etd-tamu-2004C-AERO-Griffith

217 Pages·2004·11.4 MB·English

NEW METHODS FOR ESTIMATION, MODELING AND VALIDATION OF

DYNAMICAL SYSTEMS USING AUTOMATIC DIFFERENTIATION

A Dissertation

by

DANIEL TODD GRIFFITH

Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

December 2004

Major Subject: Aerospace Engineering
NEW METHODS FOR ESTIMATION, MODELING AND VALIDATION OF

DYNAMICAL SYSTEMS USING AUTOMATIC DIFFERENTIATION

A Dissertation

by

DANIEL TODD GRIFFITH

Submitted to Texas A&M University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Approved as to style and content by:

______________________________
John L. Junkins
(Chair of Committee)

______________________________ ______________________________
Srinivas R. Vadali John E. Hurtado
(Member) (Member)

______________________________ ______________________________
Alan B. Palazzolo Walter E. Haisler
(Member) (Head of Department)

December 2004

Major Subject: Aerospace Engineering
iii
ABSTRACT

New Methods for Estimation, Modeling and Validation of Dynamical

Systems Using Automatic Differentiation. (December 2004)

Daniel Todd Griffith, B.S., Morehead State University;

B.S., University of Kentucky;

M.S., University of Kentucky

Chair of Advisory Committee: Dr. John L. Junkins

The main objective of this work is to demonstrate some new computational methods
for estimation, optimization and modeling of dynamical systems that use automatic
differentiation. Particular focus will be upon dynamical systems arising in Aerospace
Engineering. Automatic differentiation is a recursive computational algorithm, which
enables computation of analytically rigorous partial derivatives of any user-specified
function. All associated computations occur, in the background without user
intervention, as the name implies. The computational methods of this dissertation are
enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate
Embedding Method). OCEA has been recently developed and makes possible efficient
computation and evaluation of partial derivatives with minimal user coding. The key
results in this dissertation details the use of OCEA through a number of computational
studies in estimation and dynamical modeling.
Several prototype problems are studied in order to evaluate judicious ways to use
OCEA. Additionally, new solution methods are introduced in order to ascertain the
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extended capability of this new computational tool. Computational tradeoffs are studied
in detail by looking at a number of different applications in the areas of estimation,
dynamical system modeling, and validation of solution accuracy for complex dynamical
systems. The results of these computational studies provide new insights and indicate
the future potential of OCEA in its further development.
v

