Application of Multidisciplinary Design Optimization on Advanced Configuration Aircraft

Abstract

An optimization strategy is constructed to solve the aerodynamic and structural optimization problems in the conceptual design of double-swept flying wing aircraft. Aircraft preliminary aerodynamic and structural design optimization is typically based on the application of a deterministic approach of optimizing aerodynamic performance and structural weight. In aerodynamic optimization, the objective is to minimize induced drag coefficient, and the structural optimization aims to find the minimization of the structural weight. In order to deal with the multiple objective optimization problems, an optimization strategy based on collaborative optimization is adopted. Based on the optimization strategy, the optimization process is divided into system level optimization and subsystem level optimization. The system level optimization aims to obtain the optimized design which meets the constraints of all disciplines. In subsystem optimization, the optimization process for different disciplines can be executed simultaneously to search for the consistent schemes. A double-swept configuration of flying wing aircraft is optimized through the suggested optimization strategy, and the optimization results demonstrate the effectiveness of the method.

Full text

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
ABSTRACT: An optimization strategy is constructed to solve
the aerodynamic and structural optimization problems in the
conceptual design of double-swept ying wing aircraft. Aircraft
preliminary aerodynamic and structural design optimization is
typically based on the application of a deterministic approach of
optimizing aerodynamic performance and structural weight. In
aerodynamic optimization, the objective is to minimize induced
drag coefcient, and the structural optimization aims to nd
the minimization of the structural weight. In order to deal
with the multiple objective optimization problems, an optimization
strategy based on collaborative optimization is adopted. Based
on the optimization strategy, the optimization process is divided
into system level optimization and subsystem level optimization.
The system level optimization aims to obtain the optimized design
which meets the constraints of all disciplines. In subsystem
optimization, the optimization process for different disciplines
can be executed simultaneously to search for the consistent
schemes. A double-swept conguration of ying wing aircraft
is optimized through the suggested optimization strategy, and
the optimization results demonstrate the effectiveness of the
method.
KEYWORDS:Aerodynamic performance, Structural
optimization, Multiple objective optimization,
Collaborative optimization, Flying wing.
Application of Multidisciplinary
Design Optimization on Advanced
Conguration Aircraft
Yalin Pan1, Jun Huang1, Feng Li2, Chuxiong Yan1
INTRODUCTION
Flying wing conguration has been considered as an ideal
conguration of the future unmanned aerial vehicles (UAV) due
to its potential benets over conventional congurations in stealth
capability, aerodynamic performance, and structural eciency.
Several next-generation UAVs are of ying wing designs, such
as the X-45; X-47B; nEURO; etc. (Song et al. 2014; Li et al. 2014;
Bolsunovsky et al. 2001).
Compared with the conventional conguration, ying wing
aircra has become the research hotspot of advanced aircra in
recent years (Zhou and Liu 2015), and the number of ying wing
aircras which havebeendevelopedsuccessfully is far less than
the number of aircras with the conventional conguration.
e lack of statistics and practical experience about ying wing
conguration posed great dicultiesin aircra conceptualdesign.
It has been proved that multidisciplinary design optimization
(MDO) is an eective technique to deal with these problems. Now,
it has been widely used in the conceptual design of traditional
layout aircra (Piperni et al. 2007; Lee et al. 2007; Lambe and
Martins 2016).
Aircra optimization problems involve multiple objectives
and should be treated as multi-objective optimization (MOO)
problems. As a classic example, aircra preliminary aerodynamic
and structural design optimization is typically based on
the application of a deterministic approach of maximizing
lift-to-dragratio under cruising or other flight conditions
and minimizing structural weight due to applied air load
in an optimization process (Gou and Song 2006; Gao et al.
2003; Molinari et al. 2014). us, aerodynamic and structural
doi: 10.5028/jatm.v8i4.736
1.Beihang University – School of Aeronautic Science and Engineering – Beijing – China. 2.China Academy of Aerospace Aerodynamics – Beijing – China.
