Tối ưu hóa phân vùng và quyết định phối hợp trong thiết kế kỹ thuật theo phương pháp phân rã

Optimal Partitioning and Coordination Decisions in Decomposition-based Design Optimization by James T. Allison A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) in The University of Michigan 2008 Doctoral Committee: Professor Panos Y. Papalambros, Chair Professor Noboru Kikuchi Professor Romesh Saigal Associate Research Scientist Michael Kokkolaras Terrance Wagner, Ford Motor Company c James T. Allison All Rights Reserved 2008 to Ellie, Jonathan, Brian, and Michael ii Acknowledgments I have been very fortunate to study under the masterful guidance of my advisor, Panos Papalambros.

I am grateful for his remarkable support throughout my challenges and adventures at the University of Michigan; I have been inspired by his example. It was because of the opportunity to work with him that I chose to come to Michigan, and I undoubtedly made the right choice. I want to thank my dissertation committee for the time and effort they volunteered to guide my dissertation work. I want also to recognize my wife, Natalie, who has labored just as ardently as I toward my graduation, and my extended family and friends, who gave of themselves so that I could realize my ambitions.

Much of my work has been collaborative. Michael Kokkolaras has been a valuable men- tor and research collaborator throughout my graduate studies. Thanks to my affiliation with the Optimal Design Laboratory at the University of Michigan, I’ve had fantastic opportuni- ties to work with people from around the world, including Brian Roth, Emanuele Colomba, Guido Karsemakers, Simon Tosserams, David Walsh, and others. I want to thank all of my ODE friends for enriching my experiences, including Ryan Fellini, Erin MacDonald, Jeongwoo Han, Jarod Kelly, Kwang Jae Lee, Kuei-Yuan Chan, Jeremy Michalek, Subroto Gunawan, Marc Zawislak, Eric Rask, Mike Sasena, Bart Frischknecht, and many others.

I am grateful to my other friends at the U of M, including Mike Cherry, April Bryan, Natasha Chang, Eduardo Izquierdo, Brian Trease, Ken Pollary, and others. Many individuals contributed to the electric vehicle design case study. Kwang Jae Lee played an important role in system integration, optimization, and programming. Jeongwoo Han provided the Li-ion battery model, and Jarod Kelley developed the frame design and structural model.

Emanuele Colomba helped define chassis design and overall vehicle geometry. Michael Alexander assisted with structural model development. Dushyant Wadivkar, Burit Kitterungsi, and Mikael Nybacka all provided support for the vehicle dynamics model, and Hisashi Heguri generously furnished tire model data. Many experiences helped prepare me for graduate school.

My involvement with the solar car team at the University of Utah not only helped me discover my research interests, but gave me glimpses of the possible. My fellow solar car teammates, including Andy Rahden, Jayme Allred, Tadd Truscott, and Brad Hansen, played a vital role. Eberhard Bamberg, also of the University of Utah, was an important mentor who offered timely direction and iii encouraged me to seek the best possible graduate school experience. Dennis Rosier, my high school auto shop teacher, helped ignite my passion for learning, and Corinne Barney, my high school math teacher, inspired me to expand my horizons.

My parents offered regular encouragement to live to my potential, and my father provided long hours of math tutoring through my early college years that were key to my academic success. Finally, I would like to recognize support from the U. National Science Foundation, the Automotive Research Center at the University of Michigan, the Rackham Graduate School, and the University of Michigan College of Engineering and Department of Mechanical Engineering. iv Table of Contents Dedication.

iii List of Tables. viii List of Figures. ix List of Symbols. xv Chapter 1 Decomposition-based Design Optimization .1 Engineering System Design .3 Decomposition-based Design Optimization.

16 Chapter 2 Partitioning and Coordination Decisions .1 Decomposition-based System Design .2 Design Structure Matrix .3 Other Design Matrices .4 Reduced Adjacency Matrix .4 Partitioning and Coordination Decision-Making .1 Traditional Decision Techniques .2 Formal Decision Techniques. 34 v Chapter 3 Demonstration Examples .1 Air Flow Sensor Design .2 Turbine Blade Design .3 Aircraft Family Design .1 Product Families in Aircraft Design .2 Aircraft Performance Analysis .3 Aircraft Family Problem Formulation .4 Generalized Truss Design .2 Truss Design Formulation .5 Electric Water Pump Design .1 Water Pump Design .4 Motor Current Analysis .5 Motor Speed Analysis .6 Torque and Pressure Analysis. 69 Chapter 4 System Design Optimization Formulations .1 Single-Level Formulations .1 Multidisciplinary Feasible Formulation .2 Individual Disciplinary Feasible Formulation .3 All-at-Once Formulation .2 System Analysis for Single-level Formulations .1 Fixed Point Iteration .2 Example: Hidden Optima .3 Coupling Strength in Single-Level Formulations .3 Multi-Level Formulations .1 Classes of Multi-Level Formulations .2 Analytical Target Cascading .3 Example: Aircraft Family Design .4 Augmented Lagrangian Coordination .5 Example: Air Flow Sensor Design. 98 Chapter 5 Optimal Partitioning and Coordination: Theoretical Framework .4 Water Pump Electrification Example.

