Citation
Optimization of a Morphing Wing Geometry Using a Genetic Algorithm with Wind Tunnel Hardware-in-the-Loop

Material Information

Title:
Optimization of a Morphing Wing Geometry Using a Genetic Algorithm with Wind Tunnel Hardware-in-the-Loop
Creator:
Boria, Frank J
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (58 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Aerospace Engineering
Mechanical and Aerospace Engineering
Committee Chair:
Ifju, Peter
Committee Members:
Carroll, Bruce F.
Albertani, Roberto
Graduation Date:
8/11/2007

Subjects

Subjects / Keywords:
Aerodynamic coefficients ( jstor )
Aerodynamics ( jstor )
Aircraft wings ( jstor )
Airfoil camber ( jstor )
Airfoils ( jstor )
Drag coefficient ( jstor )
Genetic algorithms ( jstor )
Servomotors ( jstor )
Three dimensional imaging ( jstor )
Wind tunnels ( jstor )
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
aerodynamic, air, aircraft, algorithm, biorobots, boria, change, composite, dic, ga, genetic, hardware, loop, mav, morph, morphing, optimization, shape, uav, vehicle, vic, wing
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Aerospace Engineering thesis, M.S.

Notes

Abstract:
Advancements of compliant actuator technologies and flexible composite structures have enabled true wing morphing capabilities. The resultant effect of these new capabilities is optimal wing shapes for all flight regimes. With the ever-increasing complexity of these morphing wing structures comes the challenge of proper shape management for achieving desirable, real-time flight performance. Using a wind tunnel with sting balance as a hardware-in-the-loop objective function, a genetic algorithm is used for optimizing multiple design variable morphing wing structures. This evolutionary approach to optimization provides a more efficient means of convergence over that of other conventional optimization techniques. There are four primary subsystems utilized in the experimental setup. These include the optimization software, the servo controller, the wind tunnel, and the data acquisition software. Through the use of a simple text-format software, data is passed between each of these subsystems, thereby automating the procedure. A visual image correlation system is used independently during testing to determine the three-dimensional wing shapes of noteworthy servo positions. To demonstrate the procedure, a two design-variable morphing wing is fabricated with the capability of altering maximum camber and trailing edge reflex. Two experiments are conducted for maximizing the lift coefficient and maximizing efficiency. These experiments resulted in optimal servo position versus angle of attack shape functions. Having set the wing shape as a flat plate and again as a medium camber wing with reflex, data is again collected for comparison. These experiments resulted in a comparatively benign stall characteristic, a 63.4% increase in lift coefficient, and up to 62.1% increase in maximum efficiency over that of the fixed wing with reflex. Plotting the performance of the morphing wing with that of the two arbitrary fixed wing shapes illustrates the dramatic improvement achievable by morphing wing structures. Utilizing these procedures allows for real-time adaptive wing morphing to adjust to the instantaneous changes of flight attitude and wind conditions. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2007.
Local:
Adviser: Ifju, Peter.
Statement of Responsibility:
by Frank J Boria.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Boria, Frank J. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Classification:
LD1780 2007 ( lcc )

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hysteresis is shown. Several sweeps from maximum to minimum and intermediate servo

positions are performed to measure the effect of the hysteresis on the lift and drag coefficients.

The drag coefficient versus servo position, shown in Fig. 4-6 (B), is provided to show the

precision of the data. It is selected since it is the least precise of all data provided by the

instrumentation; this is typically an order of magnitude less than that of the lift coefficient. The

subplots shown in Fig.4-6 (C-H) are magnified data sets for lift and drag coefficients at servo

positions 1, 125, and 250. While the plots clearly show aerodynamic hysteresis does exist, the

standard deviation within a given data set is acceptable with a coefficient of variance of no more

than 2.3% for coefficient of lift (Table 4-1), 2.9% for coefficient of drag (Table 4-2), and 3.4%

for efficiency (Table 4-3).

This study shows the effect of the aerodynamic hysteresis is minimal and has little

influence on the data collected. It is in the author's opinion, as supported by this study, that the

effects due to aerodynamic hysteresis can be assumed negligible.

Initial Alpha Sweep for Predicting Convergence

To validate the procedure for determining the optimum wing shape, a preliminary set of

data was collected. The servo used in the model is capable of 1200 rotation, which is

commanded by the servo controller using position points 1 through 250. This range of servo

position is divided into 9 positions that are used to populate lift, drag, and efficiency plots. For

each servo position, data is collected for angle of attacks ranging from -50 through 300 in 2.50

increments (Figure 4-7).

In doing this it can be seen that the lift curves systematically increase as camber increases.

The drag plots show an interesting inversion in trend shape as the camber increases, which is

likely due to the aeroelastic effects of the unconstrained trailing edge. Finally, the efficiency plot













0.2

0.15

0.1

(i 0.05


-0.05

-0.1






Figure 4-5.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I
x/c


Plot of a series of airfoil shapes attained as a function of servo position.









For example, collecting data for a one design variable wing of 10 position increments over

an alpha sweep of 10 angles of attack requires 100 data points. To ensure data validity, these

same data points are typically collected multiple times to ensure precision, which increases the

number of required data points to a minimum of 200. Increasing the models capability through

the use of two design variables increases the number of required data points to 2,000.

Ultimately, the required number of data points increases by an order of magnitude with each

additional design variable. Of course this analysis assumes only 10 position increments are

possible, while the actuators used for this study have 250 position increments.

The use of response surface techniques is a reasonable approach for wings with up to three

and even four design variables. But as the number of design variables grows, it becomes

inefficient. Finding the optimal position of the determined response surface becomes more

difficult to solve. The complexity of the response surface also raises concerns for convergence

upon false, local optimums. The use of this and similar techniques for finding maximum

performance shapes for high-design variable morphing wing structures is ineffective.

Overview

To establish an effective procedure for determining optimal wing shape of a multi-variable

morphing wing, the use of a genetic algorithm with wind tunnel hardware-in-the-loop is

implemented. This procedure is used to determine a specific desired flight characteristic, such as

maximum lift or maximum efficiency. By conducting these optimization tests at several angles

of attack, it becomes possible to obtain optimal wing shapes throughout the range of angles of

attack. Utilizing these data in a control system make it possible to automate real-time wing

morphing for optimal performance during flight. It is the intent of this thesis to present and

implement such a procedure with its proficiencies and detriments.




























To my bride, Rikki









and the data is appended to the same line. The resulting line will consist of servo positions

followed by the lift coefficient, drag coefficient, coefficient of side force, coefficient of pitching

moment, and coefficient of yawing moment. The rolling moment is omitted because the system

yields invalid data. This is of no detriment to these sets of experiments since rolling moment has

no contribution in force and is not utilized as a constraint. At this point, the data acquisition

software waits for the next set of servo positions to be added to the text file. As with the

optimization software, it does this by monitoring the file size. When the new servo positions are

added to the text file, the file size will increase thereby triggering the data acquisition software

for the next set of data.

After the force and moment data have been added to the text file, the optimization software

identifies the increase in file size and retrieves the data. The next servo positions are

commanded, and thereby begin the next cycle.

As with any sting balance, there does exist the concern for signal drift. This sting balance

contains a network of strain gauges that is used to measure the elastic strain of the balance.

These strain gauges are susceptible to signal drift due to temperature variations caused by both

environment and self-heating. To manage the signal drift, the wind tunnel software counts the

number of data sets collected. After the fifteenth data set, the tunnel velocity is set to zero and

the model arm is rotated to the original angle of attack. At this point, the data acquisition

software performs an offset nullification of the strain gauge voltages. The tunnel is then brought

back up to the velocity and angle of attack required by the experiment. This simple procedure

ensures data quality and is set to coincide with the genetic algorithm population size of fifteen.

Visual Image Correlation System

Determining the shape of the morphed wing is essential to quantitatively validate the

obtained solutions. Through the use of the visual image correlation (VIC) system, a non-contact






























































5 I I I I .I


0.6

0.4 I-


** .......,**** Flat Plate
-0.2 -- -- Morphing Wing

-OA4
-5 0 5 10 15 20
Angle of Attack


250 -

200

150

100


a ..s







Servo 1
-- S~ervio 2


Angle of Attack.


Figure 5-8.


Morphing wing data for optimized lift coefficient. A) The morphing wing
performance as compared to the fixed reflex wing and flat plate. B) The optimal
servo positions as a function of angle of attack with the corresponding wing
shape.











Table 4-1. Small coeffcient of variation between the ten base data sets and the random data sets
ensures minimal effect of aerodynamic hysteresis on the coeffcient of lift.


0 Deg


0.14
1.36
1.83
0.34
1.17
0.72
0.19
0.83
0.66


10 Deg


0.32
2.20
1.48
0.21
0.98
0.63
0.38
0.25
0.40


22.5 Deg


1.79
2.28
2.27
0.25
1.45
1.05
0.30
1.36
0.96


Lift coefficient of variations


Base
Random
Overall
Base
Random
Overall
Base
Random
Overall


SP 1



SP 125



SP 250


Table 4-2. Drag data show acceptably low variation between the ten base data sets and the
random data sets.


O Deg


3.07
2.63
2.80
0.56
0.87
0.77
1.29
1.47
1.42


10 Deg


3.40
2.29
2.88
1.85
1.22
1.60
1.05
0.69


22.5 Deg


1.90
1.67
2.04
0.81
1.26
1.47
0.39
1.24


Drag coefficient of variations


Base
Random
Overall
Base
Random
Overall
Base
Random
Overall


SP 1



SP 125



SP 250


Table 4-3. Effciency is found to have a variance of the same magnitude as drag, which is
sumfcient for the procedure to correctly converge upon the optimum servo position.

Efficiency coefficient of variations / Deg 10Dg 25 e


Base
Random
Overall
Base
Random
Overall
Base
Random
Overall


3.05
3.13
3.39
0.54
0.46
0.94
1.22
1.00
1.39


2.23
1.88
2.98
0.92
0.97
1.04
0.47
1.11
0.94


SP 1



SP 125



SP 250









specified waypoint. At this point the vehicle may be required to conduct surveillance, which

would require a wing shape that would yield maximum efficiency for extended flight time. After

completion of surveillance the vehicle may be commanded to return to another waypoint where it

is required to perform a steep descent angle for landing in a small, confined field. The ability to

switch between these distinct optimal wing shape functions is necessary to maximize the overall

performance of a morphing winged aircraft as it transitions between flight modes.









Using the VIC system, a full-field, three-dimensional image of the morphed wing shape, as

shown in Figure 5-2, is developed at 16 servo positions. To illustrate how the airfoil at the wing

root relates to the airfoil at the tip, a topographic plot with airfoil "slices" from the 20% and 80%

span (Figure 5-3) is shown. These servo positions (250,230) yield a +7.1% camber and -2.6%

reflex. For comparison, these plots are also provided for servo positions 1,1 (Figure 5-4) which

is effectively an inverted wing shape of the previous. As plotted in Figure 5-5, an array of airfoil

shapes from the 20% span is illustrated to show the morphing capabilities of the model.

Comparative Lift and Efficiency Curves

In order to determine how well the morphing wing performs, the coefficient of lift and

efficiency versus angle of attack are determined for two Eixed wing shapes. The first shape is an

approximate flat-plate wing obtained by setting servo positions to (130,100) and the second is a

reflex wing obtained using servo positions (250,110). Note the abrupt stall of the flat plate

(Figure 5-6) at approximately 110 and its poor efficiency throughout the alpha sweep. The wing

with reflex has less aggressive stall characteristics at approximately 150 angle of attack with a

much higher lift coefficient than that of the flat plate wing. It also has a much higher efficiency,

which carries over a large range of angles of attack.

This data is used as a comparative tool to measure the performance of the morphing wing

shapes. The optimization procedure for maximum lift, then maximum efficiency for several

angles of attack is performed. The results from these experiments are plotted with the two fixed

wing shapes and evaluated for improved performance.

Maximizing Coefficient of Lift Curve

The optimization procedure is conducted for six angles of attack from -50 to 200 in 50

increments, which is sufficient for evaluation of its performance. The result of the experiments

yield wing shapes that produce maximum lift for a given angle of attack. By fitting a curve









LIST OF REFERENCES


[1] Haenel, R. T., "Creep Deformation of Pin-Jointed Structures," MS Thesis, The
Pennsylvania State University, Pennsylvania, 1955.

[2] Gooders, J., and Pledger, M., "Birds of North America," Edison, New Jersey: Chartwell
Books Inc., 1987.

[3] Davidson, J., Chwalowski, P., and Lazos, P., "Flight Dynamic Simulation Assessment of
a Morphable Hyper-Eliptic Cambered Span Winged Configuration," 2003 AIAA Atmospheric
Flight Mechanics Conference and Exhibit, Austin, TX, AIAA Paper 2003-5301, 2003.

[4] Shyy, W., Berg, M., and Ljungqvist, D., "Flapping and Flexible Wings For Biological
and Micro Air Vehicles," Progress in Aerospace Sciences, Vol. 35, No. 5, 1999, pp. 455-506.

[5] Ifju, P., Jenkins, D., Ettinger, S., Lian, Y., and Shyy, W., "Flexible-Wing Based Micro
Air Vehicles," AIAA Publication, AIAA Paper 2002-0705, 2002.

[6] Albertani, R., Hubner, J., Ifju, P., Lind, R., and Jackowski, J., "Experimental
Aerodynamics of Micro Air Vehicles," SAE World Aviation Congress and Exhibition, Reno,
NV, 2004.

[7] Stanford, B., Abdulrahim, M., Lind, R., Ifju, P, "Investigation of Membrane Actuation
for Roll Control of a Micro Air Vehicle," Journal of Aircraft, Vol. 44, No. 3, 2007, pp. 741-749.

[8] Gano, S., Renaud, J., Batill, S., and Tovar, A., "Shape Optimization for Conforming
Airfoils," 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials
Conference, Norfolk, Virginia, AIAA Paper 2003-1579, 2003.

[9] Gano, S., and Renaud, J., "Optimized Unmanned Aerial Vehicle with Wing Morphing for
Extended Range and Endurance," 9th AIAA/ISSMO Symposium and Exhibit on
Multidisciplinary Analysis and Optimization, Atlanta, GA, AIAA Paper 2002-5668, 2002.

[10] Waszak, M., Davidson, J., and Ifju, P., "Simulation and Flight Control of an Aeroelastic
Fixed Wing Micro Aerial Vehicle," 2002 AIAA Atmospheric Flight Mechanics Conference and
Exhibit, Monterey, CA, AIAA Paper 2002-4875, 2002.

[1l] Skillen, M., and Crossley, W., "Modeling and Optimization for Morphing Wing Concept
Generation," NASA Publication CR-2007-214860, March 2007.

[12] Albertani, R., "Experimental Aerodynamic and Static Elastic Deformation
Characterization of Low Aspect Ratio Flexible Fixed Wings Applied to Micro Aerial Vehicles,"
Ph.D. Dissertation, University of Florida, Gainesville, FL, 2005.

[13] Sytsma, M., "Aerodynamic Flow Characterization of Micro Air Vehicles Utilizing Flow
Visualization Methods," MS Thesis, University of Florida, Gainesville, FL, 2006.