Author for correspondence: Yalin Pan | Beihang University – School of Aeronautic Science and Engineering | Beijing 100191 – China | Email: pyalin@buaa.edu.cn
Received: Jul. 13, 2016 | Accepted: Sep. 21, 2016

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
64 Pan Y, Huang J, Li F, Yan C
optimization problem is a 2-objective optimization problem in
aircra design. In aerodynamic design, in order to minimize
the induced drag coecient, the shape of the li coecient
distribution along the spanwise direction is expected to be close
to an ellipse. However, under this kind of load distribution, the
structural weight is not always the lightest during the process
of structural design. us, in terms of load distribution, the
aerodynamic performance and the structural weight are usually
conicting. In MOO, the optimization objectives belong to
dierent disciplines always in conict with each other. It is
impossible to reach the optimal results for all the optimization
goals at the same time. e optimization results ought to be
a set of optimal solutions rather than an optimalsolution. is
set is known as the Pareto optimal set, and its corresponding
tradeo in objective space is known as the Pareto optimal frontier,
which is made up of the Pareto optimal points (Sanghvi et al.
2014; Huang et al. 2007; Hu and Yu 2009). Designers could
select an optimized scheme which satises the requirements
of all disciplines from the Pareto optimal set. In this article, an
optimization strategy based on collaborative optimization is
proposed to deal with the MOO problem in ying wing aircra
conceptual design. e UAV conguration used as a basis for
the MOO is shown in Fig. 1. e take-o weight of the aircra
is 20,000 kg and it is used for intelligence, surveillance, and
reconnaissance missions as a high-altitudelong-range UAV.
displayed in Fig. 3 and Fig. 4; these sections are used to t the
contour surface of the aircra. e li and the induced drag
of the UAV aremainly concernedwiththe airfoil camber. e
outline parameters are xed in the original design. It is expected
that the minimum of the induced drag coecient of the UAV
can be found by adjusting the mean lines of these sections.
Airfoil mean line
Airfoil mean line
Figure 1. CAD model of ying wing aircraft.
STATEMENT OF THE OPTIMIZATION
PROBLEM
e platform of the UAV is shown in Fig. 2. e parameters
as shown in the gure are the outline ones and they are used
to determine the planform of the UAV. e chord lengths at
dierent locations along spanwise direction are described by br ,
b2, and bt . e wing span for dierent sections are described
by l1, l2, and l3. In order to describe the sectional shape of the
UAV, section 1, section 2, section 3, and section 4 (as shown
in Fig. 2) are dened as the master sections, whose proles are
Figure 4. Prole of the other master sections.
Figure 2. Half of ying wing conguration platform.
Section 3 Section 4
Section 2Section 1
α1
α2
br
b2bt
bt
l2
l1l3
Figure 3. Prole of section 1.
Constrained by the material allowable stress and structural
deformation, it is required to nd the minimum of structural
weight by adjusting the structural dimensions. e structure of the
UAV contains outer skins and inner structural layout, as shown in
Fig. 5. e inner structural layout of the UAV is displayed clearly
in Fig. 6. For inner structure, the fuselage (Part 1) is composed
by longitudinal beams and reinforced frames, the wing closed to
the fuselage (Part 2) includes wing spars and reinforced ribs, and
the outboard wing (Part 3) includes wing spars and wing ribs. e
structural dimensions which are used as design variables include
the thickness of skin and rib, the area of spar cap and rib cap, etc.
As already mentioned, the optimization problem of this
UAV conceptual design can be formulated as follows:
• Objectives: (1) Minimized induced drag coecient;
(2) Minimized structural weight.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
65
Application of Multidisciplinary Design Optimization on Advanced Conguration Aircraft
• Design variables: (1) Parameters which are used to
describe theairfoil mean lines of the UAV; (2) Parameters
which are used to dene the structure of the UAV.