108 vi Chapter 6 Extension to Larger Systems .2 Evolutionary Algorithm for Partitioning and Coordination .1 Partition Genotype Representation .2 Sequence Genotype Representation .3 Generalized Truss Design Problem .2 Example: Eight-bar Truss. 122 Chapter 7 Consistency Constraint Allocation for Augmented Lagrangian Co- ordination .2 Linking Structure Analysis .1 Consistency Constraint Graphs .2 Valid Consistency Constraint Graphs .3 Example Consistency Constraint Graph .3 Optimal Partitioning and Coordination Decisions for Parallel ALC .4 Example: Electric Water Pump Design Problem. 138 Chapter 8 Electric Vehicle Design .2 Induction Motor Model .3 Lithium Ion Battery Model .3 Vehicle Dynamics Model .3 Quarter-Car Model .5 Mass Distribution and Packaging .6 Optimal P/C Decision Results .2 Extension of Simultaneous P/C Decision Making. 186 vii List of Tables Table 1.1 Experimental results for evaluation sequence variation .2 Experimental results for evaluation sequence and partition variation .1 Summary of formal partitioning and coordination decision methods .1 Turbine blade design parameters .2 Design variables for the aircraft family design problem .3 Design constraints for the aircraft family design problem .4 Analysis functions and design variables for the electric water pump design problem .5 Electric water pump model parameters .6 Optimization results for the electric water pump design problem .1 ALC solution progress for the air-flow sensor problem .1 Redundancy in p̂ partition representation .2 Design parameters and optimal geometry for the 8-bar truss problem .1 EV design variables .2 EV coupling variables .3 EV design constraint parameters .4 Vehicle model parameters .5 Motor model parameters .6 Vehicle dynamics model parameters .7 Mass distribution and packaging model parameters.

175 viii List of Figures Figure 1.1 Sample sequential design process: automotive example .2 Illustration of global and local optima in a nonlinear programming example 5 1.4 Process for implementing decomposition-based design optimization .5 Dissertation hypothesis: Existence of coupling between partitioning and coordination decisions .1 Input and output relationships for a system of analysis functions .2 Aspects of partitioning and coordination decisions .3 Hypergraph for relationships in Eqs.4 Digraph of functional relationships expressed in the DSM .1 Vane airflow sensor schematic (after [34]) .2 Simplified representation of a vane airflow sensor .3 Coupling relationship in airflow sensor analysis .4 GE J-79 turbojet engine turbine blades [57] .5 Turbine blade model schematic .6 Turbine blade coupling and functional relationships .7 Truss geometry and free-body diagram .8 Electrically driven centrifugal water pump [39] .9 Analysis interactions in electric water pump model .10 Schematic of permanent magnet DC motor .11 Section view of DC motor armature .12 Schematic of centrifugal water pump .13 DC motor thermal resistance model .4 Two element coupled system .5 System with multiple fixed points .6 IDF optimization space visualization .7 Coupling relationship in airflow sensor analysis .8 Comparison of MDF and IDF solution time as a function of coupling strength 81 4.9 Comparison of MDF and IDF function evaluations as a function of coupling strength .10 Turbine blade coupling and functional relationships .11 Comparison of MDF and IDF solution time as a function of coupling strength 85 4.12 Hierarchical system analysis structure .13 ATC subproblem as an optimal value function .14 Influence of β on RMS(c) (system consistency) .1 Independent (P,C) optimization approach .5 CS and SSmax histograms for first example system .6 Optimization results for A1 .7 CS and SSmax histograms for A2 .8 Optimization results for A2 .9 Optimal P/C results for pump problem .1 Typical evolutionary algorithm process .2 Genotype and phenotype representation partition size distributions .3 Subproblem sequence distribution .4 Combined subproblem sequence and partition size distribution .5 Surjective mapping from genotype space to phenotype space .6 EA results for first example system .7 EA results for second example system .8 EA results for third example system .9 Geometry and applied loads for the 8-bar truss problem .10 Non-dominated solutions for 8-bar truss problem .1 Analysis function digraph for example system .3 Condensed subproblem graph .5 Graph represtenation of consistency constraint options for x1 .6 ALC P/C results for electric water pump problem .7 Consistency constraint allocation option for point 3 .1 Vehicle systems and interactions in the EV design problem .2 Top view of EV component layout .3 Relationships between analysis functions in the EV design problem .4 Simplified overview of EV powertrain model .5 Block diagram of dynamic vehicle model .6 Simplified federal urban drive schedule .7 2 DOF vehicle pitch model .8 Slip data for electric vehicle tire .9 Diagram of an induction motor .10 Equivalent circuit of an induction motor .11 Typical IM maximum torque curve .12 Example IM efficiency map .13 Example IM power loss map with points visited during SFUDS .14 Flat-wound lithium-ion battery cell (after [68]) .15 Battery and motor power output during SFUDS cycle .16 Battery power output and charge and discharge limits during range test .17 Quarter-car vehicle suspension model .18 Sample road profile created using gaussian random number generator and digital filters .19 FEA model of the EV frame .20 Optimal partitioning and coordination decision results for the EV problem .