A Multi-Fidelity, Multi-Disciplinary Analysis and ...michael.friswell.com/PDF_Files/C386.pdf · A Multi-Fidelity, Multi-Disciplinary Analysis and Optimization Framework for the Design

American Institute of Aeronautics and Astronautics

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A Multi-Fidelity, Multi-Disciplinary Analysis and

Optimization Framework for the Design of Morphing UAV

Wings

Andrea Ciarella*, Christos Tsotskas

† and Marco Hahn

‡

Aircraft Research Association Ltd., Bedford, MK41 7PF, United Kingdom

Noud P. M. Werter§ and Roeland De Breuker

**

Delft University of Technology, 2629 HS Delft, the Netherlands

Chris S. Beaverstock††

and Michael I. Friswell‡‡

Swansea University, Swansea, Wales SA2 8PP, United Kingdom

Yosheph Yang§§

and Serkan Özgen***

Middle East Technical University, Dumlupinar Bulvari, 06800, Ankara, Turkey

Antonios Antoniadis†††

, Panagiotis Tsoutsanis‡‡‡

and Dimitris Drikakis§§§

Institute of Aerospace Sciences, Cranfield University, Cranfield, Bedfordshire, MK43 0AL, United Kingdom

A framework for the design and optimization of a morphing wing is presented. It allows

the user to simplify the design process of a morphing UAV wing with a simple and effective

interface with the possibility to easily switch between flight phases and morphing concepts.

It consists of two main solvers: a high-fidelity CFD module for detailed RANS simulation

and a fast low-fidelity module that solves the aeroelastic problem by coupling a

geometrically nonlinear structural model to a potential flow aerodynamic model. The

structure of the framework and the methodology used for the design of a morphing UAV

wing are detailed. This wing is the focus of the European FP7 CHANGE project and serves

as an example of the application of this methodology.

Nomenclature

NSGA = Non-dominated Sorting Genetic Algorithm

MOO = Multi-Objective Optimization

DoE = Design of Experiment

* Project Scientist, Computational Aerodynamics, [email protected]

† Project Supervisor, Experimental Aerodynamics, [email protected]

‡ Senior Project Scientist, Computational Aerodynamics.

§ Ph.D. Student, Faculty of Aerospace Engineering, Aerospace Structures and Computational Mechanics.

** Assistant Professor, Faculty of Aerospace Engineering, Aerospace Structures and Computational Mechanics.

†† Researcher, School of Engineering

‡‡ Professor, School of Engineering

§§ Master Student, Dept. of Aerospace Engineering

*** Professor, Dept. of Aerospace Engineering

††† Lecturer, Department of Fluid Mechanics and Computational Science

‡‡‡ Lecturer, Department of Fluid Mechanics and Computational Science

§§§ Professor, Head of Division - Engineering Sciences, Department of Fluid Mechanics and Computational Science

16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

22-26 June 2015, Dallas, TX

AIAA 2015-2326

Copyright © 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA Aviation


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LHS = Latin Hypercube Sampling

MDAO = Multi-disciplinary analysis and optimization

TRL = Technology Readiness Level

UAV = Unmanned Aerial Vehicles

CFL = Courant-Friedrichs-Lewy

1. Introduction

Shape changes have been used to modify the aerodynamic characteristics of aircraft since the early days of

flight. Among the first and most renowned example is wing warping, i.e. change in wing twist, to control rolling

motion and lateral stability. The Wright Brothers conceived this mechanism in 1899 and employed it subsequently

in all their designs1, most notably during their first successful flight demonstrating a coordinated turning manoeuvre

in 1905. Modern aircraft feature various moving parts to adjust their geometry, e.g. rudders, elevators, ailerons or

high-lift devices. These conventional systems can be seen as a form of ‘discrete morphing’ providing control

authority and improving flight performance. However, the overall performance over the complete flight envelope is

always compromised because the aircraft experiences a wide range of conditions during and between several flight

phases. Thus, discrete morphing systems are not able to respond adequately to all scenarios encountered during a

flight mission, e.g. comprising take-off, cruise, loiter and landing.

