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A Top-Down, Hierarchical, System-Of-Systems Approach to the Design of an Air Defense Weapon

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A Top-Down, Hierarchical, System-Of-Systems Approach to the Design of an Air Defense Weapon A Top-Down, Hierarchical, System-of-Systems Approach to the Design of an Air Defense Weapon A Thesis Presented to The Academic Faculty by Tommer Rafael Ender In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy School of Aerospace Engineering Georgia Institute of Technology August 2006 Copyright c 2006 by Tommer Rafael Ender A Top-Down, Hierarchical, System-of-Systems Approach to the Design of an Air Defense Weapon Approved by: Prof. Dimitri Mavris Dr. Kevin Massey Committee Chair Aerospace, Transportation, School of Aerospace Engineering and Advanced Systems Laboratory Georgia Institute of Technology Georgia Tech Research Institute Prof. Daniel Schrage Dr. E. Jeff Holder School of Aerospace Engineering Sensors and Electromagnetic Georgia Institute of Technology Applications Laboratory Georgia Tech Research Institute Dr. Neil Weston School of Aerospace Engineering Georgia Institute of Technology Date Approved: 03 July 2006 ב"ה for my family iii ACKNOWLEDGEMENTS The work presented in this document could not have been completed without the love and support of my parents, Judy and Ilan, my best friend and brother Roy, and my bashert Sonja. I would not have even considered pursuing a Ph.D. without the encouragement of my advisor Dr. Dimitri Mavris, who has supported my academic progression since my first undergraduate term at Georgia Tech. He has taught me to expect more from myself, and certainly more for myself in life. Thanks Doc. I’d also like to thank the other members of my committee who helped me along the process: Dr. Neil Weston, who was instrumental in the final round of iterations of editing this document; Dr. Daniel Schrage, who took an inspiring interest in this topic very early on and provided encouraging feedback throughout; Dr. Jeff Holder, GTRI, for helping me begin to understand the complex radar concepts I decided to tackle in this thesis; and finally, a very special thank you to Dr. Kevin Massey, GTRI, not only for the encouragement to pursue this specific topic for a Ph.D., but also for working with me every step of the way to formulate a very interesting and important problem to apply the methodology developed in this thesis. That being said, the 6-DoF trajectory analysis in this document would not have been possible without the hard work of Mike Hieges of GTRI, and the co-op students working at GTRI that I’ve had to pleasure to work with over the past few years: Kevin Guthrie, Patrick O’Leary, Ben DiFrancesco, and Kyle French - I am still very impressed how quickly you guys were able to catch on and contribute to the development of the codes used in this study. Thank you to the U.S. Army-AMRDEC and GTRI for additional computational and financial support. And many thanks to the friends I’ve made at ASDL over the years, especially iv those that helped out with my thesis review: Andrew Frits, Brian German, Peter Hollingsworth, Hernando Jimenez, Rob McDonald, Janel Nixon, Holger Pfaender, and Jack Zentner. Also a special thanks to the other students I worked with in the original methodology used in this thesis: Bjorn Cole, David Culverhouse, Jared Harrington, and to Patrick Biltgen for helping shape the story telling aspect of the method, as well as the members of the AFICE team I’ve left out. Thank you to Dr. Michelle Kirby for always making herself available for answering questions and guidance. I would finally like to thank Liz and Jason Billman for proving the occasional retreat from my normal surroundings, giving me the much needed boost to get the thesis proposal started. v TABLE OF CONTENTS DEDICATION .................................. iii ACKNOWLEDGEMENTS .......................... iv LIST OF TABLES ............................... xi LIST OF FIGURES .............................. xii LIST OF SYMBOLS OR ABBREVIATIONS .............. xviii SUMMARY .................................... xx I MOTIVATION ............................... 1 1.1 Introduction . 1 1.1.1 Top-Down Systems Engineering . 1 1.1.2 Initial Research Formulation . 2 1.1.3 Overview of Thesis . 6 1.2 Background . 7 1.2.1 The Rocket, Artillery, and Mortar (RAM) Threat in Asym- metric Warfare . 7 1.2.2 Problem Scope: Extended Area Protection & Survivability . 13 1.2.3 Approaches to the RAM Threat . 19 1.2.4 Guided Projectiles . 26 1.2.5 Summary of Discussed Solutions . 32 1.3 Paradigm Shift in Conceptual Design . 34 1.4 Disclaimer . 36 II LITERATURE SEARCH: COMBAT SYSTEM MODELING & SIM- ULATION .................................. 37 2.1 Modeling Military Operations . 38 2.1.1 General Requirements of Combat Modeling . 38 2.1.2 Large Scale Combat Computer Simulations . 