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Multidisciplinary System Design Optimization >> Content Detail



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SES #TOPICSLECTURERSKEY DATES
Module 1: Problem Formulation and Setup
1Introduction to Multidisciplinary System Design Optimization

Course Administration, Learning Objectives, Importance of MSDO for Engineering Systems, "Dairy Farm" Sample Problems
de Weck, and Willcox
2Open Lab
3Problem Formulation

Definitions, Mathematical Notation, Introduction of Design Variables, Parameters, Constraints, Objectives

Formal Optimal Design Problem Definition

Distinction between Simulation Model and Optimizer

Active Learning Exercise: In Class Role Play (Student Groups) to Find Problem Formulation for a Range of Complex Systems/Products
WillcoxAssignment 1 handed out
4Modeling and Simulation (iSIGHT CD-ROM handed out)

Design Variable -> Objective Mapping, Simulation Module Identification, Physics-based Modeling (Governing Equations) vs. Empirical Modeling, N2 Diagrams and Design Structure-Matrices (DSM), Model Fidelity and Benchmarking, Modeling Environments, Runtime Reduction Strategies

Active Learning: Find N2 Diagram for Communication Satellite
de Weck
5Lab 1: Introduction to OptimizationKim
6Decomposition and Coupling

Task Sequencing, Parallelization, Simcode-optimizer Coupling, Process Integration and Design Optimization (PIDO) Environments, Formal MDO Approaches: Collaborative Optimization (CO), Concurrent Subspace Optimization (CSSO), Bi-level Integrated System Synthesis (BLISS)
de Weck
7Design Space Exploration

Design of Experiments (DoE): Full Factorial, Monte Carlo, Parameter Study (Univariate Search), one-at-a-time, Orthogonal Arrays (Taguchi), Latin Hypercubes

Active Learning Exercise: Paper Airplane
Willcox
8Lab 1: Introduction to Optimization (cont.)Kim
Module 2: Optimization and Search Methods
9Numerical Optimization I

Existence and Uniqueness of an Optimum Solution, Karush-Kuhn-Tucker Conditions, Convex and Non-convex Spaces, Unconstrained Problems, Linear Programming

Active Learning Exercise
WillcoxAssignment 1 due

Assignment 2 handed out
10Numerical Optimization II

Constrained Problems, Reduced Gradient and Gradient Projection Methods, Penalty and Barrier Methods, Augmented Lagrangian Methods, Projected Lagrangian Methods, Convergence and Termination Criteria, Mixed-integer Programming, Examples

Active Learning Exercise
Willcox
11Open Lab
12Sensitivity Analysis

Jacobian, Hessian Matrix Properties, Sensitivity Analysis w.r.t Design Variables, Fixed Parameters and Constraints, Normalization, Finite Difference Approximation, Automatic Differentiation, ANOVA, Adjoint Methods, Examples

Active Learning Exercise
Willcox
13Guest Lecture 1

Overview of MDO, Issues in Optimization
Dr. Jaroslaw Sobieski - NASA LaRC
14Simulated Annealing (SA)

Statistical Mechanics Analogy, Simulated Annealing Algorithm, Metropolis Step, System Temperature Cooling Schedule Tuning, Strengths and Weaknesses Relative to GA, Multiobjective SA, Tabu Search, Examples
de Weck, and Dr. Cyrus Jilla
15Genetic Algorithms I

Combinatorial Optimization Problems, Overview of Heuristic (Stochastic) Search Methods, Evolutionary Computing, Basic Genetic Algorithm, Chromosome Encoding/Decoding, Selection, Crossover, Mutation Operators, Population Strategies

Active learning exercise: The binary GA game
de WeckAssignment 2 due

Assignment 3 handed out
16Genetic Algorithms II

Specialty Variants of GA's: Parallel GA's, Diffusion GA, Micro-GA and Cellular automata

Constraint Resolution, Application of GA's in Multiobjective Optimization, Mating Restrictions, Pareto Fitness Ranking, Speciation
de Weck
17Lab 2: Optimization AlgoritmsKim
18Particle Swarm Optimization Dr. Rania Hassan
19Post-optimality Analysis

Convergence for Gradient-Based and Heuristic Algorithms, Lagrange Multipliers, Duality Theory
Willcox, and de Weck
20Lab 2: Optimization AlgoritmsKim
Module 3: Multiobjective and Stochastic Challenges
21Goal Programming

Objectives Versus Constraints

Performance Targets as Equality Constraints, Isoperformance, Contour following Algorithms, Singular Value Decomposition of Jacobian, Goal Programming, Satisficing Design Philosophy, Target Cascading
de WeckAssignment 3 due

Assignment 4 handed out
22Multiobjective Optimization I

Scalar versus Vector Optimization, The Vector Maximum Problem, Edgeworth-Pareto Optimality, Generalized Karush-Kuhn-Tucker Conditions, Strong and Weak Dominance, Domination Matrix, Multiobjective Linear Programming (MOLP), Preference Weightings and Aggregation Methods (1st Generation Methods)
de Weck
23Open Lab
24Multiobjective Optimization II

Generation of Pareto Frontier (2D) and Surface (Multidimensional), Normal-boundary-intersection (NBI), Multiobjective Evolutionary (2nd Generation) Algorithms, Review of Pareto Based Fitness Ranking Schemes

Research and Industrial Examples, Tradeoff Resolution/Design Selection, Relationship with Utility and Game Theory
de Weck
25Design Space Optimization

Multi-level Optimization Problems, Design Space Optimization - Number of Design Variables as a Design Variable, Conceptual Design Optimization, S-pareto Approach to Concept Selection, Applications from Structural Topology Optimization and MEMS
Il Yong Kim
26Lab 3: Multiobjective OptimizationKim
27Approximation Methods

Design Variable Linking, Reduced-basis Methods, Response Surface Approximations, Kriging, Neural Networks as Multivariable Function Approximators, Variable-fidelity Models
WillcoxAssignment 4 due

Assignment 5 handed out
28Guest Lecture 2

MDO at General Motors (IFAD/CDQM)
Dr. Peter Fenyes, GM Research Center
29Lab 3: Multiobjective Optimization (cont.)Kim
Module 4: Implementation Issues and Real World Applications
30Robust Design

Review of Probability and Statistics, Probability Density Functions, Reliability Analysis, Taguchi Robust Design Method, Computational Issues in Robust Design Optimization
Prof. Dan Frey
31Open Lab
32Visualization Techniques

Convergence, Objective Vector and Active Constraint Set Monitoring during Optimization Execution, Multivariable Plotting Techniques: Radar Plots, Carpet Plots and Glyphs

Linking of Optimization to Dynamic (Geometric) Design Representation
WillcoxAssignment 5 due

Final Report Assignment handed out
33Computational Strategies

Parallel Computing, Grid Computing, Compiled versus Interpretive Languages
de Weck
34Open Lab
35Project Presentations IStudents
36Project Presentations IIStudents
37Project Presentations IIIStudents
38Design for Value

Net Present Value, What is Value and How do we Quantify it? How do we Design for Value? A Value Framework

Cost Models, Revenue Models, Examples from Aircraft, Spacecraft and Automotive Engineering
WillcoxFinal report (journal article paper format) due
39Course Summary

Provide Summary and Highlights of Course, Classify Materials Learned as either Principles, Methods or Tools, Give Pointers to Resources for Further Individual Learning after the Course, Give Time for Student Feedback, Course Critique
Willcox, and de Weck

 








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