Content uploaded by Gang Sun
Author content
All content in this area was uploaded by Gang Sun on Sep 24, 2019
Content may be subject to copyright.
Original Article
A review of the artificial neural
network surrogate modeling
in aerodynamic design
Gang Sun
1
and Shuyue Wang
2
Abstract
Artificial neural network surrogate modeling with its economic computational consumption and accurate generalization
capabilities offers a feasible approach to aerodynamic design in the field of rapid investigation of design space and optimal
solution searching. This paper reviews the basic principle of artificial neural network surrogate modeling in terms of data
treatment and configuration setup. A discussion of artificial neural network surrogate modeling is held on different
objectives in aerodynamic design applications, various patterns of realization via cutting-edge data technique in numerous
optimizations, selection of network topology and types, and other measures for improving modeling. Then, new frontiers
of modern artificial neural network surrogate modeling are reviewed with regard to exploiting the hidden information
for bringing new perspectives to optimization by exploring new data form and patterns, e.g. quick provision of candidates
of better aerodynamic performance via accumulated database instead of random seeding, and envisions of more physical
understanding being injected to the data manipulation.
Keywords
Artificial neural network, surrogate modeling, aerodynamic design, machine learning, optimization
Date received: 2 April 2019; accepted: 21 June 2019
Introduction
The sector of commercial aeronautics is meeting the
challenges of public expectation of cheaper fares and
reduced environmental impact upon community noise
around airports and global warming.
1
The European
Union Vision For 2025 requires progress in low-
emission energy to secure a sustainable development.
The Advisory Council for Aviation Research
(ACARE) has set a 2050 goal for civil aeronautical
industry to allow a 75% reduction in CO
2
emissions
per passenger kilometer, a 90% reduction in NO
x
emission, and a 65% reduction in the perceived
noise emission of flying aircraft.
2
Therefore, many
institutions are dedicated to research and technical
exploration in aerodynamic design and optimization.
3
For example, flight tests of the BLADE laminar wing
boast a 50% wing friction reduction and up to 5%
less CO
2
emissions; Clean Sky and SESAR projects
introduce a new generation of aircraft reducing emis-
sions by 15–20%.
4
Aerodynamic design is related to airfoil, aircraft
wing, turbine engine blades, unmanned aerial vehicle
(UAV), etc. Generally, typical aerodynamic designs
and optimizations formulate objectives, optimization
algorithms, constraint functions, and design variables.
One major obstacle is the right optimization pattern/
approach for the project. The traditional solution to
aerodynamic design problems tends to be a top-down
approach that relies on physics modeling. For exam-
ple, the inverse design of pressure distribution desig-
nating, as one of the many methods proposed in wing
drag reduction problems, modifies the geometry via
iterations until the designated pressure distribution
over surface is obtained.
5
This method is later chal-
lenged by new alternatives in terms of computational
resources consumption, e.g. heuristic algorithms com-
bined with the parametric geometry description
method.
6
Also, nonlinearity features the aerodynamic
optimization problems not only in the physics behind
flow phenomena, but also in the influence of geometry
description approach on corresponding aerodynamic
performance. Furthermore, many aerodynamic design
problems require time-consuming evaluations, com-
pared with the duration of operation of the
Proc IMechE Part G:
J Aerospace Engineering
0(0) 1–10
!IMechE 2019
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/0954410019864485
journals.sagepub.com/home/pig
1
Department of Aeronautics & Astronautics, Fudan University, China
2
AECC Commercial Aircraft Engine Co., Ltd, China
Corresponding author:
Shuyue Wang, AECC Commercial Aircraft Engine Co., Ltd, China.
Email: henri_w_91@hotmail.com
optimization algorithm. The computational resource
consumption grows rapidly with the utilization of
high-fidelity tools for simulations.
7
In addition, most
aerodynamic design problems require an appropriate
amount of sample points generated via distributing
approaches of design of experiment (DoE) methods,
e.g. D-optimality, Monte Carlo, and Latin hypercube
in multivariable design space, before the set of experi-
mental points is sent to simulator for responses.
For example, large numbers of analyses have to be
carried out in constructing Hessian at the design
point by sampling the design space when there are
many variables, particularly when using finite differ-
ence methods to evaluate gradients.
8
In fact, many
optimizations depend on some forms of internal
model for design space exploration.
9
For example,
simulations of flow field around new airfoils for dif-
ferent set of shape variables
10
or newly morphed
geometry
11
have to be conducted to populate the
design space in order to find the optimal candidate.
That is to say, obtaining enough information to pre-
dict a design landscape in a hypercube of increasing
dimensions is a barrier in many optimizations.
12
Approaches including abstraction of problem dimen-
sions and simplification of geometry topology have
been adopted in many studies to relieve this difficulty,
which yet leads to the inevitable deviation from real
design.
13
A strategy of optimization is demanded to
be efficient, intelligent, and credible for balancing the
modeling efforts and design space scope.
14
The rapid advance in data science has brought new
insights into aerodynamic design and optimization by
constructing surrogate models (also termed as meta-
model or response surfaces). The ‘‘aerodynamic
design’’ refers to the design of airfoil, wing, engine
nacelles, etc. that are components of an aircraft.
