Today's Agenda Systems Engineering Lecture 7-1 Multidisciplinary System Design ■MDO definition Optimization(MDO) Optimization problem formulation Instructor(s) MDO in the design process Prof.Jianjun Gao ■MDO challenges Department of Automation School of Electronic Information and Electrical Engineering 2014 Spring System Engineering by J.J.Gao ③cLco 国 What is MDO? Engineering Design Disciplines A methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena Aircraft: Spacecraft: Automobiles: Aerodynamics Astrodynamics Engines Optimal design of complex engineering systems which Propulsion Thermodynamics Body/chassis requires analysis that accounts for interactions amongst Structures Communications Aerodynamics the disciplines (parts of the system) Controls Payload Sensor Electronics Avionics/Software Structures Hydraulics "How to decide what to change,and to what extent to Manufacturing Optics Industrial design change it,when everything influences everything else." others Guidance Control others Ret:AIAA MDO website (Cllck Inside AIAA Technical Committees) Fairly mature,but advances in theory,methodology, computation and application foster substantial payoffs System Engineering by .Gao ③cso System Engineering by J.J.Gao ③ctse
Systems Engineering Instructor(s) + - 2014 Spring Multidisciplinary System Design Optimization(MDO) Prof. Jianjun Gao Department of Automation School of Electronic Information and Electrical Engineering Lecture 7-1 + - 2 Today䇻s Agenda System Engineering by J. J. Gao MDO definition Optimization problem formulation MDO in the design process MDO challenges + - System Engineering by J. J. Gao 3 What is MDO? + - System Engineering by J. J. Gao 4 Engineering Design Disciplines
Multidisciplinary Aspects of Design System Level Optimization Emphasis is on the multidisciplinary nature of the Why system-level,multidisciplinary optimization complex engineering systems design process.Aero- space vehicles are a particular class of such systems Disciplinary specialists tend to strive towards improvement of objectives and satisfaction of constraints in terms of the variables of their own discipline Structures Control Emphasis in recent years has In doing so they generate side effects-often unknowingly- been on advances that can that other disciplines have to absorb,usually to the Aerodynamics be achieved due to the inter- action of two or more detriment of the overall system performance disciplines. System Engineering by J.J.Gao ③cLao System Engineering by J.J.Gao ③cLco 6 Aircraft "Optimization" System Level Optimization Breguet Marketing Aero Range D Equation AI→ R- V(L/D). Vwie AR &·SFC Marketing:maximize Aero:maximize L/D passenger volume Cabin diameter →Aspect Ratio Propulsion Structures M R=Range [m] V=Flight velocity [m/s] SFC Specific Fuel Consumption [kg/s/N] L/D Lift-over-Drag ration [N/N] BPR- g gravitational acceleration [m/s?] Structures:minimize Propulsion:minimize Win=Initial (takeoff)weight [N] structural mass specific fuel consumption W=Weight at end of flight [N] (sFC)→Bypass Ratio Wie=Winbar-Wina Fuel quantity [N] →Wing-root moment System Engineering by .Gao ③ctoo System Engineering by .J.Gao ⑦ctGe 8
+ - System Engineering by J. J. Gao 5 Multidisciplinary Aspects of Design + - System Engineering by J. J. Gao 6 System Level Optimization + - System Engineering by J. J. Gao 7 Aircraft “Optimization” + - System Engineering by J. J. Gao 8 System Level Optimization
Human Aspact Quantitative vs.Qualitative It is wrong to think of MDO as"automated"or "push- button"design: Huean mveenveness,creanvit,intirton.experience Conceiving The human strengths(creativity,intuition,decision- different concepts making)and computer strengths(memory,speed, objectivity)should complement each other The human will always be the Meta-designer Evalation. selection of Challenges of defining an effective interface- c0p市店 continuous vs.discrete thinking Challenges of visualization in multidimensional space, e.g.search path from initial design to final design Human mind is the driving force in the design process.MDO is a Human element is a key component in way of formalizing the quantitative tool to apply the best trade-offs. any successful system design methodology System Engineering by J.J.Gao ③cLao System Engineering by J.J.Gao ③cLco 国 10 Architecture V.S.Design Architecture V.S.Design Architecture selects the concept,decomposition and mapping of form to function Architecture establishes the vector of design and operating parameters Design selects the values of the vector of variables This is what optimization is good for Some work in"architecture"is just an exhaustive search over the design of one architecture Design Variables X System Engineering by J.J.Gao ③cts0 11 System Engineering by .J.Gao ③ctse 12
