Multidisciplinary Engineering Design Optimization MCE 540 Graduate Course

Multidisciplinary Engineering Design Optimization (MCE 540 Graduate Course – Mechanical Engineering Department) Instructor: Dr. -Ing. Mostafa Ranjbar • Ph. D. (Dr-Ing. ), Multidisciplinary Engineering Design Optimization of Structures, Technische Universität Dresden, Germany, 2011 • M. Sc. , Vibration Monitoring and Fault Diagnosis of Structures, Tarbiat Modares University, Tehran, Iran, 2000 • B. Sc. , Mechanical Engineering, Shiraz university, Iran, 1998

LECTURE OUTLINE (see the course outline as well!) 2 Course Introduction to Optimization (Multidisciplinary) Systems Evolution of Design Process Optimization (System) Design

HOW DO WE INTEND TO DELIVER LECTURES, LABs, QUIZ and EXAM 3 LECTURES Lecture notes will be on Power Point Slides in pdf format We will have them available in class and you are welcome to take them after the class Students can bring anything they are comfortable with for taking the class notes Please equip your Laptops with ANSYS along with MATLAB, or we may use them in Computer Room

EXAM METHODS 4 EXAMS There will be Assignments and Quizzes in most of the lectures with appropriate weightage. Absentees in Quizzes will be marked ZERO. All students will submit their assignments either as a hard or soft copy (Instructor would specify in all the assignments). We expect professional reports. Late assignments without prior approval of the instructor will not be accepted. Mid Term and End Term Exams as per Department’s policy.

EVALUATIONS (Tentative) 5 Evaluation Scheme % Presentation 10 Assignments 10 Mid Term 30 Final Exam 50

CLASS PARTICIPATION Class Participation is highly recommended as this would be an interactive class. – Add on whenever you like. – Ask question as soon as it comes to mind, keeping in mind the flow of lecture. – We will write down questions that come and we would review them at the end of the semester as to what we think today and how does this change over the course of the semester. 6

KEEP IN MIND This is not a classic optimization class……. The aim is not to teach you the details of optimization algorithms, but rather To expose you to different methods To increase the understanding of optimization methods We will utilize optimization techniques – the goal is to understand enough to be able to utilize them wisely

MSDO INTRODUCTIO N TEXT BOOKS

TEXT BOOKS Lecture notes will be handed out in class ? ? But various books for reference are: TEXT BOOK: Engineering Optimization: Theory and Practice, 4 th ed. , Singiresu S. Rao, John Wiley, 2009. REFERENCE BOOK(S): Modern Heuristic Optimization Techniques, Kwang Y Lee, Mohamed A El. Sharkawi, John Wiley, 2008. Numerical Optimization Techniques for Engineering Design, Vanderplaats, Garret N, 3 rd ed. , Colorado Springs: Vanderplaats Research & Development Inc. , 2001. Optimization Techniques, George Leitmann, Academic Press, NY

BOOKS Belegundu, A. and Tirupathi, R. , Optimization Concepts and Applications in Engineering, Prentice Hall, 1999. Onwubiko, C. , Introduction to Engineering Design Optimization, Prentice Hall, 2000. Venkataraman, P. , Applied Optimization with MATLAB programming. Interscience, 2001. Goldberg, David E. Genetic Algorithms – in Search, Optimization & Machine Learning. MA: Addison. Wesley, 1989. ISBN: 0201157675 Murray B. Anderson, Genetic Algorithms In Aerospace Design: Substantial Progress, Tremendous Potential, Sverdrup Technology Inc. /TEAS Group Eglin Air Force Base, FL 32542, USA. Kennedy J, Eberhart R. and Shi, Y. H. , Swarm Intelligence, [M] Morgan Kaufmann Publishers, 2001. Kwang Y Lee, Mohamed A El-Sharkawi, Modern Heuristic Optimization Techniques, [M] John Wiley and Sons, 2008. Vanderplaats, Garret N. Numerical Optimization Techniques for Engineering Design. 3 rd ed. Colorado Springs: Vanderplaats Research & Development Inc. , 2001. ISBN: 0944956017 Gill, P. E. , W. Murray and M. H. Wright. Practical Optimization. Academic Press, 1986 Blair J. C. , Ryan R. S. , Schutzenhofer L. A. Launch Vehicle Design Process: Characterization, Technical Integration, and Lessons Learned, Marshall Space Flight Center, Alabama NASA/TP 2001– 210992, 2001 Phadke, M. S. , Quality Engineering Using Robust Design. Prentice Hall. 1989.