39 2.2 Modeling and Simulation Concepts . 41 vi 2.2.1 Deterministic Models . 44 2.2.2 Probabilistic (Stochastic) Models . 45 2.3 Survivability as a Discipline . 47 2.3.1 Susceptibility . 48 2.3.2 Vulnerability . 50 2.3.3 Powering-up/Single Sortie Probability of Damage . 51 2.4 Air Defense Systems . 53 2.4.1 Operational Requirement & System Specification . 54 2.4.2 Types of Air Defense Systems . 55 2.5 Weapon System Effectiveness Parameters . 59 2.5.1 Weapon Accuracy . 59 2.5.2 Lethality . 60 2.6 Guidance, Navigation, and Control of Related Weapon Concepts . 62 2.6.1 Guidance . 62 2.6.2 Navigation . 65 2.6.3 Control . 67 2.7 Radar Concepts . 69 2.7.1 Frequency . 69 2.7.2 Radar Range . 70 2.7.3 Signal-to-Noise Ratio . 71 2.7.4 Radar Cross Section . 72 2.7.5 Tracking Radars . 74 2.8 Chapter Conclusions . 78 III LITERATURE SEARCH: ADVANCED DESIGN METHODOLO- GIES ...................................... 80 3.1 System-of-Systems Approach . 80 3.1.1 Functional Decomposition . 84 3.1.2 Functional Composition . 86 3.1.3 System-of-System Architecture . 87 vii 3.2 Uncertainty Analysis and Quantification in the Design Process . 90 3.2.1 Forecasting . 92 3.2.2 Monte Carlo Simulation . 94 3.2.3 Filtered Monte Carlo Approach . 95 3.3 Surrogate Modeling . 96 3.3.1 Polynomial Response Surface Equations . 97 3.3.2 Neural Network Response Surface Equations . 99 3.3.3 Analysis of Variance . 105 3.4 Application of Techniques . 105 3.4.1 Response Surface Methodology & Design Space Exploration . 105 3.4.2 Top-Down Capability Based Design . 107 3.4.3 Design for Affordability . 111 3.5 Chapter Conclusions . 112 IV RESEARCH QUESTIONS & HYPOTHESES ............ 113 4.1 Problem Revisited . 113 4.2 Research Questions . 114 4.2.1 Initial Formulation Research Questions Reviewed . 114 4.2.2 Additional Research Questions . 115 4.3 Hypotheses . 118 V RESEARCH FORMULATION & APPROACH ........... 121 5.1 Decomposing the Bounded Problem . 121 5.1.1 Narrowing the Scope of Interest . 121 5.1.2 Morphological Matrix . 122 5.1.3 Hierarchical Decomposition of Proposed Solution . 133 5.1.4 Review of Morphological Matrix Selections . 136 5.2 Research Focus . 140 5.3 Modeling and Simulation Approach . 147 5.3.1 Modeling and Simulation Requirements . 147 viii 5.3.2 6-DoF Modeling . 147 5.3.3 Radar Subsystem Model . 150 5.3.4 Combined Effect of Multiple Projectiles . 153 5.3.5 Creating Surrogate Models . 154 VI IMPLEMENTATION ........................... 157 6.1 Approach Review & Implementation Introduction . 157 6.2 Preliminary Studies . 158 6.3 Initial 6-DoF Study . 159 6.3.1 Variable and Response Identification . 159 6.3.2 Surrogate Model Creation & Visualization . 162 6.3.3 Introduction of Gun Firing Noise . 166 6.3.4 Response Variability Study . 168 6.4 Addition of Radar & Guidance Update Rates . 189 6.4.1 Control State Slaved to Radar Update . 190 6.4.2 Independent Control and Radar Update Rates . 193 6.5 Effect of Firing Multiple Projectiles . 197 6.6 Subsystem Level Radar Properties . 204 6.7 Detailed 6-DoF Model . 216 6.7.1 Variable Listing . 216 6.7.2 Surrogate Modeling . 220 6.8 Assembled Hierarchal Environment . 222 6.9 Chapter Conclusions . 234 VII CONCLUSIONS .............................. 236 7.1 Review of Research Questions & Hypotheses . 236 7.1.1 First Hypothesis . 236 7.1.2 Second Hypothesis . 238 7.1.3 Third Hypothesis . 240 7.2 Summary of Contributions . 241 ix 7.3 Recommendations for Further Study . 242 APPENDIX A — PROBABILITY DISTRIBUTIONS ....... 245 APPENDIX B — PRELIMINARY RESULTS ............ 248 APPENDIX C — GUN RATE OF FIRE REGRESSION ...... 264 APPENDIX D — SUPPORTING DATA ................ 267 REFERENCES .................................. 272 VITA ........................................ 284 x LIST OF TABLES Table 1 MK 15 Phalanx Close-In Weapons System Characteristics . 22 Table 2 Ahead 35 mm Ammunition Characteristics . 24 Table 3 Summary of Relevant Unguided & Guided Alternatives . 33 Table 4 Model Types . 43 Table 5 Probability Factors that Influence Susceptibility . 49 Table 6 Attrition Kill Levels . 51 Table 7 Radar Frequency Bands . 70 Table 8 Radar Cross Section Magnitudes . 73 Table 9 Morphological Matrix of System Alternatives . 124 Table 10 Morphological Matrix of System Alternatives with Selections . 139 Table 11 Radar Noise Errors for Initial Study(1σ)............... 160 Table 12 Gun Pointing Bias for Initial Study . 161 Table 13 Discrete Variable Settings for Initial Study . 161 Table 14 Gun Firing Noise . 167 Table 15 Fixed Variables for Radar & Control Update Rate Study . 190 Table 16 Variables for Radar Update Rate Study with Control State Slaved to Radar Update . 191 Table 17 Variables for Radar Update Study with Independent Radar & Guid- ance Updates . 193 Table 18 Variables Used for Radar Subsystem Study . 205 Table 19 Detailed Study - List of Variables . 221 Table 20 Discrete Variable Settings for Detailed Study . ..
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