An inverse design method for supercritical airfoil based on conditional generative models

Author: Jing WANG, Runze LI, Cheng HE et al. [PDF]

supercritical airfoil: 超临界机翼

Introducation

Inverse Designed

Usually proceeds in two steps.

First, target distributions are generated to reflect the design goals. (be specified by an experienced aerodynamicist)

Second, optimization methods are applied to optimize the parameterized pressure distributions to obtain the target distributions.

CGAN

GAN: generator competes against discriminator

CGAN: Conditional Generative Adversarial Networks

based on a vector set of conditional data

CVAE

VAE: Variational AutoEncoder

encodes the input data to a probabilistic latent space

CVAE: Conditional Variational AutoEncoder

Method

Dataset

1. x-y coordinates

tuple(x,y) starting from the trailing edge.

only the y coordinates are involved in training

which can reduce the dimensionality of the input or output of the deep learning network to accelerate the training procedure

2. Wall Mach number distributions

壁面马系数分布

This paper only use airfoils with single shock wave concluding the weak shock pressure distribution was evaluated as the best.

3. Features of wall Mach number distributions

Features	Symbols	Implication
Suction peak	$F_{sp}$	The $x$??? and $M{a}_w$?? values at the point with the highest wall Mach number.
Start of the shock wave	$F_{sw0}$	The $x$ and $M{a}_w$ values at the start of the shock wave.
End of the shock wave	$F_{sw1}$	The $x$ and $M{a}_w$ values at the end of the shock wave.
Aft loading	$F_{al}$	The $x$ and $M{a}_w$ values at the point with the maximum difference in the wall number between the upper and lower surfaces near the trailing edge.
Maximum wall Mach number of lower surface	$F_{lm}$	The $x$ and $M{a}_w$ values at the point with the maximum wall Mach number on the lower surface.

Generative model

compare the CVAE and CVAE-GAN

use WGAN instead of traditional GANs. improves the stability of learning

The VAE decoder and the GAN generator are collapsed into one by sharing their parameters and training them jointly.

Encoder network $E$: maps the data sample $x$ to a latent representation $z$ through a learned distribution $P(z|x,c)$, where $c$ is the given condition that the data satisfy.

Generative network $G$: generates the $x^{{}^{\prime }}$ under the given latent vector $z$ and conditions $c$ by sampling from a learned distribution $P(x|z,c)$.

Loss(training stage): $L_{\text{generator?}}=\mathrm{MSE}\left(x^{\prime },x\right)+\mathrm{KL}(q(z\mid x,c)||p(z\mid x))+D(G(z))$?

Discriminative network $D$: This network is the same as that in the WGAN.

Loss(final loss): $L_{\text{discriminator?}}=D($