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SUMMARY OF LEARNING OBJECTIVES Learning Objectives: decompose and integrate multidisciplinary design models formulate meaningful problems mathematically explore design space and understand optimization critically analyze results, incl. sensitivity analysis Understand current state of the Art in MDO see depth and breadth of applications in industry & science get a feel for interaction of quantitative-qualitative design understand limitations of techniques good overview of literature in the field Research … and have fun !

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION __________________ ___AN INTRODUCTION LECTURE #1

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION LECTURE #1

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION __________________ ___ INTRODUCTION TO SYSTEM LECTURE #1

SYSTEMS 19 System: A system is a physical or virtual object that is composed of more than one element and that exhibits some behavior or performs some function as a consequence of interactions between these constituent elements. A system is a collection of interacting components.

The World Around Us “All modern products are designed as a SYSTEM”

The World Around Us AIRCRAFT SPACECRAFT AUTOMOBILES BUILDINGS Aerodynamics Astrodynamics Engines Structure & Seismology Propulsion Structures Body/chassis Space and Aesthetics Structures Communications Aerodynamics/Wind Controls Payload & Sensor Electronics HVAC Avionics/Software Optics Hydraulics Networking Manufacturing Guidance & Control Industrial design Fire & Safety Others

The World Around Us AIRCRAFT SPACECRAFT AUTOMOBILES BUILDINGS Aerodynamics Astrodynamics Engines Structure & Seismology Propulsion Structures Body/chassis Space and Aesthetics Structures Communications Aerodynamics/Wind Controls Payload & Sensor Electronics HVAC Avionics/Software Optics Hydraulics Networking Manufacturing Guidance & Control Industrial design Fire & Safety Others

The World Within Us SYSTEMS?

More Examples of Systems

More Examples of Systems SYSTEMS? Level System Subsystem Element Component Part Specific Name Launch vehicle Propulsion SRM Ignition Device Igniter

Relationships System Components A Component can itself be a SYSTEM. System . Subsystem

SYSTEM COMPLEXITY 27 Analysis codes should reside with experts ? System analysis should execute analysis codes on experts’ computers or … ? Structures Expert Aerodynamics Expert System Analysis Controls Expert

More Examples of Systems 28 COMPARTMENTALIZATION Helicopter as an example of a Multidisciplinary Complex System “Helicopters don’t fly. They beat the air into submission. ”

RS Model MODELING World The Modeling Space 29 Meta Model f(t) + input - x(t) outpu c k Physical system

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION __________________ ___ DESIGN LECTURE #1

EVOLUTION OF DESIGN PROCESS 31 HOW DO WE DEFINE DESIGN? ? ? ? ? Design of a product is an iterative focused activity that requires application of various techniques and scientific principles in fulfilling human needs with technically perfect, economically favorable and esthetically satisfactory solution. The process of conceiving and planning an object or process with a specific goal in mind.

