is the most basic and common expression.…”

Section: A Feature Extractions Of Airfoilsmentioning

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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“…The Bézier curve, B-spline and NURBS are typical polynomials that were used to derive equations of airfoil curves [4,5,12]. Among them, the Bézier curve is the most basic and common expression.…”

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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Kriging-based shape optimization framework for blended-wing-body underwater glider with NURBS-based parametrization

Cited by 30 publications

References 24 publications

A geometry-based deep learning feature extraction method for airfoils

A geometry-based deep learning feature extraction method for airfoils

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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