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Optimization And RobustnessResearch & Advanced Engineering
Optimization in Auto Industry
Ren-Jye YangSenior Technical Leader
Ford Research & Advanced Engineering TEL: (313) 549-6946
E-mail: [email protected]
2013 modeFRONTIER 2013 user's meeting
Optimization And RobustnessResearch & Advanced Engineering2
Outline� Background
� Topology Optimization
� Multidisciplinary Design Optimization (MDO)
� Restraint System Optimization
� Process Integration & Design Optimization (PIDO)
� Summary and Future Directions
Optimization And RobustnessResearch & Advanced Engineering3
Numerical Optimization
� What is Optimization– IS a general automated design tool which
systematically searches for the best design which satisfies specific criteria.
– NOT: DOE, parametric studies
� Benefits:Can be applied to a wide range of design tasks and improve the designs– Eliminates trial and error design processes– Reduces weight and lead time– Improves product quality
� Risks:– Local optimum possible– May miss important constraints
VR&D
Optimization And RobustnessResearch & Advanced Engineering4
Design -vs- Analysis
Initial Design
FEAnalysis
EvaluateResults
Initial Design
FE Analysis
Performance Measures
DesignSensitivity
OptimizationAlgorithm
Convergence ?optimalYesNo
� CAE Analysis � CAE Design
design
Optimization And RobustnessResearch & Advanced Engineering5
Optimization in Computational Mechanics
� Computation intensive functions and their sensitivities, e.g., CFD, impact, reliability constraints.
� Highly nonlinear, non-convex functions
� Numbers of constraints & design variables may be large
� Problem formulations essential
� Shape parameterization not trivial
Find design variable X that will
Minimize Fk(X)
Subject to gi(X) ≤ 0, hj(X)=0, Xl ≤ X ≤ ≤ ≤ ≤ Xu
Optimization And RobustnessResearch & Advanced Engineering6
Numerical Optimization
Analysis (& Gradients)
Approximation
Optimization
Outer Loop
Inner Loop
Optimization
Analysis
Optimization And RobustnessResearch & Advanced Engineering7
Outline� Background
� Topology Optimization
� Multidisciplinary Design Optimization (MDO)
� Restraint System Optimization
� Process Integration & Design Optimization (PIDO)
� Summary and Future Directions
Optimization And RobustnessResearch & Advanced Engineering8
Topology Optimization
� Conventional optimization techniques modify the initial design restricted to the original topology of the components
� Topology optimization helps engineers design the topology of a structure (e.g. locations of holes & stiffeners, and layout of a grillage)
P P PP
PlateTrussTruss
Optimization And RobustnessResearch & Advanced Engineering9
Topology Optimization Methods
� Homogenization Method:Bendsoe et al., Kikuchi et al., Dias, Soto, Papalambros, Olhoff, Haber, Chirehdast, etc.
� Density Method (or SIMP: Solid Isotropic Material with Penalization): Bendsoe, Rozvany, Mlejnek, Yang, Wang, Gea, Lu, etc.
� Simultaneous Analysis & DesignHaftka, Shankar, etc,
� Other Approaches:Level set, Hyper Radial Basis Function Network, Rozvany, EMRC, etc.
Optimization And RobustnessResearch & Advanced Engineering10
Homogenization Method
� Assume structure is composed of microscopic holes
� Use homogenization to determine material properties
� Design variables parameterize size and orientation of holes
� Solve optimization problem with optimality criteria method
ba
E
G
0.5 1.0
E: Young’s Modulus
G: Shear Modulus
a, bplate with holes homogenized plateunit cell
θ
Optimization And RobustnessResearch & Advanced Engineering11
Density Method
� Approach– Design variables parameterize element
densities and moduli
– Intermediate densities are penalized
– Optimization problem solved with Mathematical Programming Algorithms
� Advantages– One design variable per element
– Interfaces well with commercial FE software such as MSC and CSA Nastran
– May include multiple objectives and constraints
0 10
1
ci
ρ/ρ0
E/E0
E = c2
Eo
ρ = c ρo
Optimization And RobustnessResearch & Advanced Engineering12
Truck Frame
Finite Element Model
Topology Optimization Result
CAD Interpretation
Optimization And RobustnessResearch & Advanced Engineering13
LiftgateKnuckle
Vehicle Body
Topology Optimization Applications
Rear LCA
Typical Problem Formulation:
Min Structural Compliances
Subject to Material Usage <= 25%
Optimization And RobustnessResearch & Advanced Engineering14
Lower Control Arm - Weld Pattern Design
� Objective: Minimize total number of welds during assembly process
� Topology optimization:
• Weld element as design variables
• 350 mm weld length elimination
� Results:
• Met target after reanalysis
• Significant tooling cost saving
• Manufacturing time saving
Rear LCA
Optimization And RobustnessResearch & Advanced Engineering15
Spot Weld/Adhesive Pattern Design
� Objective: Maximize joint stiffness for 2 loads
� Design Variables: Spot weld/Adhesive
� Constraints:
adhesive <= 30% of available design spacespot weld <= 40% of available design space
Optimization And RobustnessResearch & Advanced Engineering16
3.5L-3V Front Cover Concept
Front View Rear View
Structural
Aluminum
Section
Non-Structural
Plastic Sections
Optimization And RobustnessResearch & Advanced Engineering17
3.5L-3V Front Cover Topology Optimization
� Objective: Maximize mounting natural frequencies for the alternator and power steering pump
� Constraints: – Aluminum material < 20% of available design space
– Natural frequencies > 500 hz
� Outcome:– Topology optimization showed that a structural
section was only required on upper left hand side.