DEFINITIONS AND OVERVIEW DESIGN Taylor (1959): Engineering design is the Engineering design is a process of applying various techniques and that requires application of scientific principles for the purpose of defining a various techniques and scientific device, a process, or a system in sufficient problems detail to permit its physical realization. Asimow (1962): Engineering design is a purposeful activity directed towards the goal of fulfilling human needs, particularly those which can be met by the technology factors of our culture. Goal of Engineering design is fulfilling of Human Needs

DEFINITIONS AND OVERVIEW DESIGN Feilden (1963): Mechanical engineering design is the use of scientific principles, technical information and imagination in the definition of a mechanical structure, machine or system to perform pre‐specified functions with the maximum economy and efficiency. Kesselring (1964): Designing means to find a technically perfect, economically favorable and esthetically satisfactory solution for a given task. Performing pre-specified functions with the maximum economy and efficiency Finding a technically perfect, economically favorable and esthetically satisfactory solution for a given task

DEFINITIONS AND OVERVIEW DESIGN Booker (1964): Simulating what we want to make (or do) before we make (or do) it as many times as may be necessary to feel confident in the final result. Iterative process Archer (1964): A goal‐directed problem‐solving activity. Very focused activity Reswick (1965): A creative activity ‐‐ it involves bringing into being something new and useful that has not existed previously. Creative activity Hansen (1966): Developing a technical construct is determined through prior visual thinking out. Designing is visualizing an object

DEFINITIONS AND OVERVIEW The design of any system involves several diverse disciplines with strong interaction between each other. The overall activity is therefore a typical Multidisciplinary Design and Optimization (MDO) process. MDO problems typically involve a large number of design constraints and variables. The analysis required to compute the objective and constraint functions are usually highly complex, coupled and imprecise. In such problems, traditional optimization techniques based on principles of mathematical programming have shown to be inadequate.

DEFINITIONS AND OVERVIEW DESIGN This course focuses on engineering design problems (e. g. vehicles, transportation systems, communication networks) and not primarily management problems (resource allocation, supply chain optimization, revenue management, etc. ). As such, students should have a background and interest in engineering and system or product design and have had previous exposure to optimization. The course will present many quantitative methods and tools.

DEFINITIONS AND OVERVIEW DESIGN----FINAL WORDS Design of a product is an iterative focused activity that requires application of various techniques and scientific principles in fulfilling human needs with technically perfect, economically favorable and esthetically satisfactory solution. The process of conceiving and planning an object or process with a specific goal in mind. In the context of this class this refers to the conceiving of a system that will subsequently be implemented and operated for some beneficial purpose. “WHAT DO YOU THINK? ? ? ”

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION __________________ ___ EVOLUTION OF THE DESIGN PROCESS LECTURE #1

EVOLUTION OF DESIGN PROCESS 39 Trial & Error Empirical Mathematical Deterministic (Factors of Safety) Random Experimentation Experience-based Probabilistic Stochastic (Risk Quantified) `` Graphical Approaches Computer models based on system Systematic physics Experimentation Point estimates Computer Simulations based on system physics Robust Solutions

EVOLUTION OF DESIGN PROCESS 40 CONCEPTUAL DESIGN PRELIMINARY DESIGN DETAIL DESIGN PRODUCT ATTRIBUTES 100: 1 1: 1 Conceptual design is crucial to the success of the overall design process and resulting system. It has been estimated that “at least 80% of a Mission’s life-cycle cost is locked in by the concept that is chosen” and “conceptual design decision have a 100: 1 leverage on

EVOLUTION OF DESIGN PROCESS 41 CONVENTIONAL OPTIMAL 1. Specification 2. Baseline design 3. Analysis (or experiment) 3. Analysis 4. Check performance or failure criteria 4. Check constraints 5. Is design satisfactory? 5. Does design satisfy the optimality (If yes, then stop) conditions? (If yes, then stop) 6. Change design parameters based 6. Change design parameters using

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION __________________ ___ OPTIMIZATION LECTURE #1

WHAT IS OPTIMIZATION? ● ● “Making things better” “Generating more profit” “Determining the best” “Do more with less”

WHAT IS OPTIMIZATION? “The determination of values for design variables which minimize (maximize) the objective, while satisfying all constraints” Principles of Optimal Design: Modeling and Computation 2 d Ed. by Panos Y. Papalambros and Douglass J. Wilde, Cambridge University Press, New York, 1988, 2000.