In classical aircraft design, the baseline design provides optimal performance for the most important flight phase,

e.g. cruise for commercial airliners. In order to satisfy additional constraints posed by other flight phases, however,

the baseline is modified and augmented by discrete morphing mechanisms. Consequently, the final design is

generally a compromise between several sub-optimal aerodynamic shapes. The seemingly obvious answer to this

problem is found in nature: the ‘continuous morphing’ capability of birds enables them to adjust to all flight

conditions2. This variable geometry concept, commonly referred to with the term “morphing”, is a promising

enabling technology for future aircraft generations.

A detailed overview of past and present morphing research is given in the article of Barbarino3. As the authors

point out, current morphing technology has not reached the maturity required to be adopted by major aircraft

manufacturers. Thus, Unmanned Aerial Vehicles (UAVs) provide an ideal platform for further development and

raising the Technology Readiness Level (TRL). The vision for a next-generation aircraft is to combine different

morphing concepts and to leverage their individual benefits with the aim of offering greater efficiency, versatility

and performance. In order to realise this vision a detailed evaluation of various aspects of a new design is required in

terms of flight mechanics, structural mechanics, aerodynamics, manufacture and cost. This already is a challenging

task for conventional aircraft configurations. Integrating morphing systems into the process significantly increases

the complexity, even if only a sub-set of disciplines is considered, and no transparent way of modelling feasible

solutions has yet emerged. Thus, a flexible, modular and extendable framework for analysis and optimization is

required to assist the designer throughout the product development.

The objective of the European FP7 project CHANGE (Combined morpHing Assessment software usiNG flight

Envelope data and mission based morphing prototype wing development) is to develop, build and flight-test a novel

morphing UAV. The aircraft utilizes a modular wing that incorporates several complementary morphing

technologies, with the aim of performance improvement over a range of flight missions. The baseline wing

geometry is based on a set of previously designed shapes for independent flight phases, using conventional

methods4. The CHANGE wing combines telescopic span extension and retraction, as well as different leading and

trailing edge systems, to actively modify both local camber and twist. In order to model and identify the desired

wing shape according to the mission requirements for each flight phase, a generic software framework has been

developed which is capable of optimizing the morphing aircraft.

The multi-fidelity, multi-disciplinary analysis and optimization (MDAO) framework presented in this paper

combines a parametric geometry and structural module to discretise the morphed wing, a low-fidelity aerodynamics

and structural mechanics module to perform aeroelastic calculations, as well as a high-fidelity aerodynamics module

for accurate drag prediction. It allows the selection of the flight phase and the definition of the flight conditions. The

software does not restrain the design space a priori. Thus, it has the capability to be applied to any other type of

wing and morphing technology, without having to alter the components at its core. In addition to being employed to

model the current UAV on a variety of different flight missions, the framework is also able to optimize the wing for


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various different morphing aircraft. Consequently, the software tool can guide both conceptual and detailed design,

as well as provide optimal morphing actuator settings for flight conditions not considered during the design process.

Section 2 describes the software framework with details on main modules, inputs and outputs. Section 3 presents

the methodology followed in the use of the framework for general design. A design example for the UAV wing of

the CHANGE project is presented in section 4.

2. Software framework

The intention of the CHANGE framework is to deliver a method that links several computational engineering

disciplines to guide the design and manufacture process, as well as wind-tunnel and flight testing. The MDAO

framework comprises several modules that are called in a sequential fashion, in order to deliver the desired feasible

wings for a given flight mission. A flow-chart providing a top-level overview of the analysis part of the software

framework is presented in Figure 1 and the associated implementation in PHX ModelCenter5 is provided in Figure

2. First, the input flight data and morphing design parameters are passed to the Morphing Wrapper Module to define

the morphed geometrical shape and structural characteristics of the wing. Subsequently, the Low-Fidelity Module

calculates the static aeroelastic deformation, before the High-Fidelity Module solves for the aerodynamic forces. All

results for the current configuration and flight condition are then stored for processing in a lookup table.

The framework is written to be modular and allows the user to work with a parallel computing cluster, enabling

several high-fidelity simulations at the same time, thus increasing the speed of the process. An overview of the

input data and the modelling concept, as well as more details on the different software modules, is provided in the

following sections.

