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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

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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

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

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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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