– Dual material, aluminum/plastic, structural/non-structural, solid model concept was created based on these results
• 2.5 lb weight savings vs. complete structural AL cover
• $6 piece price savings vs. complete structural AL cover
Optimization And RobustnessResearch & Advanced Engineering18
Bead Pattern Optimization
Membrane Stiffness:
Kx > Ky
Bending Stiffness:
Kx < Ky
Optimization And RobustnessResearch & Advanced Engineering19
Bead Pattern Optimization(Soto et al. ’99)
� A technique to optimally locate and orient beads in vehicle panels to maximize stiffness and natural frequencies.
topology optimization shape optimization
Optimization And RobustnessResearch & Advanced Engineering20
Examples
Optimization And RobustnessResearch & Advanced Engineering21
Design of a Negative Poisson’s Ratio Material(O. Sigmund, Denmark Technical U.)
design domain discretized by 30x30 finite elements.
This material expands vertically when stretched horizontally
Periodic material composed of repeated base cells.
Optimization And RobustnessResearch & Advanced Engineering22
Design of Compliant Mechanism(O. Sigmund et al., Denmark Technical U.)
Design of a micro-displacement amplifier
Design domain Optimal amplifier topology for 1:-3.7 amplification
Realization of the micro-amplifier
Optimization And RobustnessResearch & Advanced Engineering23
Design of MEMS(O. Sigmund et al., Denmark Technical U.)
The actuation principle is electro-thermo-mechanical, i.e. an electric input heats the structure locally due to Joule’s heating. The heating results in material expansion and thereby actuation.
Design of 2 degree-of-freedom micro-scanning device
Other Industrial Applications
Motorcycle Frame Design
Bus Frame Design
Topology Optimization Geometry Extraction
ICAD Solid Geometry
Extraction
Size and Shape Optimization
Geometry Extraction
Topology OptimizationMaterial Layout
Size and Shape OptimizationBuckling and Stress
Topology Optimization Package Space Definition
Courtesy of Airbus
Airbus A380 Droop Nose Leading Edge
Zhao Zhou Bridge (赵州桥赵州桥赵州桥赵州桥)built in Sui dynasty (581–618 AD)
by Yun Kang SUI, 2005
Optimization And RobustnessResearch & Advanced Engineering28
Recent Developments
� Extend applications from automotive, aerospace to other industries:biomedical, consumer goods, electronics, energy, heavy industry, marine, ….
� More innovative applications:ESL, inertia relief for crashworthiness design, local strain energy for designing desired load paths, ….
� Extend to other disciplines: nonlinear, transient problems, CFD, heat transfer, multiphysics, acoustics, MEMS, optics, electromagnetism, …
� Consider manufacturing constraints:no-hole option for draw-direction, stamping/sheet metal, and minimum member spacing, ….
� Other developments: Hybrid Cellular Automata, Level Set Method, Hyper Radial Basis Function Network, …
Optimization And RobustnessResearch & Advanced Engineering29
Shotgun –> door beam
Rocker
Rail –> rail extension
Subframe –> Tunnel
Compliance
0.0E+00
1.0E+06
2.0E+06
3.0E+06
4.0E+06
5.0E+06
6.0E+06
7.0E+06
0 10 20 30 40 50 60
Iteration #
Co
mp
lia
nc
e
Full Frontal Impact: IRM
Optimization And RobustnessResearch & Advanced Engineering30
Outline� Background
� Topology Optimization
� Multidisciplinary Design Optimization (MDO)
� Restraint System Optimization
� Process Integration & Design Optimization (PIDO)
� Summary and Future Directions
Optimization And RobustnessResearch & Advanced Engineering31
Multidisciplinary Design Optimization
(MDO) is a methodology for improving
design of engineering systems, e.g.,
automobile, aircraft, or spacecraft, in which
everything influences everything else.
