Simulation-Supported Decision Making

1. Simulation-Supported Decision Making Gene Allen

2. Tools for Engineers • Tools Engineers want to use to help them make better decisions: • Slide Rule • Calculator • “?” to leverage Moore’s Law

3. Successful Engineering Cultures • 1950’s U.S. Aerospace Industry • Produced: U-2, X-15, Saturn V, C-130, B-52 • U.S. Navy Nuclear Propulsion Program • Decades of dynamic operations of • hundreds of nuclear power plants without • casualties • Combined Theory and Practice • DID NOT USE COMPUTERS

4. DEVELOPING an ENGINEERING KNOWLEDGE BASE Learning Dominated by Test Eliminate Failure Modes 73% COST Certification Demonstration 10 % Engineering 15 % YEARS Initial Design 2 % • Examples of Cost to First Production • Nonrecurring Development Costs to Build Knowledge Base • Rocket Engines • SSME $ 2.8 B • F-1 $ 2.4 B • J-2 $ 1.7 B • Jet Engines • F-100 $ 2.0 B • Automobiles • 1996 Ford Taurus $ 2.8 B

5. The Fundamental Problem … Variability

6. Structural Material Scatter MATERIAL CHARACTERISTIC CV Metallic Rupture 8-15% Buckling 14% Carbon Fiber Rupture 10-17% Screw, Rivet, Welding Rupture 8% Bonding Adhesive strength 12-16% Metal/metal 8-13% Honeycomb Tension 16% Shear, compression 10% Face wrinkling 8% Inserts Axial loading 12% Thermal protection (AQ60) In-plane tension 12-24% In-plane compression 15-20% Source: Klein, M., Schueller, G.I., et.al.,Probabilistic Approach to Structural Factors of Safety in Aerospace, Proceedings of the CNES Spacecraft Structures and Mechanical Testing Conference, Paris, June 1994, Cepadues Edition, Toulouse, 1994.

7. The Deception of Precise Geometry Geometry imperfections should be described as stochastic fields.

8. Load Scatter (aerospace) LOAD TYPE ORIGIN OF RESULTS CV Launch vehicle thrust STS, ARIANE 5% Launch vehicle quasi-static loads STS, ARIANE, DELTA 30% - POGO oscillation - stages cut-off - wind shear and gust - landing (STS) Transient ARIANE 4 60% Thermal Thermal tests 8-20% Deployment shocks (Solar array) Aerospatiale 10% Thruster burn Calibration tests 2% Acoustic ARIANE 4 and STS (flight) 30% Vibration Satellite tests 20% Source: Klein, M., Schueller, G.I., et.al.,Probabilistic Approach to Structural Factors of Safety in Aerospace, Proceedings of the CNES Spacecraft Structures and Mechanical Testing Conference, Paris, June 1994, Cepadues Edition, Toulouse, 1994.

9. Simulation for Learning and Decision Making • Quickly Identify and Understand How a Product Functions: • What are the major variables driving functionality? • What are the combinations of variables that lead to problems in complex systems? • Ability Exists Today • Due to advances in compute capability Tool is a Correlation Map

10. Correlation Maps to Understand How Things Work Input Variables • Ranks input variables and • output responses • by correlation level • Follows MIT-developed • Design Structure Matrix • model format • Filters Variables Based • on Correlation Level Output Variables

11. A Correlation Map Upper right – positive correlation Lower left – negative correlation

12. Meta ModelofDesign Alternatives Generation of Correlation Maps Stochastic Simulation Template 100 MCS runs Correlation Map: - Includes All Results - Highlights Key Variables

13. Generation of Correlation Maps Correlation Map – a 2-D view of Results Data generated from Monte Carlo Analysis • Incorporates Variability and Uncertainty • Updated Latin Hypercube sampling • Independent of the Number of Variables • Results with 100 runs • Does Not Violate Physics • No assumptions of continuity • “Not elegant, only gives the right answers.”

14. Monte Carlo Results show Reality Collection of computer runs = Simulation Single computer run = Analysis Understanding the physics of a phenomenon is equivalent to the understanding of the topology and structure of these clouds.

15. Monte Carlo Analysis x1 x2 x3 y1 y2 • Sources of Variability • Material Properties • Loads • Boundary and initial conditions • Geometry imperfections • Assembly imperfections • Solver • Computer (round-off, truncation, etc.) • Engineer (choice of element type, algorithm, • mesh band-width, etc.) Solution: Establish tolerances for the input and design variables. Measure the system’s response in statistical terms.

16. Monte Carlo Simulation Basics Integration via the Monte Carlo method: Find the area under the curve, but without knowing the expression of f(x). Solution: “shoot” a large number of points into the rectangle. Calculate the number of points that fall below f(x). Dividing this number by the total number of points yields an estimate of the area. It is not necessary to know f(x). f(x)

17. Accuracy of Monte Carlo Simulation With around 100 points, the error in the area under f(x) in the previous slide is approximately 10%.