OPTIMIZATION OF A MORPHING WINTG GEOMETRY USING A GENETIC
ALGORITHM WITH WINTD TUNNEL HARDWARE-IN-THE-LOOP


















By

FRANK JO SEPH BORIA


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2007












Loop 1


Sing Balance
Data
Acquisition


Loop 2


Genetic
Algorithm


Figure 3-4.


These flowcharts illustrate how data is appended to the shared text file.


Servo
Controller









full-Hield shape and deformation tool, the wing shape can be captured and evaluated for any

given morphed configuration. A typical experimental setup with the VIC system is illustrated in

Figure 3-5. This process was developed in the mid 1990s by Helm with a reported resolution on

the order of + 0.05 mm [32].

The specimen is first uniformly painted with a low-luster color, and then painted with a

highly contrasting, random speckle pattern. Two digital cameras carefully focused on the

specimen. The cameras are triggered such that an image from each is acquired instantaneously.

A plate with high contrast dots of known diameter and spacing is used to calibrate the camera

system. Photos of the plate in different locations of the image frame and at varying angles and

rotations are taken and processed for calibration. After the calibration procedure is complete, the

precise orientation of one camera to the other is known. At this point, the system is now ready to

photograph the specimen. From these images, the software is capable of developing the full-

Hield three-dimensional shape of the specimen using stereo triangulation.

The system is also used to determine deformation of a specimen under load. By first

taking a no-load reference image of the specimen, then taking another image of the loaded

specimen, the software is capable of calculating the displacement Hield. This is useful for

determining how much deformation a wing undergoes when in flight.











80% Span
0."1
-0.1 ---
m 0 05


xr,


II :


80)% Span



D 0.5
x/c


x
lli ~I


-026 0.011 .270.060 0 07Il


Figure 5-3.


Morphed wing surface (Servo Positions: 250,230) with airfoil slices from the 20%
and 80% span yields a negative camber and negative reflex.


O
~r


20% Span



010 0 5 1
x/c


-0).078 -0.05 -0.022 0.0066 .035


Figure 5-4.


Morphed wing surface (Servo Positions: 1,1) with airfoil slices from the 20% and
80% span yields a positive camber and positive reflex.


20% Span
0.1 -

-0.1 * * *'
0 0.5 1











[ 27] Kammeyer, M., Wind Tunnel Facility Calibrations and Experimental Uncertainty, The
Boeing Company, American Institute of Aeronautics and Astronautics, 1998.

[28] Springer, A., "Uncertainty Analysis of the NASA MSFC 14-Inch Trisonic Wind Tunnel,"
1999 37" AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA-99-0684, 1999.

[29] Lopez-Anido, R., El-Chiti, F., Muszyfiski, L., Dagher, H., Thompson, L., and Hess, P.,
"Composite Material Testing Using a 3-D Digital Image Correlation System," American
Composites Manufacturers Association, Tampa, Florida, 2004.

[30] Muszyfiski, L., Lopez-Anido, R., and Shaler, S., "Image Correlation Analysis Applied to
Measurement of Shear Strains in Laminated Composites," SEM IX International Congress on
Experimental Mechanics, Orlando, Florida, 2000.

[31] Schmidt, T., Tyson, J., and Galanulis, K., "Full-Field Dynamic Displacement and Strain
Measurement Using Advanced 3-D Image Correlation Photogrammetry," Part I. Experimental
Techniques, Vol. 27, No. 3, 2002, pp. 47-50.

[32] Helm, J., McNeill, S., and Sutton, M., "Improved 3-D Image Correlation for Surface
Displacement Measurement", Optical Engineering, Vol. 35, No. 7, 1996, pp. 1911-1920.










procedure did accurately converge upon the correct servo positions. This is because although the

drag forces may be very low, they are consistently low; i.e. precise though not accurate.

These results support high confidence in the optimization procedure. The genetic

algorithm is capable of proper convergence despite the variance in collected wind tunnel data. It

is in the author' s opinion that the procedure will effectively determine optimal wing shapes for

wings with multiple design variables and of higher morphing capability.









CHAPTER 5
OPTIMIZATION OF A HIGH-FIDELITY MORPHING WING

A high-fidelity morphing wing model is fabricated to demonstrate the advantage of the

morphing wing geometry over that of conventional Eixed wing geometries. Initial coefficient of

lift and efficiency curves are developed for flat plate and reflex wings. This data is used as a

comparative tool to measure the performance of the morphing wing shapes. The optimization

procedure is conducted for maximum lift and maximum efficiency through a range of angle of

attacks. All experiments are conducted with an unconstrained genetic algorithm.

Model Description

This model is an elliptical planform, thin plate wing (Figure 5-1) consisting of a single

layer, plain weave carbon fiber skin and arced unidirectional carbon fiber spars, which follow the

outer curvature of the planform. As with the one-design-variable model, these spars transfer

loads such that when the wing shape is altered at the root, a similar shape will transfer

throughout the span of the wing. While the model is not capable of transferring the exact airfoil

from the root to the tip it does significantly change the wing shape, which is desired for this

experiment.

The model has two points of actuation, which are positioned at the quarter chord and the

trailing edge. There are two attachment points fixing the wing to the fuselage structure, which

are located at the leading edge and trailing edge. The attachment point at the leading edge

permits rotation only. The attachment point at the trailing edge permits both rotation as well as

longitudinal, linear motion. The quarter chord actuation point significantly modifies the wing

camber on the order of a 1 1%, while the trailing edge point of actuation allows for & 4% wing

reflex.











































Figure 3-5.


This illustration depicts the VIC system hardware setup about a wind tunnel test
section.














. Mean Best


. *
r***. e*


0


h-2


Generation


x x





x
x
x


200 E


xxx


150 E


100 E


X X
x


0 50 100 150
Servo 1 Position

Initial Pop~ulation


Final Pop~ulation


Member


Member


Figure 5-9.


Sample plots showing the convergence of the genetic algorithm on the optimal
servo position for maximum efficiency at 100 angle of attack.


.~ 200 ~ 200

I 11 11111111111111 1 II I ~

~'"I IIIII1IIIIIII~II~I~L LI~1 "100
rn 1 1111111111111111111 1111 v,
0 I~IIILLLLL.IlILIIL.IL11-111.1 0
0 5 10 15 20 25 0 5 10 15 20 25





.r




w/e


lip ir


_ _~ _~


IEtsr ~I


-0.0723


-0.0287


0.0149 -0.00953
Serve Position I


0.0004C62


0.0105


0.05 I-


-0.05


- Wind On


I


-0 1


0,1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 0,9


Figure 4-3.


Wing shape attained by servo position 1 with velocity at 0 and 16 m/s at 100
AOA. The top left image shows the wind off Z-coordinates of the wing in
millimeters. The top right image shows the wind on wing deformation.


I 1


Y

r


-0.0104

0.2

0.15



0.05


0,0913


0.193 -0.0110
Serve Porsition 250)


0.0303


0.0715


0 0. I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I
x/c

Wing shape attained by servo position 250 with velocity at 0 and 16 m/s at 100
AOA. The top left image shows the wind off form of the wing in millimeters.
The top right image shows the wind on wing deformation, also in millimeters.


Figure 4-4.


I i


--~IIIIEFC-i
ICL-Z1F I







































Figure 4-1.


The one-design-variable, rectangular planform model used to validate the

optimization process has a single point of actuation that alters camber.


Z [mm]
11 307
10 264
9 22102
817805
71350B


400618
2 96321
-1 92024


Figure 4-2.


The full field, three-dimensional image, developed by the VIC system, is overlaid
on an image of the morphed wing illustrating deformation in the Z-direction (left

image has 19% camber, right image has -7% camber).









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

OPTIMIZATION OF A MORPHING WINTG GEOMETRY USINTG A GENETIC
ALGORITHM WITH WINTD TUNNEL HARDWARE-IN-THE-LOOP

By

Frank Joseph Boria

August 2007

Chair: Peter Ifju
Major: Aerospace Engineering

Advancements in compliant actuator technologies and flexible composite structures have

enabled true wing morphing capabilities. The resultant effect of these new capabilities is optimal

wing shapes for all flight regimes. With the ever-increasing complexity of these morphing wing

structures comes the challenge of proper shape management for achieving desirable, real-time

flight performance.

Using a wind tunnel with sting balance as a hardware-in-the-loop obj ective function, a

genetic algorithm is used for optimizing multiple design variable morphing wing structures. This

evolutionary approach to optimization provides a more efficient means of convergence over that

of other conventional optimization techniques.

There are four primary subsystems utilized in the experimental setup. These include the

optimization software, the servo controller, the wind tunnel, and the data acquisition software.

Through the use of a simple text-format software package, data is passed between each of these

subsystems, thereby automating the procedure. A visual image correlation system is used

independently during testing to determine the three-dimensional wing shapes of noteworthy

servo positions.









CHAPTER 1
INTRODUCTION

No longer are aircraft confined to fixed wing geometries suiting a single flight regime.

The advancements of actuation and material technologies have enabled true morphing

capabilities. The resultant effect of these new capabilities is optimal wing shapes for all flight

regimes. With the ever-increasing complexity of these morphing wing structures comes the

challenge of proper shape management for achieving desirable, real-time flight characteristics.

The work presented in this thesis is one approach to such a challenge.

Emulating Biological Structures

The study of ornithology shows that each species of bird has evolved to become uniquely

specialized within their habitat. From the perspective of the aerodynamicist, designing an

aircraft to emulate the performance of the falcon for high speed dives, the eagle for highly

efficient soaring, the hovering capability of the humming bird, or the agility of the swift would

be of great value. Ultimately, however, melding each of these desirable flight characteristics on

a single aircraft is the true obj ective. Such a versatile vehicle could achieve remarkably high lift,

for maximum payload capacity, high speed, to quickly move from waypoint to waypoint, and

high efficiency. Utilizing a morphing wing structure for asymmetric deformations would yield

the ability to maneuver with high agility through complicated urban environments. Such a

vehicle could also maintain stability during the most volatile of flight conditions, such as erratic

and gusting winds among buildings and structures.

Utilizing thin plate composite materials with multiple actuation points, it is possible to

create a morphing wing capable of complex deformation. A noteworthy study on similar

materials with regard to creep is presented by Richard Thomas Haenel [1], which details the










lightweight and very effective although precaution must be taken to prevent variations in

temperature, which will affect its performance.

These, and many other, compliant forms of actuation have been developed and utilized for

morphing wing structures. Extensive work on adaptive shape change problems, which determine

methods for morphing a given curve or shape into a target curve or shape, is providing solutions

with a minimal number of actuators [18]. This work leads to the challenge of morphing a wing

not to a single target shape, but rather to adaptively morph the wing real-time during flight to

adjust to the instantaneous changes of flight attitude and wind conditions.

Optimization Techniques for Acquiring Desired Wing Shapes

The use of evolution strategies for optimization of complex design problems began back in

the early sixties [19] and has been gaining momentum over the past fifteen years. Such

strategies emphasize selection, recombination and mutation of a given population to determine

the makeup of the next population set [20]. Each of the members of this new generation is then

evaluated for fitness. Poor performing members are rej ected from the next generation while high

performing members are retained. This results in convergence upon an optimal solution after

multiple generations.

The use of a genetic algorithm (GA) has advantages over other techniques when searching

within a complex domain. Due to its evolutionary tactics, the GA is resistant to convergence on

local optimums making it better suited for finding true global optimums. It is also capable of

working with many design variables, which can be discrete, continuous, or mixed [21], [22],

[23].

As morphing wing structures become more complex, the GA solver becomes better

preferred. Studies have already shown the effective use of the GA to optimize fixed airfoil and

wing shape [24] and to better develop composite wings for desired structural characteristics [23].

























ii ******* Flat Plate

sj -- orphing Wing
-5 0 5 10 15 20 25
Angle of Atlacki










oj 250 a
o
ta 200 -' -
S1o e.I


100

50 C r Servo I
-*- Servo 2

-5 0 5 10 15
Angle of Attack



Figure 5-10. Morphing wing data for optimized efficiency. A) The morphing wing performance
as compared to the fixed reflex wing and flat plate. B) The optimal servo
positions as a function of angle of attack with the corresponding wing shape.












TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS .............. ...............4.....


LIST OF TABLES ........._._ ...... .__ ...............7....


LIST OF FIGURES .............. ...............8.....


AB S TRAC T ............._. .......... ..............._ 10...


CHAPTER


1 INTRODUCTION .............. ...............12....


Emulating Biological Structures ................. ...............12........... ....
Optimization of Morphing Wing Structures ................. ...............13........... ...
Motivation............... ...............1
Overvi ew ................. ...............14.................


2 LITERATURE REVIEW .............. ...............16....


Emulating Desirable Wing Shapes .............. ...............16....
Actuation of a Morphing Wing Structure ................. ............ ............... 17. ...
Optimization Techniques for Acquiring Desired Wing Shapes .............. ....................18
Hardware for Data Collection ................. ...............19................
Wind Tunnel Uncertainty Analysis .............. ...............19....
Visual Image Correlation System ................. ...............19................

3 EXPERIMENTAL SETUP AND DATA ANALYSIS ................... ...............2


W ind Tunnel .............. ...............20....
Servo Controller............... ...............2
Software Description .............. ...............21....
Visual Image Correlation System .............. ...............22....

4 ONE DESIGN VARIABLE MODEL .............. ...............27....


Model Description and Purpose ................. ...............27................
A Study of Aerodynamic Hysteresis .......__ ..........._ .......___ ....._ .........28
Initial Alpha Sweep for Predicting Convergence .............. ...............29....
Validation of Optimization Procedure ....._____ ................... ............3

5 OPTIMIZATION OF A HIGH-FIDELITY MORPHING WINTG .............. ..................40


Model Description .............. ..... ...............40.
Comparative Lift and Efficiency Curves ................ ...............41........... ...














- SPI
---- SP30
----SP60

~--------- SPl20

SPl50
----- SPI80
~-----SP215
-- SP250










-- SPI
---- SP30
----SP60
----SP90
-- --SPl20
SPl50
- SPl80~
----SP215
~-----SP250










---- SPI
- SP30,
~-----SP60
--------SP90
----SPl20

----SPI80
-----SP215
-- SP250


I

-l

0p 0.5

0












0.5
do


' 0.4



8 0.2


0.1











"4





za


0 5 10 15 20 25
Angle of Attack


0 5 10 15 20) 25
Angle of Attack


0 5 10 15 2025
Angle of Attack


Figure 4-7.


Lift coefficient, drag coefficient, and efficiency versus angle of attack are plotted
for several servo positions of the one design variable model.










LIST OF TABLES


Table Page

4-1 Small coefficient of variation between the ten base data sets and the random data sets
ensures minimal effect of aerodynamic hysteresis on the coefficient of lift. ................... .33

4-2 Drag data show acceptably low variation between the ten base data sets and the
random data sets............... ...............33..

4-3 Efficiency is found to have a variance of the same magnitude as drag, which is
sufficient for the procedure to correctly converge upon the optimum servo position.......33









CHAPTER 4
ONE DESIGN VARIABLE MODEL

Model Description and Purpose

To validate the procedures for data collection, a simple one-design-variable model is

utilized. This model is a thin plate wing of rectangular planform with a single point of actuation

that changes the wings camber. The wing consists of a single layer, plain weave carbon fiber

skin and horizontally aligned unidirectional spars that run from wingtip to wingtip every one

inch from the leading edge (illustrated in Figure 4-1). These spars transfer loads such that when

the wing shape is changed at the root, the same shape will be attained at the tips effectively

resulting in an extruded airfoil along the span of wing.