A surrogate model is proposed as a data-driven and
bottom-up approach used when an outcome of inter-
est cannot be easily obtained or the inner mechanism
of simulation is not assumed to be known. It can be
viewed as the response of simulator to the data points
in design space comprehensively harnessing high-
fidelity simulations and experiments to aid the
optimization, sometimes dominating the whole opti-
mization process, and sometimes functioning just as a
supplementary aid.
15
The rise of surrogate model
comes with the application of inverse design.
Traditionally, airfoil design is important for aircraft
wings, helicopter rotor blades, etc.
16
Given the bound-
ary conditions of coming flow, the airfoil shape deter-
mines its aerodynamic performance including the
pressure distribution over the surface. Navier–Stokes
equations are applied for obtaining the pressure dis-
tribution of specified airfoil shape. Then, the pressure
distribution is specified and the airfoil shape is
obtained as an output of complex aerodynamic
shape optimization procedure.
11
In this circumstance,
a surrogate model can be introduced to comprehen-
sively harness data from high-fidelity simulations and
experiments to aid the optimization. Meanwhile,
reduced-ordered modeling is a similar method that
focuses on abstract regeneration of complex flowfield
by modeling.
17
For example, the curse of the dimen-
sionality can be relieved with reduced-order modeling
in unsteady aerodynamics at varying flow condi-
tions.
18
Comparatively, surrogate modeling is more
applicable than reduced-order modeling, because the
former is more related to the input and output data of
optimization problem and is less involved in detailed
aerodynamics.
19
Therefore, this paper focuses on
surrogate model thereafter.
Artificial neural network (ANN) is proposed as a
data-driven method to transform engineering analysis
and design.
20
It emulates biological information pro-
cessing detouring the need of any objective functions;
thus it offers a feasible solution to the technological
needs in aerodynamic optimization, which will be dis-
cussed in the following section. It can be considered as
an interpolation tool for obtaining data that are not
originally present in the training data. For example,
data-fit models are generated using regression of high-
fidelity simulation data from the input to the output.
7
ANN has been widely applied in modern surrogate
modeling with its advantage of consuming trivial com-
putational effort; thus, it can be used as the assistant for
computational fluid dynamics (CFD) calculation for a
large number of designed geometry in a short time,
which greatly increases the optimization efficiency.
21
Its accurate generalization and parallel computation
capabilities in complex engineering design problems
are helpful in the rapid investigation of design space
and searching for optimalities.
12
For example, ANN
has been used to expedite decision-making process in
early stages of aircraft design process and to select
proper combination of engine thrust, wing area, and
the aircraft weight without going through elaborate
details of other direct approaches.
22
The applications
and prospects in some new frontiers of ANN surrogate
modeling will be discussed in a later section in detail.
Artificial neural network
The advanced intellectual capability and processing
power of human brains come from the biological
neural network that are composed of numerous chem-
ically connected neurons.
12
A neuron is connected to
one another with axons and dendrites; the connecting
regions between them are synapses.
23
A neuron
receives input from many sources, and then generates
a unique output that can be passed on to other
neurons in turn.
24
The complexity of biological
neural network determines the level of intelligence.
24
The architecture and strengths of synaptic connec-
tions often adapt to external stimuli, which is how
learning takes place in organisms.
25
Similarly, ANN
propagates the computed values from the input neu-
rons to the output neurons, where learning takes place
by changing the weights representing the connections
2Proc IMechE Part G: J Aerospace Engineering 0(0)
between neurons.
26
In many applications, ANN is
needed to adjust their internal structure to produce
correct outputs for sample inputs, thus approximating
the implicit relationship.
27
Various input–output functions and learning meth-
ods can be implemented in realizing neural networks.
The configuration of neural network is usually one of
the biggest problems in optimization. Figure 1 shows
the structure of perceptron as fundamental component
of ANN architecture, which contains one input node,
one hidden node, and an output node. Generally, the
paradigm of ANN is composed of a multi-layer per-
ceptron (MLP) based on feed-forward, supervised
learning, and an error back-propagation training algo-
rithm. Consider a situation where each training
instance is of the form ð
X,oÞ:each
X¼½x1,...,xd
contains dfeature variables, and o2f1, þ1gcon-
tains the observed value (which is given to the designer
as a part of the training data). The input layer contains
dnodes that transmit dfeatures
X¼½x1,...,xdwith
edges of weight
W¼½w1,...wdto an output node.
The input layer does not perform any computation
in its own right, and the linear function
W
X¼
Pd
i¼1wixiis computed at the output nodes.