- By Dr. J. Sobieski -NASA Langley
What is MDO
Optimization And RobustnessResearch & Advanced Engineering32
Typical Aerospace MDO Problem
� Effective Integration of Individual disciplines/subsystems to capture the Interactions
� Novel solution procedures to enable system level solutions
� Characteristics: large-scale, needs decomposition, computation intensive, multiple simulations
CFD Structures
Controls
Loads
Deformation
ControlSurfaceDeflns
StressPressureMoments Design space discipline 1
Design space discipline 2
Design Variables
Performance
MultidisciplinaryOptimal Design
Discipline 1 Optimum
FeasibleDesignSpace
SuboptimalDesign
Conventional Trades
MDO Search
Discipline 2 Optimum
Optimization And RobustnessResearch & Advanced Engineering33
Vehicle Attributes/Disciplines
• Vehicle Dynamics (V)
- Steering
- Handling
- Ride
- Braking
• Chassis Systems (S)
- General Vehicle
- Front Suspension
- Rear Suspension
- Steering
----------
• Aerodynamics CFD Analysis (V)
• Heat Management (V)
• Coolant Flow Simulations (S)
• Vehicle Level ClimateControl (V)
- Front End Air Flow- Front End Openings
• System Level ClimateControl (S)
- A/C Performance- Heater Performance
-----
• Chassis NVH
- Frame Principal Modes
- Frame Static Stiffness
- Static Stiff. at Frame Attach.
- PM at Frame Attachments
- Suspension Modes
• Chassis Durability
- Front Suspension
- Rear Suspension
- Frame and Mounting System
------------
• Trimmed Body Principal Modes (V)
• Trimmed Body Static Stiffness (V)
• BIP Principal Modes (S)
• PM at Body Attach. Loc.(S)
• LP6 for Body Attachments (S)
• Static Stiffness for Body
• Attachment Locations (S)
• Body SDS/WCR/FMVSS (S/C)
• Hood (S)
• Decklid (S)
• Doors (S)
• Trailer Tow (C)
• Dash/Cowl fatigue (C)
--
• FRONT IMPACT (V)
- New FMVSS 208
- NCAP
- OOP
- IIHS Offset
• SIDE IMPACT (V)
- 33.5 mph FMVSS214
- LINCAP
• Rear Impact (V)
- 35 mph RMB
- 50 mph C/C Inline
- 50 mph C/C Side
- 50 mph C/C 50% Offset
• Roof Crash (S)
• Head Impact (S)
---
• Idle Tactile (V)
• Idle Acoustic (V)
• Driveline Unbalance Tactile (V)
• Driveline Unbalance Sound (V)
• Glen Eagle Tactile (V)• Rough Road Tactile (V)
• Brake Roughness Tactile
• Impact Harshness Tactile
• R1H / CP2 Tactile (V)
• Glen Eagle Acoustic (V)
• Rough Road Acoustic (V)
• Impact Harshness Acoustic (V)
• Brake Squeal
• Exhaust NVH
• Wind Noise
• Shift Quality---
Body Structure(NVH & Durability)
Vehicle DynamicsChassis & Full Vehicle Durability
TASE* & Climate Control
SafetyVehicle NVH
Vehicle
Performance
V: Vehicle Level
S: System Level
C: Component Level
*TASE: Thermal Aerodynamics System Engineering
Optimization And RobustnessResearch & Advanced Engineering34
Typical Automotive MDO Problem
� Little or no coupling/interactions in vehicle attributes
� Coupling through common design variables
� Multiple models, multiple software
� Large number of design variables: continuous, discrete
� Large number of constraints
� Computation intensive for high fidelity models
� Highly nonlinear for many responses, e.g., restraint system responses
� Some disciplines not as mature
Optimization And RobustnessResearch & Advanced Engineering35
• Torsion Stiffness
• Bending Stiffness
• Frequencies (floor, global)
• Dynamic Equivalent Stiffness
(Y and Z for 8 mounts)
NVH
Seatbelt Pull
(FMVSS207/210/225)• Front Row Seat
• Second Row Seat
40% IIHS Frontal Offset Impact• Intrusion
Tailor Rolled Blanks
Side Impact
• IIHS
• Oblique Pole
Truck Underbody Application(Collaborated with Mubea, C. H. Chuang, et al. ‘08)
FMVSS: Federal Motor Vehicle Safety Standards
Optimization And RobustnessResearch & Advanced Engineering36
MDO Formulation
Minimize: TRB parts weightSubject to
� 40% Frontal Offset Impact (1 discipline)� Side Impact (2 disciplines)
• IIHS Side Impact• Oblique Pole Side Impact
� Seatbelt Pull - FMVSS 207/210/225, (2 disciplines)• Front row seat• Second row seat