An attachment point at the leading edge permits rotation only. An attachment point at the

70% chord permits both rotation and longitudinal motion. The unconstrained trailing edge allows

for significant deformation when under load. This deformation is an aeroelastic effect caused by

the interaction among inertial, elastic, and aerodynamic forces on the wing. Typical CFD is

expensive when attempting to model this aeroelastic effect, let alone optimize a morphing wing,

and is why this tunnel-in-the-loop procedure is of particular value. Using the VIC system, the

wing shape is determined. It is shown as a topographical overlay on an image of the wing itself

in Figure 4-2. The wind-on deformations, and the airfoils associated with each, are plotted in

Figure 4-3 for servo position 1 (a negatively cambered wing) and Figure 4-4 for servo position

250 (a highly cambered wing).

The model is capable of altering the maximum camber between -7% through 19%.

Utilizing the VIC system, 9 servo positions are selected and photographed to determine the range

of attainable wind-off wing shapes. The normalized airfoils are plotted in Figure 4-5, which help

to illustrate the magnitude of camber change.









Servo Controller

Each morphing wing developed for these experiments utilizes Futaba S3102 servo

actuators to attain the surface deformation. These servos supply 4.6 kg-cm of torque and a rate

of 600 in 0.2 seconds. Using Matlab, servo number and position are commanded through the

serial port in a 1200-baud rate, 8-bit, 1-stop, and no-parity form. A sub-module converts the

RS232 signal to transi stor-to-transistor logic. Receiving the signal on the morphing wing

structure is a custom servo controller (Figure 3-3) designed and fabricated by Scott Bowman.

This controller features 8 kilobytes of flash memory, a 16-bit high-resolution servo timer, and an

8 MHz ATMEL microprocessor. This servo controller is designed to set and hold commanded

servo positions while the wing undergoes aerodynamic loading.

Software Description

The two primary software packages used for this study are LabVIEW for wind tunnel

control and data acquisition and Matlab for wing morphing control and optimization. A flow

chart of how the information is passed between the programs is shown in Figure 3-4. To initiate

the optimization procedure, an initial population is prescribed to the genetic algorithm. When

the algorithm is started, the first member of the initial population is sent to the subroutine that

commands the servo controller. The servo controller then sets and holds each servo position

thereby morphing the wing. Simultaneously, the servo positions are sent to a text file. At this

point, the genetic algorithm waits for the force and moment data that is associated with the servo

positions to be added to the text file. It determines when this happens by monitoring the text file

size.

While the optimization software is on hold for data, the wind tunnel is brought up to the

required velocity. After the angle of attack is set, the force and moment data are determined

from the sting balance. The text file previously created by the optimization software is accessed









CHAPTER 2
LITERATURE REVIEW

Through the use of unmanned aerial vehicles it becomes possible to conduct dangerous

missions without endangering the life of a pilot. These vehicles are becoming smaller with

missions that require significant agility for navigating complex urban environments. To see a

bird navigate through such an environment will inspire the concept of its emulation. Through the

ever-maturing field of material science, the morphing capabilities of an aircraft wing are more

capable of simulating a bird in flight.

Emulating Desirable Wing Shapes

The complex system of structural members and joint articulation of a bird' s wing [2] is

difficult to duplicate mechanically with regard to function as well as low weight and high

durability. Studies associating wing shape to function are conducted to differentiate

requirements for static aerodynamics, physiology, and flapping control [3].

Understanding this differentiation leads to morphing wing structures of less complexity

than that of the birds wing. For example, while birds have many layers of feathers that are

moved around to adjust to the specific maneuver they need to perform [4], morphing wing

structures can be fabricated of thin sheet materials, which are manipulated to yield the desired

wing shape.

Currently, many unmanned aerial vehicle designs are based on a flexible wing design

developed at the University of Florida [5],[6]. These thin, flexible wings are beneficial for

dampening the effects of wind gusts and increasing stability during adverse flight conditions.

With regard to wing morphing, they are also easily manipulated for desired control and overall

flight performance using minimal actuation points. An example of this is morphing in the form

of asymmetric wing twist making it is possible to surpass the roll rates of conventional aileron









evaluation of creep with respect to material deformation. Careful design of such a wing will

yield configurations that significantly outperform conventional Eixed wing geometries.

Optimization of Morphing Wing Structures

When a given structure is created to emulate the complexities of what exists in nature, a

method must also be developed to command the structure to take a desired shape. A high Eidelity

morphing wing with several actuation points will require a complex control system. The once

rigorous determination of aerodynamic performance for conventional Eixed wing geometries has

become an even greater undertaking in multi-variable shape optimization.

While the Hield of computational fluid dynamics continues to improve, modeling complex

structures of composite makeup remains expensive. It is also difficult to accurately model the

aeroelastic effects on such a structure when it is under load. This becomes increasingly the case

when utilizing thin plate wings. While the use of a wind tunnel may also be expensive, it

provides a source for aerodynamic force data, which take full account of wing deformations due

to aeroelastic effects.

Regardless of the method used for determining aerodynamic forces, a procedure for

optimization must be properly matched to the capability of the wing structure. While a response

surface approach may be well suited for morphing wings with minimal design variables, high-

fidelity morphing wing structures may be more efficiently optimized through the use of a genetic

algorithm. The genetic algorithm is better capable of finding a global optimum more efficiently

than many strategies.

Motivation

The use of a genetic algorithm for optimizing high-fidelity, multiple design variable

morphing wing structures provides a more efficient means of convergence over that of other

conventional optimization techniques.









BIOGRAPHICAL SKETCH

Frank Boria was born in Portsmouth, New Hampshire and spent most of his childhood in

York, Maine. When he was 13 years old, he and his family moved to Fernandina Beach, Florida.

During his junior year of high school, Frank won a scholarship to train for his private pilot

license. Having trained in a Citabria 7ECA, a tandem two-seat tail-dragger, Frank received his

pilot license and developed a passion for aviation.

After high school he moved to Tallahassee, Florida where he attended Lively Technical

Center and received his Airframe and Powerplant certifieations. With these certifieations he

moved to Lake City, Florida where he spent 7 years working at TIMCO, a third-party aircraft

repair station. His experience was primarily focused on aircraft structures for DC9, Boeing 727,

and C130 aircraft. With the understanding of how to fly and maintain an aircraft, his interests

leaned toward understanding the physics of flight and the process of design.

During the final 2 years of work at TIMCO, Frank attended evening classes at Santa Fe

Community College where he received his Associate of Arts degree. He transferred to the

University of Florida where, in 2004, he received his Bachelor of Science degree in aerospace

engineering. He continued his education at the University of Florida, and in 2007, he received

his Master of Science degree in aerospace engineering with a focus on solid mechanics, design,

and manufacturing. Frank now resides in Gainesville, Florida with his beautiful bride, Rikki,

and three wonderful children, Addie, Olivia, and Christian.









ACKNOWLEDGMENTS

This work has been made possible through funding and facilities provided by the

University of Florida and BioRobots, LLC. Many thanks in particular go to Dr. Peter Ifju for his

guidance, leadership, and ability to meld science with low-quality humor. Another thank you

goes to Dr. Roberto Albertani for his guidance on wind tunnel operation and his incessant

support of the metric system, despite its obvious illogical basis (long live the slug). And yet

another thank you goes to Dr. Bruce Carroll for so strongly supporting my work during this final

task.

I thank Bret Stanford for his thoughts and input throughout my research, whose insight

and experience helped to create the framework of these experiments. I am very appreciative of

Scott Bowman for his design, fabrication, and programming of a sophisticated morphing wing

controller that was used to conduct this research.

I am forever grateful and indebted to Frank and Joanne Boria for raising me with love and

compassion while teaching me faith, respect and commitment. They are both remarkable parents

and phenomenal role models. I will always look to them for guidance.

To Julie Badger, Carl Boria, and Elizabeth Nettles, I am thankful for their strength of

support, their being there to listen, and their reminding me of birthdays and anniversaries. To

you, my brother and sisters, I gratefully dedicate the last figure of the fifth chapter.

I would like to thank my children, Addie Reith for contributing her skills in photography,

Olivia Reith for her remarkable contribution of digital photo editing, and Christian Boria for

thinking that morphing airplanes are really, really cool. I love them all.

Finally, I thank my bride, Rikki, for her never-ending support, love, and inspiration. She

has brought me great j oy, true happiness, and has taught me to live life with abandon. I am

forever thankful to her for being genuine, refreshingly enthusiastic, and mine.










[14] Bilgen, O., Kochersberger, K., Diggs, E., Kurdila, A., and Inman, D., "Morphing Wing
Aerodynamic Control via Macro-Fiber-Composite Actuators in an Unmanned Aircraft," 2007
AIAA Conference and Exhibit, Rohnert Park, CA, AIAA Paper 2007-2741, 2007.

[15] Williams, R., Inman, D., and Keats-Wilkie, W., "Nonliniear Mechanical Behavior of
Macro Fiber Composite Actuators," Center for Intelligent Material Systems and Structures,
Department of Mechanical Engineering, Virginia Polytechnic Institute and State University,
Undated material.

[16] Claverie-Bohn, C., "Dynamic Antifouling Structures and Actuators Using EAP
Composites," Ph.D. Dissertation, University of Florida, Gainesville, FL, 2004.

[17] Strelec, J., Lagoudas, D., Khan, M., and Yen, J., "Design and Implementation of a Shape
Memory Alloy Actuated Reconfigurable Airfoil," Journal ofhitelligent Material Systems and'
Structures, Vol. 14, No. 4-5, 2003, pp. 257-273.

[18] Lu, K., and Kota, S., "Design of Compliant Mechanisms for Morphing Structural
Shapes," Journal ofhitelligent Ma'~terial Systems and' Structures, Vol. 14, No. 6, 2003, pp. 379-
391.

[ 19] Rechenberg, I., "Evohitionsstrategie: Optintierung technischer Systeme nach Prinzipien
der biologischen Evohition," Frommann-Holzboog, Stuttgart, 1973.

[20] Whitley, D., "An Overview of Evolutionary Algorithms," Journal ofhifornzation and'
Software Technology, Vol. 43, 2001, pp. 817-831.

[21] Rasheed, K., and Hirsh, H., "Learning to be Selective in Genetic-Algorithm-B ased
Design Optimization," Artificial hItelligence for Engineering Design, Analysis and'
Manufacturing, Vol. 13, 1999, pp. 157-169.

[22] Herrera, F., Lozano, M., and Molina, D., "Continuous Scatter Search: An Analysis of the
Integration of Some Combination Methods and Improvement Strategies," European Journal of
Operational Research, Vol. 169, No. 2, 2006, pp. 450-476.

[23] Herrera, F., Lozano, M., and Sanchez, A., "Hybrid Crossover Operators for Real-Coded
Genetic Algorithms: An Experimental Study," Soft Comput, Vol. 9, 2005, pp. 280-298.

[24] Nauj oks, B., Willmes, L., Haase, W., Back, T., and Schtitz, M., "Multi-point Airfoil
Optimization Using Evolution Strategies," European Congress on Computational Methods in
Applied Sciences and Engineering, Barcelona, 2000.

[25] Liu, B., "Two-Level Optimization of Composite Wing Structures Based on Panel Genetic
Optimization," Ph.D. Dissertation, University of Florida, Gainesville, FL, 2001.

[26] Hemker, T., "Hardware-in-the-Loop Optimization of the Walking Speed of a Humanoid
Robot," CLAWAR 2006, Brussels, Belgium, 2006.









sufficiently throughout the range of servo positions. A large gap in the scatter will raise

concerns that the true global optimum may have been missed.

By setting the angle of attack to 100, high lift and drag forces are ensured. Three

optimization experiments are conducted to determine which servo position maximizes lift. As

shown in Figure 4- 8 (D), each experiment converged on a value that exceeded or matched the

predicted value. All three experiments converged to servo position 250, which is associated with

the greatest camber. Due to the variance in lift data, the lift coefficient associated with the

optimal servo position will never converge closer than 2.3% of one another. This does not,

however, prevent the genetic algorithm from properly converging on that optimal servo position.

Due to the low coefficient of variance and the rapid convergence on the optimum servo

position, it is in the author' s opinion that the procedure will accurately converge to the optimum

value regardless of angle of attack. For this reason, the second sets of convergence experiments

for optimal effciency are conducted.

Continuing to hold the angle of attack at 100, three convergence experiments for

determination of maximum efficiency are conducted. Since the coefficient of variance for

effciency is much higher than that of lift, other angles of attack are tested. As shown in Figure

4- 8 (F), each of the three experiments converges on servo position 134 with a maximum

effciency of 5.56. While this value is below that of the predicted value, it does exist within the

previously calculated variance and did converge on the predicted servo position.

Because the coeffcient of drag is very low at 00 and lift will become negative at -50 angle

of attack, the efficiency may vary considerably. For this reason they are tested to ensure proper

convergence. These results are plotted in Figure 4- 8 (F). As illustrated, the optimization












Maximizing Coeffieient of Lift Curve ................. ...............41........... ...
Maximizing EfH ciency Curve............... ...............43.


6 CONCLUSION AND RECOMMENDATIONS FOR FUTURE WORK ................... .....52


Conclusion ............... ........ ........... .........5
Recommendations for Future Work. ........._._.. ....__. ...............53..


LIST OF REFERENCES ........._.___..... .___ ...............55....


BIOGRAPHICAL SKETCH .............. ...............58....





0 50 100 150 200 25
Servo 1 Position


Initial Population


S200 -


o 100.

n *


Final Population









5 10 15 20 25
Member


-0.5~

-1


...8r*********


Mean *Best


1.5 E


Generation





x






x






X
X
X


200E


160 E


100 E


XXX
XXx


.1 200


o '100


0 5 10 15
IMember


20 25


Figure 5-7.


These sample plots illustrate the convergence of the genetic algorithm upon the
optimal servo position for maximum lift at 100 angle of attack.









configurations [7]. Another example is the exercise in design optimization conducted by Gano et

al. [8],[9] for a single, high endurance wing that separates into a second wing for greater agility.

Much work has been done to assess the flight characteristics of these flexible wings.

NASA has performed a control assessment and simulation of a micro air vehicle with aeroelastic

wings which adapt to the disturbances during flight [10]. Morphing wing weight equations and

an approach to size morphing aircraft [1 1] are developed to replace current methods of general

heuristics based on fixed wing aircraft. Also, extensive wind tunnel tests on a variety of flexible

wing configurations showed a decrease in wing incidence, an increase in dihedral and a shift in

maximum camber position that results in a favorable change in pitching moment and lift.

Ultimately, smoother flight characteristics are achieved over that of conventional fixed wings

[12]. A variety of experimental flow tests are conducted on these wings using surface oil flow

visualization, laser based flow visualization, and particle image velocimetry with results that

validate previously determined CFD results [13].

