July 13, 2004
-
Upload
kalia-dejesus -
Category
Documents
-
view
32 -
download
1
description
Transcript of July 13, 2004
![Page 1: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/1.jpg)
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
![Page 2: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/2.jpg)
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
![Page 3: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/3.jpg)
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
![Page 4: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/4.jpg)
4© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Goal SeekingGoal Seeking
![Page 5: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/5.jpg)
5© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Excel: Tools – Goal SeekExcel: Tools – Goal Seek
![Page 6: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/6.jpg)
6© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
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
![Page 7: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/7.jpg)
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
![Page 8: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/8.jpg)
8© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Isoperformance AnalogyIsoperformance Analogy
![Page 9: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/9.jpg)
9© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Isoperformance ApproachesIsoperformance Approaches
![Page 10: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/10.jpg)
10© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Bivariate Exhaustive Search (2D)Bivariate Exhaustive Search (2D)
![Page 11: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/11.jpg)
11© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Contour Following (2D)Contour Following (2D)
![Page 12: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/12.jpg)
12© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Progressive SplineProgressive SplineApproximation (III)Approximation (III)
![Page 13: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/13.jpg)
13© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Bivariate Algorithm Bivariate Algorithm ComparisonComparison
![Page 14: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/14.jpg)
14© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Multivariable Branch-and-BoundMultivariable Branch-and-Bound
![Page 15: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/15.jpg)
15© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Tangential Front FollowingTangential Front Following
![Page 16: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/16.jpg)
16© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Vector Spline ApproximationVector Spline Approximation
![Page 17: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/17.jpg)
17© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Multivariable AlgorithmMultivariable AlgorithmComparisonComparison
![Page 18: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/18.jpg)
18© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Graphics: Radar PlotsGraphics: Radar Plots
![Page 19: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/19.jpg)
19© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Nexus Case StudyNexus Case Study
![Page 20: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/20.jpg)
20© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Nexus Integrated ModelNexus Integrated Model
![Page 21: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/21.jpg)
21© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Nexus Block DiagramNexus Block Diagram
![Page 22: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/22.jpg)
22© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Initial Performance AssessmentInitial Performance AssessmentJJzz(p(poo))
![Page 23: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/23.jpg)
23© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Nexus SensitivityNexus SensitivityAnalysisAnalysis
![Page 24: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/24.jpg)
24© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
2D-Isoperformance Analysis2D-Isoperformance Analysis
![Page 25: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/25.jpg)
25© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Nexus MultivariableNexus MultivariableIsoperformance Isoperformance nnpp=10=10
![Page 26: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/26.jpg)
26© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Nexus Nexus Initial pInitial poo vs. Final Design p** vs. Final Design p** isoiso
![Page 27: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/27.jpg)
27© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
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
![Page 28: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/28.jpg)
28© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Raw DataRaw Data
![Page 29: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/29.jpg)
29© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
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
![Page 30: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/30.jpg)
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
![Page 31: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/31.jpg)
31© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Fitted ModelFitted Model
![Page 32: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/32.jpg)
32© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Expected PerformanceExpected Performance
![Page 33: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/33.jpg)
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
![Page 34: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/34.jpg)
34© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Get Isoperformance CurveGet Isoperformance Curve
![Page 35: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/35.jpg)
35© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
Stochastic IsoperformanceStochastic Isoperformance
![Page 36: July 13, 2004](https://reader036.fdocuments.us/reader036/viewer/2022062309/56813561550346895d9cc783/html5/thumbnails/36.jpg)
36© Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics
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”.