OPTIMIZATION Design Space: The space of working (Hill in this case) Objective: Find the Highest Point. Design Variables: Longitude and latitude.

OPTIMIZATION

OPTIMIZATION Objective Function Constraints Bounds Design Variables

SOLVING OPTIMIZATION PROBLEMS Optimization problems are typically solved using an iterative algorithm: Design variables Model Optimizer Responses Derivatives of responses (design sensitivities)

LOCAL AND GLOBAL OPTIMA LOCAL OPTIMA Local maxim a minim a maxim a Local minima GLOBAL MINIMA

Optimization Problems

Optimization Problems

MSDO Optimization: Optimization is a mathematical method and gives rise to a number of algorithmic tools. As such it represents a bridge, which enables the use of integrated multidisciplinary models to do more effective design engineering work. It should be stressed that the use of optimization is not intended to remove the human from the design loop. Rather, optimization enables engineers and system architects to explore vast design spaces, often resulting in non-intuitive insights. This may result in system designs that exhibit higher performance or are more cost -effective compared to previously considered traditional designs.

DEFINITIONS AND OVERVIEW OPTIMIZATION To find a system design that will minimize some objective function. The objective function can be a vector comprising measures of system behavior (“performance”), resource utilization (“time, money, fuel . . . ”) or risk (“stability margins…”).

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION __________________ ___ ENGINEERING DESIGN OPTIMIZATION LECTURE #1

DEFINITIONS AND OVERVIEW Engineering Design Optimization The “DO” in MDO. In industry, problems routinely arise that require making the best possible design decision. However, optimization is still underused in industry. . . Aerospace is one of the leading applications of engineering design optimization.

DEFINITIONS AND OVERVIEW Engineering Design Optimization Engineering design optimization is an emerging technology whose application both shortens design-cycle time and finds new designs that are not only feasible, but optimal, based on the design criteria. Traditional engineering design processes begin with formulating design requirements. Then, an initial design is synthesized which must be tested against the requirements. Such testing can involve building a prototype and performing an experiment. It may entail building a computer model using one of many engineering analysis codes. Of course, the design is usually validated experimentally since analysis codes are not infallible. When the design is found to be deficient in some requirement, it is changed. The change process typically involves strategies such as trial & error, use of previous experience, etc. The new design is again subjected to the test phase. The process iterates until the requirements are either met or changed to fit the performance. Often, the process is time consuming and does not produce the best design, just a feasible one.

DEFINITIONS AND OVERVIEW Engineering Design Optimization Engineering design optimization can both reduce the cycle time for the design iteration loop and find the best (optimal) design for the specifications. This process differs from the traditional process in that the iteration loop is computerized. An optimization problem is posed for which the design variables, the design objective and all constraints are specified. An optimizing algorithm, which serves as the design modifier, is coupled with an appropriate engineering analysis code such as a computational fluid dynamics (CFD) code. The analysis code performs the test phase of the iteration loop. The optimizer may function by perturbing each design variable to determine how each affects the performance and then seek a solution that optimizes the objective.

DEFINITIONS AND OVERVIEW Engineering Design Optimization An example is the design of an automobile air-conditioning duct that connects the air conditioner in the engine compartment to the air registers in the dashboard. The objective is to minimize the overall pressure drop while evenly delivering the air. The shape of the duct cross-section and the severity of the duct bends are important factors. However, changes in geometry are limited by the presence of other components behind the dashboard. The optimizer may change the shape of the initial duct design and see if the pressure is increased or reduced. It finds this out by sending a call to the analysis code. By iterating the above process, the optimizer not only finds a feasible design, but an optimal one based on the given constraints. Optionally, the designer may wish to relax constraints or otherwise modify requirements to see how this affects the performance; he may wish then to change the requirements to