Subsequently, an activation function sign of this
value in form of real number predicts the dependent
variable of
X. The activation function as the source of
nonlinearities determines the input–output relationships
of each processing unit as well as the form of the final
solution. Therefore, the prediction ^
ois computed as:
^
o¼signð
W
XÞ¼signPd
i¼1wixiwhere the sig-
moidal function sign maps a real value to either –1
or þ1, which is a common approach in the ANN con-
figuration. Appropriate activation function can provide
the desired nonlinear relationship between the input
and output vectors. The circumflex on top of the vari-
able oindicates a predicted value instead of an observed
one. The primary objective for ANN training is to
reduce the error of prediction Eð
XÞ¼o^
obetween
the observed value in the training sample and the pre-
dicted outcome. Recurrent connections can also be uti-
lized where the predicted outputs become part of the
next input vector. When the error value Eð
XÞis non-
zero, the weights in the neural network need to updat-
ing in the negative direction of error gradient.
The configuration of the value set to each neuron
and weights is the result of neural network training.
The operation of a perceptron lays foundation of
ANN; its interpretation as a computational unit is
useful because it allows to put together multiple
units in order to create powerful models in neural
network training.
25
Thereby, the basic ANN architec-
ture comprises an input layer, hidden layer(s), and an
output layer. Information processing, proceeding
from left to right within each layer of the ANN,
occurs at many simple processing units or elements.
ANN topology is established/modified according to
the detailed situation of the optimization problem: In
single-layer neural networks (Figure 1), the training pro-
cess is straightforward because the error can be com-
puted as a direct function of the weights, which allows
easy gradient computation. In multilayer networks
(Figure 2), the error is a complicated composition func-
tion of the weights in earlier layers. The gradient of a
composition function is computed using back-propaga-
tion algorithm, which leverages the chain rule of differ-
ential calculus, computing the error gradients with
respect of weights in terms of summations of local-gra-
dient products over the various paths from nodes to
outputs. The principle of weight adjusting is as follows
@L
@wðhr1,hrÞ
¼@L
@oX
½hr,hrþ1,...,hk,o2P
@o
@hkY
k1
i¼r
@hiþ1
@hi
"#
@hr
@wðhr1,hrÞ
,8r21...k
Figure 1. Basic architecture of a perceptron.
Sun and Wang 3
where Lis the error function; his the hidden layer,
with subscript indicating layer sequence; wðhr1,hrÞis
the weight value connecting layers h
r
and hr1.
25
The initialization of weight and biases for ANN is
investigated to select the effective starting points for
training network efficiently and accelerating the conver-
gence.
12
The optimal number of nodes in the hidden
layer and the optimal number of hidden layers is pro-
blem-dependent. Networks with different numbers of
neurons were evaluated to minimize the regression
error; however, these numbers should be kept low for
the computational efficiency. The number of nodes and
layers should be increased if convergence difficulties are
encountered, but should not exceed the total number of
input and output variables. A simpler network with no
hidden layers may be computationally efficient, but it
represents only linear mapping between input and
output quantities, known as flat networks and can be
inadequate to model nonlinear relationships.
ANN modeling of learning from the accumulation
of expertise have found their way into practical appli-
cations in many areas.
25
The developed techniques
assist in addressing a wide range of complex problems
in aerodynamic design, where an ANN is fed with CFD
simulation during training. For example, an aero-
dynamic database consisting of approximately 100,000
cases calculated with a full-potential code with compu-
tation of viscous effects was used for the neural network
training, with the aid of backpropagation algorithm,
scaled gradient algorithm, and Nguyen–Wridow
weight initialization.
28
Among the techniques, a surro-
gate model established/aided by neural network method
attracts many scientists due to its potential to automat-
ically give the reference geometry according to the
design target.
29
The following section will discuss in
detail the implementation of ANN in surrogate model-
ing in the field of aerodynamic design.
Surrogate model in aerodynamic design
with ANN
A surrogate model is aimed at reducing computational
resource consumption in aerodynamic design and opti-
mization. Efforts have been put so that designers get
immediate feedback within design iterations. With sur-
rogate modeling, CFD can be saved during optimiza-
tion except for final design validation. ANN is used in
many applications of surrogate models due to its huge
convenience available for problems with large amount
of data. The principle behind surrogate modeling is
that data at input and output is related through the
pattern of the trained neural network.
Direct applications of ANN surrogate modeling in
aerodynamic design
Many ANN surrogate modeling have been applied in
optimization. ANN has been implemented efficiently to
interpolate the aerodynamic pressure loads for one-
way UAV fluid structure interaction.
30
The result
shows good agreement with the actual pressure profile
on aircraft compared against two-dimensional curve
fitting with higher order polynomials. With data train-
ing, ANN is able to learn active control strategy from
experiments of mass flow rates of two jets on sides of a
cylinder.
31
Its predictive capability is shown insensitive
to numerical instabilities and convergence difficulties
typically associated with computational processes.
24
Turbomachinery uncertainty analysis requires per-
forming a large number of simulations, the computa-
tional cost of which can be greatly alleviated with
ANN surrogate modeling.
32
ANN has successfully
helped to estimate the separation point and stall
speed of cascaded fins from the relationship with the
number of fins in the cascade.
33
Surrogate models with
ANN have been shown a good alternative to conven-
tional solution with regard to the prediction of aero-
dynamic coefficients of airplanes of high accuracy.
28
ANN has been used for space mapping for transonic
airfoil aerodynamic shape optimization.
