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July 13, 2004

July 13, 2004. Guest Lecture ESD.33 “Isoperformance ”. Olivier de Weck. Why not performance-optimal ?. “The experience of the 1960’s has shown that for military aircraft the cost of the final increment of performance usually is excessive in terms of other

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July 13, 2004

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  1. July 13, 2004 Guest Lecture ESD.33 “Isoperformance” Olivier de Weck

  2. Why not performance-optimal ? “The experience of the 1960’s has shown that for military aircraft the cost of the final increment of performance usually is excessive in terms of other characteristics and that the overall system must be optimized, not just performance” Ref: Current State of the Art of Multidisciplinary Design Optimization (MDO TC) - AIAA White Paper, Jan 15, 1991

  3. Lecture 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. Goal Seeking

  5. Excel: Tools – Goal Seek

  6. Goal 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. Goal Programming vs. Isoperformance

  8. Isoperformance Analogy

  9. Isoperformance Approaches

  10. Bivariate Exhaustive Search (2D)

  11. Contour Following (2D)

  12. Progressive SplineApproximation (III)

  13. Bivariate Algorithm Comparison

  14. Multivariable Branch-and-Bound

  15. Tangential Front Following

  16. Vector Spline Approximation

  17. Multivariable AlgorithmComparison

  18. Graphics: Radar Plots

  19. Nexus Case Study

  20. Nexus Integrated Model

  21. Nexus Block Diagram

  22. Initial Performance AssessmentJz(po)

  23. Nexus SensitivityAnalysis

  24. 2D-Isoperformance Analysis

  25. Nexus MultivariableIsoperformance np=10

  26. Nexus Initial po vs. Final Design p** iso

  27. Isoperformance with Stochastic Data 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 ? FS=Wins/Decisions

  28. Raw Data

  29. 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. Model 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) Used Matlab fminunc.m for Optimal surface fit Obtain an expression for expected final standings (FSi) of individual Team i as a function of RBIiand ERAi Baseball:

  31. Fitted Model

  32. Expected Performance

  33. Expected 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 normal table lookup Error term from data

  34. Get Isoperformance Curve

  35. Stochastic Isoperformance

  36. Summary ‧ 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”.

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