Introduction to Automated Design Optimization

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Introduction to Automated Design Optimization
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Analysis versus Design
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• 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
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Design Complexity
Design Time and Cost
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Typical Design Process
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Initial Design Concept
HEEDS
Time Money Intellectual Capital
Yes
Final Design
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A General Optimization Solution
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Automotive Civil
Infrastructure Biomedical
Aerospace
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Automated Design Optimization
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Basic Procedure
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Automated Design Optimization
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Identify Objective(s) Constraints Design
Variables Analysis Methods Note These
definitions affect subsequent steps
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Automated Design Optimization
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Automated Design Optimization
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Automated Design Optimization
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New Design (HEEDS)
Extract Results from Output File
Converged?
No
Yes
Optimized Design(s)
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CAE Portals
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When
What
Where
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Tangible Benefits
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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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Return on Investment
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• 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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Topology Optimization
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• Suggests material placement or layout based on
  load path efficiency
• Maximizes stiffness
• Conceptual design tool
• Uses Abaqus Standard FEA solver

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When to Use Topology Optimization
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• Early in the design cycle to find shape concepts
• To suggest regions for mass reduction

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Design of Experiments
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• 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

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When to Use Design of Experiments
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• Following optimization
• To identify parameters that cause greatest
  variation in your design

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Parameter Optimization
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Minimize (or maximize) F(x1,x2,,xn)
such that Gi(x1,x2,,xn) lt 0,
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
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Objective Search the performance design
landscape to find the highest peak or lowest
valley within the feasible range

• Typically dont 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
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• Design Space depends on
• Number, type and range of variables and
  responses
• Objectives and constraints

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SHERPA Search Algorithm
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• 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

• 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

• Both single and multi-objective capabilities

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SHERPA Benchmark Example
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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
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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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Advantages of SHERPA
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• 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
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• 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
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Shape Design Variables
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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
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• 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
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Validation
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Lower Rail Benefits
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• 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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Future Gen Passenger Compartment
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Side Impact Roof Crush Mass
improvement in safety cage 30 kg (about 23)
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Sensor Magnetic Flux Linearity
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Displacement
N
S
6.0 mm
S
N
Magnetic Circuit
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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

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Front Suspension
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Picture taken from MSC/ADAMS Manual
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Problem Statement
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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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Piston Design for a Diesel Engine
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• 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
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• 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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Soft Tissue Membrane Inflation
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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
Courtesy of Jeffrey Bischoff, Zimmer Inc.
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Optimization Progression
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R2 1.6 1.8
2.0
0 50
100 150
Iteration
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Polymer Property Calibration
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Rate Sensitive Polymer Neo-Hookean material
model with a four-term Prony series Five
undetermined coefficients (design variables)
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Stent Shape Optimization
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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
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Stent Subsystem Design Model
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Stent Baseline and Final Designs
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• BASELINE DESIGN
• (Provided)

FINAL DESIGN (Found by HEEDS)
Max. Strain 0.99
Max. Strain 3.3
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Example Frame Torsional Stiffness
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Goal Maximize torsional stiffness with no
increase in mass
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Loading and Optimization Statement
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Objective Minimize deflection of unsupported
corner Constraints mass lt baseline
model max von mises stress lt baseline
model first 3 modal frequencies gt baseline
model
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Design Variables
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10 shape parameters 5 each for two cross
members 7 thickness variables 3 each for two
cross members 1 for the longitudinal rails
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Design Results
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• 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
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• 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
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• Baseline

HEEDS 30 reduction in failure index
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Deflection
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• Baseline

HEEDS 15 reduction in deflection
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Buckling
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• Baseline

HEEDS 80 increase in buckling load
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Design of a Composite Wing
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• Buckling Load increased by 80
• Failure index decreased by 30
• Bending stiffness increased by 15
• Mass increased by 6

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Rubber Bushing
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Parametric model 6 parameters
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Rubber Bushing Target Response
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Rubber Bushing Final Design
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Final design
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Rubber Bushing Response
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