34
ANN has
been trained by the data of fuselage drag coefficient
obtained by accumulated experimental results con-
ducted in wind tunnel to be capable of fuselage drag
coefficient estimation for each parameter values of
fuselage shape with respect to inputs without rigorous
computations.
20
It has also helped to achieve optimal
profiles for minimizing time-averaged drag and buffet
magnitude in the supercritical airfoil design.
10
The numerical search for the optimum shape is of
great interest for aircraft and turbomachinery
designers. The authors of this paper have both been
dedicated to an applicable airfoil/wing inverse design
method with the help of ANN and database (Figure 3)
in a design for a transonic swept wing of a passenger
jet.
16
It can directly generate profiles fitting the
requested aerodynamic performance with trained
neural network, avoiding the repetitive cut-and-try.
35
Variation, improvement, and development of ANN
surrogate modeling
Selection of type of neural network. The type of neural
network is an important option that lays influence
Figure 2. Basic architecture of a multilayer perceptron.
4Proc IMechE Part G: J Aerospace Engineering 0(0)
on the effect of the ANN surrogate modeling. There
was an intensive comparative study on the approxi-
mation performance of three prospective surrogate
models: ANN, radial basis function (RBF), and sup-
port vector regression.
32
The result shows that ANN
outperforms others, but it may alter if the problem is
changed because ANN needs a certain data set to be
effectively trained. A data set is an assembly of data.
Different surrogate modeling approaches, e.g. RBF,
Kriging, and support vector regression, etc., have
been compared to bring the efficient global optimiza-
tion closer to reality.
8
It is certain that the best selec-
tion of ANN architecture always accomplishes with
different data sets of problem.
20
The outcomes can be
influenced by many factors, and therefore there is no
simple deduction to which type of surrogate model
outperforms others. The main approaches in the fron-
tiers of ANN surrogate modeling proposed to
enhance the estimating abilities by recent studies are
discussed as follows.
Treatment to the input and output data for neural network
training. Conventionally, the input data to the ANN is
simply geometric parameters in geometry-aerody-
namic performance surrogate modeling, e.g. wing
planform, airfoil geometry and flight condition,
etc.
28
For example, wing planform parameters of
UAV design were determined through an aero-
dynamic optimization process using both genetic
algorithms (GAs) and ANNs.
36
The number of par-
ameters should be kept as little as possible; otherwise
the sufficiency of sample data would be difficult to be
satisfied in the network training. A class/shape func-
tion transformation (CST) geometry parametrization
method represents an accurate UAV aerofoil with 10
geometry design variables.
12
Parametric section
(PARSEC) is compared with other kinds of paramet-
rization method and is evaluated as appropriate for
airfoil description due to its accuracy and
intuitiveness.
16
ANN designers are inspired by the idea that the
outcome of data training may largely be dependent
on the form the input data takes. On one hand, the
form of input data should be excluded with nonmea-
ningful information so that the training can be guided
with some kind of direction. On the other hand, the
form itself may hinder the ANN to automatically
relate the crucial physical meaning that effectively
decides the output data (e.g. aerodynamic perform-
ance) during training. For example, the geometric rep-
resentations are sometimes not effective for neural
network training since the hidden semantic meaning
of the vectors of input data varies.
37
Data tend to lose
its apparent physical meaning in the process of par-
ametrization and normalization. Obviously, the data
form has influence on the information where the data
are transmitted to the neural network during training.
Some knowledge of aerodynamic optimization that is
not expressed in data will never be ‘‘understood’’ by
the neural network.
The aerodynamic performance of an airfoil is func-
tion of its geometrical shape, which implies in many
situations (especially when the target aerodynamic
performance is not multi-objective) where there may
be more than one set of geometrical shape that fits the
aerodynamic feature given by designers. Under this
circumstance, classification via self-organizing map-
ping (SOM) can relieve this challenge, applications
of which can be seen in Figures 4 and 7, where data-
base of airfoils are classified into several groups
according to the similarity of feature data.
Therefore, new forms of geometric representation
method are proposed specifically to the network train-
ing. Geometry data instead of abstract parameters can
be directly input into deep learning network in the
form of coordinate of wing profile points, or even in
the form of tensors that records the connection of the
concerned point with other neighboring points, with-
out the need for complex parametrization.
38
Even at
the output, the form can be extended to two-dimen-
sional and three-dimensional pressure distribution
over a solid body of aircraft, which can be beneficial
for aerodynamic design.
11
For example, a signed dis-
tance function (SDF) sampled on a Cartesian grid was
proposed as a universal representation for different
geometries, which is shown to be effective for convo-
lutional neural networks.
37
SDF not only provides
local geometry details, but also contains additional
information of the global geometry structure.
Another solution is data filtering via principal com-
ponent analysis (PCA), a statistical procedure that
uses an orthogonal transformation to convert a set
of observations of possibly correlated variables into
Figure 3. An airfoil database for inverse design.
Sun and Wang 5
a set of values of linearly uncorrelated variables ‘‘prin-
cipal components’’. PCA reduces the dimensions of
the problem with kernel function in interpolating non-
linear problems, thus saving computational resources.