Figure 1 – Top-level overview of the software framework.

Figure 2 – Software framework in PHX ModelCenter.


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A. Modelling concept overview

Aero-structural problems are governed by multiple disciplines and are characterized by high levels of

complexity. Frequently, a large number of variables participate in the problem formulation and link to a number of

objectives, which are subject to various constraints. A morphing wing adds to the complexity of the problem

because the aerodynamic performance and the stresses on the wing will change for each morphing configuration.

Therefore, two different types of main input are considered in the software framework to represent the CHANGE

wing:

1. Flight parameters: They define the flight conditions encountered during various phases of a specified

flight mission, e.g. a typical reconnaissance mission illustrated in Figure 3.

Figure 3 – Flight phases during a typical reconnaissance mission.

2. Morphing parameters: They control the shape change according to the actuation settings of the morphing

technologies in the wing. A schematic of the modular morphing wing used in CHANGE is shown in Figure

4. It contains several regions: an inner fixed wing (IFW, orange regions) with different leading and trailing

edge morphing devices (blue regions); and an outer morphing wing (OMW) with telescopic span and fixed

cross section (green regions). Since various leading and trailing edge morphing technologies can be

attached to the wing box, the morphing parameters also define the respective structural properties of the

resulting wing shape.

Figure 4 – Schematic of the modular morphing wing used in CHANGE.

A top-level overview of the analysis part is presented in Figure 5. First, the material data and morphing design

parameters are passed to the Morphing Wrapper Module to define the morphed geometrical shape and structural

characteristics of the wing. Subsequently, incorporating the flight conditions, the Low-Fidelity Module calculates the

static aeroelastic deformation and low-fidelity aerodynamic data using the deformed wing shape. The results of all

simulations are analysed in the Pareto Front Module which filters the data and selects the simulation to run in the


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High-Fidelity Module. The High-Fidelity Module calculates the wing aerodynamic characteristics. All results for the

current configuration and flight condition are then stored for processing in a lookup table.

Figure 5 – Schematic of the analysis framework.

A detailed view of the framework within ModelCenter is presented in Figure 6. The left part of this figure shows

the control variables and the right part illustrates the structure of the code including data links (black arrows). Two

different inputs are considered: the flight conditions for the individual flight phase and the morphing parameters

defining the morphing characteristics of the UAV.

Figure 6 – Analysis framework in PHX ModelCenter.


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B. Morphing Wrapper

The Morphing Wrapper6 generates the geometric, mass and structural models that are used in the analysis

modules, as shown in Figure 7.

Figure 7 – Overview of the Morphing Wrapper Module.

The input to the module is a set of morphing parameters and the geometry and structural models that they drive.

The morphing parameters are a set of values to configure the morphing systems available. The morphing parameters

are abstract, in the sense that a morphing parameter can directly or indirectly represent positions of morphing

actuators, from which the effect on the geometry and structure is modelled. The models contain information

regarding the baseline, un-morphed configuration, and also functions to enable the effect of morphing on the

geometric and structural models. The functions use the morphing parameters to model the actuation of the morphing

system(s) on the platform, and then generate a morphed geometry and structure for aero-structural analysis. The

basis of the geometry is formed of a series of connected panels that form an aerodynamic lifting surface. Each panel

is defined by two cross-sections, an inboard and outboard. Each cross-section is defined by a set of points in a 2D

plane, where the cross-sections are connected, as can be observed in Figure 8.

Figure 8 – Morphing panel definition.

For the geometry, the functions within the Morphing Wrapper ensure that only the boundary for generating and

transferring aerodynamic loads to the structure is modelled. Points internal to a volume are removed, where the

interface between panels is modified such that the surface is continuous. In addition to modifying the geometry,

using similar treatment, the structure is also modified. The structure is defined for each panel. The properties are

derived from a set of nodes, which are connected by laminated material. For overlapping sections, a new partitioned

panel is defined, with appropriate cross-section limits set. The structural properties within this section include the

effect of all cross-sections that contribute toward the structural properties in a panel section

Additional input for the material properties, such as Young’s modulus, torsional stiffness and material density, is

required. The material properties can also be applied to laminates. The laminates define a series of layers at a

specified orientation. This ensures that the directional properties of a laminate applied between nodes are correct.

