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INCLAN-DISSERTATION-2021.Pdf A METHOD FOR SYSTEM OF SYSTEMS DEFINITION AND MODELING USING PATTERNS OF COLLECTIVE BEHAVIOR A Dissertation Presented to The Academic Faculty by Eric Inclan In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Aerospace Engineering Georgia Institute of Technology May 2021 COPYRIGHT © 2021 BY ERIC INCLAN A METHOD FOR SYSTEM OF SYSTEMS DEFINITION AND MODELING USING PATTERNS OF COLLECTIVE BEHAVIOR Approved by: Dr. Dimitri Mavris, Advisor Dr. Jean Charles Domerçant School of Aerospace Engineering Georgia Tech Research Institute Georgia Institute of Technology Dr. Michael J. Steffens Dr. Santiago Balestrini-Robinson School of Aerospace Engineering Georgia Tech Research Institute Georgia Institute of Technology Dr. Daniel P. Schrage School of Aerospace Engineering Georgia Institute of Technology Date Approved: April 29, 2021 DEDICATION To my family iii ACKNOWLEDGEMENTS First and foremost, I would like to thank Dr. Mavris for his sense of humor, patience, leadership, and support. Your feedback has always been as accurate and valuable as it has been incisive. I will undoubtedly be a better scientist and engineer for it, and I am grateful for all the guidance you have given me. I want to thank all of the Georgia Tech faculty and staff that I had the privilege to learn from and work for, for embodying a level of professionalism, talent, depth of understanding, empathy, and diligence that is very hard to find, let alone in one place. I would like to thank my lab-mates, and in particular John Mines, Stephanie Zhu, Arturo Santa, and Katie Handschuh Fuerst, for listening when I needed someone to talk to. I would also like to thank Stephanie Zhu for the late nights we spent debating the finer points of fluid mechanics and pouring over this and that equation. I would like to thank my mother, my wife, and my son for their love and for inspiring me to press forward. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS iv LIST OF FIGURES viii LIST OF SYMBOLS AND ABBREVIATIONS xiii SUMMARY xiv CHAPTER 1. Introduction and Background 1 1.1 Foreword 1 1.2 Department of Defense Acquisition 2 1.3 Paradigm Shifts in USN Ship Design, Acquisition, and Modeling 5 1.4 Navy Fleet Synthesis Studies 9 1.5 System of Systems 16 1.6 Complex Behavior 21 1.7 Emergent Behavior 33 CHAPTER 2. Modeling Challenges and Definitions 55 2.1 Measures of Merit 55 2.2 The Limitations of Modeling & Simulation 59 2.2.1 Complexity-Appropriate Simulation and Tool Choices 68 2.2.2 Emergent Behavior within the Scope of Simulated SoS 71 2.2.3 Response to a Relevant Polemic 77 2.3 Defining Property, Behavior, and Interaction 81 2.4 A Notional Adversarial Model 83 CHAPTER 3. Patterns and Emergence 87 3.1 Pattern Recognition 89 3.2 Self-Organization 93 3.3 A Canonical Example of Self-Organization 99 3.4 Synthesis of Key Observations: Measuring versus Modeling Emergence 105 CHAPTER 4. Complexity and Emergence Defined 108 4.1 A Pragmatic Definition of Emergence 111 4.2 Requirements for Simulating Emergence in SoS 113 4.3 Traceability and Associating Self-Organization with Emergent Properties 117 4.3.1 Hypothesis 1: Upper Bound on the Number of Properties 118 4.3.2 Hypothesis 2: Property Identification and Association 119 4.3.3 Definition 2a: Property Distinctiveness 125 4.3.4 Definition 2b: Interaction Detection and Association 127 4.4 Systems Science Research Q&A Summary 132 CHAPTER 5. Experiment Procedures and Exploitation Analysis 137 5.1 Tools for Data Mining 141 5.1.1 Statistical Measures 141 v 5.1.2 Candidate Property Identification 143 5.1.3 Model Complexity Calculations 146 5.2 Self-Organization Detection Tool Workflows 157 5.2.1 Tool 1: Fast Fourier Transform (FFT) 159 5.2.2 Tool 2: Fourier Series (FS) Curve Fitting 165 5.3 Behavior Association (Curve-Fitting) Tool Workflows 169 5.3.1 Time intervals using SISSO 174 5.3.2 Contrasting With Other Behavior Association Studies 178 5.4 Stability Analysis Method for Emergence Exploitation 190 5.5 Hypothesis Testing Procedure 197 5.5.1 Hypothesis 1 Testing 198 5.5.2 Hypothesis 2 Testing 201 5.6 Boids Study 208 5.7 Adversarial Boids Study 213 CHAPTER 6. The Boids Model Case Study 222 6.1 Case 1a: Boids versus Flock 222 6.2 Case 1b: Flock versus Flock 227 6.2.1 Stable / Independent 229 6.2.2 Interaction Phase Data 238 6.2.3 Re-stabilization 249 6.2.4 Interact. / Re-stab. Phase Data 261 6.2.5 Full Time-Series Data (H2 property interchangeability) 268 6.2.6 Critical Analysis of H2-related results 280 6.2.7 H1 Falsification Test 289 CHAPTER 7. Adversarial Boids Case Study 291 7.1 SO Detection 291 7.2 Sensitivity Analysis 297 7.3 Hypothesis 3 Statement 298 7.4 H3 Falsification Test 301 7.4.1 Pilot Behavior Rules Modification 302 7.4.2 Experiment Results 305 7.4.3 Reductionist vs. Non-Reductionist