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