DEFINITIONS AND OVERVIEW Engineering Design Optimization, in its broadest sense, can be applied to solve any engineering problem e. g. 1. Running a business to maximize profit, minimize loss, maximize efficiency, or minimize risk. 2. It might mean designing a bridge to minimize weight or maximize strength. It might mean selecting a flight plan for an aircraft to minimize time or fuel use. 3. Design of water resources systems for maximum benefit 4. Planning the best strategy to obtain maximum profit in the presence of a competitor 5. Planning of maintenance and replacement of equipment to reduce operating costs The power of optimization methods to determine the best case without actually testing all possible cases comes through the use of a modest level of mathematics and at the cost of performing iterative numerical calculations using clearly defined logical procedures or algorithms implemented on computing machines.

DEFINITIONS AND OVERVIEW OPTIMIZATION Modern computers, with their incredibly fast computational power, have turned optimization theory into a rapidly growing branch of applied mathematics. Methods such as Genetic Algorithm Tabu Search Method Simulated Annealing …. have all been successfully used in finding optimum solutions.

DEFINITIONS AND OVERVIEW CONVENTIONAL OPTIMAL 1. Specification 2. Baseline design 3. Analysis (or experiment) 3. Analysis 4. Check performance or failure criteria 4. Check constraints 5. Is design satisfactory? 5. Does design satisfy the optimality (If yes, then stop) conditions? (If yes, then stop) 6. Change design parameters based on 6. Change design parameters using an intuition and heuristics, return to 3. optimization strategy, return to 3.

MULTIDISCIPLINARY SYSTEM DESIGN OPTIMIZATION LECTURE #1

MSDO Design technique is a significant element in product development process. For example, effect of design of the performance and productivity of new product is about 70% while design technique requires just 5% of product cost. Importance of design technique has more emphasis as complexity of product is getting increased. However, the most of product design rely on the experience and intuition of designer and trial and error method. So, the application of advanced design techniques is insufficient. In recent years, scale of simulation model and design problem is getting greatly increased and design and analysis environments more demand multidisciplinary simulation and design optimization instead of the conventional single-disciplinary simulation.

MSDO Since interaction effects exit in the complex system such as airplane, automobile, optimization of such a complex system is hard to be solved by conventional optimization technique which considering just single disciplinary. So, multidisciplinary design optimization (MDO) techniques which consider a number of conflicting design requirements have been developed. MDO technique is an integrated design technique which enables an efficient and accurate design. So, study about MDO is active in recent year. To treat a number of conflicting design requirements from the various disciplines, development of a MDO technique which enables integration,

MSDO We actively study about a decomposition method, MDO methodology, and application of MDO to design of industrial product. To effectively perform multidisciplinary analysis (MDA) and MDO by applying parallel computing, a decomposition technique which decomposes a complex system into a number of subsystems is developed. Also, MDO technique has been successfully applied to the real world engineering design problem such as airplane, automobile, home appliance and ship

MSDO Multidisciplinary System Design Optimization (MSDO) deals with the optimization of several engineering disciplines simultaneously. MSDO gives the engineer the opportunity to find the optimal solution of some system accounting for the interactions between the different disciplines. It should be noted that the multidisciplinary solution might not be the solution for any one discipline analyzed separate from the other disciplines, but is the best solution accounting for the interactions.

MSDO Multidisciplinary Design Optimization (MDO) deals with the optimal design of complex engineering systems which requires analysis that accounts for interactions amongst the disciplines (or parts of the system) and seeks to synergistically exploit these interactions. MDO has become vital in design environments in the past decades as designs are becoming more and more complex.

