Engineering Technology Associates, Inc.

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Accelerating Innovation through Automated Design
Optimization Erik D. Goodman Professor, ECE,
ME MSU VP 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
HEEDS
Yes
Final Design
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Automated Design Process
Execute the Analyses
Yes
Optimized Design(s)
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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 days
• significant cost reduction

• Accelerates product and process innovation
• increased competitive advantage

• Integrates and leverages existing investment in
  CAD/CAE tools and hardware better utilization
  of capital

• Improves design robustness
• six sigma

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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
absorbed 20 reduction in mass Composite
wing 80 increase in buckling load 15
increase in stiffness Bumper 20 reduction in
mass with 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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Topology Optimization

• Suggests material placement or layout based on
  load path efficiency
• Maximizes stiffness
• Conceptual design tool
• Works with commercial FEA solvers

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Parameter Optimization
Minimize (or maximize) F(x1,x2,,xn)
such that Gi(x1,x2,,xn) i1,2,,p Hj(x1,x2,,xn) 0, j1,2,,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 dont 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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SHERPA a Hybrid, Adaptive Method

• Hybrid
• Multiple methods used simultaneously, not
  sequentially
• Takes advantage of best attributes of each method
• Both global and local search techniques are used

• 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

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SHERPA Benchmark Example
Find the cross-sectional shape of a cantilevered
I-beam with a tip load (4 design vars)
Design variables H, h1, b1, b2 Objective
Minimize mass Constraints Stress, Deflection
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SHERPA Benchmark Example
Find the cross-sectional shape of a cantilevered
I-beam with a tip load (4 design vars)
Effectiveness and Efficiency of Search (Goal
1)
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SHERPA Benchmark Example
Find the cross-sectional shape of a cantilevered
I-beam with a tip load (4 design vars)
Robustness of Search (Goal 0)
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Example Hydroformed Lower Rail
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Shape Design Variables
67 design variables 66 control points and one
gage thickness
z
y
rigid wall
lumped mass
x
arrows indicate directions of offset
crush zone
cross-section
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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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Formability Results

• Manual Optimization HEEDS
  Optimization
• (55
  improvement)

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Rubber Bushing
Parametric model 6 parameters
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Rubber Bushing Target Response
F o r c e (N)
Displacement (mm) 10 mm
Load deflection curve when the bushing is loaded
to the left Load 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
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Bushing Benefits

• HEEDS found solution 100 compliant to
  requirements
• Solution found was non-intuitive

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Sensor Magnetic Flux Linearity
Displacement
N
S
6.0 mm
S
N
Magnetic Circuit
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Sensor Magnetic Flux Linearity

• 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

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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.
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Results
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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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HEEDS COMPOSE

• 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

New design proposal
Updated boundary conditions
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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
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

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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
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Shape Design Variables
67 design variables 66 control points and one
gage thickness
z
y
rigid wall
lumped mass
x
arrows indicate directions of offset
crush zone
cross-section
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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
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Energy Absorbed
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HEEDS CIA Example Agent Topology
Lower Compartment Rail Example 19 Agents/19
CPUs
High Resolution
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Red Cedar Technology East 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

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Stent Shape Optimization
LOADCASE 1 Expand the stent in the radial
direction by 8.23226 mm.
LOADCASE 2 Crimp the annealed stent by 2.0 mm.
ANNEAL
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Stent Subsystem Design Model
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Stent Baseline and Final Designs

• BASELINE DESIGN
• (Provided)

FINAL DESIGN (Found by HEEDS)
Max. Strain 0.99
Max. Strain 3.3