These laminates can then be applied between nodes in a cross-section, where the connectivity is defined under one

format, and the node positions and indices in another. When combined, this data provides the necessary data to

compute the structural properties of a cross-section of a panel. Using this structure, along with the morphed wing,

Inboard Nodes

Outboard Nodes

Panel Assembly

Direction

N Panels to define

surface


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enables aero-structural data to be generated for analysis. The final output defines a series of sections, with structural

properties defined between the cross-sections.

The morphing design variables used to control the shape of the wing are used as design variables in the

optimization process and are presented in Table 1.

Table 1 – Morphing design variables.

LEconcept Concept used for the

leading edge. 1 indicates the TuDelft

7 concept

2 indicates the DLR8 concept

TEconcept Concept used for the

trailing edge 1 indicates the TuDelft

7 concept

2 indicates the METU9 concept

LEact1 Inboard leading edge

actuator setup Varies from 0 (no actuation) to 100 (maximum actuation).

LEact2 Outboard leading edge


TEact1 Inboard trailing edge


TEact2 Outboard trailing edge


Not used in METU concept

UBIact10

Span morphing

parameter Varies from 0 (no actuation, fully extended wing, 2 m wingspan) to 100

(maximum actuation, retracted wing, 1.6 m wingspan)

C. Low-Fidelity Module

The Low-fidelity Module11

is used to perform the aeroelastic assessment of the different morphing concepts.

Figure 9 shows a schematic overview of the Low-fidelity Module.

Figure 9 – Overview of the Low-Fidelity Module.

The inputs to the module are the wing geometry and structural characteristics from the Morphing Wrapper. The

wing geometry is specified by means of an aerodynamic cross-section at a number of spanwise locations. In order to

obtain the full shape of the wing, these cross-sections are linearly interpolated to obtain the aerodynamic surface

mesh. The wing structural characteristics are defined by means of structural cross-sections at the same spanwise

stations as the wing geometry. Nodal coordinates and the connectivity between these nodes define the cross-

sectional geometry. In order to complete the structural definition, a (composite) laminate is assigned to each cross-

sectional element. This allows for the modelling of any arbitrary structural cross-section made out of any arbitrary

material distribution. Finally, to complete definition of the inputs for the Low-fidelity Module, the flight condition

and the aircraft weight need to be specified in the framework’s main input. This aircraft weight will be used to trim

the aircraft for target lift.

The cross-sectional modeller computes the cross-sectional properties of the three-dimensional wing geometry

along the span and allows for the condensation of the full three-dimensional wing structural model to a one-

dimensional reduced-order model. The cross-section is discretised using linear Hermitian shell elements with a

constant thickness and constant material properties. Using sufficient elements allows for any arbitrary composite

cross-section, including thickness variation, to be modelled efficiently. The main advantage of creating a one-

dimensional structural model is that it reduces computational time significantly, thus making it suitable for

implementation in an optimization procedure. The output of this module is the Timoshenko cross-sectional stiffness

matrix, which not only accounts for extension and bending of the wing, but also shear effects that can become

important depending on the material thickness and material lay-up used.

The static aeroelastic analysis module uses a structural model based on linear Timoshenko beam elements, which

are embedded in a co-rotational framework to obtain a geometrically non-linear structural solution. Additionally, a


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vortex lattice method is used as the aerodynamic model, such that any planform and level of camber can be

modelled, while still obtaining an efficient model suitable for optimization. Both models are closely coupled and a

non-linear static aeroelastic equilibrium solution is obtained by using load control and the Newton-Raphson root

finding algorithm. The induced drag of the wing is computed by means of a Trefftz plane analysis. All analyses are

performed at a trimmed flight condition. This allows for a comparison of the performance of different morphing

wings in the optimization framework.

The Low-Fidelity Module provides the aeroelastically deformed wing geometry under 1-g loading as output. This

serves as input for the high-fidelity aerodynamic analysis. Furthermore, the cross-sectional modeller is used to

compute the skin strains from the beam deformation and hence assess the structural performance of the wing.