MSDO Industry, government, and academic collaborations have advanced multidisciplinary design optimization (MDO) while broadening its applications. SGI and Ford use MDO and response surface models for rapid visualization of design alternatives Penn State collaborated with Boeing and Lockheed Martin Space Systems to develop visualization interfaces to support design decision-making Sandia National Labs continues investigating optimization under uncertainty and surrogate-based optimization NASA-Langley is developing robust optimization methods for aerodynamics and multidisciplinary aero-structural design University of Utah is developing an approach to optimize structural problems Georgia Tech is using MDO to design energetic materials Russia’s Central Aerohydrodynamic Institute is using MDO to develop new concepts for different types of airplanes

MSDO Multidisciplinary: A key component of this course is learning how to integrate different models from various disciplinary fields together into a single macro-model. All too often specialists in different fields (structures, fluids, propulsion, controls etc. ) exert a great deal of effort modeling and designing within their area of expertise with little understanding of how their design decisions affect other subsystems within the entire macro-system. Also frequently lacking is an understanding of how such design decisions impact system lifecycle cost and program risk. Understanding of and fluency in integrated, multidisciplinary modeling is essential to the success of contemporary and future complex systems.

DEFINITIONS AND OVERVIEW MULTIDISCIPLINARY Comprised of more than one traditional disciplinary area described by governing equations from various physical, economic, social fields. A key component of this course is learning how to integrate different models from various disciplinary fields together into a single macro-model. (MDO FORMULATIONS) All specialists in different fields (structures, fluids, propulsion, controls etc. ) exert a great deal of effort modeling and designing within their area of expertise with little understanding of how their design decisions affect other subsystems within the entire macro-system.

DEFINITIONS AND OVERVIEW MULTIDISCIPLINARY Also frequently lacking is an understanding of how such design decisions impact system lifecycle cost and program risk. Understanding of and fluency in integrated, multidisciplinary modeling is essential to the success of contemporary and future complex systems.

DEFINITIONS AND OVERVIEW SYSTEM A system is a physical or virtual object that is composed of more than one element and that exhibits some behavior or performs some function as a consequence of interactions between these constituent elements. A system is a collection of interacting components.

INTRODUCTION TO MSDO HISTORICAL PERSPECTIVE

MDO: Historical Perspective The need for MDO can be better understood by considering the historical context of progress in aerospace vehicle design. 1903 – Wright Flyer makes the first manned and powered flight. 1927 – Charles Lindbergh crosses the Atlantic solo and nonstop 1935 – DC-3 enters service 1958 – B 707 enters service 1970 – B 747 enters service 1974 – A 300 enters service 1976 – Concorde enters service

MDO: Historical Perspective (1970 -1990 Cold War and Maturity) Big slump in world economy (“oil crisis” 1973), airline industry and end of Apollo program leads to a reduction of engineering workforce around 25%. Two major new developments: Computer aided design (CAD), Procurement policy changes for airlines and the military. Earlier quest for maximum performance has been superseded by need for a “balance” among performance, life-cycle cost, reliability, maintainability and other “-ilities” Reflected by growth in design requirements. Competition in airline industry drives operational efficiency.

MDO: Historical Perspective (Growth in Design Requirements)

MDO: Historical Perspective (1990 Present) Multidisciplinary design extended to other industries: spacecraft, automobiles, electronics and computers, transportation, energy and architecture Thrusts in government and industry to improve productivity and quality in products and processes

MDO: Historical Perspective (1990 Present) Design process: Globalization results in distributed, decentralized design teams, high performance PC has replaced centralized super-computers, disciplinary design software (Nastran, CAD/CAM) very mature, Internet and LAN’s allow easy information transfer. Advances in optimization algorithms: e. g. Genetic Algorithms, Simulated Annealing, Particle Swarm Optimization, MDO software, e. g. i. SIGHT, Model Center …

INTRODUCTION TO MSDO OVERVIEW

MDO: Overview Multidisciplinary design optimization (MDO) deals with the optimization of several engineering disciplines simultaneously. MDO gives the engineer the opportunity to find the optimal solution of some system accounting for the interactions between the different disciplines. It should be noted that the multidisciplinary solution might not be the solution for any one discipline analyzed separate from the other disciplines, but is the best solution accounting for the interactions. The MDO field has become vital in design environments in the past decades as designs are becoming more and more complex.

