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CAE-Based Design Optimization
Dong-Hoon Choi
Director, the Center of Innovative Design Optimization Technology (iDOT)Professor, School of Mechanical Engineering
Hanyang University, Seoul, Korea
September 1, 2006
2
Brief Introduction of iDOT
Brief Introduction of iDOT
Sequential Approximate Optimization
Outline
Applications
3
Brief Introduction of iDOT
Automation
Integration Optimization
Cost Reduction
Shorter Design Cycle
Improved ProductQuality
MultidisciplinaryDesign
Optimization
Development ofComputingTechnology
Advance inOptimizationTechnology
Why MDO ?
Motivation
4
Brief Introduction of iDOT
Research and development ofResearch and development ofmultidisciplinary design multidisciplinary design optimization methodsoptimization methods
Transfer of promising MDO Transfer of promising MDO technology to industry technology to industry
Train industry designers and Train industry designers and educate students on MDO educate students on MDO methods and design proceduresmethods and design procedures
MDOMDOResearchResearch
IndustrialIndustrialApplicationApplication
Training andTraining andEducationEducation
iDOT InternationalInternationalCooperationCooperation
iDOT Mission
5
Brief Introduction of iDOT
The Center ofinnovative Design Optimization Technology
Selected as one of the Engineering Research Centers of excellence by Korean government in 1999
Located at Hanyang University in Seoul, Korea
Supported for 9 years by the KOrean Science and Engineering Foundation (KOSEF)
14 Professors from 7 universities4 Research Staffs4 Computer Programmers2 Administrators
81 Graduate Students
A research alliance with ASDL since 1999
6
Brief Introduction of iDOT
Research Topics
Computing Infrastructure
Integrated Design
ApplicationTechnology
Design Process
Management
OptimizationFormulation
MDOMethods
ApproximateOptimization
GlobalOptimization
MDOKernel
PIDO Tool
“The Ultimate Design Machine”
DB CAD
ElectromagneticAnalysis
Fluids
Dynamics
Structures
Users
Optimization Methods
PIDO : Process Integration and Design Optimization
Research Areas
7
Brief Introduction of iDOT
DOE Module(s)
GlobalOptimizer(s)
Resources
Visual Modeling
ScriptManager
Other Resource(s)
PROCESS Manager
Component Manager
Optimization Schedule Template Manager
DATABASE Manager
USER INTERFACE
ScriptParser
CO MDF IDF …
MDO Kernel
Message Manager
I/O Manager
Com
ponent Abstract Layer
LocalOptimizer(s)
Non Linear Analysis
Crash Analysis
Experimental Results
ApproximationModule(s)
Com
ponent Abstract Layer
EMDIOS Architecture
8
Brief Introduction of iDOT
AerospaceAutomotivesBiotechnologyElectronicsInformation TechnologyMarine TechnologyMaterialsMechanicalMEMS DevicesNuclearRailway Vehicles
2152
13226
26222
Applications (2001-2005):74 Design Optimizations
9
Brief Introduction of iDOT
ResearchResearch& Development& Development
PIDOPIDOTechnologyTechnologyTransferTransfer CommercializationCommercialization
& Maintenance& Maintenance
FRAMAX is a spin-off company of iDOT,having the world-class PIDO technologies
(Founded in June, 2003). Developmentof PIDO Tool
Customizationof Design S/W
EngineeringConsulting
FRAMAX: a Spin-off Company of iDOT
10
Sequential Approximate Optimization
Outline
Brief Introduction of iDOT
Sequential Approximate Optimization
Applications
11
Sequential Approximate Optimization
SOFTWARE
Higher
Efficiency
DistributedDistributedParallelParallel
ComputingComputingTechniqueTechnique
SequentialSequentialApproximationApproximationOptimizationOptimizationTechniqueTechnique
HARDWARE
How to Enhance the Computational Performance?