Actuation of a Morphing Wing Structure

Advancements in actuator technologies for these compliant wing structures, such as Macro

Fiber Composites (MFC), Electroactive Polymers (EAP), and Smart Memory Alloys (SMA), are

yielding lightweight, capable devices. The thin, compliant MFC is a type of piezoceramic

composite actuator that is constructed of orthogonal layers of unidirectional piezoceramic fibers

and copper electrodes encased in layers of acrylic and Kapton [14]. These actuators have been

reported to produce high strain levels on the order of 2000 CLE [15]. Alternatively, the EAP

actuator is similar to muscle tissue with regard to stress and force capability. This actuator is

capable of large-scale linear motion [16]. Another source of actuation is through the use of an

SMA mechanism. These mechanisms consist of a metallic alloy that act as linear actuators by

contracting when heated and returning to their original shape when cooled [17]. This actuator is
































O 2007 Frank Joseph Boria









To demonstrate the procedure, a two design-variable morphing wing is fabricated with the

capability of altering camber and trailing edge reflex. Two experiments are conducted for

maximizing the lift coefficient and maximizing efficiency. These experiments result in optimal

servo position versus angle of attack shape functions. Setting the wing shape as a flat plate and

again as a medium camber wing with reflex provides comparative data. These experiments

resulted in a comparatively benign stall characteristic, a 63.4% increase in lift coefficient, and up

to 62. 1% increase in maximum efficiency over that of the Eixed wing with reflex. Plotting the

performance of the morphing wing, with that of the two arbitrary Eixed wing shapes, illustrates

the dramatic improvement achievable by morphing wing structures. Utilizing these procedures

allows for real-time adaptive wing morphing to adjust to the instantaneous changes of flight

attitude and wind conditions.









Maximizing Efficiency Curve

Efficiency is calculated by dividing the lift coefficient by the drag coefficient. As

determined in Chapter 4, the coefficient of variance with such a calculation is significantly

greater than that associated with the lift coefficient alone. For this reason, it may take as many as

three times the number of generations for the genetic algorithm to converge on the optimal servo

positions as compared to the prior set of experiments. The optimization procedure is conducted

at seven angles of attack, which are sufficient to populate an efficiency curve. This efficiency

curve is then compared to the efficiencies of the flat plate and reflex wings.

It is seen in Figure 5-9 (top) the algorithm requires approximately 20 generations before

convergence. Note how the mean performance varies throughout the experiment while the best

performance will improve incrementally. This is due to the increased complexity of the

obj ective function and the increase in the variance in data. As a result, the genetic algorithm

selects much broader and more diverse servo positions to find the optimal region. The scatter

plot in Figure 5-9 (center) best illustrates the diversity in selected servo positions. The final

graphs of the same figure show the varied, well distributed initial population (bottom left) and

the final, converged upon optimum servo positions (bottom right).

The performance of the morphing wing with the two fixed wing geometries are plotted in

Figure 5-10 (A). Morphing the wing to the determined optimal shapes through the alpha sweep

provides a significant improvement in efficiency up to the region of stall. Notably, at 2.50 angle

of attack, the morphing wing has twice the efficiency value as that of the other wings. Having

completed the tests for maximization of efficiency, the plot of optimal servo positions versus

angle of attack is acquired and plotted in

Figure 5-10 (B).






































Servo Position 1


Servo Position I


A 250


B


0.45

0.4

0 35

0.3

0 2(


200

150

100

50


0 10 20
Data Set Number


II x Consecu~tive
Scattered



50 100 150 200 250
Servo Position


C -0.206


0.057

0.056

0D 055

0.054

0.053

0.052


-0.208

S-0.21

u -0.212

-0.214


-0.216


0.167


S0.166

e 0.165

0.164


0.061


0 0605


0 Og


Servo Position 125


Servo Position 125


0.594

0.592

0.59
0.588

0.586
0.584


9 .2

S0.198




0,'194


Servo Position 250


Servo Position 250


Figure 4-6.


Results of an aerodynamic hysteresis study depict the servo scatter and data
coefficient of variance for multiple servo positions.









































~I ~ ~I


*******~~ Filat Plate


167


8~ t


Serve 2


Figure 5-5.


An illustration of the intermediate wing shapes from the 20% span shows the
morphing capability of the two-design-variable model.


...........,- Flat Plate

0 10 20 30
A ngle of Attack


0.2 t


-0.2

-0.4L
-10


0 10
Anrgle of Attack


Figure 5-6.


The lift coefficient and efficiency is plotted using set flat plate and reflex wing
geometries.











A 250

200

S150




0 ~o






C 1.5





g .
"e


200

S150
o,
E 10

50to

0o


1.


1 23 4 567 89 1011
Member


1 2 345 67 89 1011
Member


50 100 150 200 250
Servo Position


-5 0 5 10 15 20 25 30
Andec of Attack


E 7

6

>.5


50 100 150 200 250
Servo Position


-5 0 5 10 15 20 25 30
Angle of Attack


Figure 4- 8. Resulting data illustrate the effectiveness of the optimization procedure. A) Initial
population. B) Final population. C) Coeffieient of lift servo scatter.
D) Morphing wing performance comparison for lift coefficient. E) Efficiency
servo scatter. F) Morphing wing performance comparison for efficiency.









These results support high confidence in the optimization procedure. The genetic

algorithm is capable of proper convergence despite the variance in collected wind tunnel data. It

is in the author' s opinion that the procedure will effectively determine optimal wing shapes for

morphing wings of many design variables and higher morphing capability.

Recommendations for Future Work

There are many valuable wing shape functions that can be attained using this procedure

which have yet to be explored. By simply applying constraints to the genetic algorithm many

new ideas for flight optimization arise.

One such experiment could be to vary the wing shape as a function of velocity to attain a

desired lift. For a given angle of attack, a high velocity would yield minimal camber while a low

velocity would yield a comparatively high camber. Such a shape function would minimize drag

thereby increasing efficiency.

Another interesting study would be to apply the constraint of a desired pitching moment

for each angle of attack to ensure longitudinal stability. Using this constraint while maximizing

lift at very high angles of attack could result in the mitigation of wing stall. Such a wing shape

function would yield a controlled, rate of descent flight mode useful in an auto-land feature.

Of course these shape functions are of no value unless they are utilized in an on-board

control system for real-time wing morphing. Such a control system will receive data such as

angle of attack or velocity and in response, command the position of the actuators. The servo

controller produced by Scott Bowman, which is utilized exclusively for this research, is capable

of such a task.

In a given mission profie for an aerial vehicle, several flight modes may be commanded.

For example, at takeoff the vehicle may require a wing shape that maximizes rate of climb.

When required altitude is met, another wing shape may be commanded to maximize speed to a










5-3 Morphed wing surface (Servo Positions: 250,230) with airfoil slices from the 20%
and 80% span yields a negative camber and negative reflex ................. .....................46

5-4 Morphed wing surface (Servo Positions: 1,1) with airfoil slices from the 20% and
80% span yields a positive camber and positive reflex. ............. .....................4

5-5 An illustration of the intermediate wing shapes from the 20% span shows the
morphing capability of the two design-variable model. ................ ............... ...._...47

5-6 The lift coefficient and efficiency is plotted using set flat plate and reflex wing
geom etries. .............. ...............47....

5-7 These sample plots illustrate the convergence of the genetic algorithm upon the
optimal servo position for maximum lift at 100 angle of attack. ............. ....................48

5-8 Morphing wing data for optimized lift coefficient. A) The morphing wing
performance as compared to the fixed reflex wing and flat plate. B) The optimal
servo positions as a function of angle of attack with the corresponding wing shape........49

5-9 These sample plots illustrate the convergence of the genetic algorithm upon the
optimal servo position for maximum efficiency at 100 angle of attack. ................... .........50

5-10 Morphing wing data for optimized efficiency. A) The morphing wing performance
as compared to the fixed reflex wing and flat plate. B) The optimal servo positions
as a function of angle of attack with the corresponding wing shape. ............. .................5 1










LIST OF FIGURES


Figure Page

3-1 Closed-loop wind tunnel at the University of Florida is pictured with a 24-inch test
secti on ........... ............... ...............24.......

3-2 Digital protractor is used to measure the angle of the sting balance that mounts to the
U-shape model arm. ............. ...............24.....

3-3 The servo controller (background) is used to set and hold servo positions, while the
serial port adapter (foreground) converts signals from RS232 to TTL. ............................24

3-4 Data exchange between software applications. ............. ...............25.....

3-5 The VIC system hardware setup about a wind tunnel test section.. ............ ..................26

4-1 The one design variable, rectangular planform model used to validate the
optimization process has a single point of actuation that alters camber. ...........................34

4-2 The full field, three-dimensional image, developed by the VIC system, is overlaid on
an image of the morphed wing illustrating deformation in the Z-direction. ...................34

4-3 Wing shape attained by servo position 1 with velocity at 0 and 16 m/s at 100 AOA.
The top left image shows the wind off Z-coordinates of the wing in millimeters. The
top right image shows the wind on wing deformation ................. .......... ...............35

4-4 Wing shape attained by servo position 250 with velocity at 0 and 16 m/s at 100 AOA....35

4-5 Plot of a series of airfoil shapes attained as a function of servo position. .........................36

4-6 Results of an aerodynamic hysteresis study depict the servo scatter and data
coefficient of variance for multiple servo positions. ................ ................. ..........37

4-7 Lift coefficient, drag coefficient, and efficiency versus angle of attack are plotted for
several servo positions of the one design variable model ................. ................ ...._.3 8

4-8 Resulting data illustrate the effectiveness of the optimization procedure. A) Initial
population. B) Final population. C) Coefficient of lift servo scatter. D) Morphing
wing performance comparison for lift coefficient. E) Efficiency servo scatter.
F) Morphing wing performance comparison for efficiency. ............. .....................3

5-1 The two design-variable model morphs the wing geometry through change of camber
and reflex. ............. ...............45.....

5-2 The full field, three-dimensional image, developed by the VIC system, is overlaid on
an image of the morphed wing illustrating deformation in the Z-direction. ...................45









Above the servo positions are the optimized wing shapes rotated to the corresponding

angle of attack. Using the equations of these curves in a control system, maximum efficiency as

a function of angle of attack can be achieved. These unpredictable curves illustrate the need for

optimization procedures for highly complex morphing wing structures.









CHAPTER 6
CONCLUSION AND RECOMMENDATIONS FOR FUTURE WORK

Conclusion

A procedure has been established to achieve proper shape management of morphing wing

structures. It has been demonstrated that utilizing a genetic algorithm with wind tunnel

hardware-in-the-loop is an effective means of determining optimal wing shape functions. The

use of these shape functions enables a morphing aircraft to achieve optimal flight performance in

all flight regimes.

To demonstrate the procedure, a two design-variable morphing wing is fabricated with the

capability of altering maximum camber and trailing edge reflex. Two experiments are conducted

for maximizing the lift coefficient and maximizing efficiency, which resulted in optimal servo

position versus angle of attack shape functions. For a performance comparison, the wing shape

is set as a flat plate and again as a medium camber wing with reflex. These fixed wing shapes

are tested for lift and efficiency performance from -50 to 250 angle of attacks.

Plotting the performance of the morphing wing with that of the two fixed wings illustrates

the dramatic improvement achieved by morphing wing structures. In particular, while the slope

of the lift coefficient curve remains the same for each data set, the morphing wing shows a

63.4% improvement over the fixed reflex wing. Another remarkable attribute of the morphing

wing is its benign stall characteristics. While more data must be collected to determine the

wings performance at angles of attack greater than 200, it is clear that such a wing can be used to

control and mitigate wing stall.

The experiments for determining maximum efficiency show an equally impressive increase

in performance. Considering the range of -50 to 50 angle of attacks, typical for straight and level

flight and subtle altitude changes, efficiency increases as much as 62.1%.










By collecting data for set servo positions over an array of angle of attacks, the performance

trends of the model become clear. The now predictable performance of this wing is used to

determine whether proper convergence of the genetic algorithm occurs. When it is confirmed

that convergence is achieved repeatedly, the process can then be used to optimize performance

for complex, high fidelity wings capable of sophisticated wing morphing.

A Study of Aerodynamic Hysteresis

Aerodynamic hysteresis occurs when the detached, low Reynolds number flow

inconsistently reattaches thereby resulting in varied performance. Repeatability of wing

performance is essential when conducting optimization tests since the genetic algorithm will

semi-randomly alter servo position while conducting its search. In an effort to determine if

aerodynamic hysteresis exists, a series of tests are conducted.

Five servo positions are used to represent the extremes and intermediate positions within

the range of servo motion. While holding the angle of attack and airspeed constant, ten

consecutive data sets are collected for each of the five servo positions. The standard deviation is

calculated for each of these data sets. This standard deviation is a measure of instrument

precision and is independent of aerodynamic hysteresis.

Data is then collected as the servo positions are varied between the extremes and

intermediate servo positions to measure any effect caused by aerodynamic hysteresis. The data

is sorted into common servo positions and the standard deviation is calculated. If the standard

deviation of the original data sets and the varied data sets coincides within a common range,

aerodynamic hysteresis will have been proven not to exist.

Tests are conducted at 00, 100, and 22.50 angles of attack, which represent low drag, high

lift, and near-stall flight regimes. Within Figure 4-6, eight plots are provided to illustrate the

results of the study. In Fig. 4-6 (A), the servo position variation used to induce aerodynamic









Another study used a sequential surrogate optimization approach with hardware-in-the-loop as

its objective function [25]. While the study was specific to determining the maximum walking

speed of a humanoid robot [26], this use of hardware-in-the-loop is well suited for determining

optimal wing shape for a morphing wing.

Hardware for Data Collection

Wind Tunnel Uncertainty Analysis

By testing the morphing wing in a wind tunnel with a six degree-of-freedom sting balance

to measure forces and moments, an array of performance data is collected. Using the sting

balance as a hardware-in-the-loop objective function, the GA morphs the wing shape for each

member of a given generation. A fitness value for each member is calculated from data received

from the sting balance. Critical to the use of any hardware-in-the-loop optimization procedure is

a determination of the measurement uncertainty for evaluation of data quality. Such an

evaluation of wind tunnel and sting balance performance is documented in [27] and [28].

Visual Image Correlation System

Using the digital image correlation (a.k.a. visual image correlation or VIC) system, a three-

dimensional non-contact full-Hield measurement of strain and displacements can be attained for a

given structure of composite material [29]. It has successfully been used to determine strains in

specimens of fiber reinforced polymer composites [30]. This system is well suited to determine

wing shapes for differing morphed positions while under flight loads. The supporting principles,

specifications, calibration procedures, and applications are well documented in [31].









shows a complex trend, which would have been difficult to predict. By plotting the convergence

data against these plots it becomes clear if the genetic algorithm is finding the true optimum.

Validation of Optimization Procedure

Using the genetic algorithm with the wind tunnel hardware in the loop, tests for

determining servo positions associated with optimal lift and efficiency are conducted. The

optimization procedure is first tested multiple times at set angles of attack to ensure repeatable

convergence on the optimum position. This demonstrates the data collected to be both

sufficiently accurate and precise for this procedure. The optimization procedure is then tested at

several other angles of attack and is compared to the previously acquired alpha sweeps presented

in Figure 4-7. Showing that the converged upon optimal values coincide or exceed predicted

values validates the optimization procedure.

Since the lift forces yield a lower standard deviation than that of the drag forces, it is used

for the initial convergence tests. When calculating efficiency, the lift is divided by the drag

resulting in a much greater coefficient of variance than that of the two individual components.

These tests are conducted after convergence for maximum lift is achieved.

