1. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 1 July 13, 2004 Guest Lecture ESD.33 “Isoperformance ” Olivier de Weck

2. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 4 Goal Seeking

5. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 5 Excel: Tools – Goal Seek

6. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 7 Goal Programming vs. Isoperformance

8. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 8 Isoperformance Analogy

9. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 9 Isoperformance Approaches

10. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 10 Bivariate Exhaustive Search (2D)

11. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 11 Contour Following (2D)

12. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 12 Progressive Spline Approximation (III)

13. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 13 Bivariate Algorithm Comparison

14. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 14 Multivariable Branch-and-Bound

15. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 15 Tangential Front Following

16. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 16 Vector Spline Approximation

17. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 17 Multivariable Algorithm Comparison

18. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 18 Graphics: Radar Plots

19. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 19 Nexus Case Study

20. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 20 Nexus Integrated Model

21. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 21 Nexus Block Diagram

22. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 22 Initial Performance Assessment J z (p o )

23. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 23 Nexus Sensitivity Analysis

24. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 24 2D-Isoperformance Analysis

25. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 25 Nexus Multivariable Isoperformance n p =10

26. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 26 Nexus Initial p o vs. Final Design p** iso

27. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 27 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 Data FS=Wins/Decisions

28. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 28 Raw Data

29. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 30 Step 1: Obtain an expression from model for expected performance of a “system” for individual design i as a function of design variables x 1,I and x 2,i 1.1 assumed model E [ J i ] = a 0 + a 1 ( x 1,i ) + a 2 ( x 2,i ) + a 12 ( x 1,i - x 1 )( x 2,i - x 2 ) (1) 1.2 model fitting General mean E [ FS i ] = m + a ( RBI i ) + b ( ERA i ) +c ( RBI i – RBI )( ERA i – ERA ) Model Used Matlab fminunc.m for Optimal surface fit Baseball: Obtain an expression for expected final standings (FS i ) of individual Team i as a function of RBI i and ERA i

31. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 31 Fitted Model

32. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 32 Expected Performance

33. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 33 Expected Performance Baseball: Performance criterion - User specifies a final desired standing of FS i =0.550 Confidence Level - User specifies a.80 confidence level that this is achieved Spec is met if for Team i: E [ FS i ] =.550 +zσ r =.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. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 34 Get Isoperformance Curve

35. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 35 Stochastic Isoperformance

36. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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”.