• Constraints: (1) Aerodynamic requirements; (2)
Structural requirements.
weight of the UAV. e constraint function of system optimization
is used to make the schemes of dierent subsystem optimizations
consistent. In this article, only the state variables of aerodynamic
discipline which are used to describe the load distribution on the
aircra surfaces are dened as the global design variables (i.e.
the design variables in system level optimization). e design
parameters which only have impact to 1 discipline are dened
as local design variables (i.e. the design variables in subsystem
level optimization). Since the airfoil mean lines of the master
sections have inuence mainly on aerodynamic performance but
have little eect on structure weight, the parameters which are
used to describe the airfoil mean lines are local design variables.
e structural dimensions have inuence mainly on structure
weight and impact on aerodynamic performance slightly, so these
parameters are also local design variables. e load distribution can
be described by li coecient curve and it is generated by tting
the li coecient of the sections along its spanwise direction. e
li coecient curve is described by a cubic polynomial function.
e tting function is shown as follows:
Skin
Ineer Structure
Skin
Part 1 Part 2 Part 3
Figure 6. Inner structure of the UAV.
Figure 5. Structural layout of the UAV.
OPTIMIZATION STRATEGY
Aerodynamic and structural optimization problem is a typical
MOO problem in aircra design, and the 2 disciplines are always
in conict. e improvement of aerodynamic performance oen
brings an increase in structural weight, and the decrease in it usually
causestheexpenseof aerodynamic performance (Chu 2011; Ma et
al. 2009). In MOO, there oen exists a set of optimal solutions, and
none can be said to be better than any other without any further
information. In order to coordinate the relationship between
aerodynamic and structure of the UAV, an optimization strategy
based on collaborative optimization is used to deal with the MOO
problem. e optimization process can be divided into 2 levels
which include the system level optimization and the subsystem level
optimization. e system level optimization transfers the global
design variables to the subsystem level optimization. In the subsystem
level optimization, these global design variables are dened as
target values. e state variables of each discipline are optimized to
approximate these target values throughoptimizationalgorithm.
us, the optimized designs for dierent disciplines are consistent.
e system level optimization aims to search for the design
scheme with minimum induced drag coecient and structural
Cl (η) = a3∙η3 + a2∙η2 + a1∙η1 + a0(1)
where: η = y/b; y represents the coordinates of the UAV
spanwise direction; b is half of the span; theshapeoftheload
distribution curve is determined by the function coecients
(i.e. a0, a1, a2, and a3). The global design variables can be
represented by a0, a1, a2, and a3.
e subsystem level optimization is integrated with the system
level optimization, and the goal of aerodynamic optimization is
to achieve the minimumof dierencebetweenthe state variables
and global design variables under the constraints of aerodynamic
characteristics by changing the camber curve shapes of master
sections airfoils. Constrained by the material allowable stress and
structural deformation, the structure optimization aims to nd
the minimum of structural weight by adjusting the structural
dimensions. e frame of the method for aerodynamic and structural
multiple-objective design optimization is depicted in Fig. 7.
In the optimization strategy, thenon-dominated sorting
genetic algorithm (NSGA-ⅱ)is adopted for system optimization.
e formulation of system level optimization is stated as follows:
• Objectives: minimized induced drag coecient (CDi)
and structural weight (W).
• Design variables: parameters which are used to dene
the li coecient distribut ion along spanwise direction,
such as a0; a1; a2 and a3.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
66 Pan Y, Huang J, Li F, Yan C
• Constraints: the scheme optimized by the subsystem
optimization is consistent with the design oered by
the system (J1 = 0).
e sequential quadratic programming algorithm is used for
aerodynamic optimization. e formulation of aerodynamic
optimization problem is as follows:
• Given conditions: cruise Mach number is 0.8, and
cruise altitude is 18 km.
• Objective: to minimize the differencebetween
the state variables and the global design variables,
J1 = ∑
3
i = 0 (ai – a0
i)2.
• Design variables: the parameters for describing the
airfoil mean lines of master sections.
