Download - Accelerating Innovation through Automated Design Optimization Erik D. Goodman Professor, ECE, ME
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Accelerating Innovation through Automated Design Optimization
Erik D. GoodmanProfessor, ECE, ME
MSUVP Technology
Red Cedar Technology, Inc.
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Analysis versus Design
• Analysis
Given: system properties and loading conditions
Find: responses of the system
• Design
Given: loading conditions and targets for response
Find: system properties that satisfy those targets
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Design Complexity
Design Complexity
Design Time and Cost
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Typical Design Process
Initial Design Concept
Specific Design Candidate
Build Analysis Model(s)
Execute the Analyses
Design Requirements Met?
Final Design
Yes
No
ModifyDesign
(Intuition)
HEEDS
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Automated Design Process
Initial Design Concept
Representative Design(s)
Build Analysis Model(s)
Optimized Design(s)
Yes
Convergence Criterion Met?
ModifyDesign
(HEEDS)
No
Design Model(HEEDS)
Execute the Analyses
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Main Benefits
• Automates search for design alternatives with improved performance and cost
more efficient and thorough search
• Reduces design time from weeks to dayssignificant cost reduction
• Integrates and leverages existing investment in CAD/CAE tools and hardware better utilization of capital
• Improves design robustness six sigma
• Accelerates product and process innovationincreased competitive advantage
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Example Application Areas
Automotive Civil Infrastructure
Biomedical Aerospace
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Examples of Benefits*
Crash rails: 100% increase in energy absorbed20% reduction in mass
Composite wing: 80% increase in buckling load15% increase in stiffness
Bumper: 20% reduction in masswith equivalent performance
Coronary stent: 50% reduction in strain
* Percentages relative to best designs found by experienced engineers
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Some Common Types of Structural Optimization
• Sizing Optimization• Design variables are thickness or cross-sectional area of
each member
• Domain is fixed
• Shape Optimization• Design variables are boundary shape parameters
• Domain is the design variable
• Topology Optimization• Design variables are geometric features such as number,
location and shape of holes, or connectivity of the domain
• Sometimes called material layout or material distribution
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Suggests material placement or layout based on load path efficiency Maximizes stiffness Conceptual design tool Works with commercial FEA solvers
Topology Optimization
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Parameter Optimization
Minimize (or maximize): F(x1,x2,…,xn)
such that: Gi(x1,x2,…,xn) < 0, i=1,2,…,p
Hj(x1,x2,…,xn) = 0, j=1,2,…,q
where: (x1,x2,…,xn) are the n design variables
F(x1,x2,…,xn) is the objective (performance) function
Gi(x1,x2,…,xn) are the p inequality constraints
Hj(x1,x2,…,xn) are the q equality constraints
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Parameter Optimization
Objective:Search the performance design landscape to find the highest peak or lowest valley within the feasible range
• Typically don’t know the nature of the surface before search begins
• Local searches may yield only incremental improvement
• Number of parameters may be large (1 – 1,000)• Evaluations may be expensive
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Optimization Scenarios
Seek small improvements to an existing design
• Local search, small variable range
•Manual iterations reduce work needed by optimizer
Seek best design or concept within a large design space
• Global search, large variable range
• Very little initial effort used to set up analysis
• Optimizer reduces need for manual iterations
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Some Unique Features in Tool You Are Using
SHERPA – Simultaneous Hybrid Exploration that is Robust, Progressive and Adaptive
A hybrid, adaptive search method that works for nearly all problems Makes product optimization accessible to non-experts Increases robustness of most searches
CIA – Cooperative Independent Agents Allows more effective search of challenging problems via decomposition Speeds search by using inexpensive models to guide refined models
COMPOSE – COMPonent Optimization within a System Environment
Reduces design time by factor of 10 – 1,000 for certain problems Allows search over large number of design variables Makes intractable problems solvable
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• Adaptive Each method adapts itself to the design space Master controller determines which methods get used and how much Efficiently learns about design space and effectively searches even very