Finally, the module provides the trimmed angle of attack, the wing lift and induced drag, the load distribution on the

wing, and the root bending moments as outputs.

D. High-Fidelity Module

The High-Fidelity Module is the component of the framework that provides high-fidelity CFD RANS simulation

results, using as input the wing geometry and the flow conditions provided by the Low-Fidelity Module. The main

practical difference between the codes is in the drag calculation. While the Low-Fidelity Module calculates only the

induced drag, the High-Fidelity Module calculates the total drag including profile drag. The schematic of the High-

Fidelity Module is presented in Figure 10 and shows its three main components, namely:

WingBuilder

Solar mesher12

SU2 solver13

Figure 10 – Overview of the High-Fidelity Module.

Each one of these components is independent and flexible, allowing the user to have control of all the main

parameters of the components directly through PHX ModelCenter. The outputs of this module are the aerodynamic

characteristics of the wing for the defined flight phase, in terms of lift coefficient, drag coefficient, moment

coefficients, surface pressure coefficient and skin friction coefficient distributions.

The first component of this module is the WingBuilder, a tool that converts the aeroelastically deformed wing

sections provided by the Low-Fidelity Module into a complete three-dimensional CAD file suitable for mesh

generation with Solar. This CAD file contains the wing geometry and the flow domain. The code uses cubic spline

or linear interpolation depending on user setup to reconstruct the geometry based on the initial sections. The other

tasks of the component are to provide the boundary condition information and to write the Solar setup files. The user


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has access to control parameters in order to improve the quality of the geometry, in terms of surface reconstruction,

number of points used and domain size.

The second component is the Solar mesher. A fully automatic methodology to obtain a high-quality and wall-

resolved mesh has been implemented. The user can control the density of the mesh and the first cell height, giving

the possibility to refine the mesh if the quality is not acceptable. The output will be a complete three-dimensional

mesh in the format requested by the SU2 flow solver.

The third component is the CFD RANS solver. In this module the incompressible version of the RANS solver

SU2 is used with a bespoke target-lift script. This code was selected because of its good balance between

performance and accuracy. In addition, SU2 is Open Source, which makes it easy to distribute among the partners.

The high-fidelity simulations run at target-lift coefficient defined from the Low-Fidelity module. The user can

control, through the main interface of the framework, all the numerical parameters of the solver, such as numerical

scheme, CFL number, convergence criterion etc. The data generated via SU2 are used to validate the Low-Fidelity

module in all flight phases and to improve data accuracy where the low-fidelity methodology is not adequate, for

example, where boundary-layer effects are significant.

3. Optimization methodology

The process used here is composed of multiple and computationally demanding applications to design, assess

and optimize the shape of the wings of a UAV. A Design of Experiments (DoE) technique is combined with Multi-

Objective Optimization (MOO) algorithms to produce a range of solutions to reveal the trade-off between

performance indices. These were selected to mitigate the high computational cost and to quickly drive the process.

At the end of the process several non-dominated solutions, also known as the Pareto Front, will be revealed to allow

the user to make an informed decision about the desired wing shapes.

The objective of DoE is to capture the behaviour and the sensitivity of the problem space with the least possible

number of simulations, to save computational time and cost. Thereafter, because of the complexity of the problem, a

local-search based MOO algorithm is used to discover design points with the best possible behaviour. It will be

guided by the previously found sensitivities. The trade-off of these solutions will be further analysed to identify the

most significant features that contribute to the best behaviour. However, the main disadvantage of such algorithms is

the selection of the initial search point. As a single decision, this determines the overall performance of the

optimizer. In addition, because of the size of the design space, this weakness had to be addressed. Therefore, it was

decided to combine the optimizer with methods from statistics and multivariate analysis to enhance its functionality.