• Constraints: to design li coecient (CL = 0.362).
e sequential quadratic programming algorithm is adopted
for structural optimization. e formulation of the structural
optimization problem is as follows:
• Objective: minimized structural weight (W).
• Design variables: (1) the areas of spar caps, ribs, and
reinforced frames; (2) the thicknesses of the webs of
spars, ribs, and reinforced frames; (3) the thicknesses
of wing skins; (4) the stiener areas of the webs. Eighty-
six dimensions in total are used as design variables.
• Constraints: (1) the axial stress of the rods ≤ 450 MPa;
(2) the shear stress of the plates ≤ 250 MPa; (3) the dis-
placement of wing tip ≤ 5% of the semi span of the wing.
e nal result can be obtained by iterating the system level
and the subsystem level optimizations until converging to the
optimum values. e subsystem optimizations are executed as
the global variables are updated.
AIRCRAFT MODEL AND ANALYSIS
METHODS
Executing optimization process automatically is necessary
forsolvingcomplex optimization problems. To implement the
procedure of aerodynamic and structural optimization for
the UAV conceptual design, some important technologies, like
parametric geometry description and automatic execution of
aerodynamic computing and structure calculation, are essential.
ese approaches which will be used in the optimization are
explained in the following subsections.
GENERATING PARAMETRIC MODEL
As for all optimization tasks, the complexity of the problem
is directly coupled to the parameterization of the geometry. Of
highest relevance is the number of parameters that are required
to ensure valid modeling. e most important characteristic
of the CAD model is to be highly exible in order to represent
a variety of designs as large as possible. Secondly the model
must be robust and reliable, since there will not be a specialist
manually entering new parameters and supervising the update
process (Amadori et al. 2008; Sripawadkul et al. 2010; Wang et
al. 2013). Flying wing conguration has the characteristics of
simple shape and blended wing body, and the UAV can be seen
as a special wing which is connected together by 3 segments.
e important content of theCAD model parameterizationis
to describe parametric airfoils shape of the UAV.
In the article, the airfoil profile is described by the
superposition of camber distribution and thickness distribution.
e function which is used to explain the camber distribution
is shown as follows:
Figure 7. Optimization strategy for multi-objective optimization
in aircraft conceptual design.
System level optimization
Aerodynamic optimization Structural optimization
Objective:
Objective:
Constraint:
Constraint:
Design variables:
Design variables:
Aerodynamic calculation
aerodynamic requirements
minimized
minimized structural weight W
minimized induced drag coecientt CDi
J0
XA = {parameters of master sections}
Objective:
Constraint:
Design variables:
strength, stiness, etc.
minimized
XB = {dimensions of structural}
XACDi , ai
Structural analysis
WXB
J1 = ∑ (a1 – a1)2
0
3
t = 0
w
f (x) = c1 ∙ sin (π ∙ x) + c2 ∙ sin (π ∙ x1.5) +
+ c3 ∙ sin (π ∙ x2) + c4 ∙ sin (π ∙ x2.5)(2)

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
67
Application of Multidisciplinary Design Optimization on Advanced Conguration Aircraft
The coefficients of the function are derived from four
characteristic parameters of the airfoil mean line, such as
relativecamber (C), relativecamber location (XC), the angle
between leading edge of camber line and chord line (αLE), and the
angle between trailing edge of camber line and chord line (αTE).
e geometricsignicance of these parameters is shown in Fig. 8.
rough aerodynamic performance calculation, the li
drag ratio and the li coecients of the sections along the UAV
spanwise direction corresponding to design li coecient can
be generated and outputted.
STRUCTURAL ANALYSIS
e structural model is more complex than the aerodynamic
one due to the structural layout in the inertial model of the
UAV. The features of the structural layout are defined by
the number and positions of the spars, as well as the number
and orientation of the ribs. These parameters are used for
splitting the geometric model surface of the UAV in CATIA.
en the split model is transmitted to MSC.PATRAN to generate
the structural layout model and the nite element model (FEM),
which is shown in Fig. 10. In the FEM of the structure, the skins
and webs of spars, ribs, and reinforced frames are modeled by
plates, and the spars and the stieners for webs are modeled
by rods. e dimension parameters of the FEM include thickness
of skin and rib, area of spar caps and rib caps, etc.