Motivation
12
Sequential Approximate Optimization
Before Schmit and Farshi (1974)
ExactFunction & Gradient Values
New Design
Iterative Numerical Optimization Loop
After Schmit and Farshi (1974)
ApproximateFunction & Gradient Values
New Design
Iterative Numerical Optimization Loop
High Fidelity Model Low Fidelity Model
High Fidelity Model
Decouple an Expensive Analysisfrom Iterative Optimization Process
ExactFunction & Gradient Values
ApproximateOptimum
Approximation
Why Approximate Optimization ?
13
Sequential Approximate Optimization
High Fidelity Model
Optimizer
Low Fidelity Model
High Fidelity Model
Optimizer
Exact Optimization SAO
High Fidelity Modelrequires 2hr per analysis
Low Fidelity Modelrequires 0.05 sec per analysis
40 x 2hr = 80 hr
4 x 2hr
40 x 0.05sec
24 hr6 sec
x 1=8hr
x 1=2sec
x 2=16hr
x 2=4sec
x 3=24hr
x 3=6sec
Efficiency of Sequential Approximate Optimization (SAO)
14
Sequential Approximate Optimization
f
xx
f
f
x
Quadratic Simple Cubic
Using Quadratic Function
real function real function
real function
SequentialSequentialApproximateApproximateOptimizationOptimization
ApproximateApproximateOptimizationOptimization
AO vs. SAO
15
Sequential Approximate Optimization
Local/GlobalOptimizers
UL
f
xxxxhxgx
00
Min.s.t.
hg ~,~,~f
x
xApproximate Model
Manager
Approximate ModelDeveloper
Analysis orExperimental Data
x
hg ~,~,~f
SAOManager
Define approximate optimization problem
Convergence Checking
0~0~
~
xh
xgxfMin.
s.t.
xx0
SAO Framework of iDOT
16
Sequential Approximate Optimization
Approximate ModelDeveloper
One-Point Approximation
Two-Point Approximation
New Two-Point Approximation MethodSTDQAO
Linear, Reciprocal, Conservative
TPEA, TANA, TANA1, TANA2, TANA3
Typical Local Approximation Methods
Typical RSM based on Experimental Design
Alphabetic Optimality CriteriaD-optimal Design
New RSM based on Experimental Design`Augmented D-optimal DesignSubspace CCD/SCDPQRSM
KrigingRBF (Radial Basis Function)SVR (Support Vector Regression)MARS (Multivariate Adaptive Regression Splines)
Quadratic Approximation ModelingCCD, SCD and BBD
Approximate Model Developer
17
Sequential Approximate Optimization
1x1Lx 1
Ux
2Lx
2Ux
0kx
2x: Trust region
*kx
k
1x1Lx 1
Ux
2Lx
2Ux
01kx
2x
: New Trust region
1k k
: Previous Trust region
Approximate OptimizationApproximate Optimization
STARTSTART
1determine
Build Approximate ModelBuild Approximate Model
Converge ?Converge ?
STOPSTOP
Update Trust RegionUpdate Trust Region
Build Approximate Modelin the new Trust region
Build Approximate Modelin the new Trust region
k+1 k=
Evaluate the exact function valueat the approximate optimum
Evaluate the exact function valueat the approximate optimum
Yes
No
k=k+1
SAO using Trust Region Concept
18
Sequential Approximate Optimization
0 *k kk0 *k k
f x - f x=
f x - f x
k
k
k k
if 0, approximation is badif 1, approximation is excellentif > 1 or 0,1 , moving in the right direction.