complicated spaces
• Hybrid Multiple methods used simultaneously, not sequentially Takes advantage of best attributes of each method Both global and local search techniques are used
SHERPA – a Hybrid, Adaptive Method
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Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars)
b1
b2
h1
h1
H
P
L
Design variables: H, h1, b1, b2
Objective: Minimize mass
Constraints: Stress, Deflection
SHERPA Benchmark Example
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Effectiveness and
Efficiency of Search
(Goal = 1)
1
1.2
1.4
1.6
1.8
2
50 75 100 150 250 500
Maximum allowable evaluations
Nor
mal
ized
ave
rage
bes
t sol
utio
n SHERPAGASANLSQPRSM
Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars)
SHERPA Benchmark Example
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Robustness of Search
(Goal = 0)0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
50 75 100 150 250 500
Maximum allowable evaluations
Stan
dard
dev
iatio
n of
bes
t sol
utio
n SHERPAGASANLSQPRSM
Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars)
SHERPA Benchmark Example
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Example: Hydroformed Lower Rail
Crush zoneCrush zone
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Shape Design Variables
rigid walllumped mass
arrows indicate directions of offsetcrush zone
x
z
y
cross-section
67 design variables:66 control points and one gage thickness
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Optimization Statement
• Maximize energy absorbed in crush zone• Identify the rail shape and thickness• Subject to constraints on:
• Peak force• Mass• Manufacturability
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HEEDS Optimized Design
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HEEDS Optimized Design
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Validation
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Lower Rail Benefits
Compared to 6-month manual design effort:• Peak force reduced by 30%• Energy absorption increased by 100%• Weight reduced by 20%• Overall crash response resulted in equivalent
of FIVE STAR rating
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Hydroforming Process Optimization
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Hydroforming Model
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Formability Optimization
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Manual Optimization
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HEEDS Optimization
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Manual Optimization HEEDS Optimization (55% improvement)
Formability Results
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Rubber Bushing
Parametric model: 6 parameters
Fixed D1
D1
D1
D2
D4
D5
θ
D3
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Rubber Bushing Target Response
Displacement (mm) 10 mm
Force
(N)
Load deflection curve when the bushing is loaded to the leftLoad –deflection curve while the bushing is loaded to the right
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Rubber Bushing Final Design
Final design:
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Rubber Bushing Response
Stiffness Comparison Chart
0.00E+00
1.00E+07
2.00E+07
3.00E+07
4.00E+07
5.00E+07
6.00E+07
7.00E+07
8.00E+07
9.00E+07
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Deflection (mm)
Forc
e (0
.001
N)
Design Curve
Final Curve
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Bushing Benefits
• HEEDS found solution 100% compliant to requirements
• Solution found was non-intuitive
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Magnetic Circuit
6.0 mm
N
N S
S
Displacement
Rack
Cover
Magnets
Hall-effect DeviceHolder
Sensor – Magnetic Flux Linearity
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Compared to previous best design found:
• Linearity of response ~ 7 times better
• Volume reduced by 50%
• Setup & solution time was 4 days, instead of 2-3 weeks
Sensor – Magnetic Flux Linearity
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Piston Design for a Diesel Engine
• Piston pin location is optimized to reduce piston slap in a diesel engine at 1100, 1500, 2000, and 2700 RPM
• Design Variables:– Piston Pin X location– Piston Pin Y location
• Design Objectives:– Minimize maximum piston
impact with the wall– Minimize total piston impact
with the wall throughout the engine cycle.
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Piston Design for a Diesel Engine
• 110 designs were evaluated for each engine speed (440 runs of CASE)
• Total computational time was approximately 0.5 days using a 2.4 GHz processor.
• Optimized pin offset was essentially identical to what was found experimentally on the dynamometer.
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Front Suspension
Picture taken from MSC/ADAMS Manual
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Problem Statement
Determine the optimum location of the front suspension hard points to produce the
desired bump steer and camber gain.