The initial population is user defined and is equally distributed throughout the servo

position range. Setting the initial population in this manner, shown in Figure 4- 8 (A),

significantly reduces the required number of generations to convergence. This occurs because

the lift and efficiency curves as a function of servo position are simple polynomial curves

without complex local minimums. A sample of the final generation is plotted in Figure 4- 8 (B),

which shows convergence on an optimum with subtle deviations from that optimum.

The genetic algorithm selected servo positions, or servo scatter, are plotted in Figure 4- 8

(C) and (E). Note the cluster of data points near the optimum servo positions where the

algorithm narrowed its search. This plot is useful to visually ensure the algorithm searched










This thesis consists of six chapters. The first chapter outlines the intent and scope of the

investigation. The second chapter details a literature review of prior work related to morphing

wing structures, optimization procedures, and wind tunnel operation and data collection. The

third chapter describes the experimental setup with detail on the wind tunnel and the visual

image correlation system hardware. Also described in this chapter are the optimization software,

the interaction among the programs, and the experimental procedure for error minimization. The

fourth chapter describes the preliminary one design variable model used to validate the

optimization procedure. The fifth chapter describes the multi design variable model used to

illustrate the improved performance the morphing wing has over that of conventional fixed

wings. The sixth chapter closes with a conclusion of the investigation and suggests

recommendations for future work.




























Figure 5-1.


The two-design-variable model morphs the wing geometry through change of
camber and reflex.


Z [mm]
1100603


Figure 5-2.


The full field, three-dimensional image, developed by the VIC system, is overlaid
on an image of the morphed wing illustrating deformation in the Z-direction.









CHAPTER 3
EXPERIMENTAL SETUP AND DATA ANALYSIS

There are four primary subsystems utilized in the experimental setup. These include the

optimization software, the servo controller, the wind tunnel, and the data acquisition system.

Through the use of simple text-format software, data is passed between each of these

subsystems. This cooperative scheme of utilizing previously independent software programs

provides a means for automating the optimization procedure. The visual image correlation

system is used independently during testing to determine the three-dimensional wing shapes of

noteworthy servo positions.

Wind Tunnel

The primary piece of hardware used for this optimization procedure is the closed-loop

wind tunnel model 407B (Figure 3-1), which is manufactured by Engineering Laboratory

Design. This low-speed, low-turbulence tunnel has been reported to have less than 0.2%

turbulence [13] along the centerline of its 33-inch test section. The tunnel is capable of

producing airspeeds of 2 m/s to 45 m/s with its 250HP motor and 2-stage axial fan.

Extending from the sidewall of the test section is a U-shape model arm (Figure 3-2) that

supports the 6 degree-of-freedom sting balance and rotates the balance/model assembly to the

commanded angle of attack. It is the sting balance that provides all force and moment data to the

software through a National Instruments SCXI 1000 frame. The sting balance, produced by

Aerolab model 01-15, is capable of measuring loads on the order of 0.01 N [13].

Several LabVIEW virtual instruments (VI) are used to control the wind tunnel speed,

temperature, model angle of attack, and sting balance voltage data acquisition. As detailed later

in this chapter, automation of the optimization procedure is achieved by calling these subroutine

VIs from within a primary VI which exchanges loads data with the genetic algorithm software.









through these datum points a simple polynomial equation is calculated. It is this equation that

correlates maximum lift to angle of attack.

The genetic algorithm is capable of converging within just six generations when using a

well distributed initial population as illustrated in Figure 5-7 (bottom left). The topmost plot in

the same figure shows the rapid convergence of the mean performance with the best

performance. The rate of convergence can also be seen from the lack of diversity of the servo

scatter. The pattern of the initial population is still easily defined because the algorithm

immediately hones in on the region of the optimal position. Note that in this case, a second

optimization procedure is conducted, this time with an initial population narrowed around the

optimal region. Once again the algorithm hones almost immediately on the optimum servo

positions, which is well illustrated in the bottom right plot in Figure 5-7. This is a special case

due to the simplicity of the objective function and the small coefficient of variance in the data.

In the following maximum efficiency tests it is shown that convergence will not occur so rapidly.

The performance of the morphing wing as compared to the two fixed wing geometries is

plotted in Figure 5-8 (A). By morphing the wing throughout the alpha sweep, a much greater lift

coefficient is obtained. Note the benign stall characteristics of the morphing wing, which has

little decrease in lift from 15-200. No tests are conducted beyond the 200 angle of attack due to

the vibrations encountered within this stall region.

Having completed the tests for maximization of lift coefficient, the plot of optimal servo

positions versus angle of attack is acquired and plotted in Figure 5-8 (B). As is expected, the

maximum lift at any given angle of attack will have no reflex and is why the second servo

always converges to position 1. These servo position curves can now be used in a control

system, with angle of attack as input, to yield maximum lift performance.























Figure 3-1.


The closed-loop wind tunnel at the University of Florida is pictured with a 24-
inch test section (image provided by Michael Sytsma).


Figure 3-2.


A digital protractor is used to measure the angle of the sting balance that mounts
to the U-shape model arm.


Figure 3-3.


The servo controller (background) is used to set and hold servo positions, while
the serial port adapter (foreground) converts signals from RS232 to TTL.




Full Text

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OPTIMIZATION OF A MORPHING WING GEOMETRY USING A GENETIC ALGORITHM WITH WIND TUNNEL HARDWARE-IN-THE-LOOP By FRANK JOSEPH BORIA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007 1

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2007 Frank Joseph Boria 2

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To my bride, Rikki 3

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ACKNOWLEDGMENTS This work has been made possible through funding and facilities provided by the University of Florida and BioRobots, LLC. Many thanks in particular go to Dr. Peter Ifju for his guidance, leadership, and ability to meld science with low-quality humor. Another thank you goes to Dr. Roberto Albertani for his guidance on wind tunnel operation and his incessant support of the metric system, despite its obvious illogical basis (long live the slug). And yet another thank you goes to Dr. Bruce Carroll for so strongly supporting my work during this final task. I thank Bret Stanford for his thoughts and input throughout my research, whose insight and experience helped to create the framework of these experiments. I am very appreciative of Scott Bowman for his design, fabrication, and programming of a sophisticated morphing wing controller that was used to conduct this research. I am forever grateful and indebted to Frank and Joanne Boria for raising me with love and compassion while teaching me faith, respect and commitment. They are both remarkable parents and phenomenal role models. I will always look to them for guidance. To Julie Badger, Carl Boria, and Elizabeth Nettles, I am thankful for their strength of support, their being there to listen, and their reminding me of birthdays and anniversaries. To you, my brother and sisters, I gratefully dedicate the last figure of the fifth chapter. I would like to thank my children, Addie Reith for contributing her skills in photography, Olivia Reith for her remarkable contribution of digital photo editing, and Christian Boria for thinking that morphing airplanes are really, really cool. I love them all. Finally, I thank my bride, Rikki, for her never-ending support, love, and inspiration. She has brought me great joy, true happiness, and has taught me to live life with abandon. I am forever thankful to her for being genuine, refreshingly enthusiastic, and mine. 4

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES...........................................................................................................................7 LIST OF FIGURES.........................................................................................................................8 ABSTRACT...................................................................................................................................10 CHAPTER 1 INTRODUCTION.............................................................................................................12 Emulating Biological Structures........................................................................................12 Optimization of Morphing Wing Structures......................................................................13 Motivation..........................................................................................................................13 Overview............................................................................................................................14 2 LITERATURE REVIEW..................................................................................................16 Emulating Desirable Wing Shapes....................................................................................16 Actuation of a Morphing Wing Structure..........................................................................17 Optimization Techniques for Acquiring Desired Wing Shapes........................................18 Hardware for Data Collection............................................................................................19 Wind Tunnel Uncertainty Analysis............................................................................19 Visual Image Correlation System...............................................................................19 3 EXPERIMENTAL SETUP AND DATA ANALYSIS.....................................................20 Wind Tunnel......................................................................................................................20 Servo Controller.................................................................................................................21 Software Description.........................................................................................................21 Visual Image Correlation System......................................................................................22 4 ONE DESIGN VARIABLE MODEL...............................................................................27 Model Description and Purpose.........................................................................................27 A Study of Aerodynamic Hysteresis..................................................................................28 Initial Alpha Sweep for Predicting Convergence..............................................................29 Validation of Optimization Procedure...............................................................................30 5 OPTIMIZATION OF A HIGH-FIDELITY MORPHING WING....................................40 Model Description.............................................................................................................40 Comparative Lift and Efficiency Curves...........................................................................41 5

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Maximizing Coefficient of Lift Curve...............................................................................41 Maximizing Efficiency Curve............................................................................................43 6 CONCLUSION AND RECOMMENDATIONS FOR FUTURE WORK........................52 Conclusion.........................................................................................................................52 Recommendations for Future Work...................................................................................53 LIST OF REFERENCES...............................................................................................................55 BIOGRAPHICAL SKETCH.........................................................................................................58 6

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LIST OF TABLES Table Page 4-1 Small coefficient of variation between the ten base data sets and the random data sets ensures minimal effect of aerodynamic hysteresis on the coefficient of lift.....................33 4-2 Drag data show acceptably low variation between the ten base data sets and the random data sets.................................................................................................................33 4-3 Efficiency is found to have a variance of the same magnitude as drag, which is sufficient for the procedure to correctly converge upon the optimum servo position.......33 7

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LIST OF FIGURES Figure Page 3-1 Closed-loop wind tunnel at the University of Florida is pictured with a 24-inch test section............................................................................................................................24 3-2 Digital protractor is used to measure the angle of the sting balance that mounts to the U-shape model arm............................................................................................................24 3-3 The servo controller (background) is used to set and hold servo positions, while the serial port adapter (foreground) converts signals from RS232 to TTL.............................24 3-4 Data exchange between software applications..................................................................25 3-5 The VIC system hardware setup about a wind tunnel test section....................................26 4-1 The one design variable, rectangular planform model used to validate the optimization process has a single point of actuation that alters camber............................34 4-2 The full field, three-dimensional image, developed by the VIC system, is overlaid on an image of the morphed wing illustrating deformation in the Z-direction.......................34 4-3 Wing shape attained by servo position 1 with velocity at 0 and 16 m/s at 10 AOA. The top left image shows the wind off Z-coordinates of the wing in millimeters. The top right image shows the wind on wing deformation.......................................................35 4-4 Wing shape attained by servo position 250 with velocity at 0 and 16 m/s at 10 AOA....35 4-5 Plot of a series of airfoil shapes attained as a function of servo position..........................36 4-6 Results of an aerodynamic hysteresis study depict the servo scatter and data coefficient of variance for multiple servo positions..........................................................37 4-7 Lift coefficient, drag coefficient, and efficiency versus angle of attack are plotted for several servo positions of the one design variable model..................................................38 4-8 Resulting data illustrate the effectiveness of the optimization procedure. A) Initial population. B) Final population. C) Coefficient of lift servo scatter. D) Morphing wing performance comparison for lift coefficient. E) Efficiency servo scatter. F) Morphing wing performance comparison for efficiency..............................................39 5-1 The two design-variable model morphs the wing geometry through change of camber and reflex...........................................................................................................................45 5-2 The full field, three-dimensional image, developed by the VIC system, is overlaid on an image of the morphed wing illustrating deformation in the Z-direction.......................45 8

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5-3 Morphed wing surface (Servo Positions: 250,230) with airfoil slices from the 20% and 80% span yields a negative camber and negative reflex.............................................46 5-4 Morphed wing surface (Servo Positions: 1,1) with airfoil slices from the 20% and 80% span yields a positive camber and positive reflex.....................................................46 5-5 An illustration of the intermediate wing shapes from the 20% span shows the morphing capability of the two design-variable model.....................................................47 5-6 The lift coefficient and efficiency is plotted using set flat plate and reflex wing geometries..........................................................................................................................47 5-7 These sample plots illustrate the convergence of the genetic algorithm upon the optimal servo position for maximum lift at 10 angle of attack........................................48 5-8 Morphing wing data for optimized lift coefficient. A) The morphing wing performance as compared to the fixed reflex wing and flat plate. B) The optimal servo positions as a function of angle of attack with the corresponding wing shape........49 5-9 These sample plots illustrate the convergence of the genetic algorithm upon the optimal servo position for maximum efficiency at 10 angle of attack.............................50 5-10 Morphing wing data for optimized efficiency. A) The morphing wing performance as compared to the fixed reflex wing and flat plate. B) The optimal servo positions as a function of angle of attack with the corresponding wing shape.................................51 9

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science OPTIMIZATION OF A MORPHING WING GEOMETRY USING A GENETIC ALGORITHM WITH WIND TUNNEL HARDWARE-IN-THE-LOOP By Frank Joseph Boria August 2007 Chair: Peter Ifju Major: Aerospace Engineering Advancements in compliant actuator technologies and flexible composite structures have enabled true wing morphing capabilities. The resultant effect of these new capabilities is optimal wing shapes for all flight regimes. With the ever-increasing complexity of these morphing wing structures comes the challenge of proper shape management for achieving desirable, real-time flight performance. Using a wind tunnel with sting balance as a hardware-in-the-loop objective function, a genetic algorithm is used for optimizing multiple design variable morphing wing structures. This evolutionary approach to optimization provides a more efficient means of convergence over that of other conventional optimization techniques. There are four primary subsystems utilized in the experimental setup. These include the optimization software, the servo controller, the wind tunnel, and the data acquisition software. Through the use of a simple text-format software package, data is passed between each of these subsystems, thereby automating the procedure. A visual image correlation system is used independently during testing to determine the three-dimensional wing shapes of noteworthy servo positions. 10

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To demonstrate the procedure, a two design-variable morphing wing is fabricated with the capability of altering camber and trailing edge reflex. Two experiments are conducted for maximizing the lift coefficient and maximizing efficiency. These experiments result in optimal servo position versus angle of attack shape functions. Setting the wing shape as a flat plate and again as a medium camber wing with reflex provides comparative data. These experiments resulted in a comparatively benign stall characteristic, a 63.4% increase in lift coefficient, and up to 62.1% increase in maximum efficiency over that of the fixed wing with reflex. Plotting the performance of the morphing wing, with that of the two arbitrary fixed wing shapes, illustrates the dramatic improvement achievable by morphing wing structures. Utilizing these procedures allows for real-time adaptive wing morphing to adjust to the instantaneous changes of flight attitude and wind conditions. 11

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CHAPTER 1 INTRODUCTION No longer are aircraft confined to fixed wing geometries suiting a single flight regime. The advancements of actuation and material technologies have enabled true morphing capabilities. The resultant effect of these new capabilities is optimal wing shapes for all flight regimes. With the ever-increasing complexity of these morphing wing structures comes the challenge of proper shape management for achieving desirable, real-time flight characteristics. The work presented in this thesis is one approach to such a challenge. Emulating Biological Structures The study of ornithology shows that each species of bird has evolved to become uniquely specialized within their habitat. From the perspective of the aerodynamicist, designing an aircraft to emulate the performance of the falcon for high speed dives, the eagle for highly efficient soaring, the hovering capability of the humming bird, or the agility of the swift would be of great value. Ultimately, however, melding each of these desirable flight characteristics on a single aircraft is the true objective. Such a versatile vehicle could achieve remarkably high lift, for maximum payload capacity, high speed, to quickly move from waypoint to waypoint, and high efficiency. Utilizing a morphing wing structure for asymmetric deformations would yield the ability to maneuver with high agility through complicated urban environments. Such a vehicle could also maintain stability during the most volatile of flight conditions, such as erratic and gusting winds among buildings and structures. Utilizing thin plate composite materials with multiple actuation points, it is possible to create a morphing wing capable of complex deformation. A noteworthy study on similar materials with regard to creep is presented by Richard Thomas Haenel [1], which details the 12