Trust region ratio
0
1
* 0 s
2 * 0 s
1 2
= 0.25= 1
2 if x - x ==
1 if x - x <
= 0.25, = 0.75
R. Flecher, Practical Methods of Optimization, 1987
0 *k kf x - f x
f
originalfunction
approximatefunction
*f x
*f x
0f x0f x
*x0x x
,,
k k+1 k1 0
k k+1 k1 2 1k k+1 k
2 2
1 2
if 0 < , =if < =if =where, 0 < <
Trust radius
0 *k kf x - f x
Trust Region Concepts (1/2)
19
Sequential Approximate Optimization
* 0 k
0 1 2 * 0 k
2 if x - x == 0.25, = 0.75, = 0.25, = 1.0, =
1 if x - x <
1 = 0.25 2 = 0.75
2
1 = 1.331
1 = 4.000
excellent goodgoodbadright
directionright
direction
k+1 k2
0 *k+1 k
=x = x
k+1 k1
0 *k+1 k
=x = x
k+1 k0
0 *k+1 k
=x = x
(reject)
0 0
k+1 k0
k+1 kx ==
x
1x
2x
0kx
*kx
2x
0kx
*kx
1x
2x
0kx
*kx
1x
2x
0kx
*kx
previous trust region
new trust region
1x
2x
0kx
*kx
0 *k kk0 *k k
f x - f x=
f x - f x
Trust Region Concepts (2/2)
20
Sequential Approximate Optimization
START
DOE
BuildApproximate Model
ApproximateOptimization
ModelManagement
Converged?
END
Approximate
Build Approximate Model
DOE
x
xf
x
xf
x
xf
x
xf
: Trust Region
: Design Regionx
xf
x
xf
x
xf
x
xf
Model Management
SAO - Function Based Approximation Methods
21
Sequential Approximate Optimization
1x
3x
2x
1x
3x
2x333231
232221
131211
HHHHHHHHH
H
kTk
Tkk
kkTk
Tkkkk
kk yyy
HHHHH
1
111
333231
232221
131211
HHHHHHHHH
H
1x
3x
2x
1x
3x
2x
33
22
11
HH
HH
3231
2321
1312
HHHHHH
H
333231
232221
131211
HHHHHHHHH
H
DO
EM
ath
em
atica
l Pro
gra
mm
ing
Conventional Quadratic Modeling PQRSM
Concept ofthe Progressive Quadratic Response Surface Method
22
Sequential Approximate Optimization
: Trust regionx
( )f x
xf ( )f x xf
( )f x
( )f xx
x
xf
( )f x
( )f x
Update Trust RegionUpdate Trust Region
Approximate OptimizationApproximate Optimization
1 n nnumber ofunknowns
Only 2n+1 Experimental pointsare required!!
1 n n n(n-1)/2number of unknowns
At least(n+1)(n+2)/2Experimental
pointsare required!!
20
1 1 1
ndv ndv ndv ndv
i i ii i ij i ji i i j i
f x x x xx
20
1 1 1
ndv ndv ndv ndv
i i ii i ij i ji i i j i
f x x x xx
Make Full Quadratic Approximate ModelMake Full Quadratic Approximate ModelResponse Surface Method
PQRSM
3-points polynomialinterpolation
Quasi-Newtonmethod
Least Square Method
Hessian term
0
11
22
33
H12 13
21 23
31 32
H 12 13
21 23
31 32
11
22
33
H3-points polynomial
interpolationQuasi-Newton
method
+
1x1Lx 1
Ux
2Lx
2Ux
11x 12x
22x
21x
0x
2x
: Trust regionDOEDOE
“2n+1”points
PQRSM Procedure
23
Sequential Approximate Optimization
1
1
22221 70sin1.011
n
kkkkk xxxxf xMinimize
1,,2,1,0.1,2.1 1 nkxx kk
Initial Values:
Optimum Values:
,0.1,,0.1,0.1at,0.0 * Tf xx
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35 40 45 50
Number of Design Variables
Num
ber
of C
umul
ativ
e Fu
nctio
n E
valu
atio
ns
PQRSMD-optimalCCD
66,91,81196
345
859
316
1201
559
2051
1038
2122
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35 40 45 50
Number of Design Variables
Num
ber
of C
umul
ativ
e Fu
nctio
n E
valu
atio
ns
PQRSMD-optimalCCD
66,91,81196
345
859
316
1201
559
2051
1038
2122
Total Number of Function Evaluations
Noisy Mathematical Function
24
Sequential Approximate Optimization
1. Gear Reducer Design
2. Rosen-Suzuki Problem
3. Two-DOF linear dynamic
absorber design
4. Elasto-plastic Ten-member
Truss Design
5. Design of a Tracked Vehicle
Performance comparison between PQRSM, D-optimal, and CCD
0
0.5
1
1.5
2
2.5
3
1 2 3 4 5
Problem Number
Rela
tive N
um
be
r o
f A
na
lyse
s PQRSM
D-opt.
