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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