MDO: Overview Most modern engineering systems are multidisciplinary and their analysis is often very complex, involving hundreds computer programs, many people in different locations. This makes it difficult for companies to manage the design process. In the early days, design teams tended to be small an were managed by a single chief designer who knew most about the design details and could make all the important decisions. Modern design projects are more complex and problem has to be decomposed and each part tackled by a different team. The way these teams should interact is still being debated by managers, engineers and

MDO: Framework

MDO: Overview AIRCRAFT DESIGN Aircraft design can start with very rough sketches, as did the human powered airplane, the Gossamer Condor, or Wright Flyer.

MDO: Overview AIRCRAFT DESIGN Practical development often proceeds without detailed simulation.

MDO: Overview AIRCRAFT DESIGN Modern aircraft design is strongly dependent on computational simulation: computation-based design. Significant challenge: integration of high-fidelity modeling in multiple disciplines.

MDO: Overview AIRCRAFT DESIGN Problem formulation is not obvious and requires engineering judgment. One can only make one thing best at a time. ”

MDO: Overview ATC: ROUTE OPTIMIZATION

WHY MDO? ? ? Multidisciplinary Design Optimization (MDO) can be defined as a formal methodology for the design of complex coupled systems in which the synergistic effects of coupling between various interacting disciplines/phenomena are explored and exploited at every stage of the design process.

WHY MDO? ? ? To enable the design of high performance products. Balance product performance considerations manufacturing, economics, and life cycle issues. Achieve design process timetable compression. Achieve Economic competitiveness with

ABOUT THE COURSE

ABOUT THE COURSE This course is focused on developing a deeper understanding of “Multidisciplinary Design and Optimization” as a Discipline that requires a well defined set of design methods and procedures. The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context. The focus will be equally strong on all three aspects of the problem: 1. The multidisciplinary character of engineering systems; 2. Design of these complex systems, and 3. Tools for optimization Using a decision‐making framework, emphasis is placed on understanding basic quantitative methods employed for making design decisions, building mathematical models, and accounting for interdisciplinary interactions.

OBJECTIVES To learn how MDO can support the product development process of complex, multidisciplinary engineered systems. To learn how to rationalize and quantify a system architecture or product design problem by selecting appropriate objective functions, design variables, parameters and constraints To subdivide a complex system into smaller disciplinary models, manage their interfaces and reintegrate them into an overall system model.

OBJECTIVES To be able to use various gradient based optimization techniques such as Sequential Quadratic Programming various Heuristic Optimization Techniques such as Genetic Algorithm Simulated Annealing Particle Swarm Optimization Ant Colony Optimization Tabu Search Hybrid optimization methods Hyper heuristic search methods.

OBJECTIVES To make the selection of the optimization method which is most suitable to the problem at hand. Perform a critical evaluation and interpretation of simulation and optimization results, including sensitivity analysis and exploration of performance, cost and risk tradeoffs. To get familiar with the basic concepts of multi-objective optimization, including the conditions for optimality and the computation of the Pareto front. To acquire critical reasoning with respect to the validity and fidelity of MDO models.

OBJECTIVES Fundamental objectives of the course will be; 1. To learn how optimization as a methodology can support the design of of complex, multidisciplinary engineered systems. 2. To learn how to rationalize and quantify a system architecture problem by selecting appropriate objective functions, design variables, parameters and constraints. 3. To subdivide a complex system into smaller disciplinary models, manage their interfaces and reintegrate them into an overall system model. 4. To be able to use various optimization techniques from various classes of optimization. 5. To make the selection of the optimization technique this is most suitable to the problem at hand. 6. Perform a critical evaluation and interpretation of simulation and optimization results, including sensitivity analysis and exploration of performance, cost and risk tradeoffs. 7. To get familiar with the basic concepts of multi-objective optimization, including the conditions for optimality and the computation of the Pareto front.

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