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Improved Robustness Formulations and A IMPROVED ROBUSTNESS FORMULATIONS AND A SIMULATION-BASED ROBUST CONCEPT EXPLORATION METHOD A Thesis Presented to The Academic Faculty by Markus Rippel In Partial Fulfillment of the Requirements for the Degree Master of Science in Mechanical Engineering in the George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology December 2009 IMPROVED ROBUSTNESS FORMULATIONS AND A SIMULATION-BASED ROBUST CONCEPT EXPLORATION METHOD Approved by: Dr. Janet K. Allen, Advisor G. W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Dr. Farrokh Mistree G. W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Dr. Seung-Kyum Choi G. W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Date Approved: November 16, 2009 ACKNOWLEDGEMENTS During my time as a Masters student at Georgia Tech, I was extremely lucky to learn with and from great educators, teachers, classmates and friends. Here, I want to thank especially those, who supported me during my research and the completion of this thesis. First of all, I thank my advisor Dr. Janet K. Allen for her inspiration, support and guidance during my entire time at Georgia Tech. She always encouraged me to accept the challenge of research, which gave me a great insight to academia and on which I grew both intellectually and personally. I am also very thankful to my committee member Dr. Farrokh Mistree, the most dedicated educator I have met, for his support and contributions to my thesis. His insights and his consistent encouragement to think critically were major success factors over the course of my research. Furthermore, I owe great thanks to my committee member Dr. Seung-Kyum Choi, without whose guidance and support this thesis would have been nearly impossible. He provided great insights to statistics in engineering design and assisted during the generation of ideas for answering my research questions. I also thank Dr. Jitesh Panchal, Dr. Dirk Schaefer and Dr. Matthias Messer for their guidance, insights and friendship. For his help with the application of JavaDSIDES, I owe great thanks to Dr. Matthew Marston. His patience in answering my questions and integrating my suggestions to JavaDSIDES were of enormous help for the progress of my research. For providing the simulation code for the LCA heat exchanger example I thank Dr. Carolyn C. Seepersad, iii Dr. Hae-Jin Choi and Dr. Marco Gero Fernández. I am also thankful to Dr. Wei Chen, on whose PhD work my research is built, for her insights to RCEM. Furthermore, I thank all faculty and students in the Systems Realization Laboratory both in Atlanta and in Savannah for being a great research family. Special thanks go to Timothy Dietz, Jiten Patel, Alex Ruderman, Chenjie Wang, Julie Bankston and Andrew Hyder for their friendship and encouragement during my time at Georgia Tech. I owe the greatest thanks to my family, especially my mother, for their continuous support and encouragement during the course of my entire studies both in Germany and in the United States. Finally, I thank the Federation of German-American Clubs (VDAC) and the German Academic Exchange Service for their support prior to and during my studies at Georgia Tech. Furthermore, I acknowledge the funding sources, which made this thesis possible: • NSF grant DMI-060259 SACE: Statistics Aided Computer Experiments • Georgia Tech Savannah • The Center for Computational Materials Design; a joint project between Georgia Tech and the Pennsylvania State University iv TABLE OF CONTENTS ACKNOWLEDGEMENTS ............................................................................................... iii LIST OF TABLES ............................................................................................................. ix LIST OF FIGURES ........................................................................................................... xi LIST OF SYMBOLS ....................................................................................................... xvi SUMMARY ...................................................................................................................... xx CHAPTER 1 FOUNDATIONS FOR ROBUST CONCEPT EXPLORATION ................ 1 1.1 Motivation and Background for Developing Robust Concept Exploration Methods............................................................................................................. 3 1.1.1 Engineering Design Processes ................................................................... 5 1.1.2 Uncertainty in Engineering Design and the Concept of Robust Design ... 7 1.2 Frame of Reference ............................................................................................... 9 1.2.1 Robust Design and Multi-Objective Concept Exploration ........................ 9 1.2.2 Multi-Objective Decision-Making and the Compromise Decision Support Problem ................................................................................................ 12 1.2.3 Uncertainty Analysis and the Probabilistic Collocation Method ............ 13 1.3 Research Focus and Contributions ...................................................................... 14 1.3.1 Research Questions and Hypotheses ....................................................... 15 1.3.2 Research Contributions ........................................................................... 17 1.4 Validation and Verification of this Thesis .......................................................... 18 1.4.1 Quadrant 1: Theoretical Structural Validity ............................................ 20 1.4.2 Quadrant 2: Empirical Structural Validity .............................................. 20 1.4.3 Quadrant 3: Empirical Performance Validity .......................................... 21 1.4.4 Quadrant 4: Theoretical Performance Validity ....................................... 21 1.4.5 Implementation of the Validation Framework in this Thesis .................. 21 1.5 Chapter Synopsis ................................................................................................. 27 CHAPTER 2 ROBUST DESIGN: REVIEW OF LITERATURE AND IDENTIFICATION OF RESEARCH OPPORTUNITIES ........................... 28 v 2.1 Multi-Objective Decision Support and the Decision Support Problem Technique ......................................................................................................................... 28 2.2 Robust Design and Robust Concept Exploration ................................................ 33 2.2.1 Taguchi’s Robust Design ........................................................................ 34 2.2.2 Limitations and Improvements of Taguchi’s Robust Design Methodology .............................................................................................................. 37 2.2.3 The Robust Concept Exploration Method ............................................... 42 2.2.4 Limitations of RCEM .............................................................................. 46 2.3 The Probabilistic Collocation Method ................................................................ 47 2.4 New Computational Framework for RCEM ....................................................... 51 2.4.1 Adaptive Linear Programming and DSIDES .......................................... 52 2.4.2 New Computational Framework with JavaDSIDES and MATLAB Integration ............................................................................................ 54 2.5 Chapter Synopsis ................................................................................................. 56 CHAPTER 3 MODIFYING THE ROBUST CONCEPT EXPLORATION METHOD . 58 3.1 Characteristics and Limitations of RCEM .......................................................... 59 3.2 Advancements of RCEM ..................................................................................... 71 3.2.1 Nominal Value Shift ................................................................................ 71 3.2.2 Alternative Methods for Variance Approximation ................................. 75 3.2.3 Assessment of Alternative Methods ........................................................ 80 3.2.4 Critical Evaluation of Results and Introduction of the Modified RCEM 93 3.3 Guide for Validation of the First Research Questions ........................................ 95 3.3.1 Theoretical Structural Validity ................................................................ 95 3.3.2 Empirical Structural Validity .................................................................. 96 3.3.3 Empirical Performance Validity .............................................................. 97 3.3.4 Theoretical Performance Validity ........................................................... 97 3.4 Chapter Synopsis ................................................................................................. 97 CHAPTER 4 MULTI-OBJECTIVE ROBUST DESIGN OF A PRESSURE VESSEL .. 99 4.1 The Robust Design of a Pressure Vessel ........................................................... 100 4.2 Validation and Verification with the Example .................................................. 104 4.2.1 Empirical Structural Validation ............................................................. 104 4.2.2 Empirical Performance Validation ........................................................ 106 4.3 Application of the Modified RCEM to the Design of a Pressure Vessel .......... 109 4.3.1 Clarification and Formulation of the Design Problem .........................
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