Explanations 311 7.4.4 A Remark on Hypothesis Testing 312 7.4.5 A Persistent Ambiguity 312 CHAPTER 8. UAV Swarming Case Study 314 8.1 Pattern Recognition 319 8.1.1 Simulation Settings and Modifications 319 8.1.2 Results 322 8.2 Behavior Association 326 8.2.1 Simulation Settings and Modifications 328 8.2.2 Results 332 8.3 Exploitation Analysis 342 8.3.1 Measures of Merit 342 8.3.2 Sensitivity Analysis 345 vi 8.3.3 Simulation Settings and Modifications 349 8.3.4 Results: Swarm Yaw Case Study 351 8.3.5 Results: Swarm Principal Axis Length Case Study 355 8.4 Comments on Negative Emergence and Assured Autonomy 359 CHAPTER 9. Conclusions and Future Work 362 9.1 Summary of Method and Research Findings 365 9.2 Future Work 370 APPENDIX A. Supplemental Material 376 A.1 On Hypergraphs 376 A.2 Additional Arguments on Simulated SoS 377 A.3 Equation-Free Modeling 381 A.4 Periodicity Revisited 384 A.5 A Canonical Example of Emergence 385 A.6 Time-series using SISSO 387 A.7 Property Down-Selection Considerations 390 A.8 Brief Review of Time-series Analysis Using Granger Causality 391 A.9 Reasons for No Emergence or Surprise (in Simulation) 393 A.10 Comments on Causation and Graphs 394 A.11 Brief Review of Other Symbolic Regression Tools 400 A.12 Contrasting with Other Behavior Association Studies (Extended) 402 A.13 Emergence and Self-Organization as Latent Nodes 410 A.14 Additional Comments Relating to Tests of Hypothesis 2 413 REFERENCES 419 vii LIST OF FIGURES Figure 1 –The Major Phases of the Defense Acquisition Process ...................................... 3 Figure 2 –A notional system decomposition for an Arleigh-Burke Class Flight IIA destroyer performing a Search and Rescue (SAR) mission. ............................................. 12 Figure 3 – Continuation of the notional system decomposition from Figure 2. ............... 14 Figure 4 – Graphical depiction of the term system reproduced from [53]. ....................... 18 Figure 5 – Various distinctions between systems and SoS, reproduced from [54] .......... 19 Figure 6 – The impact of system complexity factors on decision making, reproduced from [61]. ................................................................................................................................... 22 Figure 7 – Stair-Climbing Machine Concepts in [71] ...................................................... 24 Figure 8 – Suggested Functional Decomposition for Coupled Stair-Climber .................. 25 Figure 9 –Measure of Merit Hierarchy, reproduced from [147] ....................................... 56 Figure 10 – MOE development method by Sproles, reproduced from [150] ................... 58 Figure 11 – List of “complexity-appropriate” tools and approaches [70] ........................ 69 Figure 12 – Progression of realism: As interactions (white arrows) lead to self-organized systems and SoS, the systems either (+) possess, (?) may possess, or (×) do not possess idealizations and forms of uncertainty. ............................................................................. 73 Figure 13 –Directed multi-edge graph of precision-strike behavior: Ford’s proposed Interoperability View [26] ................................................................................................ 82 Figure 14 – John Boyd’s OODA Loop, reproduced from [187]....................................... 85 Figure 15 –NetLogo GUI and flocking simulation (a) before and (b) after ~3,000 iterations ............................................................................................................................ 88 Figure 16 – Graphical depiction of self-organization and emergence in [206] ................ 97 Figure 17 – NetLogo Flock Patterns ................................................................................. 99 Figure 18 – Boids self-organization and model compression ......................................... 102 Figure 19 – Pictorial representation of Hypothesis 2 (weak association) ....................... 131 Figure 20 – Knowledge gaps in relation to existing literature ........................................ 133 Figure 21 – Bridge across knowledge gaps (simplified Figure 20) ................................ 139 Figure 22 – Input-Process-Output diagram for emergent behavior exploitation method 140 Figure 23 – Time complexity for n-digit number by operation / function...................... 150 Figure 24 - Input-Process-Output diagram for pattern recognition step ......................... 158 Figure 25 – Fast Fourier Transform (-FFT) applied to “clean” time series (-TS) data (a) sum of sine waves, (b) constant non-zero signal ............................................................ 160 Figure 26 – Fast Fourier Transform (-FFT) applied to “mixed” time series (-TS) data (a) piecewise
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