� NVH (4 disciplines)• Torsion and bending stiffness• Normal modes (front floor, rear floor, overall torsion, and overall
bending)• Dynamic equivalent stiffness (Y- and Z-directions for 8 mounts)
With respect to� Thickness of upper and lower bounds
47 Responses
FMVSS: Federal Motor Vehicle Safety Standards
Optimization And RobustnessResearch & Advanced Engineering37
Parameterization
9 segments on CM #1
9 segments on CM #2
9 segments on Rear Sill11 segments on CM #4
18 segments on Side Sills
9 segments on CM #3
Total Number of segments: 65
Optimization And RobustnessResearch & Advanced Engineering38
Design Variables Summary
Independent DV: 15
12
3
15
4
151
1
1
2
44
4
5
5
6
7
7
7
7
8
8
9
10
10
11
11
12
12 13
13
14
� Symmetry� Connection� Transition
� Gauge can vary with a 2:1 ratio� 100mm transition required for
1mm gauge change
Optimization And RobustnessResearch & Advanced Engineering39
CM#2
0.60
1.10
1.60
2.10
0 500 1000 1500
Vehicle Y Coordinate (mm)
Thic
kness (
mm
)
MDO
1 lbs (8.3%) weight saving
Side Sills (L/R)
0.600
1.100
1.600
2.100
2.600
3.100
3.600
0 500 1000 1500 2000
Vehicle Y Coordinate (mm)
Thic
kness (
mm
)
6 lbs (17.6%) weight saving
Optimization And RobustnessResearch & Advanced Engineering40
Outline� Background
� Topology Optimization
� Multidisciplinary Design Optimization (MDO)
� Restraint System Optimization
� Process Integration & Design Optimization (PIDO)
� Summary and Future Directions
Optimization And RobustnessResearch & Advanced Engineering41
Technical Challenges
� Highly Nonlinear, Non-convex Functions
� Discrete/Continuous Variables
� Multi-modalities, Instabilities� Large Number of Constraints
Unbelted
In-Position
HIII 50s
Belted
In-Position
HIII 50s
OOPO
HIII 50s
OOPO
HIII 05s
Unbelted
In-Position
HIII 05
Belted
In-Position
HIII 05
Present &
Future Interplay
FMVSS 208 Frontal Impact Test Suite
Optimization And RobustnessResearch & Advanced Engineering42
Structure Target Setting & Restraint Selection
A1
A2
a
b
Design Variables
Crush Distance
Front End Length
Stiffness
Intrusion
Restraint Selection
NCAP Performance
Objectives:
Min Crush Distance
Min Cost
Optimize Performance
OutputInput Simulation
Responses
Optimization And RobustnessResearch & Advanced Engineering43
Restraint System Design(Zhou et al., intl J Vehicle Safety, ‘05)
� Objective: minimize vehicle crush distance
� Design variables (10): bi-level crash pulse, restraint variables, e.g., load limiter load level
� Constraints (60): 12 constraints for each crash mode, 12*5 models = 60
� Optimization Method: Genetic Algorithm
� 50th belted dummy at 35 mph
� 50th belted dummy at 30 mph
� 5th belted dummy at 30 mph
� 50th unbelted dummy at 25 mph
� 5th unbelted dummy at 25 mph
Optimization And RobustnessResearch & Advanced Engineering44
Design Variables
Design Variable
Symbol Description
X1PulA Vehicle Front End
Length
X2 PulA1 Pulse 1st level
X3 PulA2 Pulse 2nd level
X4ColLoaB Adaptive Belted
column load
X5ColLoaU Adaptive Unbelted
column load
X6 VenBel Belted Vent Size
X7 VenUBel Unbelted Vent Size
X8 PBucFla Pyro Buckle Flag
X9 PRetFla Pyro Retractor Flag
X10Emr Retractor Load
Limiter load level
A
B C
Acc. PulA1
PulA2
Crush
D E
F
Crash Acceleration versus Crush
Bi-Level Pulse
Optimization And RobustnessResearch & Advanced Engineering45
Constraints Constraints Symbol Description
Yi1 (i=1-5) Hic15 15 ms HIC
Yi2 (i=1-5) ChestRCum Peak chest G
Yi3 (i=1-5) CheDefMax Chest deflection
Yi4 (i=1-5) FemLfPk Left femur load
Yi5 (i=1-5) FemRtPk Right femur load
Yi6 (i=1-5) NecFxMin neck shear -
Yi7 (i=1-5) NecFxMax neck shear +
Yi8 (i=1-5) NecFzMin Neck compression
Yi9 (i=1-5) NecFzMax Neck tension
Yi10 (i=1-5) NecMyMin Neck extension
Yi11 (i=1-5) NecMyMax Neck flexion
Yi12 (i=1-5) NijIndMax Neck injury criteria
Note: i represents different MADYMO model.