In the inverse design model of stall lift robustness for
high-lift device, PCA is applied to operate on the
input data to the network being trained and obtains
satisfactory result (Figure 5).
39
Similarly, there are also studies about the treat-
ment of output data of neural network training. For
example, grouped method of data handling (GDMH)
neural network can be used in order to transform dis-
crete CFD data into continuous function.
40
The para-
mount goal of GDMH modeling is to generate a
quadratic polynomial function in a feed-forward net-
work whose coefficients are obtained with regression
technique. By means of a complex polynomial
function, the generic form of relation between the
input and output variables can be expressed as
Ivakhnenko polynomial.
Utilization of various levels of information. As a matter of
fact, the data in the design space can be classified by
the information conveyed by data itself.
41
Different
levels of information hidden in physics can be
extracted via different procedures. For example, mul-
tiple design alternatives have to be quickly iterated in
preliminary design to make initial decisions without
high-fidelity simulations. Similarly, the multilevel sur-
rogate modeling (also termed as variable-resolution
model) is proposed to obtain the optimal area in the
design space quickly, after which the search for the
optimal point location is held in the neighboring
region of a smaller area in design space thus saving
computational resource. Designers can even directly
apply the deep learning approximation model in
design space exploration algorithms without training
extra lower-dimensional surrogate models.
37
One such
application is a multilevel surrogate-based aerofoil
shape optimization.
42
As three fundamental parts of
ANN, i.e. the form that input data takes, the type,
topology and configuration of neural network, and
the form the output data takes, the data flow should
be complete as well as well-arranged. The progress
can also be made at the procedure of surrogate mod-
eling, which can be in new form other than simple
data bunching.
Unexploited hidden information in optimization
ANN is used to utilize the resource of accumulated
airfoil data so that it can be able to learn from large
amount of data, instead of using rule-based program-
ming.
43
There is still room for improvement in making
ANN learn in a ‘‘smarter’’ way. The hidden informa-
tion has to be exploited so that the design space con-
tains new perspectives beneficial to optimization.
Take drag reduction for example: the flow phenom-
enon involves many factors that may have impact on
the aerodynamic performance, e.g. the position and
vibrating frequency of separating in buffets in the
boundary layer of transonic airfoil; the peak of pres-
sure value over the surface that indicates shock wave
position and the distribution of the pressure that
determines the profile drag of an aircraft wing; the
location and emerging time of vortex cores; the distri-
bution of boundary layer thickness. A good surrogate
model should contain the above information during
neural network training, while does not mix all the
useful information into a mess.
It is known that different aerodynamic perform-
ances of two airfoils are result of their different geom-
etry.
44
In this approach, ANN is expected to correlate
the relationship; thereby new airfoil geometry that
leads to better aerodynamic performance will be
able to be produced. The authors of this paper have
Figure 5. Framework of the PCA–ANN-based inverse design
model.
Figure 4. Classification of airfoil database via SOM.
6Proc IMechE Part G: J Aerospace Engineering 0(0)
done similar research in exploiting airfoil database of
geometry and aerodynamic performance from accu-
mulated experiment and CFD calculation results
based on ANN.
45
The proposed approach ‘‘database
self-expansion’’ is focused on quickly providing new
airfoil candidate that has better aerodynamic per-
formance (Figure. 6), which is different from other
algorithms e.g. particle swarm optimization, ant
colony optimization, etc. The database is classified
for data concentration via SOM, as is shown in
Figure 7. Conclusively, the comparisons of geometry
before and after optimization are shown in Figure 8.
The corresponding comparison of aerodynamic per-
formance is shown in Figure 9.
Collaboration with other optimization algorithms. The pos-
sibilities of combining the advantages of different
optimization algorithms are studied by many
researchers. The heuristic algorithm of GA is usually
chosen due to its simplicity to implement, their
robustness, and flexibility in different situation of
various problems. One big disadvantage associated
with GA is that they are computationally time-con-
suming especially in aerodynamic optimization where
a CFD solver is used for the fitness function evalu-
ation. This makes the use of ANN an efficient way to
reduce the computational time, since ANN decouples
the aerodynamic solver from the optimization process
where the GA operates simultaneously with ANN.
36
ANN is employed as one of the reliable and fast meth-
ods of predicting aerodynamic coefficients to
select optimized airfoils
10
as well as a lift-drag ratio
optimization for airfoil
46
with GA. Approximated
pre-evaluations based on ANN are used in a hybrid
optimization procedure with GA to determine airfoil
shape in three-dimensional wing design to benefit
from the accumulated knowledge thus reducing
Figure 6. Illustration of database self-expansion flow chart.
Figure 7. SOM geometry classification situation.
Sun and Wang 7
the number of CFD evaluations required at each
generation.
47
There are also other types of combination of opti-
mization algorithms with ANN. A hybrid model that
combines state-space model (supported by wind-
tunnel experimental data) and ANN is proposed to
describe the aircraft unsteady aerodynamic character-
istics.