18. Monte Carlo Simulation Results Number of 2D Views of Results = Sum of all integers from 1 to (Number of Variables -1) 12 of the 78 2D views that resulted from a simulation with 6 outputs from a scan of 7 inputs with uniform distributions.

19. Understanding Monte Carlo Simulation Results Simulation generates a large amount of data. • A typical simulation run requires around 100 solver executions. • Each combination of hundreds to thousands of variables produces a point cloud. • In each cloud: • POSITION provides information on PERFORMANCE • SCATTER represents QUALITY • SHAPE represents ROBUSTNESS

20. Understanding Monte Carlo Simulation Results KEY: • REDUCE the Multi-Dimensional Cloud to EASILY UNDERSTOOD INFORMATION HOW: • Condense into a CORRELATION MAP • Variables are sorted by the strength of their relationships

21. Meta ModelofDesign Alternatives Generation of Correlation Maps Stochastic Simulation Template 100 MCS runs Correlation Map: - Includes All Results - Highlights Key Variables

22. First World-wide Stochastic Crash(BMW-CASA, August 1997) • Stochastic material properties, • thicknesses and stiffnesses • (70 variables), initial and boundary • conditions. • 128 Monte Carlo samples on • Cray T3E/512 (Stuttgart Univ.) • 1 week-end of execution time.

23. Crash: Identifying Risks Deterministic result: optimistic. Most likely result (trend): realistic and robust. Firewall displacement Initial design optimum? Angle of impact Courtesy, BMW AG

24. Design Improvement Process Iteration 1 2 Target Performance 3 4

25. Design ImprovementChange Design Variables to Improve Design 40% offsetrigid wall US-NCAP Courtesy of BMW AG Problem: Reduce weight by 15 kg without reducing performance

26. Design Improvement -0.25 -0.15 -0.05 0.05 0.15 0.25 Initial design Deformations (mm) Mass (kg) 12, 20, 47, 88, 103, 4, 9, 39, 82 184.6 Final design (Improved, not Optimal) Deformations (mm) Mass (kg) 17, 23, 49, 87, 108, 6, 10, 46, 86 169.3 Cost = 90 executions of PAM-Crash Courtesy of BMW AG

27. Design Improvement Problem: reduce mass, maintain safety and stiffness Result: 16 kg mass reduction 20% reduction of A-pillar deformation 40% reduction of dashboard deformation Cost = 60 runs (tolerances in all materials and thicknesses) of PAM-Crash and MSC.Nastran Courtesy, Nissan Motor Company

28. Design Improvement Problem: reduce mass, maintain safety and stiffness Result: 10 kg mass reduction Cost = 85 runs of PAM-Crash and MSC.Nastran Courtesy, UTS

29. Design Improvement Satellite Dispenser Problem: reduce mass, maintain stiffness Result: Over 70 kg mass reduction Cost = 60 runs of MSC.Nastran (1048 design variables) Courtesy EADS-CASA

30. Design Improvement Problem: Find a layup so as to achieve: • mass reduction • technological requirement • static relief factor and buckling performance Highly Complex Problem • multi target • 6 objectives (1 linear static + 5 buckling) • 10 boundary conditions • discrete variables type • plyshape • angle ply • high variables number (~ 650 to 1000) • 180 different plies shape • a layup contains 350 to 500 plies • a layup contains 300 to 400 ply angles • Result: • 6% mass reduction, satisfying constraints Courtesy, Alenia Aeronautica

31. Spot-weld Failure and NVH Courtesy GMC Outliers (plots have been scaled between 0 and 1). 10% panel thickness variation + random elimination of 5% of welds.

32. Application of Simulation COMMERCIAL APPLICATION HISTORY COST COST Certified Product Certified Product TIME TIME AUTOMOTIVE INDUSTRY NEW CAR DESIGN REDUCED FROM 60 MONTHS TO 26 MONTHS COMMERCIAL AEROSPACE COMPOSITE BODY ON BOEING 787 U.S. DEFENSE INDUSTRY NO CHANGE?

33. Process for Decision Support • Model a multi-disciplinary design-analysis process • Randomize the process model • Run Monte Carlo simulation of the model • Process Results • Correlation Maps showing Influence • Outlier identification showing anomalies • Direction for Design Improvement

34. Correlation Maps - Filter Complexity while Modeling Reality • Identify what influences functionality • Address Uncertainty and Variation • Provides credibility in modeling & simulation • Results clouds represent what is possible • Easy to use • No methods or algorithms to learn • Reduces risk through better engineering • Takes all inputs into account vice using initial • assumptions • Changing the general engineering process

35. Acknowledgement • I acknowledge with gratitude the contributions to this presentation made by: • Dr. Jacek Marczyk – Ontonix • Dr. Edward Stanton – MSC (retired)