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evaluation of creep with respect to material deformation. Careful design of such a wing will yield configurations that significantly outperform conventional fixed wing geometries. Optimization of Morphing Wing Structures When a given structure is created to emulate the complexities of what exists in nature, a method must also be developed to command the structure to take a desired shape. A high fidelity morphing wing with several actuation points will require a complex control system. The once rigorous determination of aerodynamic performance for conventional fixed wing geometries has become an even greater undertaking in multi-variable shape optimization. While the field of computational fluid dynamics continues to improve, modeling complex structures of composite makeup remains expensive. It is also difficult to accurately model the aeroelastic effects on such a structure when it is under load. This becomes increasingly the case when utilizing thin plate wings. While the use of a wind tunnel may also be expensive, it provides a source for aerodynamic force data, which take full account of wing deformations due to aeroelastic effects. Regardless of the method used for determining aerodynamic forces, a procedure for optimization must be properly matched to the capability of the wing structure. While a response surface approach may be well suited for morphing wings with minimal design variables, high-fidelity morphing wing structures may be more efficiently optimized through the use of a genetic algorithm. The genetic algorithm is better capable of finding a global optimum more efficiently than many strategies. Motivation The use of a genetic algorithm for optimizing high-fidelity, multiple design variable morphing wing structures provides a more efficient means of convergence over that of other conventional optimization techniques. 13

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For example, collecting data for a one design variable wing of 10 position increments over an alpha sweep of 10 angles of attack requires 100 data points. To ensure data validity, these same data points are typically collected multiple times to ensure precision, which increases the number of required data points to a minimum of 200. Increasing the models capability through the use of two design variables increases the number of required data points to 2,000. Ultimately, the required number of data points increases by an order of magnitude with each additional design variable. Of course this analysis assumes only 10 position increments are possible, while the actuators used for this study have 250 position increments. The use of response surface techniques is a reasonable approach for wings with up to three and even four design variables. But as the number of design variables grows, it becomes inefficient. Finding the optimal position of the determined response surface becomes more difficult to solve. The complexity of the response surface also raises concerns for convergence upon false, local optimums. The use of this and similar techniques for finding maximum performance shapes for high-design variable morphing wing structures is ineffective. Overview To establish an effective procedure for determining optimal wing shape of a multi-variable morphing wing, the use of a genetic algorithm with wind tunnel hardware-in-the-loop is implemented. This procedure is used to determine a specific desired flight characteristic, such as maximum lift or maximum efficiency. By conducting these optimization tests at several angles of attack, it becomes possible to obtain optimal wing shapes throughout the range of angles of attack. Utilizing these data in a control system make it possible to automate real-time wing morphing for optimal performance during flight. It is the intent of this thesis to present and implement such a procedure with its proficiencies and detriments. 14

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This thesis consists of six chapters. The first chapter outlines the intent and scope of the investigation. The second chapter details a literature review of prior work related to morphing wing structures, optimization procedures, and wind tunnel operation and data collection. The third chapter describes the experimental setup with detail on the wind tunnel and the visual image correlation system hardware. Also described in this chapter are the optimization software, the interaction among the programs, and the experimental procedure for error minimization. The fourth chapter describes the preliminary one design variable model used to validate the optimization procedure. The fifth chapter describes the multi design variable model used to illustrate the improved performance the morphing wing has over that of conventional fixed wings. The sixth chapter closes with a conclusion of the investigation and suggests recommendations for future work. 15

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CHAPTER 2 LITERATURE REVIEW Through the use of unmanned aerial vehicles it becomes possible to conduct dangerous missions without endangering the life of a pilot. These vehicles are becoming smaller with missions that require significant agility for navigating complex urban environments. To see a bird navigate through such an environment will inspire the concept of its emulation. Through the ever-maturing field of material science, the morphing capabilities of an aircraft wing are more capable of simulating a bird in flight. Emulating Desirable Wing Shapes The complex system of structural members and joint articulation of a birds wing [2] is difficult to duplicate mechanically with regard to function as well as low weight and high durability. Studies associating wing shape to function are conducted to differentiate requirements for static aerodynamics, physiology, and flapping control [3]. Understanding this differentiation leads to morphing wing structures of less complexity than that of the birds wing. For example, while birds have many layers of feathers that are moved around to adjust to the specific maneuver they need to perform [4], morphing wing structures can be fabricated of thin sheet materials, which are manipulated to yield the desired wing shape. Currently, many unmanned aerial vehicle designs are based on a flexible wing design developed at the University of Florida [5],[6]. These thin, flexible wings are beneficial for dampening the effects of wind gusts and increasing stability during adverse flight conditions. With regard to wing morphing, they are also easily manipulated for desired control and overall flight performance using minimal actuation points. An example of this is morphing in the form of asymmetric wing twist making it is possible to surpass the roll rates of conventional aileron 16

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configurations [7]. Another example is the exercise in design optimization conducted by Gano et al. [8],[9] for a single, high endurance wing that separates into a second wing for greater agility. Much work has been done to assess the flight characteristics of these flexible wings. NASA has performed a control assessment and simulation of a micro air vehicle with aeroelastic wings which adapt to the disturbances during flight [10]. Morphing wing weight equations and an approach to size morphing aircraft [11] are developed to replace current methods of general heuristics based on fixed wing aircraft. Also, extensive wind tunnel tests on a variety of flexible wing configurations showed a decrease in wing incidence, an increase in dihedral and a shift in maximum camber position that results in a favorable change in pitching moment and lift. Ultimately, smoother flight characteristics are achieved over that of conventional fixed wings [12]. A variety of experimental flow tests are conducted on these wings using surface oil flow visualization, laser based flow visualization, and particle image velocimetry with results that validate previously determined CFD results [13]. Actuation of a Morphing Wing Structure Advancements in actuator technologies for these compliant wing structures, such as Macro Fiber Composites (MFC), Electroactive Polymers (EAP), and Smart Memory Alloys (SMA), are yielding lightweight, capable devices. The thin, compliant MFC is a type of piezoceramic composite actuator that is constructed of orthogonal layers of unidirectional piezoceramic fibers and copper electrodes encased in layers of acrylic and Kapton [14]. These actuators have been reported to produce high strain levels on the order of 2000 [15]. Alternatively, the EAP actuator is similar to muscle tissue with regard to stress and force capability. This actuator is capable of large-scale linear motion [16]. Another source of actuation is through the use of an SMA mechanism. These mechanisms consist of a metallic alloy that act as linear actuators by contracting when heated and returning to their original shape when cooled [17]. This actuator is 17

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lightweight and very effective although precaution must be taken to prevent variations in temperature, which will affect its performance. These, and many other, compliant forms of actuation have been developed and utilized for morphing wing structures. Extensive work on adaptive shape change problems, which determine methods for morphing a given curve or shape into a target curve or shape, is providing solutions with a minimal number of actuators [18]. This work leads to the challenge of morphing a wing not to a single target shape, but rather to adaptively morph the wing real-time during flight to adjust to the instantaneous changes of flight attitude and wind conditions. Optimization Techniques for Acquiring Desired Wing Shapes The use of evolution strategies for optimization of complex design problems began back in the early sixties [19] and has been gaining momentum over the past fifteen years. Such strategies emphasize selection, recombination and mutation of a given population to determine the makeup of the next population set [20]. Each of the members of this new generation is then evaluated for fitness. Poor performing members are rejected from the next generation while high performing members are retained. This results in convergence upon an optimal solution after multiple generations. The use of a genetic algorithm (GA) has advantages over other techniques when searching within a complex domain. Due to its evolutionary tactics, the GA is resistant to convergence on local optimums making it better suited for finding true global optimums. It is also capable of working with many design variables, which can be discrete, continuous, or mixed [21], [22], [23]. As morphing wing structures become more complex, the GA solver becomes better preferred. Studies have already shown the effective use of the GA to optimize fixed airfoil and wing shape [24] and to better develop composite wings for desired structural characteristics [23]. 18

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Another study used a sequential surrogate optimization approach with hardware-in-the-loop as its objective function [25]. While the study was specific to determining the maximum walking speed of a humanoid robot [26], this use of hardware-in-the-loop is well suited for determining optimal wing shape for a morphing wing. Hardware for Data Collection Wind Tunnel Uncertainty Analysis By testing the morphing wing in a wind tunnel with a six degree-of-freedom sting balance to measure forces and moments, an array of performance data is collected. Using the sting balance as a hardware-in-the-loop objective function, the GA morphs the wing shape for each member of a given generation. A fitness value for each member is calculated from data received from the sting balance. Critical to the use of any hardware-in-the-loop optimization procedure is a determination of the measurement uncertainty for evaluation of data quality. Such an evaluation of wind tunnel and sting balance performance is documented in [27] and [28]. Visual Image Correlation System Using the digital image correlation (a.k.a. visual image correlation or VIC) system, a three-dimensional non-contact full-field measurement of strain and displacements can be attained for a given structure of composite material [29]. It has successfully been used to determine strains in specimens of fiber reinforced polymer composites [30]. This system is well suited to determine wing shapes for differing morphed positions while under flight loads. The supporting principles, specifications, calibration procedures, and applications are well documented in [31]. 19

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CHAPTER 3 EXPERIMENTAL SETUP AND DATA ANALYSIS There are four primary subsystems utilized in the experimental setup. These include the optimization software, the servo controller, the wind tunnel, and the data acquisition system. Through the use of simple text-format software, data is passed between each of these subsystems. This cooperative scheme of utilizing previously independent software programs provides a means for automating the optimization procedure. The visual image correlation system is used independently during testing to determine the three-dimensional wing shapes of noteworthy servo positions. Wind Tunnel The primary piece of hardware used for this optimization procedure is the closed-loop wind tunnel model 407B (Figure 3-1), which is manufactured by Engineering Laboratory Design. This low-speed, low-turbulence tunnel has been reported to have less than 0.2% turbulence [13] along the centerline of its 33-inch test section. The tunnel is capable of producing airspeeds of 2 m/s to 45 m/s with its 250HP motor and 2-stage axial fan. Extending from the sidewall of the test section is a U-shape model arm (Figure 3-2) that supports the 6 degree-of-freedom sting balance and rotates the balance/model assembly to the commanded angle of attack. It is the sting balance that provides all force and moment data to the software through a National Instruments SCXI 1000 frame. The sting balance, produced by Aerolab model 01-15, is capable of measuring loads on the order of 0.01 N [13]. Several LabVIEW virtual instruments (VI) are used to control the wind tunnel speed, temperature, model angle of attack, and sting balance voltage data acquisition. As detailed later in this chapter, automation of the optimization procedure is achieved by calling these subroutine VIs from within a primary VI which exchanges loads data with the genetic algorithm software. 20

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Servo Controller Each morphing wing developed for these experiments utilizes Futaba S3102 servo actuators to attain the surface deformation. These servos supply 4.6 kgcm of torque and a rate of 60 in 0.2 seconds. Using Matlab, servo number and position are commanded through the serial port in a 1200-baud rate, 8-bit, 1-stop, and no-parity form. A sub-module converts the RS232 signal to transistor-to-transistor logic. Receiving the signal on the morphing wing structure is a custom servo controller (Figure 3-3) designed and fabricated by Scott Bowman. This controller features 8 kilobytes of flash memory, a 16-bit high-resolution servo timer, and an 8 MHz ATMEL microprocessor. This servo controller is designed to set and hold commanded servo positions while the wing undergoes aerodynamic loading. Software Description The two primary software packages used for this study are LabVIEW for wind tunnel control and data acquisition and Matlab for wing morphing control and optimization. A flow chart of how the information is passed between the programs is shown in Figure 3-4. To initiate the optimization procedure, an initial population is prescribed to the genetic algorithm. When the algorithm is started, the first member of the initial population is sent to the subroutine that commands the servo controller. The servo controller then sets and holds each servo position thereby morphing the wing. Simultaneously, the servo positions are sent to a text file. At this point, the genetic algorithm waits for the force and moment data that is associated with the servo positions to be added to the text file. It determines when this happens by monitoring the text file size. While the optimization software is on hold for data, the wind tunnel is brought up to the required velocity. After the angle of attack is set, the force and moment data are determined from the sting balance. The text file previously created by the optimization software is accessed 21

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and the data is appended to the same line. The resulting line will consist of servo positions followed by the lift coefficient, drag coefficient, coefficient of side force, coefficient of pitching moment, and coefficient of yawing moment. The rolling moment is omitted because the system yields invalid data. This is of no detriment to these sets of experiments since rolling moment has no contribution in force and is not utilized as a constraint. At this point, the data acquisition software waits for the next set of servo positions to be added to the text file. As with the optimization software, it does this by monitoring the file size. When the new servo positions are added to the text file, the file size will increase thereby triggering the data acquisition software for the next set of data. After the force and moment data have been added to the text file, the optimization software identifies the increase in file size and retrieves the data. The next servo positions are commanded, and thereby begin the next cycle. As with any sting balance, there does exist the concern for signal drift. This sting balance contains a network of strain gauges that is used to measure the elastic strain of the balance. These strain gauges are susceptible to signal drift due to temperature variations caused by both environment and self-heating. To manage the signal drift, the wind tunnel software counts the number of data sets collected. After the fifteenth data set, the tunnel velocity is set to zero and the model arm is rotated to the original angle of attack. At this point, the data acquisition software performs an offset nullification of the strain gauge voltages. The tunnel is then brought back up to the velocity and angle of attack required by the experiment. This simple procedure ensures data quality and is set to coincide with the genetic algorithm population size of fifteen. Visual Image Correlation System Determining the shape of the morphed wing is essential to quantitatively validate the obtained solutions. Through the use of the visual image correlation (VIC) system, a non-contact 22

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full-field shape and deformation tool, the wing shape can be captured and evaluated for any given morphed configuration. A typical experimental setup with the VIC system is illustrated in Figure 3-5. This process was developed in the mid 1990s by Helm with a reported resolution on the order of 0.05 mm [32]. The specimen is first uniformly painted with a low-luster color, and then painted with a highly contrasting, random speckle pattern. Two digital cameras carefully focused on the specimen. The cameras are triggered such that an image from each is acquired instantaneously. A plate with high contrast dots of known diameter and spacing is used to calibrate the camera system. Photos of the plate in different locations of the image frame and at varying angles and rotations are taken and processed for calibration. After the calibration procedure is complete, the precise orientation of one camera to the other is known. At this point, the system is now ready to photograph the specimen. From these images, the software is capable of developing the full-field three-dimensional shape of the specimen using stereo triangulation. The system is also used to determine deformation of a specimen under load. By first taking a no-load reference image of the specimen, then taking another image of the loaded specimen, the software is capable of calculating the displacement field. This is useful for determining how much deformation a wing undergoes when in flight. 23

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Figure 3-1. The closed-loop wind tunnel at the University of Florida is pictured with a 24-inch test section (image provided by Michael Sytsma). Figure 3-2. A digital protractor is used to measure the angle of the sting balance that mounts to the U-shape model arm. Figure 3-3. The servo controller (background) is used to set and hold servo positions, while the serial port adapter (foreground) converts signals from RS232 to TTL. 24