48
Thereby, the separation point model in state-
space representation is reserved to describe the time
delay of the unsteady aerodynamic responses, while
the conventional polynomial model is replaced by
ANN to improve accuracy and universality. An archi-
tecture combining a variational autoencoder mapping
shapes to latent representations and Gaussian process
regression is jointly trained to generate improved
shapes in the two-dimensional case.
9
A novel algo-
rithm to estimate the optimum value of the fuselage
drag coefficient is designed by integrating ANN into
the algorithm of simultaneous perturbation stochastic
approximation (SPSA).
20
There are also attempts of using different
approaches within the domain of ANN surrogate
modeling, although the basic pattern is quite similar
to one another. For example, the surrogate models by
implementing enhanced neural networks (ENNs)
have been conducted in establishing a hybrid opti-
mizer, which is executed to search for the first tenta-
tive optimal point.
12
The analysis code is performed
on the tentative optimal point to check the difference
between the surrogate model ENN and the analysis
code.
Deep learning in surrogate modeling. In MLP architec-
ture, the learning capability can be increased by
adding hidden layers and/or units in hidden layer.
However, the trade-off space between the network
size and the learning capability is mainly determined
by stereotyped variability due to the underlying
assumption of ‘‘fully-connected’’ network structure.
In this context, ‘‘deep learning’’ has attracted many
studies in recent years, although it is just a sub-
concept under ANN. Compared with its conventional
MLP counterparts, deep learning is equipped with
more training layers and characterized layer (e.g. con-
volutional layer and pooling layer in the famous
LeNet-5).
49
Conventional MLP are compared with
the convolutional neural network (CNN) results: the
deep learning surrogate modeling exhibits a competi-
tive prediction accuracy with minimal constraints in
geometric representation.
50
Deep learning is enabled
to learn invariant high-level features when the data
have strong spatial and/or temporal correlations.
Despite the limitation in application (e.g. progress
are mostly seen in the frontier of image recognition)
and the requirement of sample data of higher magni-
tude, deep learning is beneficial in the field of aero-
dynamic design surrogate model because it no longer
needs the a priori treatment to the input data (e.g. the
hand-crafting of features by experts), thus human
experience can be less relied on and new perspective
of design space can be created.
There are an increasing number of applications of
deep learning in aerodynamic design, most of which
takes different forms than conventional ANN,
although the principle of surrogate model is not chan-
ged. CNN is able to estimate the velocity field two
orders of magnitude faster than GPU-accelerated
CFD solver and four orders of magnitude faster
than a CPU-based CFD solver at a cost of a low
error rate.
37
In a long endurance UAV aerofoil
design optimization, repetitively enhanced neural net-
works (RENN) method is developed and presented
for complex and implicit engineering design problems,
which constructs an accurate surrogate model and
avoids over-fitting during neural networks training
from supervised learning data.
12
The optimizer seeks
a tentative optimum point, which is then repetitively
added into the supervised learning data until tolerance
is reached. CNN has been applied to map airfoil
shapes to pressure distribution under the framework
of classification problem using discretized pressure
coefficient.
51
In the testing phase, a new pressure coef-
ficient distribution is given to the CNN model,
Figure 9. The skin friction coefficient C
f
and pressure coef-
ficient C
p
distribution at specified position of nacelle surface
before and after database self-expansion.
Figure 8. Comparison of initial airfoil and the new airfoil’s
upper curve by database self-expansion.
8Proc IMechE Part G: J Aerospace Engineering 0(0)
generating an airfoil shape that is close to the asso-
ciated airfoil with an average L
2
error of less than 2%.
Using conditional generative adversarial networks
(cGAN), new data-driven models are trained by
deep learning for direct generation of solutions to
steady-state heat conduction and incompressible
fluid flow purely on observation without knowledge
of underlying physical models.
52
Conclusions
ANN surrogate modeling offers a feasible approach to
aerodynamic design in the field of rapid investigation of
design space and optimal solution searching. The direct
motive of a surrogate model is to establish a data-driven
and bottom-up approach used when an outcome of
interest cannot be easily obtained. The principle behind
surrogate modeling is that data at input and output are
related through the pattern of the trained neural net-
work. Introducing the basic principle of ANN as an
excellent surrogate modeling method, this paper focuses
on its data treatment and configuration setup.
ANN has successfully helped in direct applications
of ANN surrogate modeling in aerodynamic design.
For example, the numerical search for the optimum
shape is of great interest for aircraft and turboma-
chinery designers. This paper discusses the selection
of the type of neural network that may have influence
on the optimization effect. It is noted that ANN needs
a certain data set to be effectively trained. Treatment
to the input and output data for neural network train-
ing has also been discussed. In particular, new forms
of geometric representation method are proposed spe-
cifically to the network training.
ANN not only performs well in surrogate model-
ing, but also produces potential advantages in opti-
mization. New frontiers of modern ANN surrogate
modeling are reviewed in this paper. As for the util-
ization of various levels of information, the multilevel
surrogate modeling is proposed to obtain the optimal
area in the design space quickly thus saving compu-
tational resource. There has also been attempts of
sorting out optimization direction in the accumulated
database. Also, there are many types of combination
of optimization algorithms with ANN. Lastly, deep
learning is beneficial to the field of aerodynamic
design surrogate model because it no longer needs
the a priori treatment to the input data and thus
human experience can be relied less. Meanwhile,
new perspective of design space can be created.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of
this article.