+ - System Engineering by J. J. Gao 9 Human Aspact + - System Engineering by J. J. Gao 10 Quantitative vs. Qualitative + - System Engineering by J. J. Gao 11 Architecture V.S. Design + - System Engineering by J. J. Gao 12 Architecture V.S. Design
Today's Agenda Optimization methods have been combined with design synthesis and parametric analysis for ca.40 years ■MDO definition Traditionally used graphical methods to find maximum or minimum of a multivariate function("carpet plot"),but.... Optimization problem formulation MDO in the design process "peaks" Graphics break down above 3-4 dimensions ■MDO challenges Where is max J(x)? Caution:local extrema 一Where is min J(x)? Design variable x1 System Engineering by J.J.Gao ③cLe0 国倒 13 System Engineering by J.J.Gao ③cLco 国 14 Combinatorial Explosion The General Model Any design can be defined by a vector in Quantitative side of the design problem may be formulated multidimensional space,where each design as a problem of Nonlinear Programming (NLP) variable represents a different dimension minJ x.p This is the problem formulation For n>3 a combinatorial "explosion"takes place that we will discuss this semester. and the design space cannot be computed and s.tg(k,p)≤0 plotted in polynomial time h(K,P)=0 where J=[J,x…J.x了 B≤X,≤xB（G=l…m) X=x1…x…Xm Numerical optimization offers an alternative to the graphical approach and"brute force"evaluation g=[8(…8()] h=[h()…h(x)] During past three decades much progress has been made in numerical optimization System Engineering by J.J.Gao ③coo 15 System Engineering by .J.Gao ③ctse 16
+ - 13 Today䇻s Agenda System Engineering by J. J. Gao MDO definition Optimization problem formulation MDO in the design process MDO challenges + - System Engineering by J. J. Gao 14 + - System Engineering by J. J. Gao 15 Combinatorial Explosion + - System Engineering by J. J. Gao 16 The General Model
Objectives Design Variables The objective can be a vector J of z system responses Design vector x contains n variables that form the design space or characteristics we are trying to maximize or minimize During design space exploration or optimization we change the [S] Often the objective is a entries of x in some rational fashion to achieve a desired effect cost scalar function,but for X;can be… range [km] real systems often we aspect ratio [- attempt multi-objective weight [kg] 2 transmit power [W] optimization: Real: xi∈R J= X3 #of apertures[日] data rate [bps] X= x→J(☒ Integer: ri∈Z orbital altitude [km] : Binary: c∈{0,1} Some objectives can be ROI [%] Boolean:xiE {true,false} conflicting. control gain [V/V] System Engineering by J.J.Gao ③cLao 国 17 System Engineering by J.J.Gao ③cLco 国 18 Parameters Constraints Constraints act as boundaries of the design space x and typically occur due to finiteness of resources or Parameters p are quantities that affect the objective technological limitations of some design variables. J,but are considered fixed,i.e.they cannot be changed by the designers. Often.but not always.optimal designs lie at the intersection of several active constraints Sometimes parameters p can be turned into design variables x to enlarge the design space. Inequality constraints: gX≤0j=1,2…,m1 Sometimes parameters p are former design variables that were fixed at some value because they were Equality constraints:x=0k=1,2....,m found not to affect any of the objectives or because Bounds::xB≤x,≤xgi=l,2,n their optimal level was predetermined. Objectives are what we are trying to achieve Constraints are what we cannot violate Design variables are what we can change System Engineering by J.Gao ③ctGe 19 System Engineering by J.J.Gao ③ct6e 20
+ - System Engineering by J. J. Gao 17 Objectives + - System Engineering by J. J. Gao 18 Design Variables + - System Engineering by J. J. Gao 19 Parameters Parameters p are quantities that affect the objective J,but are considered fixed, i.e. they cannot be changed by the designers. Sometimes parameters p can be turned into design variables x to enlarge the design space. Sometimes parameters p are former design variables that were fixed at some value because they were found not to affect any of the objectives J or because their optimal level was predetermined. + - System Engineering by J. J. Gao 20 Constraints