Figure 8. The meaning of camber parameters.
Y
XC
X
C
αLE αTE
AERODYNAMIC COMPUTING
In order to get the induced drag coecient and li coecient
distribution along spanwise direction corresponding to design
li coecient of the UAV, a panel code (Panair) is adopted. Panel
codes are numerical schemes for solving the Prandtl-Glauert
equation for linear, inviscid, irrotational ow about aircra ying
at subsonic or supersonic speeds (Lehmkuehler et al. 2012).
Compared to CFD codes, Panair has advantages in terms of speed
and ease of meshing. e surface mesh information of the UAV
required for aerodynamic analysis is shown in Fig. 9. Pointwise
soware is used to divide quad surface mesh of the UAV model.
An auxiliary numerical code is written to transform the surface
mesh into the le which will be transmitted to Panair.
Aerodynamic performance is calculated through the
following steps: (1) generating the mesh le of the UAV in
Pointwise based on CAD model; (2) generating the le which
will be transferred to Panair; (3) executingPanair program
to calculate the licoecient of the UAV at dierent attack
angles; (4) calculating the attack angle corresponding to design
li coecient; (5) computing the aerodynamic performance
of the UAV at design point; (6) deleting the les which are
generated in the procedure.
Figure 9. Aerodynamic model of the UAV.
y
Figure 10. Finite element model for the UAV structure.
By using the FEM of the UAV structure, the optimization
process can be used. e structural optimization is carried
out by running MSC.NASTRAN soware. It aims to search
for the values of structural design variables which minimize
structural weight in the condition when the material allowable
stress, structural deformation, and geometry dimensions are
satised. e structural weight optimized is necessary for overall
performance calculation.
OPTIMIZATION PROCESS
In this article, iSIGHT is adopted to integrate all the
sowareandprograms we used (Koch et al. 2002). In order
to improve the optimizationeciency, a surrogate model is
constructed before MDO. Since aerodynamic problems are oen
highly non-linear, the surrogate model chosen in this article is

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
68 Pan Y, Huang J, Li F, Yan C
the Radial Basis Function Neural Network (RBFNN). e input
data of the surrogate model including the camber parameters
of master sections and the output parameters are a0; a1; a2; a3
and CDi. In the surrogate model, 370 sample points are selected
randomly in design space to construct the surrogate model.
Other 185 sample points are selected as the error analysis points
of the surrogate model. In order to improve the credibility of
the surrogate model, 370 new sample points are selected to
reconstruct the surrogate model. e error analysis results of
the nal surrogate model for the output parameters are shown
in Table 1. Six new sample points which are selected from
the design space are calculated by Panair and the surrogated
model, respectively, and the results are shown in Table 2. Once
the surrogate model is built with given exact function data, it
can eciently be in the exploration of the design space and the
MDO by replacing the original code.
Figure 11 shows the detailed procedure for dealing with
the MOO problem of the UAV. e optimization process is
carried out step by step following the owchart. Each system
level optimization iterates, during which the global variables
can be updated and then the subsystem level optimization is
completed once.
Responses 1 2 3 4 5 6
a0
Panair 2.028481 2.135833 2.099838 2.129787 2.089403 2.056113
RBFNN 2.029884 2.135446 2.097253 2.130500 2.092359 2.056392
a1
Panair −3.284242 −3.56747 −3.718978 −3.458064 −3.533423 −3.257147
RBFNN −3.287965 −3.56777 −3.70466 −3.461285 −3.549795 −3.262633
a2
Panair 2.760191 2.858455 3.431695 2.571950 3.064149 2.578853
RBFNN 2.760020 2.860046 3.409363 2.578452 3.089931 2.589869
a3
Panair −1.422091 −1.35417 −1.733668 −1.181949 −1.54088 −1.298712
RBFNN −1.419876 −1.35518 −1.72302 −1.185902 −1.553252 −1.304347
CDi
Panair 0.003510 0.003480 0.003470 0.003410 0.003470 0.003480
RBFNN 0.003505 0.003478 0.003472 0.003405 0.003473 0.003477
Table 1. Approximation error analysis.