Funding
The author(s) received no financial support for the research,
authorship, and/or publication of this article.
ORCID iD
Shuyue Wang https://orcid.org/0000-0001-8452-5602
References
1. Abbas A, De Vicente J and Valero E. Aerodynamic
technologies to improve aircraft performance. Aerosp
Sci Technol 2013; 28: 100–132.
2. Botez RM. Green aircraft minimum fuel consumption
methodologies. In: Oral or poster sessions, during
the GLOREP 2018 conference, Timisoara, Romania,
15–17 November 2018.
3. ACARE. Aeronautics and air transport beyond vision
2020 (towards 2050), 2010.
4. Sky C. Clean sky. European Union Funding for Research
and Innovation, 2018.
5. Green BE, Whitesides JL, Campbell RL, et al. Method
for the constrained design of natural laminar flow air-
foils. J Aircraft 1997; 34: 706–712.
6. Wang S, Sun G and Li C. Natural laminar flow opti-
mization of transonic nacelle based on differential evo-
lution algorithm. J Aerosp Eng 2019. DOI: 10.1061/
(ASCE)AS.1943-5525.0001028.
7. Kani JN and Elsheikh AH. Dr-rnn: a deep residual
recurrent neural network for model reduction. arXiv
preprint arXiv:170900939, 2017.
8. Forrester AI and Keane AJ. Recent advances in surro-
gate-based optimization. Prog Aerosp Sci 2009; 45:
50–79.
9. Eismann S, Bartzsch S and Ermon S. Shape optimiza-
tion in laminar flow with a label-guided variational
autoencoder. arXiv preprint arXiv:171203599, 2017.
10. Xu Z, Saleh JH and Yang V. Optimization of supercrit-
ical airfoil design with buffet effect. AIAA J 2018.
11. Sekar V, Zhang M, Shu C, et al. Inverse design of airfoil
using a deep convolutional neural network. AIAA J
2019.
12. Van Nguyen N, Lee J, Tyan M, et al. Repetitively
enhanced neural networks method for complex engin-
eering design optimisation problems. Aeronaut J 2015;
119: 1253–1270.
13. Samareh JA. A survey of shape parameterization tech-
niques. ntrsnasagov 1999.
14. Andrado
´ttir S and Prudius AA. Balanced explorative
and exploitative search with estimation for simulation
optimization. Informs J Comput 2009; 21: 193–208.
15. Barton RR. Simulation optimization using metamodels.
In: Proceedings of the 2009 winter simulation conference
(WSC), 2009, pp.230–238. New York: IEEE.
16. Sun G, Sun Y and Wang S. Artificial neural network
based inverse design airfoils and wings. Aerosp Sci
Technol 2015; 42: 415–428.
17. Yu J and Hesthaven JS. Flowfield reconstruction
method using artificial neural network. AIAA J 2018;
57: 482–498.
18. Kou J and Zhang W. Multi-kernel neural networks for
nonlinear unsteady aerodynamic reduced-order model-
ing. Aerosp Sci Technol 2017; 67: 309–326.
19. Parish EJ and Duraisamy K. A paradigm for data-
driven predictive modeling using field inversion and
machine learning. J Comput Phys 2016; 305: 758–774.
20. Oktay T, C¸ elik H and Uzun M. A novel learning algo-
rithm to estimate the optimum fuselage drag coefficient.
Sakarya Univ J Sci 2017; 21: 63–68.
Sun and Wang 9
21. Iuliano E and Pe
´rez EA. Application of surrogate-based
global optimization to aerodynamic design. New York:
Springer, 2016.
22. Oroumieh MAA, Malaek SMB, Ashrafizaadeh M, et al.
Aircraft design cycle time reduction using artificial
intelligence. Aerosp Sci Technol 2013; 26: 244–258.
23. Hopfield JJ. Neural networks and physical systems with
emergent collective computational abilities. Proc Natl
Acad Sci 1982; 79: 2554–2558.
24. Berke L, Patnaik S and Murthy P. Optimum design
of aerospace structural components using neural net-
works. Comput Struct 1993; 48: 1001–1010.
25. Aggarwal CC. Neural networks and deep learning.
New York: Springer, 2018.
26. Agarwal A and Biegler LT. A trust-region framework
for constrained optimization using reduced-order mod-
eling. Optim Eng 2013; 14: 3–35.
27. Nilsson NJ. Introduction to machine learning. An early
draft of a proposed textbook. 1998. http://robotics stan-
ford edu/people/nilsson/mlbook html
28. Secco NR and Mattos BSd. Artificial neural networks
to predict aerodynamic coefficients of transport air-
planes. Aircraft Eng Aerosp Technol 2017; 89: 211–230.
29. Kocuk B, Altinel _
IK and Aras N. Approximating the
objective function’s gradient using perceptrons for con-
strained minimization with application in drag reduc-
tion. Comput Oper Res 2015; 64: 139–158.