The three-fold idea is to obtain a global preliminary understanding of the problem space, to resolve its sensitivity

and then to appropriately deploy an optimizer in the most promising region, to explore and capture the optimal

behaviour. The aim is to create a sampling plan that uniformly samples the design space and will be used to obtain

global information about the problem. This will help to decide the initial point, the search step and other

configuration settings before launching the optimizer. A variant of Latin Hypercube Sampling (LHS) is enhanced

with orthogonality criteria and utilized in this framework. This method evenly samples the entire design space to

efficiently capture the complexity of the problem. The number of points to sample is pre-determined and is a

fraction of the computational budget considered for the case. This is combined with a lookup table to save

information generated from each simulation and to avoid repeating computation in future stages.

Following the sampling plan provided by the improved LHS, each of the points is evaluated through the defined

objective function. Then, these are ranked for Pareto-dominance, where the non-dominated set is formed. Among

the fitness points of the Pareto Front, one of them is selected randomly and its corresponding decision variables

serve as the initial point for the next phase. If more than one set of decision variables have the same fitness, one of

them will be selected randomly. At this point, all the pairs of decision variables and fitness points will be inserted

into the lookup table.

The second step uses the Pareto Front to estimate the sensitivity of the current optimal set. At the beginning of

this phase, the covariance matrix of the optimal set is calculated. Thereafter, Principal Component Analysis is

applied on the covariance matrix. This returns the principal component coefficients, where the order of the

component’s variance reflects the importance of each component to the data set. The higher the variance of a

decision variable, the more sensitive the optimal set is to a change of that variable. Hence, depending on the search


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state, a larger or smaller step should be selected appropriately. Nevertheless, because the current data set is the

optimal discovered so far, the result of the second step represents the global importance of each decision variable to

the problem. It is noteworthy that this is not the absolute sensitivity of the problem, because it is highly dependent

on the sampled designs. The significance could be used either to reduce the dimensionality of the problem or to

assist in the selection of the initial search step for the third phase. The latter will be applied before launching the

optimization algorithm, because the effectiveness of the whole process is not compromised.

Before beginning the final optimization, a number of important elements are determined; this will make the

optimization search more effective. In particular, the initial point is selected to start from one of the extremes of the

Pareto Front. The search step and the range for each decision variable are individually specified and the remaining

optimization is performed. The algorithm chosen for the optimization phase is the NSGA- II14

; it is a multi-objective

optimization that uses a Non-dominated Sorting Genetic Algorithm (NSGA). Instead of finding the best design, it

tries to find a set of best designs using an elitist approach to preserve best designs from previous generations. If a

design is close to another design, a process called "sharing" is used to penalize such points.

4. Application of the framework

The framework described above has been used in the design process of the CHANGE UAV wing. In this paper,

only results for the landing phase are presented. The reason behind this choice is the fact that it is one of the most

difficult due to the high angle of attack required and it is also a phase where a conventional wing operates outside

the optimal performance region. The aim of the exercise is to find a wing with:

1. Lowest drag possible

2. Low bending moment

3. Angle of attack far from the stall region.

4. Low sensitivity to small changes on the morphing variables.

The requirements of this flight phase are presented in Table 2. From an altitude of 1000ft, the UAV must land

with a descent angle of 10° at a rate of descent of 2.3 m/s.

Table 2: Landing flight phase mission profile

Rate of descent [m/s] Descent angle[°] Altitude[ft]

2.3 -10.0 1000

A. Design of Experiment analysis

The design process follows the methodology described in Section 3. After inserting the mission profile into the

framework, a set of 8000 low-fidelity simulations were run using the full range of the design variables. The number

of simulations chosen was based on the computational budget for this analysis. At the end of this stage the results

were analysed in terms of sensitivities to find the relation between inputs and outputs.

The Principal Component Analysis of the Low-Fidelity Module results, in terms of drag, bending moment and

angle of attack against the design variables presented in Table 1, are presented in Figure 11, Figure 12 and Figure

13, respectively. These plots outline the effect on an output variable with respect to an input variable change. Figure

11 and Figure 12 show that both drag and bending moment are affected primarily by the UBIAct. This effect

dominates the others by a large margin. Of course, this effect was predictable and verifies the correctness of the

framework, as drag and bending moment are strongly linked to span extension. Figure 13 shows that the span

extension and the trailing edge actuator (TEAct1) are the dominant factors for the angle of attack.