CCD
0.27
0.75 0.75
0.170.28
2.61
1.24 1.24
1 1 1 1 1
Test Problems
25
Sequential Approximate Optimization
ipii xy
pi is determined to matchii y
gy
g 11~ yy
n
iii
iTPEA yy
yggg
12,
22
~ yyy2,
1,21 lnln1i
i
iii x
xx
gx
gp xx
xg
ixg 1x
ixg 2x
1x 2x ix
1xg
2xg
yg
iyg 1y
iyg 2y
1y 2y iy
1yg
1~ yg
2yg
Fadel et al.TPEA
Wang & GrandhiTANA-1 & -2
Xu & GrandhiTANA-3
Wang & GrandhiTANA
Kim et al.TDQA
1990 1994 1995 1998 2001
Two-Point Approximation
26
Sequential Approximate Optimization
n
iiiiii
n
i i
yyGyyy
ggg1
22,2,
1
22
~ yyy
Two-Point Diagonal Quadratic Approximation
Intervening Variable with Shifting Constant ci Diagonal Hessian having different signed values Gi
Correction Coefficient
1
g
ix
To define an intervening variable whenthe design variable value is near zeroor negative
11~ xx gg
To match the function at x1
ipiii cxy
0otherwise,1,if
i
Liii
cxcx
iiiii y
gy
gyy
G 21
2,1,21 yy
Curvatures of different signs along each variable axis
1y2y
( )g y
A New Two-Point Approximation
27
Sequential Approximate Optimization
STDQAO
STDQAO:Sequential Two-point Diagonal Quadratic Approximate Optimization
28
Sequential Approximate Optimization
1. Welded Beam Design
2. Gear Reducer Design
3. Rosen-Suzuki Problem
4. Piston Design Problem
5. Three-bar truss design problem
6. Ten-bar truss design problem Case 1a
7. Ten-bar truss design problem Case 1b
8. Ten-bar truss design problem Case 2a
9. Ten-bar truss design problem Case 2b
Performance comparison between TDQA and TANA3
: Convergence failed
: Prematurely converged
Problem Number
Num
ber
of A
nlay
ses
TDQATANA3
Test Problems
29
Sequential Approximate Optimization
Outline
Brief Introduction of iDOT
Sequential Approximate Optimization
Applications
30
Sequential Approximate Optimization
Go
Go
Go
Go
Go
Go
NEXT
AerospaceAutomotivesBiotechnologyElectronicsInformation Technology
Marine TechnologyMaterialsMechanicalMEMS DevicesNuclearRailway Vehicles
2152
132
26
26222
ApplicationsApplications
ABS Controller (Simulink & CarSim)
Air Bearing Surface of HDD (in-house code)
Switched Reluctance Motor (SRM Analyzer)
Hydro-Pneumatic Suspension Unitof a Tracked Vehicle
Automotive Body Structure (MSC/NASTRAN)
Go Drum Washer Suspension System (DADS & ANSYS)
Heat Sink for a 40A-Drive PackageSystem of an Elevator (FLUENT)
(RecurDyn-alpha)
31
Sequential Approximate Optimization
Application 1: 40A-Drive Package System
Model : 40A Drive Package System
- Heat Sink (188 x 400 x 60 mm)- IGBTs (46,007 / 42,438 W/m2)- Fan (Model : 3112KL-05W-B50)
Schematics of Drive Package System
7.52
1.5 (B2)
94
537
(t)
2.0 (B1)
Schematics and baseline geometry of heat sink
IGBT_1
Duct Heat SinkReactor
IGBT_2
Optimization of Heat Sink
Numerical Methodology
- FLUENT : Predict Flow andThermal Fields in System
- SQP (Sequential Quadratic Programming Method): Propose the optimal variables numerically
- Batch-process : Integrate CFD(FLUENT) and CAO (SQP)
Objective
- To obtain the optimum design variables
(B1, B2, and t ) by minimizing
(1) the pressure drop (2) the temperature rise, simultaneously
Objective functions
Design variables
32
Sequential Approximate Optimization
Application 1: 40A-Drive Package System
Pathlines for understanding the flow fields
Optimum variables ( Temp. rise is less than 35 K)
Results
Comments
- Optimization is strongly needed to guarantee the thermalstability of IGBTs
- It is easily applicable to the other specification of heat sink- As shown the above table, pressure drop increases while
temperature rise decreases. - Note that, in optimum model, the value of pressure drop is
ranged in the characteristic curve of fan.
