Model Implementation and Validation

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1 Anonymous MIT students 1

2 Introduction Problem Statement Design of Experiment e Sensitivity i t Analysis Agenda Model Implementation and Validation Single Objective Optimization Multi objective Optimization Conclusions 2

3 9Introduction Problem Statement Design of Experiment e Sensitivity i t Analysis Agenda Model Implementation and Validation Single Objective Optimization Multi objective Optimization Conclusions 3

4 Problem Statement Maximize the Return On Investment (ROI) by changing the physical Space Shuttle External Fuel Tank design variables while satisfying the given mechanical requirements (Volume, Stress, Vibrations) at a fixed specific Payload. 4

5 Problem Statement (cont ) ROI = Tank Weight Revenue (tax payers) (Launch Fixed Costs + Tank Cost) (Launch Fixed Costs + Tank Cost) 5

6 9Introduction 9Problem Statement Design of Experiment e Sensitivity i t Analysis Agenda Model Implementation and Validation Single Objective Optimization Multi objective Optimization Conclusions 6

7 Model implementation and validation Objectives Design Variables Constraint t (7) (6) (5) Total surface of the tank Tank weight Total seam cost Delta payload Payload launched ROI Nose cone height Radius of the hemisphere Length of the cylindrical body Nose cone thickness Cylinder thickness Hemisphere thickness Aspect ratio of cone Volume Stress (cylinder nose, hemisphere, nose cone) Vibration Parameters (10) Cost of material/unit Cost Seam/unit Material weight/unit Liquid fuel pressure Payload 1 Payload 2 Nominal Payload Profit ratio Vibration constant Fixed launch cost per weight Charge to customer for launching payload per unit weight 7

8 Model implementation and validation (cont ) PSM32 8

9 Model implementation and validation (cont ) N2 Matrix 9

10 Model implementation and validation (cont ) Block Diagram 10

11 Model implementation and validation (cont ) Model Validation The given nominal values of the real External Tank were used in the model formulas Outputs verified the model as valid, but with low fidelity E.g.: Nominal Tank Weight = 27, [Kg] Model Tank W eight = 21, [Kg] 11

12 9Introduction 9Problem Statement Design of Experiment e Sensitivity i t Analysis Agenda 9Model Implementation and Validation Single Objective Optimization Multi objective Optimization Conclusions 12

13 Design of Experiment DOE factors and levels Main effects 18-Orthogonal array X 0 = ROI 0 =

14 9Introduction 9Problem Statement 9Design g of Experiment e Sensitivity i t Analysis Agenda 9Model Implementation and Validation Single Objective Optimization Multi objective Optimization Conclusions 14

15 Single Objective Optimization i Best solution by Genetic Algorithm 15

16 Single Objective Optimization i ROI=0.060 ROI=0.090 ROI=0.226 ROI=0.283 ROI=0.284 Pre DOE DOE SQP SQP GA Scaling 16

17 9Introduction 9Problem Statement 9Design g of Experiment e Sensitivity i t Analysis Agenda 9Model Implementation and Validation 9Single Objective Optimization Multi objective Optimization Conclusions 17

18 Sensitivity Analysis Normalize Gradient es n Variable Design 18

19 Sensitivity Analysis Constraint Form Value at x* Active? Vibration constraint Volume constraint Eq. Cylinder stress constraint 1 VF/VFallo wed 0 1 Vtank/Vno minal 0 Scyl/Sallo wed 1 0 ~ 0 Yes ~ 0 Yes ~ 0 Yes Eq. Shem/Sall ~ 0 Yes Hemisphere owed 1 0 stress constraint Eq. Cone stress constraint Scon/Sallo wed 1 0 ~ 0 Yes 19

20 9Introduction 9Problem Statement Agenda 9Model Implementation and Validation 9Design g of Experiment e 9Single Objective Optimization 9Sensitivity Analysis Multi objective Optimization Conclusions 20

21 Multi Objective Optimization i Weight [Kg] AWS-Pareto Front MAX ROI MIN WEIGHT -(ROI) 21

22 9Introduction 9Problem Statement Agenda 9Model Implementation and Validation 9Design g of Experiment e 9Single Objective Optimization 9Sensitivity Analysis 9Multi objective Optimization Conclusions 22

23 Conclusions Single Objective Optimization Multi Objective Optimization 23

24 MIT OpenCourseWare ESD.77 / Multidisciplinary System Design Optimization Spring 2010 For information about citing these materials or our Terms of Use, visit:

Multidisciplinary Design Optimization of the Space Shuttle External Tank

6.888/ESD.77J Multidisciplinary System Multidisciplinary Design Optimization of the Space Shuttle External Tank Mo-Han Hsieh Christopher Michael Lawson May 7th, 24 Outline Motivation Problem Statement