Figure 14 shows how the effect of UBIAct is conflicting between drag and bending moment: low values of UBIAct

(wing fully extended) provide minimum induced drag and maximum values of bending moment. This means also

that the problem is non-trivial. A single solution that simultaneously optimizes both objectives does not exist.

Instead, a Pareto front of optimal solutions is obtained. From an aerodynamic point of view, it was decided that the

angle of attack for this flight phase must be lower than 7 degree. The solutions within this constraint are also

presented in Figure 14. .


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Figure 11 – Principal component analysis based on the drag. The red line rapresents the cumulative effect of the

design variables.

Figure 12 – Principal component analysis based on the bending moment. The red line rapresents the cumulative

effect of the design variables.


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Figure 13 – Principal component analysis based on the angle of attack. The red line rapresents the cumulative

effect of the design variables.

a) Bending Moment b) Drag

Figure 14 – Effect of UBIAct setting on bending moment and drag.

Figure 15 shows the Pareto Front of the High-Fidelity Module solutions as extracted by the Pareto Front Module.

The comparison of low-fidelity and high-fidelity solvers is presented in Figure 16 in the form of parallel coordinate

plots. The automatic Pareto Front Module selected a total of 120 high-fidelity simulations. To minimize the

computational requirement, the High Fidelity Module has a parameter that allows the user to automatically stop

simulations that are converging near the stall region or with angle of attack greater than a selected value, in this case

15°. With this in mind, 60 acceptable high-fidelity solutions were obtained. The lower part of Figure 16 shows that

after limiting the angle of attack of the high-fidelity toolset to 7 degree, the region of minimum drag between the

two solvers live in harmony, but, as expected, the actual values differ. The same conclusion can be drawn for the

bending moment.


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This analysis allows two important conclusions to be made:

1. The low-fidelity and the high-fidelity solver are consistent for the landing flight phase and the constraints

considered.

2. Due to the enhanced drag prediction, the optimal configuration must be selected with the high-fidelity

toolset

Figure 15 – High-fidelity results and corresponding Pareto Front.


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a) Full set of simulations.

b) Filtered set of simulations. Angle of attack less than 7 degrees.

Figure 16 – Comparison of low-fidelity and high-fidelity results.

After the principal component analysis the ranges of the design variable for the optimization stage were defined.

Figure 17 illustrates the process used. The process starts with the full set of solutions (a), all DoE data points are

filtered with the angle of attack constraint, (b). This step outlined that the only trailing edge concept that can achieve

the required angle of attack constraint is the TEconcept = 2, the METU concept. The METU concept just uses

TEAct1, hence TEAct2 is removed from the analysis, this is done by fixing its value for the rest of the computation.

The next step is to limit the value of the drag to a range that is 5% from the minimum (c) and after that limit the

bending moment range to 5% variation from this local minimum (d). The choices made are based on the

understanding of the problem and the required solution, other choices are possible, leading to a different set of the

design variables.


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a) Full set of solutions b) Limiting the angle of attack to 7 degree

c) Limiting the drag d) Limiting the bending moment

Figure 17 – Parallel coordinate plot of the DoE data points with the angle of attack constraint

Summarising the above the TEconcept used for the optimization stage is TEconcept = 2 that correspond to METU

trailing edge concept. TEact1 ranges between 0% and 25%. The TEact2 is fixed, because is not used. UBIAct ranges

between 0% and 10%, which correspond to large span. LEconcept, LEact1, LEact2 are not limited during the

optimization

B. Optimization analysis

After the DoE stage, an optimization stage was run to determine the optimal values of the design variables. The

number of simulations budgeted for this stage was 1500. The result of this optimization is presented in Figure 18.

The upper part shows the full set of simulations, while the lower part is filtered for minimum drag. The high-fidelity

parallel coordinates plot is presented in Figure 19. All lines represent multi-objective solutions found during the

optimization, where the final wing is highlighted in blue. This final optimal wing was chosen because it has the

minimum drag.


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a) Full set of simulations.

a) Filtered set of simulations. Low drag and low bending moment.

Figure 18 – Low-fidelity optimization results.


