l11b - Issues in Optimization Jaroslaw Sobieski NASA...

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Issues in Optimization Jaroslaw Sobieski NASA Langley Research Center Hampton Virginia NASA Langley Research Center Hampton, VA 23681; MS240 LaRC/SMC/ACMB Copyright NASA, Jaroslaw Sobieski, 2003
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How to know whether optimization is needed
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How to recognize that the problem at hand needs optimization. • General Rule of the Thumb: there must be at least two opposing trends as functions of a design variable Analysis x f1 f1 f2 f2 f1 f2 x
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Power Line Cable tout cable slack cable h Length(h) A(h) Volume(h) A L V min • Given: • Ice load • self-weight small • h/span small tout h slack
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Wing Thin-Walled Box Lift •Top cover panels are compressed b thickness t •Buckling stress = f(t/b) 2 b few many Cover weight Rib total weight Wing box weight min ribs ribs
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Multistage Rocket fuel drop when burned number of segments fuel weight segment junctions weight rocket weight 2 3 min weight to carry up = less fuel more weight to carry up • More segments (stages) = less • More segments = more junctions = • Typical optimum: 2 to 4. Saturn V
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Under-wing Nacelle Placement longer body to rotate for take-off = more weight fore nacelle aft shock wave drag nacelle wing underside shock wave impinges on forward slope = drag moves with it = larger tail (or drag weight Range max • Inlet ahead of wing max. depth = • Nacelle moved aft = landing gear
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National Taxation tax paid on $ earned revenue collected max incentive to work 0 % average 100 % tax rate • More tax/last $ = less reason to strive to earn • More tax/$ = more $ collected per “unit of economic activity”
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National Taxation revenue collected max tax paid on $ earned incentive to work 0 % average 100 % tax rate • More tax/last $ = less reason to strive to earn • More tax/$ = more $ collected per “unit of economic activity” • What to do: • If we are left of max = increase taxes • If we are right of max = cut taxes
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Nothing to Optimize Rod P Newton A cm 2 • Monotonic trend • No counter-trend σ σ allowable • Nothing to optimize N/cm 2 A
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Various types of design optima
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Design Definition: Sharp vs. constraints - 0 contours Shallow - bad side of 1 2 1 2 band point constraints - 0 contours X X Objective Constraint descent • Near-orthogonal intersection defines a design point • Tangential definition identifies a band of of designs X
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Multiobjective Optimization trade- both Q = 1/(quality & f 1 off both performance & f 2 comfort) $ 1 4 $ 4 pareto-frontier 2 3 3 2 design & manufacturing sophistication 1 Q pareto-optimum V&W R&R
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A Few Pareto-Optimization Techniques • Reduce to a single objective: F = Σ i w i f i where w’s are judgmental weighting factors • Optimize for f 1 ; Get f* 1; ; •Set a floor f 1 >= f* i ; Optimize for f 2 ; get f 2 ; • Keep floor f 1 , add floor f 2 ; Optimize for f 3 ; • Repeat in this pattern to exhaust all f’s; • The order of f’s matters and is judgmental • Optimize for each f independently; Get n optimal designs; i Find a compromise design equidistant from all the above.
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This note was uploaded on 11/08/2011 for the course AERO 16.810 taught by Professor Olivierdeweck during the Winter '07 term at MIT.

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l11b - Issues in Optimization Jaroslaw Sobieski NASA...

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