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Loop 1 Loop 2 Figure 3-4. These flowcharts illustrate how data is appended to the shared text file. 25

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Figure 3-5. This illustration depicts the VIC system hardware setup about a wind tunnel test section. 26

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CHAPTER 4 ONE DESIGN VARIABLE MODEL Model Description and Purpose To validate the procedures for data collection, a simple one-design-variable model is utilized. This model is a thin plate wing of rectangular planform with a single point of actuation that changes the wings camber. The wing consists of a single layer, plain weave carbon fiber skin and horizontally aligned unidirectional spars that run from wingtip to wingtip every one inch from the leading edge (illustrated in Figure 4-1). These spars transfer loads such that when the wing shape is changed at the root, the same shape will be attained at the tips effectively resulting in an extruded airfoil along the span of wing. An attachment point at the leading edge permits rotation only. An attachment point at the 70% chord permits both rotation and longitudinal motion. The unconstrained trailing edge allows for significant deformation when under load. This deformation is an aeroelastic effect caused by the interaction among inertial, elastic, and aerodynamic forces on the wing. Typical CFD is expensive when attempting to model this aeroelastic effect, let alone optimize a morphing wing, and is why this tunnel-in-the-loop procedure is of particular value. Using the VIC system, the wing shape is determined. It is shown as a topographical overlay on an image of the wing itself in Figure 4-2. The wind-on deformations, and the airfoils associated with each, are plotted in Figure 4-3 for servo position 1 (a negatively cambered wing) and Figure 4-4 for servo position 250 (a highly cambered wing). The model is capable of altering the maximum camber between % through 19%. Utilizing the VIC system, 9 servo positions are selected and photographed to determine the range of attainable wind-off wing shapes. The normalized airfoils are plotted in Figure 4-5, which help to illustrate the magnitude of camber change. 27

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By collecting data for set servo positions over an array of angle of attacks, the performance trends of the model become clear. The now predictable performance of this wing is used to determine whether proper convergence of the genetic algorithm occurs. When it is confirmed that convergence is achieved repeatedly, the process can then be used to optimize performance for complex, high fidelity wings capable of sophisticated wing morphing. A Study of Aerodynamic Hysteresis Aerodynamic hysteresis occurs when the detached, low Reynolds number flow inconsistently reattaches thereby resulting in varied performance. Repeatability of wing performance is essential when conducting optimization tests since the genetic algorithm will semi-randomly alter servo position while conducting its search. In an effort to determine if aerodynamic hysteresis exists, a series of tests are conducted. Five servo positions are used to represent the extremes and intermediate positions within the range of servo motion. While holding the angle of attack and airspeed constant, ten consecutive data sets are collected for each of the five servo positions. The standard deviation is calculated for each of these data sets. This standard deviation is a measure of instrument precision and is independent of aerodynamic hysteresis. Data is then collected as the servo positions are varied between the extremes and intermediate servo positions to measure any effect caused by aerodynamic hysteresis. The data is sorted into common servo positions and the standard deviation is calculated. If the standard deviation of the original data sets and the varied data sets coincides within a common range, aerodynamic hysteresis will have been proven not to exist. Tests are conducted at 0, 10, and 22.5 angles of attack, which represent low drag, high lift, and near-stall flight regimes. Within Figure 4-6, eight plots are provided to illustrate the results of the study. In Fig. 4-6 (A), the servo position variation used to induce aerodynamic 28

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hysteresis is shown. Several sweeps from maximum to minimum and intermediate servo positions are performed to measure the effect of the hysteresis on the lift and drag coefficients. The drag coefficient versus servo position, shown in Fig. 4-6 (B), is provided to show the precision of the data. It is selected since it is the least precise of all data provided by the instrumentation; this is typically an order of magnitude less than that of the lift coefficient. The subplots shown in Fig.4-6 (C-H) are magnified data sets for lift and drag coefficients at servo positions 1, 125, and 250. While the plots clearly show aerodynamic hysteresis does exist, the standard deviation within a given data set is acceptable with a coefficient of variance of no more than 2.3% for coefficient of lift (Table 4-1), 2.9% for coefficient of drag (Table 4-2), and 3.4% for efficiency (Table 4-3). This study shows the effect of the aerodynamic hysteresis is minimal and has little influence on the data collected. It is in the authors opinion, as supported by this study, that the effects due to aerodynamic hysteresis can be assumed negligible. Initial Alpha Sweep for Predicting Convergence To validate the procedure for determining the optimum wing shape, a preliminary set of data was collected. The servo used in the model is capable of 120 rotation, which is commanded by the servo controller using position points 1 through 250. This range of servo position is divided into 9 positions that are used to populate lift, drag, and efficiency plots. For each servo position, data is collected for angle of attacks ranging from -5 through 30 in 2.5 increments (Figure 4-7). In doing this it can be seen that the lift curves systematically increase as camber increases. The drag plots show an interesting inversion in trend shape as the camber increases, which is likely due to the aeroelastic effects of the unconstrained trailing edge. Finally, the efficiency plot 29

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shows a complex trend, which would have been difficult to predict. By plotting the convergence data against these plots it becomes clear if the genetic algorithm is finding the true optimum. Validation of Optimization Procedure Using the genetic algorithm with the wind tunnel hardware in the loop, tests for determining servo positions associated with optimal lift and efficiency are conducted. The optimization procedure is first tested multiple times at set angles of attack to ensure repeatable convergence on the optimum position. This demonstrates the data collected to be both sufficiently accurate and precise for this procedure. The optimization procedure is then tested at several other angles of attack and is compared to the previously acquired alpha sweeps presented in Figure 4-7. Showing that the converged upon optimal values coincide or exceed predicted values validates the optimization procedure. Since the lift forces yield a lower standard deviation than that of the drag forces, it is used for the initial convergence tests. When calculating efficiency, the lift is divided by the drag resulting in a much greater coefficient of variance than that of the two individual components. These tests are conducted after convergence for maximum lift is achieved. The initial population is user defined and is equally distributed throughout the servo position range. Setting the initial population in this manner, shown in Figure 48 (A), significantly reduces the required number of generations to convergence. This occurs because the lift and efficiency curves as a function of servo position are simple polynomial curves without complex local minimums. A sample of the final generation is plotted in Figure 48 (B), which shows convergence on an optimum with subtle deviations from that optimum. The genetic algorithm selected servo positions, or servo scatter, are plotted in Figure 48 (C) and (E). Note the cluster of data points near the optimum servo positions where the algorithm narrowed its search. This plot is useful to visually ensure the algorithm searched 30

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sufficiently throughout the range of servo positions. A large gap in the scatter will raise concerns that the true global optimum may have been missed. By setting the angle of attack to 10, high lift and drag forces are ensured. Three optimization experiments are conducted to determine which servo position maximizes lift. As shown in Figure 48 (D), each experiment converged on a value that exceeded or matched the predicted value. All three experiments converged to servo position 250, which is associated with the greatest camber. Due to the variance in lift data, the lift coefficient associated with the optimal servo position will never converge closer than 2.3% of one another. This does not, however, prevent the genetic algorithm from properly converging on that optimal servo position. Due to the low coefficient of variance and the rapid convergence on the optimum servo position, it is in the authors opinion that the procedure will accurately converge to the optimum value regardless of angle of attack. For this reason, the second sets of convergence experiments for optimal efficiency are conducted. Continuing to hold the angle of attack at 10, three convergence experiments for determination of maximum efficiency are conducted. Since the coefficient of variance for efficiency is much higher than that of lift, other angles of attack are tested. As shown in Figure 48 (F), each of the three experiments converges on servo position 134 with a maximum efficiency of 5.56. While this value is below that of the predicted value, it does exist within the previously calculated variance and did converge on the predicted servo position. Because the coefficient of drag is very low at 0 and lift will become negative at -5 angle of attack, the efficiency may vary considerably. For this reason they are tested to ensure proper convergence. These results are plotted in Figure 48 (F). As illustrated, the optimization 31

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procedure did accurately converge upon the correct servo positions. This is because although the drag forces may be very low, they are consistently low; i.e. precise though not accurate. These results support high confidence in the optimization procedure. The genetic algorithm is capable of proper convergence despite the variance in collected wind tunnel data. It is in the authors opinion that the procedure will effectively determine optimal wing shapes for wings with multiple design variables and of higher morphing capability. 32

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Table 4-1. Small coefficient of variation between the ten base data sets and the random data sets ensures minimal effect of aerodynamic hysteresis on the coefficient of lift. 0 Deg 10 Deg 22.5 Deg Lift coefficient of variations % % % Base 0.14 0.32 1.79 Random 1.36 2.20 2.28 SP 1 Overall 1.83 1.48 2.27 Base 0.34 0.21 0.25 Random 1.17 0.98 1.45 SP 125 Overall 0.72 0.63 1.05 Base 0.19 0.38 0.30 Random 0.83 0.25 1.36 SP 250 Overall 0.66 0.40 0.96 Table 4-2. Drag data show acceptably low variation between the ten base data sets and the random data sets. 0 Deg 10 Deg 22.5 Deg Drag coefficient of variations % % % Base 3.07 3.40 1.90 Random 2.63 2.29 1.67 SP 1 Overall 2.80 2.88 2.04 Base 0.56 1.85 0.81 Random 0.87 1.22 1.26 SP 125 Overall 0.77 1.60 1.47 Base 1.29 1.05 0.39 Random 1.47 0.69 1.24 SP 250 Overall 1.42 1.01 1.11 Table 4-3. Efficiency is found to have a variance of the same magnitude as drag, which is sufficient for the procedure to correctly converge upon the optimum servo position. 0 Deg 10 Deg 22.5 Deg Efficiency coefficient of variations % % % Base 3.05 3.49 2.23 Random 3.13 3.03 1.88 SP 1 Overall 3.39 3.22 2.98 Base 0.54 1.64 0.92 Random 0.46 1.40 0.97 SP 125 Overall 0.94 1.51 1.04 Base 1.22 1.31 0.47 Random 1.00 0.53 1.11 SP 250 Overall 1.39 1.00 0.94 33

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Figure 4-1. The one-design-variable, rectangular planform model used to validate the optimization process has a single point of actuation that alters camber. Figure 4-2. The full field, three-dimensional image, developed by the VIC system, is overlaid on an image of the morphed wing illustrating deformation in the Z-direction (left image has 19% camber, right image has % camber). 34

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Figure 4-3. Wing shape attained by servo position 1 with velocity at 0 and 16 m/s at 10 AOA. The top left image shows the wind off Z-coordinates of the wing in millimeters. The top right image shows the wind on wing deformation. Figure 4-4. Wing shape attained by servo position 250 with velocity at 0 and 16 m/s at 10 AOA. The top left image shows the wind off form of the wing in millimeters. The top right image shows the wind on wing deformation, also in millimeters. 35

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Figure 4-5. Plot of a series of airfoil shapes attained as a function of servo position. 36

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Figure 4-6. Results of an aerodynamic hysteresis study depict the servo scatter and data coefficient of variance for multiple servo positions. 37

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Figure 4-7. Lift coefficient, drag coefficient, and efficiency versus angle of attack are plotted for several servo positions of the one design variable model. 38

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Figure 48. Resulting data illustrate the effectiveness of the optimization procedure. A) Initial population. B) Final population. C) Coefficient of lift servo scatter. D) Morphing wing performance comparison for lift coefficient. E) Efficiency servo scatter. F) Morphing wing performance comparison for efficiency. 39

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CHAPTER 5 OPTIMIZATION OF A HIGH-FIDELITY MORPHING WING A high-fidelity morphing wing model is fabricated to demonstrate the advantage of the morphing wing geometry over that of conventional fixed wing geometries. Initial coefficient of lift and efficiency curves are developed for flat plate and reflex wings. This data is used as a comparative tool to measure the performance of the morphing wing shapes. The optimization procedure is conducted for maximum lift and maximum efficiency through a range of angle of attacks. All experiments are conducted with an unconstrained genetic algorithm. Model Description This model is an elliptical planform, thin plate wing (Figure 5-1) consisting of a single layer, plain weave carbon fiber skin and arced unidirectional carbon fiber spars, which follow the outer curvature of the planform. As with the one-design-variable model, these spars transfer loads such that when the wing shape is altered at the root, a similar shape will transfer throughout the span of the wing. While the model is not capable of transferring the exact airfoil from the root to the tip it does significantly change the wing shape, which is desired for this experiment. The model has two points of actuation, which are positioned at the quarter chord and the trailing edge. There are two attachment points fixing the wing to the fuselage structure, which are located at the leading edge and trailing edge. The attachment point at the leading edge permits rotation only. The attachment point at the trailing edge permits both rotation as well as longitudinal, linear motion. The quarter chord actuation point significantly modifies the wing camber on the order of 11%, while the trailing edge point of actuation allows for 4% wing reflex. 40

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Using the VIC system, a full-field, three-dimensional image of the morphed wing shape, as shown in Figure 5-2, is developed at 16 servo positions. To illustrate how the airfoil at the wing root relates to the airfoil at the tip, a topographic plot with airfoil slices from the 20% and 80% span (Figure 5-3) is shown. These servo positions (250,230) yield a +7.1% camber and .6% reflex. For comparison, these plots are also provided for servo positions 1,1 (Figure 5-4) which is effectively an inverted wing shape of the previous. As plotted in Figure 5-5, an array of airfoil shapes from the 20% span is illustrated to show the morphing capabilities of the model. Comparative Lift and Efficiency Curves In order to determine how well the morphing wing performs, the coefficient of lift and efficiency versus angle of attack are determined for two fixed wing shapes. The first shape is an approximate flat-plate wing obtained by setting servo positions to (130,100) and the second is a reflex wing obtained using servo positions (250,110). Note the abrupt stall of the flat plate (Figure 5-6) at approximately 11 and its poor efficiency throughout the alpha sweep. The wing with reflex has less aggressive stall characteristics at approximately 15 angle of attack with a much higher lift coefficient than that of the flat plate wing. It also has a much higher efficiency, which carries over a large range of angles of attack. This data is used as a comparative tool to measure the performance of the morphing wing shapes. The optimization procedure for maximum lift, then maximum efficiency for several angles of attack is performed. The results from these experiments are plotted with the two fixed wing shapes and evaluated for improved performance. Maximizing Coefficient of Lift Curve The optimization procedure is conducted for six angles of attack from -5 to 20 in 5 increments, which is sufficient for evaluation of its performance. The result of the experiments yield wing shapes that produce maximum lift for a given angle of attack. By fitting a curve 41

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through these datum points a simple polynomial equation is calculated. It is this equation that correlates maximum lift to angle of attack. The genetic algorithm is capable of converging within just six generations when using a well distributed initial population as illustrated in Figure 5-7 (bottom left). The topmost plot in the same figure shows the rapid convergence of the mean performance with the best performance. The rate of convergence can also be seen from the lack of diversity of the servo scatter. The pattern of the initial population is still easily defined because the algorithm immediately hones in on the region of the optimal position. Note that in this case, a second optimization procedure is conducted, this time with an initial population narrowed around the optimal region. Once again the algorithm hones almost immediately on the optimum servo positions, which is well illustrated in the bottom right plot in Figure 5-7. This is a special case due to the simplicity of the objective function and the small coefficient of variance in the data. In the following maximum efficiency tests it is shown that convergence will not occur so rapidly. The performance of the morphing wing as compared to the two fixed wing geometries is plotted in Figure 5-8 (A). By morphing the wing throughout the alpha sweep, a much greater lift coefficient is obtained. Note the benign stall characteristics of the morphing wing, which has little decrease in lift from 15-20. No tests are conducted beyond the 20 angle of attack due to the vibrations encountered within this stall region. Having completed the tests for maximization of lift coefficient, the plot of optimal servo positions versus angle of attack is acquired and plotted in Figure 5-8 (B). As is expected, the maximum lift at any given angle of attack will have no reflex and is why the second servo always converges to position 1. These servo position curves can now be used in a control system, with angle of attack as input, to yield maximum lift performance. 42

