introduction to automated design optimization
DESCRIPTION
ME 475. Introduction to Automated Design Optimization. Analysis versus Design. ME 475. Analysis Given: system properties and loading conditions Find: responses of the system Design Given: loading conditions and targets for response - PowerPoint PPT PresentationTRANSCRIPT
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Introduction to Automated Design Optimization
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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
YesNo
ModifyDesign
(Intuition)
Time
Money
Intellectual Capital
HEEDS
$
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A General Optimization Solution
Automotive Civil Infrastructure
Biomedical Aerospace
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Automated Design Optimization
Create Parameterized Baseline Model
Create HEEDS Design Model
Execute HEEDS Optimization
Plan Design Study
Basic Procedure:
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Automated Design Optimization
Identify: Objective(s)ConstraintsDesign VariablesAnalysis Methods
Note: These definitions affect subsequent steps
Create Parameterized Baseline Model
Create HEEDS Design Model
Execute HEEDS Optimization
Plan Design Study
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Automated Design Optimization
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Create Parameterized Baseline Model
Create HEEDS Design Model
Execute HEEDS Optimization
Plan Design Study
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Automated Design Optimization
9
Create Parameterized Baseline Model
Create HEEDS Design Model
Execute HEEDS Optimization
Plan Design Study
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Automated Design Optimization
Create Parameterized Baseline Model
Create HEEDS Design Model
Execute HEEDS Optimization
Plan Design Study Modify Variables in Input File
Execute Solver in Batch Mode
Extract Results from Output File
Optimized Design(s)
Yes
NewDesign
(HEEDS)
NoConverged?
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CAE Portals
“When”
“What”
“Where”
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Tangible Benefits*
Crash rails: 100% increase in energy absorbed
20% 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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Return on Investment
• Reduced Design Costs• Time, labor, prototypes, tooling• Reinvest savings in future innovation projects
• Reduced Warranty Costs• Higher quality designs• Greater customer satisfaction
• Increased Competitive Advantage• Innovative designs• Faster to market• Savings on material, manufacturing, mass, etc.
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Suggests material placement or layout based on load path efficiency
Maximizes stiffness Conceptual design tool Uses Abaqus Standard FEA solver
Topology Optimization ME 475
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When to Use Topology Optimization
• Early in the design cycle to find shape concepts• To suggest regions for mass reduction
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Design of Experiments
• Determine how variables affect the response of a particular design
Design sensitivities
• Build models relating the response to the variables
Surrogate models, response surface models
B
A
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When to Use Design of Experiments
• Following optimization
• To identify parameters that cause greatest variation in your design
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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 surface before search begins
• Search algorithm choice depends on type of design landscape
• Local searches may yield only incremental improvement
• Number of parameters may be large
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Selecting an Optimization Method
Design Space depends on:
•Number, type and range of variables and responses
•Objectives and constraints
Gradient-Based
Simplex
Simulated Annealing
Response Surface
Genetic Algorithm
Evolutionary Strategy
Etc.
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Adaptive Each “method” adapts itself to the design space Master controller determines the contribution of each
“method” to the search process Efficiently learns about design space and effectively
searches even very complicated spaces
Hybrid Blend of “methods” used simultaneously, not sequentially Aspects of evolutionary methods, simulated annealing,
response surface methods, gradient methods, and more Takes advantage of best attributes of each approach Global and local search performed together
SHERPA Search Algorithm
Both single and multi-objective capabilities
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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 ME 475
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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 ME 475
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Advantages of SHERPA Efficient
Requires fewer evaluations than other methods for many problems
Rapid set up – no tuning parameters Solution the first time more often, instead of iterating to
identify the best method or the best tuning parameters Robust
Better solutions more often than other methods for broad classes of problems
Global and local optimization at the same time Easy to Use
Only one parameter – number of allowable evaluations Need not be an expert in optimization theory
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Nonlinear Optimization Problems
• Usually involve nonlinear or transient analysis
• Gradients not accurate, not available, or expensive
• Multi-modal and or noisy design landscape
• Moderate to large CPU time per evaluation
• In other words, most engineering problems
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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
• Identify the rail shape and thickness• Maximize energy absorbed in crush zone• Subject to constraints on:
• Peak force• Mass• Manufacturability
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Optimized Design ME 475
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Validation ME 475
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Lower Rail Benefits
Compared to 6 month manual search:• Peak force reduction by 30%• Energy absorption increased by 100%• Weight reduction by 20%• Overall crash response resulted in equivalent
of FIVE STAR rating
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Side Impact Roof Crush
Mass improvement in safety cage:30 kg (about 23%)
Future Gen Passenger CompartmentME 475
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Magnetic Circuit
6.0 mm
N
N S
S
Displacement
Rack
Cover
Magnets
Hall-effect DeviceHolder
Sensor – Magnetic Flux Linearity ME 475
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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 ME 475
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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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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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A biaxial stress state suitable for interrogating nonlinear anisotropic properties of membranous soft tissue can be realized using membrane inflation
Orthotropic nonlinear elasticity: four material parameters
Drexler et al., J. Biomech. 40 (2007), 812-819
Soft Tissue Membrane Inflation
Courtesy of Jeffrey Bischoff, Zimmer Inc.
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Optimization Progression
0 50 100 150Iteration
R2
1
.6
1.8
2
.0ME 475
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Polymer Property Calibration
Rate Sensitive Polymer:
Neo-Hookean material model with a four-term Prony series
Five undetermined coefficients (design variables)
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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 ME 475
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Stent – Subsystem Design Model ME 475
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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 ME 475
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Example: Frame Torsional Stiffness
Goal: Maximize torsional stiffness with no increase in mass
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Loading and Optimization Statement
Objective:Minimize deflection of unsupported corner
Constraints:mass < baseline modelmax von mises stress < baseline modelfirst 3 modal frequencies > baseline model
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Design Variables
10 shape parameters: 5 each for two cross members
7 thickness variables: 3 each for two cross members1 for the longitudinal rails
t3
t2
t4
t1x2
x1
x5
x3
x4 t3t3
t2t2
t4t4
t1t1x2
x1
x5
x3
x4
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Design Results
Torsional stiffness increased by 12%
• height of cross members increased
• cross member locations moved toward the ends
• connection plate thicknesses decreased
• cross member thicknesses increased
• thickness of the rails remained constant
Baseline Design
Optimized Design
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Design of a Composite Wing
• Design variables:– Number of plies– Orientation of plies– Skin, spars, tip
• Objectives, Constraints:– Minimize mass– Buckling, stiffness, failure
constraints• Analysis Tool:
– Abaqus
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Failure Index
Baseline
HEEDS: 30% reduction in failure index
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Deflection
Baseline
HEEDS: 15% reduction in deflection
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Buckling
Baseline
HEEDS: 80% increase in buckling load
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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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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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