Constraints versus Objectives Example Problem Statement It can be difficult to choose whether a Minimize the take-off weight of the aircraft by condition is a constraint or an objective. changing wing geometric parameters while For example:should we try to minimize cost, satisfying the given range and playload requirement at the given cruise speed. or should we set a constraint stating that cost should not exceed a given level. Sometimes,the initial formulation will need to Question:What is the objective,design variable, be revised in order to fully understand the parameters and constraint? design space. In some formulations,all constraints are treated as objectives(physical programming). System Engineering by J.J.Gao ③cLao 国 21 System Engineering by J.J.Gao ③ctco 国 22 Group Exercise Today's Agenda For your group's system: ■MDO definition 1.Consider the preliminary design phase. Identify: Optimization problem -important disciplines formulation -potential objective functions MDO in the design process -potential design variables -system parameters ■MDO challenges -constraints and bounds 2.Report out System Engineering by J.J.Gao ③ctGe 国 23 System Engineering by .J.Gao ③ctGe 国 24
+ - It can be difficult to choose whether a condition is a constraint or an objective. For example: should we try to minimize cost, or should we set a constraint stating that cost should not exceed a given level. Sometimes, the initial formulation will need to be revised in order to fully understand the design space. In some formulations, all constraints are treated as objectives (physical programming). System Engineering by J. J. Gao 21 Constraints versus Objectives + - Minimize the take-off weight of the aircraft by changing wing geometric parameters while satisfying the given range and playload requirement at the given cruise speed. System Engineering by J. J. Gao 22 Example Problem Statement Question: What is the objective, design variable, parameters and constraint? + - System Engineering by J. J. Gao 23 Group Exercise + - 24 Today䇻s Agenda System Engineering by J. J. Gao MDO definition Optimization problem formulation MDO in the design process MDO challenges
What MDO really does MSDO Framework MDO mathematically traces a path in the design space Design Vector Simulation Model Objective Vector from some initial design x towards improved designs 「1 Discipline A Discipline B (with respect to the objective J). J. It does this by operating on a large number of variables Discipline C and functions simultaneously-a feat beyond the power of the human mind. Coupling Multiobjective Optimization Approximation The path is not biased by intuition or experience. Optimization Algorithms Methods This path instead of being invisible inside a "black box" Numerical Techniques Sensitivity Tradespace (direct and penalty methods) becomes more visible by various MDO techniques such Analysis Exploration as sensitivity analysis and visualization Heuristic Techniques Coupling (DOE) (SA,GA) Isoperfommance Optimization does not remove the designer from Output Evaluation the loop,but it helps conduct trade studies Massachusetts Institute af Technology-Prof de Weck and Prot Wicox System Engineering by J.J.Gao CLCO 国 25 System Engineering by J.J.Gao ③cLGo 国 26 Simulation versus Optimization Typical Process in MDO (1) Define overall system requirements There are two distinct components of the MSDO (2) Define design vector x.objective J and constraints process: (3) System decomposition into modules The optimization algorithm decides how to move (4) Modeling of physics via governing equations at the module level-module execution in isolation through the design space. (5) Model integration into an overall system simulation The simulation model evaluates designs chosen by the (6) Benchmarking of model with respect to a known optimizer.Both objective functions and constraints must system from past experience,if available be evaluated. (7) Design space exploration(DoE)to find sensitive and important design variables x, Sometimes,disciplinary simulation models can be used (8) Formal optimization to find min J(x) in an optimization framework,but often they are not (9) Post-optimality analysis to explore sensitivity and appropriate. tradeoffs:sensitivity analysis,approximation methods,isoperformance,include uncertainty System Engineering by J.J.Gao ③ctGe 27 System Engineering by Gao ③c1G0 28
