1© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

July 13, 2004July 13, 2004

Guest Lecture ESD.33

“Isoperformance”

Olivier de Weck

2© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Why not performance-optimal ?Why not performance-optimal ?

“The experience of the 1960’s has shown that formilitary aircraft the cost of the final increment ofperformance usually is excessive in terms of othercharacteristics and that the overall system must beoptimized, not just performance”

Ref: Current State of the Art of Multidisciplinary Design Optimization(MDO TC) - AIAA White Paper, Jan 15, 1991

3© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Lecture OutlineLecture Outline

‧ Motivation - why isoperformance ? ‧ Example: Goal Seeking in Excel ‧ Case 1: Target vector T in Range

= Isoperformance ‧ Case 2: Target vector T out of Range

= Goal Programming ‧ Application to Spacecraft Design ‧ Stochastic Example: Baseball

4© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Goal SeekingGoal Seeking

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Excel: Tools – Goal SeekExcel: Tools – Goal Seek

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Goal Seeking and Equality ConstraintsGoal Seeking and Equality Constraints

• Goal Seeking – is essentially the same as

finding the set of points x that will satisfy the

following “soft” equality constraint on the

objective:

Find all x such that

7© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Goal Programming vs. IsoperformanceGoal Programming vs. Isoperformance

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Isoperformance AnalogyIsoperformance Analogy

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Isoperformance ApproachesIsoperformance Approaches

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Bivariate Exhaustive Search (2D)Bivariate Exhaustive Search (2D)

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Contour Following (2D)Contour Following (2D)

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Progressive SplineProgressive SplineApproximation (III)Approximation (III)

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Bivariate Algorithm Bivariate Algorithm ComparisonComparison

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Multivariable Branch-and-BoundMultivariable Branch-and-Bound

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Tangential Front FollowingTangential Front Following

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Vector Spline ApproximationVector Spline Approximation

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Multivariable AlgorithmMultivariable AlgorithmComparisonComparison

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Graphics: Radar PlotsGraphics: Radar Plots

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Nexus Case StudyNexus Case Study

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Nexus Integrated ModelNexus Integrated Model

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Nexus Block DiagramNexus Block Diagram

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Initial Performance AssessmentInitial Performance AssessmentJJzz(p(poo))

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Nexus SensitivityNexus SensitivityAnalysisAnalysis

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2D-Isoperformance Analysis2D-Isoperformance Analysis

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Nexus MultivariableNexus MultivariableIsoperformance Isoperformance nnpp=10=10

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Nexus Nexus Initial pInitial poo vs. Final Design p** vs. Final Design p** isoiso

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Example: Baseball season has started

What determines success of a team ?

Pitching Batting

ERA RBI

Earned Run Average” “Runs Batted In”

How is success of team measured ?

Isoperformance with Stochastic DataIsoperformance with Stochastic Data

FS=Wins/Decisions

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Raw DataRaw Data

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Stochastic Isoperformance (I)Stochastic Isoperformance (I)

Step-by-step process for obtaining (bivariate)

isoperformance curves given statistical data:

Starting point, need:

- Model - derived from empirical data set

- (Performance) Criterion

- Desired Confidence Level

30© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Step 1: Obtain an expression from model for expected

performance of a “system” for individual design i

as a function of design variables x1,I and x2,i

1.1 assumed model

E[Ji] = a0+a1(x1,i)+a2(x2,i)+a12(x1,i - x1)(x2,i - x2) (1)

1.2 model fitting

General mean

E[FSi] = m + a(RBIi) + b(ERAi) +c(RBIi – RBI)(ERAi – ERA)

ModelModel

Used Matlabfminunc.m forOptimal surface fit

Baseball:

Obtain an expression for expected final standings (FSi) ofindividual Team i as a function of RBIi and ERAi

31© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Fitted ModelFitted Model

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Expected PerformanceExpected Performance

33© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Expected PerformanceExpected Performance

Baseball:

Performance criterion

- User specifies a final desired standing of FSi=0.550

Confidence Level

- User specifies a .80 confidence level that this is achieved

Spec is met if for Team i:

E[FSi] = .550 +zσr = .550 + 0.84(0.0493) = .5914

If the final standing of team I is to equal or exceed

.550 with a probability of .80, then the expected

final standing for Team I must equal 0.5914

From normaltable lookup

Error termfrom data

34© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics

Get Isoperformance CurveGet Isoperformance Curve

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Stochastic IsoperformanceStochastic Isoperformance

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SummarySummary

‧ Isoperformance fixes a target level of

“expected” performance and finds a set of

points (contours) that meet that requirement

‧ Model can be physics-based or empirical

‧ Helps to achieve a “balanced” system

design, rather than an “optimal design”.