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

YEARSInitial Design

EliminateFailure Modes

Engineering

Demonstration

73%

15 %

10 %

2 %

Certification

CO

ST

Examples of Cost to First Production Examples of Cost to First Production Nonrecurring Development Costs to Build Knowledge BaseNonrecurring 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 …

VariabilityVariability

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

InputVariables

OutputVariables

• Ranks input variables and output responses by correlation level

• Follows MIT-developed Design Structure Matrix model format

• Filters Variables Based on Correlation Level

11

Upper right –positive correlation

Lower left –negative correlation

A Correlation Map

12

Meta Modelof

Design Alternatives

Correlation Map:

- Includes All Results

- Highlights Key Variables

Stochastic Simulation Template 100 MCS runs

Generation of Correlation Maps

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

Understanding the physics of a phenomenon is equivalent to the understanding of the topology and structure of these clouds.

Singlecomputerrun =Analysis

Collectionof computerruns =Simulation

15

Monte Carlo Analysis

Solution:Establish tolerances for the input and design variables.

Measure the system’s response in statistical terms.

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.)

x1

x2

x3

y1

y2

16

Monte Carlo Simulation Basics

f(x)

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).

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

12 of the 782D views that resulted from a simulation with6 outputs froma scan of 7 inputs with uniformdistributions.

Number of 2D Views of Results = Sum of all integers from 1 to (Number of Variables -1)

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 Modelof

Design Alternatives

Correlation Map:

- Includes All Results

- Highlights Key Variables

Stochastic Simulation Template 100 MCS runs

Generation of Correlation Maps

22

• 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.

First World-wide Stochastic Crash(BMW-CASA, August 1997)

23

Crash: Identifying Risks

Deterministic result: optimistic.

Most likely result (trend): realistic and robust.

optimum?

Initial design

Firewall displacement

Angle of impactCourtesy, BMW AG

24

Design Improvement Process

1 2

3 4

TargetPerformance

Iteration

25

Design ImprovementChange Design Variables to Improve Design

Problem:Reduce weight by 15 kg without reducing performance

US-NCAP

40% offsetrigid wall

Courtesy of BMW AGCourtesy of BMW AG

26

Design Improvement

Initial designDeformations (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

-0.25-0.15-0.050.050.150.25

Courtesy of BMW AG

27

Design Improvement

Problem: reduce mass, maintain safety and stiffnessResult:16 kg mass reduction20% reduction of A-pillar deformation40% reduction of dashboard deformationCost = 60 runs (tolerances in all materials andthicknesses) of PAM-Crash and MSC.Nastran

Courtesy, Nissan Motor Company

28

Design Improvement

Courtesy, UTSCourtesy, UTS

Problem: reduce mass, maintain safety and stiffnessResult: 10 kg mass reductionCost = 85 runs of PAM-Crash and MSC.Nastran

29

Design Improvement

Courtesy EADS-CASA

MODE 1 (9.7Hz) MODE 2 (9.74Hz)

Problem: reduce mass, maintain stiffnessResult: Over 70 kg mass reductionCost = 60 runs of MSC.Nastran (1048 design variables)

Satellite DispenserSatellite DispenserSatellite DispenserSatellite Dispenser

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 ply shape 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

Outliers (plots have been scaled between 0 and 1).

Spot-weld Failure and NVH

Courtesy GMC

10% panel thickness variation + random elimination of 5% of welds.

32

HISTORY COMMERCIAL APPLICATIONCOST

TIME

COST

TIME

Application of Simulation

CertifiedProduct

CertifiedProduct

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

1.Model a multi-disciplinary design-analysis process

2.Randomize the process model3.Run Monte Carlo simulation of the model4.Process Results

• Correlation Maps showing Influence• Outlier identification showing anomalies• Direction for Design Improvement

34

• 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

Correlation Maps - Filter Complexity while Modeling Reality

35

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

Acknowledgement