HEEDS Toe Curve Optimization
-25
-20
-15
-10
-5
0
5
10
15
20
25
-0.1 0 0.1 0.2 0.3
<- Toe Out (deg) Toe in ->
<- R
ebou
nd L
F W
heel
Tra
vel (
mm
) Jou
nce
->
Toe - Initial Design
Toe - Target
HEEDS Camber Curve Optimization
-25
-20
-15
-10
-5
0
5
10
15
20
25
-1 -0.8 -0.6 -0.4 -0.2 0
Camber (deg)
<- R
ebou
nd L
F W
heel
Tra
vel (
mm
) Jou
nce
->
Camber - Initial Design
Camber - Target
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Results
HEEDS Toe Curve Optimization
-25
-20
-15
-10
-5
0
5
10
15
20
25
-0.1 0 0.1 0.2 0.3
<- Toe Out (deg) Toe in ->
<- R
ebou
nd L
F W
heel
Tra
vel (
mm
) Jou
nce
->
Toe - Initial DesignToe - TargetToe - Final Design
HEEDS Camber Curve Optimization
-25
-20
-15
-10
-5
0
5
10
15
20
25
-1 -0.8 -0.6 -0.4 -0.2 0
Camber (deg)
<- R
ebou
nd L
F W
heel
Tra
vel (
mm
) Jou
nce
->
Camber - Initial DesignCamber - Target
Camber - Final Design
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Suspension Benefits
• Compliance to targets found with in half a day by an engineer new to HEEDS
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Strategies / Algorithms
Search Strategies(e.g., CIA, COMPOSE)
Search Algorithms(e.g., SHERPA)
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HEEDS COMPOSE
• COMPOSE – COMPonent Optimization within a System Environment
• New method for enabling high fidelity design of subsystems in highly coupled complex systems (101 – 103 times speedup)
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New design
proposal
Updated boundary conditions
• Based on decomposition• Most CPU effort to design
subsystem (component)• Small number (3-8) of system
level analyses• Full coupling maintained
between system and subsystem• Large number of variables can
be studied• CPU time reduced by factor of
10 – 1,000
HEEDS COMPOSE
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Vehicle Rail – Shape Optimization
Objective : Maximize Energy Absorbed
Constraint : Reaction Force
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Subsystem Model
Boundary Conditions from System Model
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Subsystem Design Variables
Individually designed rails
7 Cross-sections on each rail
10 Design- Master Points on each cross-section
Total of 140 Shape Design variables ***
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Rail Optimization Results
0 5 10 15 20 256.2
6.25
6.3
6.35
6.4
6.45
6.5
6.55
Cycle no
Sys
tem
ene
rgy
abso
bed
1xE
7
0 5 10 15 20 252
2.5
3
Cycle no
Ene
rgy
abso
rbed
1xE
7
Local EAGlobal EA
Rail Energy Absorbed System Energy Absorbed (30% increase) (5.5% increase)
(Optimization over 140 variables using only 6 system evaluations.)
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CIA: Cooperative Independent Agents
DIFFERENT search agents at the same time, working with – DIFFERENT TOOLS– DIFFERENT views of the problem
Team: Intellectual Diversity
OptimalDesign
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Approaches to Heterogeneous Agents
Agents might differ according to their:• Physical/spatial domain• Temporal extent of simulation• Number of design variables• Resolution of design variables• Stochasticity of variables• Performance measures• Loading cases• Constraint enforcement• Analysis models• Search methods• …
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Hydroformed Lower Rail
Crush zoneCrush zone
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Shape Design Variables
rigid walllumped mass
arrows indicate directions of offsetcrush zone
x
z
y
cross-section
67 design variables:66 control points and one gage thickness
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Optimization Statement
• Maximize energy absorbed in crush zone• Identify the rail shape and thickness• Subject to constraints on:
• Peak force• Mass• Manufacturability
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Simple, Three-Agent Topology
Treat DIFFERENTLY:• crush time simulated ( reduces CPU
time )• discretization of design variables ( reduces design space )
F
t
Coarse 1
2
3
t=6 ms
t=14 ms
t=10 ms Medium
Refined
CrushTime
Design Variable Discretization
AgentTopology
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Energy Absorbed
3000
4000
5000
6000
7000
8000
9000
0 100 200 300 400 500 600 700 800Number of Evaluations
Ener
gy (J
)
1 agent
3 agents
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HEEDS CIA – Example Agent Topology
0
3
9
1
4 5 6 7
10 11 12 13 14 15 16 17
2
8
18
Low Resolution
Medium Resolution
Axial Load Case (Deterministic)
Offset Load Case (Deterministic)
Stochastic Load Cases(and Stochastic Design Variables)
CrushTime 3.8 ms
CrushTime 8.4 ms CrushTime 12.6 ms
Lower Compartment Rail Example – 19 Agents/19 CPU’s
High Resolution
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Red Cedar TechnologyEast Lansing, MI
USA
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Extra Slides
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Design of a Composite Wing
• Design variables:– Number of plies– Orientation of plies– Skin, spars, tip
• Objectives:– Minimize mass– Buckling, stiffness, failure
constraints
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Design of a Composite Wing
• Buckling Load increased by 80%• Failure index decreased by 30%• Bending stiffness increased by 15%• Mass increased by 6%
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 5 10 15 20 25 30 35 40Cycle Number
Nor
mal
ized
Con
stra
ints
&
Obj
ectiv
e
Mass
Failure Index
Deflection
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LOADCASE 1
Expand the stent in the radial direction by 8.23226 mm.
LOADCASE 2
Crimp the annealed stent by 2.0 mm.
ANNEAL
Stent Shape Optimization
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Stent – Subsystem Design Model
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BASELINE DESIGN (Provided)
FINAL DESIGN (Found by HEEDS)
Max. Strain = 3.3% Max. Strain = 0.99%
Stent – Baseline and Final Designs