To my parents

Dan and Barbara

and

my brothers and sisters

Christie, Ryan and Andy
vi
ACKNOWLEDGMENTS

Setting upon any of life’s journeys requires the support and guidance of many
people. Many people have shared equally the successes and disappointments which
have arisen while on the path to completing this dissertation. Of course, there are many
who have made technical contributions that aided me in meeting my educational
objectives and, more specifically to completing this work, many have made meaningful
contributions. I have benefited greatly, as well, from the support of many people in my
personal life who have done so much to shape me into who I am today.
I am greatly indebted to my graduate advisor, Dr. John Junkins. I thank him for
welcoming me to study with him at Texas A&M in August 2000. I, of course,
acknowledge the technical contributions he has made toward completing this
dissertation. He has been a source of knowledge on many subjects, and has given me a
glimpse into the fundamental principles which unify many technical areas. He has been
a source of inspiration to me whether it be in the classroom, in a research meeting or in
passing in the hallway, and gave his time freely to me whenever it was needed. I
especially appreciate the guidance and words of encouragement he provided during my
toughest times and most misguided moments. I appreciate the financial support he
provided over my first year of study and during the latter months while I completed this
dissertation. My earnest hope is that I take a great deal from my experiences with Dr.
Junkins to my professional life since I feel the impact he has had on me is significant in
many ways, not only for the technical knowledge and the large-scale perspective I have
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gained from him, but also for the passion he has for his work and students. I could not
be more pleased with the time I spent with him at Texas A&M.
My parents, Dan and Barbara, have always been my biggest asset in their constant
support, by the example they set, and for the drive and confidence they have instilled in
me my entire life. They have, most importantly, tempered my ambition by
demonstrating the balance in life that I strive for in order to be truly happy and
completely successful.
My most joyous moments have come since meeting the most special person in my
life, my fiancé Loraine. Her support has inspired me to work diligently and focus on the
completion of this dissertation. She has sacrificed a great deal by understanding the
importance of this dissertation to me and has supported me in more ways than I could
ever expect or deserve. I could not have completed this without her love and support.
I acknowledge the tremendous impact that Dr. James Turner has had on technical
merit of this dissertation. I thank him for the countless instances he has given his time to
share his technical expertise. I appreciate his sense of humor and the passion he has for
his work. It was entirely my pleasure to have the opportunity to work with him.
I am very thankful for the insights and valuable time of my committee members Dr
S. Rao Vadali, Dr. John E. Hurtado, and Dr. Alan Palazzolo. Dr. Vadali has provided
me with a fine example in the thoughtfulness of his classroom teaching. I am thankful
for the time he devoted to me as I learned much about optimization. I am indebted to
Dr. Hurtado for many inspiring lectures and conversations regarding advanced topics in
dynamics. I am thankful for his practical, informal style of teaching and mentoring.
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I am thankful for the support of the American Society for Engineering Education in
awarding three years of financial assistance to support my doctoral studies through the
National Defense Science and Engineering Fellowship Program from 2001-2004.
The Aggie campus is unlike any other in this nation. I appreciate the caring nature,
togetherness and values of the people of Texas A&M and College Station, Texas. In my
time in College Station, I am quite thankful for the community of St. Mary’s Catholic
Church, especially Father Mike Sis, for providing me with great words of wisdom and
perspectives on living. I shared many good times with many new friends and colleagues
at Texas A&M. I am thankful to have had two wonderful friends as office mates. Chad
Searcy has been and is a friend who has truly enhanced my experience at Texas A&M
by showing me the ropes when I arrived in College Station. I appreciate his kindness
and generosity, and our many discussions on politics. Rajnish Sharma has been an
exceptional person to share a workspace with in my last days at Texas A&M. I
appreciate his warm personality and have taken a great deal from his relaxed attitude
regarding life and work.
I would like to acknowledge two friends who have made the times away from my
desk very enjoyable. Lisa Biggs has been a great friend, and someone who has many
times given me a good perspective on what is truly important. I thank her for her
friendship. I am also very thankful for the times I have spent with Andy Sinclair. I had
the pleasure of enjoying many discussions with him on Southeastern Conference (SEC)
sports. Although he leans toward the University of Florida Gators (and I the University
of Kentucky Wildcats), I am very happy for the sense of home I received from our
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discussions. I am also very happy for the significant technical discussions we had, many
of which led us to hours of research on the dynamics encountered in the game of golf.
The match play feature of the Tiger Woods golf game executed on the PlayStation II
game system proved to be an ideal testbed for this study.
I would also like to thank Art and Rocio Fano for welcoming me into their family.
Art and Rocio have made the last year of my studies very enjoyable through their
warmth and thoughtful attention.
There are many others who have I have not mentioned here by name who I would
like to thank. I sincerely thank them as well.
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TABLE OF CONTENTS

Page

ABSTRACT…………………………………………………………………………. iii

DEDICATION………………………………………………………………………. v

ACKNOWLEDGMENTS…………………………………………………………… vi

TABLE OF CONTENTS……………………………………………………………. x

LIST OF TABLES………………………………….……………………………….. xii

LIST OF FIGURES………………………………………………………………….. xiv

CHAPTER

I INTRODUCTION…………………………………………………… 1

II OVERVIEW OF COMPUTERIZED DIFFERENTIATION……….. 5

2.1 Symbolic Differentiation………………………………… 5
2.2 Automatic Differentiation……………………………….. 6
2.3 Overview of OCEA……………………………………… 7

III ESTIMATION AND CONTROL OF DYNAMICAL SYSTEMS…. 14

3.1 Review of First-order Algorithms……………………….. 15
3.2 Higher-order Generalized Sensitivity Calculations……… 22
3.3 Higher-order Algorithms………………………………… 38
3.4 Numerical Examples…………………………………….. 50
3.5 Summary…………………………………………………. 74

IV MODELING OF DYNAMICAL SYSTEMS……………………….. 75

4.1 Overview………………………………………………… 76
4.2 Equations of Motion Formulation……………………….. 77
4.3 Formulation via Lagrange’s Equation…………………… 81
4.4 Numerical Integration of Equations of Motion………….. 94
4.5 Numerical Examples…………………………………….. 96
4.6 Comparison with Hard-coding Equations of Motion……. 114
4.7 Summary…………………………………………………. 118