Decision Making Strategies for Probabilistic Aerospace - SMARTech

243 Pages·2006·13.05 MB·English

Decision Making Strategies for Probabilistic Aerospace
Systems Design
A Thesis
Presented to
The Academic Faculty
by
Nicholas Keith Borer
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
School of Aerospace Engineering
Georgia Institute of Technology
May 2006
Copyright (cid:176)c 2006 by Nicholas Keith Borer
Decision Making Strategies for Probabilistic Aerospace
Systems Design
Approved by:
Dr. Dimitri Mavris Craig Nickol
Professor, Faculty Advisor Aerospace Engineer
Georgia Institute of Technology NASA Langley Research Center
Dr. Daniel Schrage Sharon Padula
Professor Senior Research Scientist
Georgia Institute of Technology NASA Langley Research Center
Dr. Alan Wilhite
Professor
Georgia Institute of Technology
Date Approved: 21 February 2006
It would be well if engineering were less thought of, and even defined, as the art of
constructing. In a certain important sense it is rather the art of not constructing; or,
to define it rudely but not inaptly, it is the art of doing that well with one dollar,
which any bungler can do with two after a fashion.
- Arthur Mellen Wellington, The Economic Theory of the Location of Railways
To mom and dad, for their love,
patience, and unwavering support
ACKNOWLEDGEMENTS
I would like to extend thanks to the many individuals who have helped me through this
endeavor. Dr. Dimitri Mavris, my advisor, has given years of support and encouragement
throughout my tenure at Georgia Tech. I cannot say enough about the opportunities he
has provided for me and am grateful to have had the chance to work with him all these
years. Dr. Daniel Schrage and Dr. Alan Wilhite both bring their considerable experience
in aerospace systems design to my reading committee and I feel privileged to be able to
receive their comments. Craig Nickol of NASA Langley served as my advisor for the GSRP
fellowshipand hasgivenmeinvaluableadvice andsupportsince hefirst cameto NASA.His
experiences with the Multi-mission Maritime Aircraft (MMA/P-8A) while at the Naval Air
Systems Command provided much insight into the practical world of multi-mission systems
design. Sharon Padula of NASA was kind enough to meet with me several times during my
stay at Langley. She and Dr. Wu Li provided much-needed input regarding optimization
and decomposition techniques during our many conversations. They also kept me honest
when it came to some of the mathematical techniques I was experimenting with.
ManyothersatNASALangleyprovidedguidance,encouragement,andhelpbothduring
and after my visits. I would like to extend thanks to my first GSRP technical advisor Bob
McKinley, Branch Head Bill Kimmel, and everyone at the Aerospace Systems Analysis
Branch for their support.
ASDLatGeorgiaTechhasprovidedmewithawealthofcontacts,experiences,andmost
importantly,goodfriends. IwouldliketothankDr.MichelleKirbyandJeffSchuttefortheir
assistance with the QuEST technology study and for providing the models used to develop
the reduced-order surfaces seen in Chapter VII. Newly-minted Dr. Michael Buonanno, who
wasalsoaGSRPfellowwithme,providedvaluablehelpwithafewMatlabmodelsaswellas
agoodsoundingboardforideas. Dr.BryceRoth,nowanemployeeatGETransportationin
Cincinnati, providedsoundadvice. HealsointroducedmetotheCommemorativeAirForce
v
and vintage aircraft restoration. Rob McDonald spent many hours chewing over various
ideas, algorithms, ponderings, LATEX queries...and also made a good carpool partner down
to the CAF. During the final weeks of writing, I accosted many ASDLer’s and forced them
to proofread a chapter. If there is a typo, misspelling, or grammatical error within this
document, it is not for lack of trying to eliminate them all.
I will not attempt to list all of my friends at Georgia Tech who have made the past
several years so much fun...to do so would take up far too much room. I would like to give
aspecialthankstoTheGoldenPheasantregularsformanychallengingnightsofthree-man,
the back-porch crew at Rocky who cannot be deterred even in sub-freezing temperatures,
all of the current and former residents of Casa de Shalimar, and who can forget The Day of
Chili? My time in Atlanta has been very enjoyable because of you, making my upcoming
departure that much more bittersweet. I’ll save a seat at Fenway for you.
My family and friends from around the globe have given their encouragement and love
throughout my life no matter where I hang my hat. I’ve been a long way from home for a
long time, and I could not have made it without your understanding and support. Mom,
Randy, Dad, Laura, Scott, Mike, Jon...thanks.
Last but certainly not least, I would like to thank Mary Margaret Stoeckle for her years
ofpatienceandsupport, nevermindfillingoutthelion’sshareofmybibliographydatabase.
I’m looking forward to finally being able to share the same area code with you.
