Transcript Simulation-Supported Decision Making Gene Allen

Simulation-Supported
Decision Making
Gene Allen
Tools for Engineers
Tools Engineers want to use to
help them make better decisions:
• Slide Rule
• Calculator
• “?” to leverage Moore’s Law
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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
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DEVELOPING an ENGINEERING KNOWLEDGE BASE
COST
Learning Dominated by Test
Eliminate
Failure Modes
73%
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
• F-1
• J-2
Jet Engines
• F-100
Automobiles
• 1996 Ford Taurus
$ 2.8 B
$ 2.4 B
$ 1.7 B
$ 2.0 B
$ 2.8 B
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The Fundamental Problem …
Variability
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Structural Material Scatter
MATERIAL
CHARACTERISTIC
CV
Metallic
Rupture
Buckling
8-15%
14%
Carbon Fiber
Rupture
10-17%
Screw, Rivet, Welding
Rupture
8%
Bonding
Adhesive strength
Metal/metal
12-16%
8-13%
Honeycomb
Tension
Shear, compression
Face wrinkling
16%
10%
8%
Inserts
Axial loading
12%
Thermal protection (AQ60)
In-plane tension
In-plane compression
12-24%
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.
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The Deception of Precise Geometry
Geometry imperfections should be described as stochastic fields.
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Load Scatter (aerospace)
LOAD TYPE
ORIGIN OF RESULTS
CV
Launch vehicle thrust
STS, ARIANE
5%
Launch vehicle quasi-static loads
- POGO oscillation
- stages cut-off
- wind shear and gust
- landing (STS)
STS, ARIANE, DELTA
30%
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.
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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
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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
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A Correlation Map
Upper right –
positive correlation
Lower left –
negative correlation
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Generation of Correlation Maps
100
MCS
runs
Stochastic Simulation Template
Meta Model
of
Design Alternatives
Correlation Map:
- Includes All Results
- Highlights Key Variables
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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.”
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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.
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Monte Carlo Analysis
x1
y1
x2
x3
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.)
y2
Solution:
Establish tolerances for the
input and design variables.
Measure the system’s
response in statistical terms.
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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)
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Accuracy of Monte Carlo Simulation
With around 100 points, the error in the area under f(x) in the previous
slide is approximately 10%.
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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.
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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
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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
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Generation of Correlation Maps
100
MCS
runs
Stochastic Simulation Template
Meta Model
of
Design Alternatives
Correlation Map:
- Includes All Results
- Highlights Key Variables
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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.
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Crash: Identifying Risks
Deterministic result: optimistic.
Most likely result (trend): realistic and robust.
Firewall displacement
Initial design
optimum?
Courtesy, BMW AG
Angle of impact
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Design Improvement Process
Iteration
Target
Performance
1
2
3
4
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Design Improvement
Change Design Variables to Improve Design
US-NCAP
40% offset
rigid wall
Courtesy of BMW AG
Problem: Reduce weight by 15 kg without reducing performance
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Design Improvement
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
-0.25
-0.15
-0.05
0.05
0.15
0.25
Courtesy of BMW AG
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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
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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
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Design Improvement
Satellite Dispenser
Problem: reduce mass, maintain
stiffness
Result: Over 70 kg mass reduction
Cost = 60 runs of MSC.Nastran
(1048 design variables)
MODE 1 (9.7Hz)
MODE 2 (9.74Hz)
Courtesy EADS-CASA
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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
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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.
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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?
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Process for Decision Support
1. Model a multi-disciplinary designanalysis process
2. Randomize the process model
3. Run Monte Carlo simulation of the model
4. Process Results
• Correlation Maps showing Influence
• Outlier identification showing anomalies
• Direction for Design Improvement
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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
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Acknowledgement
I acknowledge with gratitude the contributions
to this presentation made by:
• Dr. Jacek Marczyk – Ontonix
• Dr. Edward Stanton – MSC (retired)
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