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Figure 19 – High-fidelity optimization results and final solution.

C. Final wing aerodynamic analysis

The parameters of the chosen optimal wing shown in Figure 19 are:

LEconcept = 1. The selected concept for this flight phase is the TUDelft leading edge.

TEconcept = 2. The selected concept for this flight phase is the METU trailing edge.

LEact1 = 95.

LEact2 = 10.

TEact1 = 18

TEact2 =20. Not used

UBIact = 1. Almost full extension

The surface pressure contours of the final wing are presented in Figure 20. It is possible to notice some spikes on

the pressure distribution due to the wing deformation.

Figure 20 – Pressure distribution on the final wing.


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Table 3 presents the angle of attack, bending moment and drag of the final wing from the High-Fidelity Module

simulation. This design has minimum drag and a bending moment that is 30% higher than the minimum value

achieved by other morphing settings.

Table 3 - Final wing aerodynamic data

Angle of Attack Bending Moment [Nm] Drag [N]

5.77 105.47 17.49

Considering the actual value of the design parameters for the leading edge:

LEact1 = 95 implies that the leading edge is deformed in order to generate high lift near the root of the

wing

LEact2 = 10 implies that the deformation is reduced in order to generate less lift in the central wing area

In conclusion the optimization framework provides a wing with higher loading near the root and less loading

toward the tip in order to reduce the bending moment, see Figure 21.

Figure 21 – Spanwise loading distribution.

Nine sections have been used to extract the pressure distribution, the exact locations are presented in Table 4 and

the geometrical position within the wing is shown in Figure 22.

Table 4 – Spanwise slices locations

Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9

0.01 m 0.25m 0.5 m 0.75 m 1 m 1.25 m 1.5 m 1.75 m 1.97 m

Figure 23 display the pressure distributions on these slices. It is possible to see the effect of the morphing

mechanism on the inboard pressure distribution. The lower plot shows smoother pressure distributions if compared

to the upper, with the exception of the last section in which the flow is fully separated. In Figure 24, the section at

0.5 is shown to demonstrate how the pressure ‘bumps’ are related to the morphing mechanism. The dash-dot line

highlights this effect for the trailing edge mechanism.


19

Figure 22 – Location of the sections for the span-wise pressure distribution

a) Inboard wing

b) Outboard wing

Figure 23 – Pressure distribution

Root Tip


20

Figure 24 – Pressure distribution relation with morphing mechanism. The section geometry is presented in

black

5. Conclusions

An optimization framework for the design of a morphing UAV wing has been described. The framework is

multi-disciplinary in nature, taking into account both structural and aerodynamic effects, and multi-fidelity, in that

both low- and high-fidelity aerodynamic capabilities are deployed. The framework has been constructed to allow

complex multi-objective design problems to be examined in a simple and efficient manner, using user-friendly

interfaces. A high degree of automation has been built into the framework, but the ability for the user to interact

effectively with the design process remains, to give freedom for knowledge-based intervention to take place.

The framework has been demonstrated through application to a UAV with various morphing mechanisms: span

extension and smooth deflection of leading- and trailing-edge devices. This UAV is part of a European FP7 project

called CHANGE. The UAV mission has several phases, all of which have been optimized with the framework, but

only optimization of the landing phase is shown herein. The multiple design objectives led to a selection of several

possible morphing set-ups; a single optimum was then chosen based on minimising the drag. In this context, the

importance of using high-fidelity drag computations was demonstrated.

The next phases of the CHANGE project are wind-tunnel testing, to test the morphing mechanisms and to

validate the numerical simulations, and finally a flight test to demonstrate the benefits of the multi-faceted morphing

UAV.

Although the optimization framework has been applied here to a low-speed morphing UAV, it is general in its

applicability and could equally be applied to higher speed morphing vehicles.

Acknowledgements

The work presented herein has been partially funded by the European Community's Seventh Framework

Programme (FP7) under the Grant Agreement 314139. The CHANGE project (Combined morphing assessment

software using flight envelope data and mission based morphing prototype wing development) is a Level 1 project

funded under the topic AAT.2012.1.1-2. involving 9 partners. The project started on 1st 2012 August.


21

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