+ - System Engineering by J. J. Gao 25 What MDO really does + - System Engineering by J. J. Gao 26 MSDO Framework + - System Engineering by J. J. Gao 27 Simulation versus Optimization + - System Engineering by J. J. Gao 28 Typical Process in MDO
In Practice... MDO Uses (0) Step through(1)-(8) The 'MD'portion of 'MDO'is important on its own (ii)The optimizer will use an error in the problem setup to Often MDO is used not to find the truly optimal determine a mathematically valid but physically design,but rather to find an improved design.or even unreasonable solution a feasible design... OR The optimizer will be unable to find a feasible solution (satisfies all constraints) Range of design objectives (iii)Add,remove or modify constraints and/or design variables (iv)Iterate until an appropriate model is obtained Although MDO is an automated formalization of the design Feasible Improved Optimal Pareto process,it is a highly interactive procedure... System Engineering by J.J.Gao ③cLao 国 29 System Engineering by J.J.Gao ③cLco 30 Today's Agenda Fidelity/expense of disciplinary models: Fidelity is often sacrificed to obtain models with short computation times. Complexity: ■MDO definition Design variables,constraints and model interfaces must be managed carefully. Optimization problem 。Communication formulation The user interface is often very unfriendly and it can be difficult to change problem parameters. MDO in the design process 。Flexibility ■MDO challenges .It is easy for an MDO tool to become very specialized and only valid for one particular problem. How do we prevent MDO codes from becoming complex,highly specialized tools which are used by a single person (often the developer!)for a single problem? System Engineering by J.J.Gao ③ctGe 31 System Engineering by J.J.Gao ③c1Ge 32
+ - System Engineering by J. J. Gao 29 In Practice... + - System Engineering by J. J. Gao 30 MDO Uses + - 31 Today䇻s Agenda System Engineering by J. J. Gao MDO definition Optimization problem formulation MDO in the design process MDO challenges + - Fidelity/expense of disciplinary models: Fidelity is often sacrificed to obtain models with short computation times. Complexity: Design variables, constraints and model interfaces must be managed carefully. Communication The user interface is often very unfriendly and it can be difficult to change problem parameters. Flexibility It is easy for an MDO tool to become very specialized and only valid for one particular problem. System Engineering by J. J. Gao 32 How do we prevent MDO codes from becoming complex, highly specialized tools which are used by a single person (often the developer!) for a single problem?
Fidelity vs.Expense Breadth vs.Depth high fidelity how to high fidelity (e.g.CFD,FEM) can we do s-design how to better? implement? (e.g. practeal? CFD.FEM) implement? ② intermediate intermediate fidelity fidelity e.g.vortex lattice. increasing difficulty (e.g.vortex increasing difficulty beam theory) lattice,beam can the theory) can the empirical Pesults be empirical 石 Tesults be models Level of MSDO believed? relations System Breadth believed? trade limited full focus on a all critical complete studies optimization/iteration MDO subsystem constraints system System Engineering by J.J.Gao ③cLao 国倒 33 System Engineering by J.J.Gao ③cLco 国 34 MDO Pros and Cons Summary Advantages MDO is not a stand-alone,automated design process reduction in design time systematic,logical design procedure MDO is a valuable tool that requires substantial human handles wide variety of design variables constraints interaction and complements other design tools not biased by intuition or experience Elements of an MDO framework Disadvantages ·MDO Challenges computational time grows rapidly with number of dv's numerical problems increase with number of dv's limited to range of applicability of analysis programs will take advantage of analysis errors to provide mathematical design improvements difficult to deal with discontinuous functions System Engineering by J.J.Gao ③ctoo 35 System Engineering by .J.Gao ⑦c1Ge 国 36
+ - System Engineering by J. J. Gao 33 Fidelity vs. Expense + - System Engineering by J. J. Gao 34 Breadth vs. Depth + - System Engineering by J. J. Gao 35 MDO Pros and Cons + - System Engineering by J. J. Gao 36 Summary