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MIT ESD 77 - Multidisciplinary System Design Optimization

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1© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxAnas AlfarisProblem FormulationLecture 2Multidisciplinary System Design Optimization (MSDO)2© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxToday’s Topics• MDO definition• Optimization problem formulation• MDO in the design process• MDO challenges3© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxMDO DefinitionWhat is MDO ?• A methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena• Optimal design of complex engineering systems which requires analysis that accounts for interactions amongst the disciplines (= parts of the system)• “How to decide what to change, and to what extent to change it, when everything influences everything else.”Ref: AIAA MDO website http://www.aiaa.org (Click Inside AIAA, Technical Committees)4© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Design DisciplinesAircraft:AerodynamicsPropulsion StructuresControlsAvionics/SoftwareManufacturingothersSpacecraft:AstrodynamicsThermodynamicsCommunicationsPayload & SensorStructuresOpticsGuidance & ControlAutomobiles:EnginesBody/chassisAerodynamicsElectronicsHydraulicsIndustrial designothersFairly mature, but advances in theory, methodology,computation and application foster substantial payoffs5© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxMultidisciplinary Aspects of DesignEmphasis is on the multidisciplinary nature of thecomplex engineering systems design process. Aero-space vehicles are a particular class of such systems.StructuresAerodynamicsControlEmphasis in recent years has been on advances that can be achieved due to the inter-action of two or more disciplines.6© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxSystem Level OptimizationWhy system-level, multidisciplinary optimization ?• Disciplinary specialists tend to strive towards improvement of objectives and satisfaction of constraints in terms of the variables of their own discipline• In doing so they generate side effects - often unknowingly-that other disciplines have to absorb, usually to the detriment of the overall system performance7© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxAircraft “Optimization”Marketing: maximize passenger volume Cabin diameterAero: maximize L/D Aspect Ratio Structures: minimizestructural mass Wing-root momentPropulsion: minimizespecific fuel consumption (SFC) Bypass RatioDARMBPR8© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxSystem-level Optimization( / )lninitialfinalWV L DRg SFC WBréguetRangeEquationR = Range [m]V = Flight velocity [m/s]SFC = Specific Fuel Consumption [kg/s/N]L/D = Lift-over-Drag ration [N/N]g = gravitational acceleration [m/s2]Winitial= Initial (takeoff) weight [N]Wfinal = Weight at end of flight [N]Wfuel=Winitial-Wfinal Fuel quantity [N]AllStructuresPropulsionAeroMarketing9© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxHuman Interface Aspects of DesignIt is wrong to think of MDO as “automated” or “push-button” design:• The human strengths (creativity, intuition, decision-making) and computer strengths (memory, speed, objectivity) should complement each other• The human will always be the Meta-designer• Challenges of defining an effective interface –continuous vs. discrete thinking• Challenges of visualization in multidimensional space, e.g. search path from initial design to final designHuman element is a key component inany successful system design methodology10© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxQuantitative vs. QualitativeHuman mind is the driving force in the design process. MDO is a way of formalizing the quantitative tool to apply the best trade-offs. Image by MIT OpenCourseWare.Qualitative Effort StreamQuantitative Effort StreamTimeAnswerAnswerAnswer AnswerQuestionQuestionQuestionQuestionNew Vehicle DesignParallel, qualitative, and quantitative efforts in design.Human inventiveness, creativity, intuition, experience Quantitative, objective, computationalConceiving different conceptsEvaluation, selection of concepts11© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxArchitecture vs. 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 architectureInitial WaterSurface AreaQuantityMaterial Thickness Material Well ThicknessLength, width, HeightWhole Product SystemCoolerBox with BottomTopIceDesign Variables XOperating parameters PImage by MIT OpenCourseWare.12© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxOptimization Problem Formulation13© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxOptimization Aspects of Design• Optimization methods have been combined with design synthesis and parametric analysis for ca. 40 years• Traditionally used graphical methods to find maximum or minimum of a multivariate function (“carpet plot”), but….Graphics break downabove 3-4 dimensionsObjective J(x)Where is min J(x) ?Where is max J(x) ?Caution: local extrema !“peaks”14© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxCombinatorial Explosion• Any design can be defined by a vector in multidimensional space, where each design variable represents a different dimension• For n > 3 a combinatorial “explosion” takes place and the design space cannot be computed and plotted in polynomial time• Numerical optimization offers an alternative to the graphical approach and “brute force” evaluationDuring past three decades much progress hasbeen made in numerical optimization15© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxFormal Notation,,1,..., )min ,s.t. , 0 , =0(i LB i i UBinx x xJ x pg(x p)h(x p)This is the problem formulationthat we will discuss this semester.Quantitative side of the design problem may be formulatedas a problem of Nonlinear Programming (NLP)121111where


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