30. Mazhar F, Khan AM, Chaudhry IA, et al. On using
neural networks in uav structural design for CFD data
fitting and classification. Aerosp Sci Technol 2013; 30:
210–225.
31. Jean R, Miroslav K and Atle J. Artificial neural
networks trained through deep reinforcement learning
discover control strategies for active flow control. arXiv
preprint arXiv:180807664, 2018.
32. Ju Y, Zhang C and Ma L. Artificial intelligence meta-
model comparison and application to wind turbine
airfoil uncertainty analysis. Adv Mech Eng 2016; 8:
1687814016647317.
33. Sinha M, Kuttieri RA, Ghosh AK, et al. High angle of
attack parameter estimation of cascaded fins using
neural network. J Aircraft 2013; 50: 272–291.
34. Koziel S and Leifsson L. Knowledge-based airfoil shape
optimization using space mapping. In: 30th AIAA
applied aerodynamics conference, New Orleans,
Louisiana, 2012, p.3016.
35. Chen J, Sun G and Jin X. Intelligent aerodynamic
design for airfoil based on artificial neural network
method. In: 2nd international conference on computer
and automation engineering, ICCAE, Singapore, 2010,
pp.428–436.
36. Boutemedjet A, Samardzˇ ic
´M, Rebhi L, et al. Uav aero-
dynamic design involving genetic algorithm and artifi-
cial neural network for wing preliminary computation.
Aerosp Sci Technol 2019; 84: 464–483.
37. Guo X, Li W and Iorio F. Convolutional neural net-
works for steady flow approximation. In: Proceedings
of the 22nd ACM SIGKDD international conference on
knowledge discovery and data mining,ACM,San
Francisco, California, 2016, pp.481–490.
38. Chen H, Deng K and Li R. Utilization of machine
learning technology in aerodynamic optimization.
Acta Aeronaut Astronaut Sin 2019; 40.
39. Wang X, Wang S, Tao J, et al. A pca–ann-based inverse
design model of stall lift robustness for high-lift device.
Aerosp Sci Technol 2018; 81: 272–283.
40. Safikhani H and Jamalinasab M. Pareto optimization
of two-element wing models with morphing flap using
computational fluid dynamics, grouped method of data
handling artificial neural networks and genetic algo-
rithms. Int J Eng-Trans A 2018; 31: 666–672.
41. Timnak N, Jahangirian A and Seyyedsalehib S. An
optimum neural network for evolutionary aerodynamic
shape design. Scient Iran Trans B 2017; 24: 2490–2500.
42. Koziel S and Leifsson L. Multi-level surrogate-based
airfoil shape optimization. In: 51st AIAA aerospace
sciences meeting including the new horizons forum and
aerospace exposition, Dallas, Texas, 2013, p.778.
43. Ram RKG, Cooper YN, Bhatia V, et al. Design
optimization and analysis of naca 0012 airfoil using
computational fluid dynamics and genetic algorithm.
Appl Mech Mater 2014; 664: 111–116.
44. Ganesh Ram R, Cooper YN, Bhatia V, et al. Design
optimization and analysis of naca 0012 airfoil using
computational fluid dynamics and genetic algorithm.
Appl Mech Mater 2014; 664: 111–116.
45. Wang S, Sun G, Chen W, et al. Database self-expansion
based on artificial neural network: an approach in air-
craft design. Aerosp Sci Technol 2018; 72: 77–83.
46. Haryanto I, Utomo TS, Sinaga N, et al. Optimization
of maximum lift to drag ratio on airfoil design based on
artificial neural network utilizing genetic algorithm.
Appl Mech Mater 2014; 493: 123–128.
47. Duvigneau R and Visonneau M. Hybrid genetic algo-
rithms and artificial neural networks for complex design
optimization in CFD. Int J Numer Methods Fluids 2004;
44: 1257–1278.
48. Guang O, Jun L and Ping Z. Aircraft unsteady
aerodynamic hybrid modeling based on state-space
representation and neural network. In: International
conference on pattern recognition applications and meth-
ods, vol. 2, Porto, Portugal, 2017, pp.232–239.
49. LeCun Y, Bottou L, Bengio Y, et al. Gradient-based
learning applied to document recognition. Proc IEEE
1998; 86: 2278–2324.
50. Zhang Y, Sung WJ and Mavris DN. Application of
convolutional neural network to predict airfoil lift
coefficient. In: 2018 AIAA/ASCE/AHS/ASC structures,
structural dynamics, and materials conference,
Kissimmee, Florida, 2018, p.1903.
51. Yilmaz E and German B. A convolutional neural
network approach to training predictors for airfoil
performance. In: 18th AIAA/ISSMO multidisciplinary
analysis and optimization conference, Denver,
Colorado, 2017, p.3660.
52. Farimani AB, Gomes J and Pande VS. Deep learning
the physics of transport phenomena. arXiv preprint
arXiv:170902432, 2017.
10 Proc IMechE Part G: J Aerospace Engineering 0(0)