Thank you all – without you, I could accomplish nothing.
vi
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
LIST OF SYMBOLS OR ABBREVIATIONS . . . . . . . . . . . . . . . . . . xvi
SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Multi-Mission Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Requirements Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 6
II REQUIREMENTS AND AIRCRAFT SIZING. . . . . . . . . . . . . . . 9
2.1 The Engineering Design Process . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Requirements Specification . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Traditional Single-Objective Approaches . . . . . . . . . . . . . . . . . . . 14
2.3 Modern Sizing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Multidisciplinary Design Optimization and Statistical Techniques . 17
2.3.2 Evolving Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Multi-Mission Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Shortfalls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2 Multipoint Sizing for Multi-Mission Vehicles . . . . . . . . . . . . . 24
III DESIGN AND DECISION MAKING . . . . . . . . . . . . . . . . . . . . 26
3.1 Pareto Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Axiomatic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Multiple Criteria Decision Making Techniques . . . . . . . . . . . . . . . . 31
3.3.1 The Ideal Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.2 Simple Additive Weighting . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.3 TOPSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.4 Compromise Programming . . . . . . . . . . . . . . . . . . . . . . . 39
vii
3.3.5 MCDM for Systems Design . . . . . . . . . . . . . . . . . . . . . . 40
IV DECISION MAKING FOR LARGE-SCALE PROBLEMS . . . . . . . 42
4.1 Generalized Probabilistic MCDM Formulation . . . . . . . . . . . . . . . . 43
4.2 Case Study: Notional Multi-Role Fighter . . . . . . . . . . . . . . . . . . . 45
4.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Results and Implications . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 MCDM Example Application . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.1 Multiple Criteria Beam Design . . . . . . . . . . . . . . . . . . . . 50
4.3.2 Polynomial Surrogate Modeling . . . . . . . . . . . . . . . . . . . . 54
4.4 Initial Experiments for Beam Design Problem . . . . . . . . . . . . . . . . 57
4.4.1 Resolution of Nondominated Solutions . . . . . . . . . . . . . . . . 58
4.4.2 Deterministic Decision Making. . . . . . . . . . . . . . . . . . . . . 61
4.4.3 Design to Probabilistic Requirements . . . . . . . . . . . . . . . . . 65
4.4.4 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
V IMPORTANCE AND INTERDEPENDENCE . . . . . . . . . . . . . . . 72
5.1 Characterizing Relative Importance . . . . . . . . . . . . . . . . . . . . . . 73
5.1.1 Entropy and Static Relative Importance . . . . . . . . . . . . . . . 74
5.1.2 Constraints, Thresholds, and Dynamic Relative Importance . . . . 82
5.1.3 Experiments with Modified Relative Importance Models . . . . . . 86
5.2 Requirements Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.1 Decomposition Techniques for Linear Systems . . . . . . . . . . . . 98
5.2.2 Singular Value Decomposition for Response Surface Equations . . . 99
5.2.3 Multidimensional Visualization with Characteristic Requirements . 106
5.2.4 Interdependent Relative Importance Modeling . . . . . . . . . . . . 110
VI METHODSFORPROBABILISTICLARGE-SCALEDECISIONMAK-
ING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.1 Requirements Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 Concept Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.3 Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3.1 Surrogate Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4 Relative Importance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
viii
6.4.1 Identification of User Preferences . . . . . . . . . . . . . . . . . . . 129
6.4.2 Entropy Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.4.3 Interdependence Evaluation . . . . . . . . . . . . . . . . . . . . . . 130
6.4.4 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.5 Probabilistic Considerations . . . . . . . . . . . . . . . . . . . . . . 133
6.5 Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.5.1 Computational Cost . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.6 Multidimensional Visualization . . . . . . . . . . . . . . . . . . . . . . . . 137
VIIEXAMPLE APPLICATION: TRANSPORT DESIGN . . . . . . . . . . 142
7.1 Requirements Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 Concept Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.3 Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.3.1 Creation of Surrogate Models . . . . . . . . . . . . . . . . . . . . . 149
7.4 Relative Importance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.4.1 User Preferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.4.2 Entropy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7.4.3 Interdependence Analysis. . . . . . . . . . . . . . . . . . . . . . . . 154
7.4.4 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.5 Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.6 Multidimensional Visualization . . . . . . . . . . . . . . . . . . . . . . . . 167
7.6.1 Requirements Decomposition . . . . . . . . . . . . . . . . . . . . . 171
7.7 Goal Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
VIIICONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . . . 178
8.1 Contributions to Aerospace Systems Design . . . . . . . . . . . . . . . . . 178
8.2 Lessons from Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.3 Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8.4 New Research Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.5 Caveat Cursor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
APPENDIX A RESPONSE SURFACE METHODOLOGY . . . . . . . . 186
APPENDIX B SINGULAR VALUE DECOMPOSITION . . . . . . . . . 195
ix
APPENDIX C BASELINE INPUTS FOR LONG-RANGE TRANSPORT
TECHNOLOGY STUDY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
APPENDIXD VALIDATIONOFREDUCED-ORDERRESPONSESUR-
FACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
x