i = 1 means 50th belted dummy at 35 mph speed
i = 2 means 50th belted dummy at 30 mph speed
i = 3 means 5th belted dummy at 30 mph speed
i = 4 means 50th unbelted dummy at 25 mph speed
i = 5 means 5th unbelted dummy at 25 mph speed
Optimization And RobustnessResearch & Advanced Engineering46
Top Two Designs
Optimization And RobustnessResearch & Advanced Engineering47
5th Belted Dummy at 30MPH Speed
0%
20%
40%
60%
80%
100%
120%
Hic
15C
hest
GC
hest
Df
FemL
FemR
Fx-
Fx+ Fz-
Fz+
My-
M
y+
Nij
Baseline Design
Design 1
Design 2
Optimization And RobustnessResearch & Advanced Engineering48
Outline� Background
� Topology Optimization
� Multidisciplinary Design Optimization (MDO)
� Restraint System Optimization
� Process Integration & Design Optimization (PIDO)
� Summary and Future Directions
Optimization And RobustnessResearch & Advanced Engineering49
Step 4: Perform MADYMO Simulations and Extract Occupant Injury Numbers
Step 2: Define PAB Shape VariablesConvert MADYMO PAB mesh to a Hypermesh readable format (e.g. Nastran)Create shape variables in Hypermesh using global morphing technique, and save the file in hm formatCreate a Hypermesh command file to perform shape change in batch mode
System Integration and Automation of PAB Shape Design Process
Morphing
Step 3: Perform PAB Shape ChangesChange values of shape variablesRun Hypermesh to perform PAB shape morphing in batchUpdate PAB finite element mesh file with the new PAB shape
Step 1: Prepare and Correlate MADYMO Models for Multiple Crash ScenariosPAB model as an include filePAB FE mesh as an include file for the PAB model
Input File for PAB Shape Design Variables
Output Files for Occupant Response Numbers
Optimization And RobustnessResearch & Advanced Engineering50
Flowchart for Airbag Shape Design
Engineering Data Mining
Color: gray feasible, yellow unfeasible
bubble size: safety index
Color: vehicle type, bubble size: safety indexColor represents safety index
Color: dark gray feasible, yellow
unfeasible
Optimization And RobustnessResearch & Advanced Engineering52
Summary
� PIDO is essential for product development
� MDO is a key enabler for light weight structure design
� GA becomes more popular
� Need to change mindset from “Analysis” to “Design”
� Optimization technologies are well developed and can be applied to a wide range of design tasks
� Make optimization standard enterprise practice will have a competitive advantage
PIDO: Process Integration and Design Optimization
Optimization And RobustnessResearch & Advanced Engineering53
Future Directions
� Methodology:– User friendly system well developed but need more – Integration of PIDO and database management – How to handle computation intensive applications– Advanced optimization algorithms for direct MDO– Others: manufacturing process optimization, reliability-
based design optimization (RBDO), robust design, cluster analysis/engineering data mining, global optimization, etc.
� Hardware/Software:– Seamless high performance computation
throughout inhomogeneous platforms/computers– Web-based, enterprise collaborative and distributed
system– MPI implementation, GPU (Graphics Processing Unit),
Cloud computingPIDO: Process Integration and Design Optimization
MPI: Message Passing Interface
Optimization And RobustnessResearch & Advanced Engineering54
Thank you for your attention!