Variables Average Maximum Root Mean Square R-squared
a00.00508 0.02527 0.00677 0.99909
a10.00456 0.02435 0.006 0.99912
a20.00423 0.02318 0.00551 0.99911
a30.00423 0.02274 0.00545 0.99909
CDi 0.0134 0.04002 0.01572 0.9927
Table 2. Comparison of calculation results by Panair and RBFNN model.
Figure 11. Flowchart of aerodynamic and structural
multidisciplinary design optimization.
Global design variables
X0 = {a0, a1, a2, a3}
Update
Update
Initial scheme of the UAV
Parametric geometry denition
DOE
Generate
CAD model
Generate
CAD model
aerodynamic
Data le for
analysis
Aerodynamic
calculation
a0, a1, a2
a3, CDi
a0, a1, a2
a3, CDi
J1, CDi
Aerodynamic
optimization
Data
processing
Structural
layout
Structural
optimization
Structural
optimization
Parameters
of master
sections
Generation
of FEM
Generation
of FEM
Surrogate
model
Surrogate
model
Parameters
of master
sections
J
W
W
o o o o

J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.63-70, Jan.-Mar., 2017
69
Application of Multidisciplinary Design Optimization on Advanced Conguration Aircraft
OPTIMIZATION RESULTS
Based on the given optimization strategy, the optimization
process is executed automatically. Figure 12 provides the Pareto
fronts which are the solutions of minimizing both the induced
drag coecient and structural weight. An optimal point can
be selected from the Pareto optimal solution set according to
the design requirements. performance of design 1 is better than the 2 other solutions;
design 3 is the best one with respect to structural weight;
and design 2 is a solution which is a compromise of the induced
drag coecient and structural weight.
CONCLUSION
In this paper, an investigation has been made to study
aerodynamic and structural optimization of ying wing aircra.
A multi-objective optimization strategy based on collaborative
optimization strategy is proposed. During the optimization process,
the parallel computing in subsystem optimization is used, which
improves the eciency of optimization. e optimization result
is a Pareto optimal set, which provides the designer with more
options. A ying wing conguration of aircra is optimized by
the strategy, and the optimization results demonstrate that the
present method can eciently nd the Pareto optimal set.
AUTHORS’ CONTRIBUTIONS
Pan Y and Huang J conceived the idea and co-wrote the
main text; Li F and Yan C constructed the numerical models
for multidisciplinaryanalysis; Yan C processed the calculation
data. All authors discussed the results and commented on the
manuscript. is paper was carried out through the collaboration
of all authors.
Figure 12. Pareto optimal front obtained from system level
optimization.
7600
7400
7200
7000
6800
6600
6400
3 4 5 6 7 8 9 10 11 12
3
C
2
B
A
1
C
Di
/10
–3
W (kg)
e Pareto optimal front can be divided into 3 typical
subsets, including subset A, subset B, and subset C.
ese subsets correspond to 3 typical subsets of the Pareto
optimal solution set, respectively. The subset A is a set
of optimization solutions with smaller induced drag coecient.
e subset C represents the optimization solutions which
have lighter structural weight. e subset B lying between subsets
A and C is the trade-o between aerodynamic performance
and structural weight, so it has both relatively smaller induced
drag coecient and lighter structural weight. e choice for
a solution from each subset as the typical sample and the
aerodynamic performance and structural weight of selected
samples are listed in Table 3, which shows that the aerodynamic
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Number of the
sample CDi W (kg)
1 0.00323511 7,582
2 0.00454684 6,632
3 0.01012 6,409

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