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Maximizing Efficiency Curve Efficiency is calculated by dividing the lift coefficient by the drag coefficient. As determined in Chapter 4, the coefficient of variance with such a calculation is significantly greater than that associated with the lift coefficient alone. For this reason, it may take as many as three times the number of generations for the genetic algorithm to converge on the optimal servo positions as compared to the prior set of experiments. The optimization procedure is conducted at seven angles of attack, which are sufficient to populate an efficiency curve. This efficiency curve is then compared to the efficiencies of the flat plate and reflex wings. It is seen in Figure 5-9 (top) the algorithm requires approximately 20 generations before convergence. Note how the mean performance varies throughout the experiment while the best performance will improve incrementally. This is due to the increased complexity of the objective function and the increase in the variance in data. As a result, the genetic algorithm selects much broader and more diverse servo positions to find the optimal region. The scatter plot in Figure 5-9 (center) best illustrates the diversity in selected servo positions. The final graphs of the same figure show the varied, well distributed initial population (bottom left) and the final, converged upon optimum servo positions (bottom right). The performance of the morphing wing with the two fixed wing geometries are plotted in Figure 5-10 (A). Morphing the wing to the determined optimal shapes through the alpha sweep provides a significant improvement in efficiency up to the region of stall. Notably, at 2.5 angle of attack, the morphing wing has twice the efficiency value as that of the other wings. Having completed the tests for maximization of efficiency, the plot of optimal servo positions versus angle of attack is acquired and plotted in Figure 5-10 (B). 43

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Above the servo positions are the optimized wing shapes rotated to the corresponding angle of attack. Using the equations of these curves in a control system, maximum efficiency as a function of angle of attack can be achieved. These unpredictable curves illustrate the need for optimization procedures for highly complex morphing wing structures. 44

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Figure 5-1. The two-design-variable model morphs the wing geometry through change of camber and reflex. Figure 5-2. The full field, three-dimensional image, developed by the VIC system, is overlaid on an image of the morphed wing illustrating deformation in the Z-direction. 45

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Figure 5-3. Morphed wing surface (Servo Positions: 250,230) with airfoil slices from the 20% and 80% span yields a negative camber and negative reflex. Figure 5-4. Morphed wing surface (Servo Positions: 1,1) with airfoil slices from the 20% and 80% span yields a positive camber and positive reflex. 46

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Figure 5-5. An illustration of the intermediate wing shapes from the 20% span shows the morphing capability of the two-design-variable model. Figure 5-6. The lift coefficient and efficiency is plotted using set flat plate and reflex wing geometries. 47

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Figure 5-7. These sample plots illustrate the convergence of the genetic algorithm upon the optimal servo position for maximum lift at 10 angle of attack. 48

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Figure 5-8. Morphing wing data for optimized lift coefficient. A) The morphing wing performance as compared to the fixed reflex wing and flat plate. B) The optimal servo positions as a function of angle of attack with the corresponding wing shape. 49

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Figure 5-9. Sample plots showing the convergence of the genetic algorithm on the optimal servo position for maximum efficiency at 10 angle of attack. 50

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Figure 5-10. Morphing wing data for optimized efficiency. A) The morphing wing performance as compared to the fixed reflex wing and flat plate. B) The optimal servo positions as a function of angle of attack with the corresponding wing shape. 51

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CHAPTER 6 CONCLUSION AND RECOMMENDATIONS FOR FUTURE WORK Conclusion A procedure has been established to achieve proper shape management of morphing wing structures. It has been demonstrated that utilizing a genetic algorithm with wind tunnel hardware-in-the-loop is an effective means of determining optimal wing shape functions. The use of these shape functions enables a morphing aircraft to achieve optimal flight performance in all flight regimes. To demonstrate the procedure, a two design-variable morphing wing is fabricated with the capability of altering maximum camber and trailing edge reflex. Two experiments are conducted for maximizing the lift coefficient and maximizing efficiency, which resulted in optimal servo position versus angle of attack shape functions. For a performance comparison, the wing shape is set as a flat plate and again as a medium camber wing with reflex. These fixed wing shapes are tested for lift and efficiency performance from -5 to 25 angle of attacks. Plotting the performance of the morphing wing with that of the two fixed wings illustrates the dramatic improvement achieved by morphing wing structures. In particular, while the slope of the lift coefficient curve remains the same for each data set, the morphing wing shows a 63.4% improvement over the fixed reflex wing. Another remarkable attribute of the morphing wing is its benign stall characteristics. While more data must be collected to determine the wings performance at angles of attack greater than 20, it is clear that such a wing can be used to control and mitigate wing stall. The experiments for determining maximum efficiency show an equally impressive increase in performance. Considering the range of -5 to 5 angle of attacks, typical for straight and level flight and subtle altitude changes, efficiency increases as much as 62.1%. 52

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These results support high confidence in the optimization procedure. The genetic algorithm is capable of proper convergence despite the variance in collected wind tunnel data. It is in the authors opinion that the procedure will effectively determine optimal wing shapes for morphing wings of many design variables and higher morphing capability. Recommendations for Future Work There are many valuable wing shape functions that can be attained using this procedure which have yet to be explored. By simply applying constraints to the genetic algorithm many new ideas for flight optimization arise. One such experiment could be to vary the wing shape as a function of velocity to attain a desired lift. For a given angle of attack, a high velocity would yield minimal camber while a low velocity would yield a comparatively high camber. Such a shape function would minimize drag thereby increasing efficiency. Another interesting study would be to apply the constraint of a desired pitching moment for each angle of attack to ensure longitudinal stability. Using this constraint while maximizing lift at very high angles of attack could result in the mitigation of wing stall. Such a wing shape function would yield a controlled, rate of descent flight mode useful in an auto-land feature. Of course these shape functions are of no value unless they are utilized in an on-board control system for real-time wing morphing. Such a control system will receive data such as angle of attack or velocity and in response, command the position of the actuators. The servo controller produced by Scott Bowman, which is utilized exclusively for this research, is capable of such a task. In a given mission profile for an aerial vehicle, several flight modes may be commanded. For example, at takeoff the vehicle may require a wing shape that maximizes rate of climb. When required altitude is met, another wing shape may be commanded to maximize speed to a 53

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specified waypoint. At this point the vehicle may be required to conduct surveillance, which would require a wing shape that would yield maximum efficiency for extended flight time. After completion of surveillance the vehicle may be commanded to return to another waypoint where it is required to perform a steep descent angle for landing in a small, confined field. The ability to switch between these distinct optimal wing shape functions is necessary to maximize the overall performance of a morphing winged aircraft as it transitions between flight modes. 54

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LIST OF REFERENCES [1] Haenel, R. T., Creep Deformation of Pin-Jointed Structures, MS Thesis, The Pennsylvania State University, Pennsylvania, 1955. [2] Gooders, J., and Pledger, M., Birds of North America, Edison, New Jersey: Chartwell Books Inc., 1987. [3] Davidson, J., Chwalowski, P., and Lazos, P., Flight Dynamic Simulation Assessment of a Morphable Hyper-Eliptic Cambered Span Winged Configuration, 2003 AIAA Atmospheric Flight Mechanics Conference and Exhibit, Austin, TX, AIAA Paper 2003-5301, 2003. [4] Shyy, W., Berg, M., and Ljungqvist, D., Flapping and Flexible Wings For Biological and Micro Air Vehicles, Progress in Aerospace Sciences, Vol. 35, No. 5, 1999, pp. 455-506. [5] Ifju, P., Jenkins, D., Ettinger, S., Lian, Y., and Shyy, W., Flexible-Wing Based Micro Air Vehicles, AIAA Publication, AIAA Paper 2002-0705, 2002. [6] Albertani, R., Hubner, J., Ifju, P., Lind, R., and Jackowski, J., Experimental Aerodynamics of Micro Air Vehicles, SAE World Aviation Congress and Exhibition, Reno, NV, 2004. [7] Stanford, B., Abdulrahim, M., Lind, R., Ifju, P, Investigation of Membrane Actuation for Roll Control of a Micro Air Vehicle, Journal of Aircraft, Vol. 44, No. 3, 2007, pp. 741-749. [8] Gano, S., Renaud, J., Batill, S., and Tovar, A., Shape Optimization for Conforming Airfoils, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia, AIAA Paper 2003-1579, 2003. [9] Gano, S., and Renaud, J., Optimized Unmanned Aerial Vehicle with Wing Morphing for Extended Range and Endurance, 9th AIAA/ISSMO Symposium and Exhibit on Multidisciplinary Analysis and Optimization, Atlanta, GA, AIAA Paper 2002-5668, 2002. [10] Waszak, M., Davidson, J., and Ifju, P., Simulation and Flight Control of an Aeroelastic Fixed Wing Micro Aerial Vehicle, 2002 AIAA Atmospheric Flight Mechanics Conference and Exhibit, Monterey, CA, AIAA Paper 2002-4875, 2002. [11] Skillen, M., and Crossley, W., Modeling and Optimization for Morphing Wing Concept Generation, NASA Publication CR-2007-214860, March 2007. [12] Albertani, R., Experimental Aerodynamic and Static Elastic Deformation Characterization of Low Aspect Ratio Flexible Fixed Wings Applied to Micro Aerial Vehicles, Ph.D. Dissertation, University of Florida, Gainesville, FL, 2005. [13] Sytsma, M., Aerodynamic Flow Characterization of Micro Air Vehicles Utilizing Flow Visualization Methods, MS Thesis, University of Florida, Gainesville, FL, 2006. 55

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[14] Bilgen, O., Kochersberger, K., Diggs, E., Kurdila, A., and Inman, D., Morphing Wing Aerodynamic Control via Macro-Fiber-Composite Actuators in an Unmanned Aircraft, 2007 AIAA Conference and Exhibit, Rohnert Park, CA, AIAA Paper 2007-2741, 2007. [15] Williams, R., Inman, D., and Keats-Wilkie, W., Nonliniear Mechanical Behavior of Macro Fiber Composite Actuators, Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Undated material. [16] Claverie-Bohn, C., Dynamic Antifouling Structures and Actuators Using EAP Composites, Ph.D. Dissertation, University of Florida, Gainesville, FL, 2004. [17] Strelec, J., Lagoudas, D., Khan, M., and Yen, J., Design and Implementation of a Shape Memory Alloy Actuated Reconfigurable Airfoil, Journal of Intelligent Material Systems and Structures, Vol. 14, No. 4-5, 2003, pp. 257-273. [18] Lu, K., and Kota, S., Design of Compliant Mechanisms for Morphing Structural Shapes, Journal of Intelligent Material Systems and Structures, Vol. 14, No. 6, 2003, pp. 379-391. [19] Rechenberg, I., Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, FrommannHolzboog, Stuttgart, 1973. [20] Whitley, D., An Overview of Evolutionary Algorithms, Journal of Information and Software Technology, Vol. 43, 2001, pp. 817-831. [21] Rasheed, K., and Hirsh, H., Learning to be Selective in Genetic-Algorithm-Based Design Optimization, Artificial Intelligence for Engineering Design, Analysis and Manufacturing, Vol. 13, 1999, pp. 157-169. [22] Herrera, F., Lozano, M., and Molina, D., Continuous Scatter Search: An Analysis of the Integration of Some Combination Methods and Improvement Strategies, European Journal of Operational Research, Vol. 169, No. 2, 2006, pp. 450-476. [23] Herrera, F., Lozano, M., and Snchez, A., Hybrid Crossover Operators for Real-Coded Genetic Algorithms: An Experimental Study, Soft Comput, Vol. 9, 2005, pp. 280. [24] Naujoks, B., Willmes, L., Haase, W., Bck, T., and Schtz, M., Multi-point Airfoil Optimization Using Evolution Strategies, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, 2000. [25] Liu, B., Two-Level Optimization of Composite Wing Structures Based on Panel Genetic Optimization, Ph.D. Dissertation, University of Florida, Gainesville, FL, 2001. [26] Hemker, T., Hardware-in-the-Loop Optimization of the Walking Speed of a Humanoid Robot, CLAWAR 2006, Brussels, Belgium, 2006. 56

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[27] Kammeyer, M., Wind Tunnel Facility Calibrations and Experimental Uncertainty, The Boeing Company, American Institute of Aeronautics and Astronautics, 1998. [28] Springer, A., Uncertainty Analysis of the NASA MSFC 14-Inch Trisonic Wind Tunnel, 1999 37th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA-99-0684, 1999. [29] Lopez-Anido, R., El-Chiti, F., Muszyski, L., Dagher, H., Thompson, L., and Hess, P., Composite Material Testing Using a 3-D Digital Image Correlation System, American Composites Manufacturers Association, Tampa, Florida, 2004. [30] Muszyski, L., Lopez-Anido, R., and Shaler, S., Image Correlation Analysis Applied to Measurement of Shear Strains in Laminated Composites, SEM IX International Congress on Experimental Mechanics, Orlando, Florida, 2000. [31] Schmidt, T., Tyson, J., and Galanulis, K., Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3-D Image Correlation Photogrammetry, Part I. Experimental Techniques, Vol. 27, No. 3, 2002, pp. 47-50. [32] Helm, J., McNeill, S., and Sutton, M., Improved 3-D Image Correlation for Surface Displacement Measurement, Optical Engineering, Vol. 35, No. 7, 1996, pp. 1911-1920. 57

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BIOGRAPHICAL SKETCH Frank Boria was born in Portsmouth, New Hampshire and spent most of his childhood in York, Maine. When he was 13 years old, he and his family moved to Fernandina Beach, Florida. During his junior year of high school, Frank won a scholarship to train for his private pilot license. Having trained in a Citabria 7ECA, a tandem two-seat tail-dragger, Frank received his pilot license and developed a passion for aviation. After high school he moved to Tallahassee, Florida where he attended Lively Technical Center and received his Airframe and Powerplant certifications. With these certifications he moved to Lake City, Florida where he spent 7 years working at TIMCO, a third-party aircraft repair station. His experience was primarily focused on aircraft structures for DC9, Boeing 727, and C130 aircraft. With the understanding of how to fly and maintain an aircraft, his interests leaned toward understanding the physics of flight and the process of design. During the final 2 years of work at TIMCO, Frank attended evening classes at Santa Fe Community College where he received his Associate of Arts degree. He transferred to the University of Florida where, in 2004, he received his Bachelor of Science degree in aerospace engineering. He continued his education at the University of Florida, and in 2007, he received his Master of Science degree in aerospace engineering with a focus on solid mechanics, design, and manufacturing. Frank now resides in Gainesville, Florida with his beautiful bride, Rikki, and three wonderful children, Addie, Olivia, and Christian. 58