Comparison with Experimental Data
- For the temp. rise, difference is only 1.2 KGood agreement with the experimental data
Isotherms for understanding the temp. fields
Vortex flow
10.7
7
t
34.93 K ( )
38.66 K ( )
Temp. Rise
43.3 Pa1.52Baseline
1.9
B2
Optimal 50.3 Pa2.6
Pre. DropB1
• Ambient temp. : 318 K (45 oC)• Max. temp. of baseline geometry : 356.66K, Max. temp. of optimization : 352.93 K
Max. Temp : 352.93 K
Unit : [mm]
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3333
Applications
For higher areal density For higher areal density …………
• Reduced flying height (as low as 10 nm)• Complicated geometry of ABS
Application 2: Head-Disk Interface (HDI)
3434
Applications
h*
radius
radius
U
L
radius
U
L
hglide
rotational vel.
halt
radius
Uniform FH (Fly Height) (target FH = 9 nm)Uniform FH (Fly Height) (target FH = 9 nm)
Limited Pitching (between 250 and 300 Limited Pitching (between 250 and 300 rad)rad)
Limited Rolling (between Limited Rolling (between --5 and 5 5 and 5 rad)rad)
Altitude Insensitivity (80% FH @10k ft)Altitude Insensitivity (80% FH @10k ft)
Fast TOV (80% FH @ra=15 mm/skew=Fast TOV (80% FH @ra=15 mm/skew=--25.54, rpm=2.5K)25.54, rpm=2.5K)
Application 2: Design Requirements
3535
Applications
•• Design variables: S1~S10, recess depth, and shallow stepDesign variables: S1~S10, recess depth, and shallow step•• Using SAEUsing SAE’’s shape function for design variable linking s shape function for design variable linking --> [shape.in]> [shape.in]
Application 2: Design Variables
3636
Applications
2 2max min
min
max
, 1 ~ 8, ,
0.5*( 9 ) 0.5*( 9 )
:250 ,
: 300 ,
:
1
2
3
find
min. nm nm
subject to g rad
g µrad
g
i s i recess shallow
F hINT hINT
Pitch
Pitch
min
max
max
1
5 ,
: 5 ,
: 9 (1 0.8)*9 ,
: 0.8*9 ,
0.02
4
5
6
rad
g µrad
g nm
g nm
where -0.05 mm mm
ALT
FAST
Roll
Roll
nm hINT
hINT
s
2
3
4
5
6
0.020.020.050.050.05
-0.05 mm mm
-0.05 mm mm
-0.02 mm mm
-0.05 mm mm
-0.05 mm mm
-0
sssss
7
8
0.050.052
0.2
.02 mm mm
-0.02 mm mm
1 m m 0.1 m m
ss
recessshallow
Application 2: Mathematical Formulation
3737
Applications
Uniform FH , Limited Pitching , Limited RollingUniform FH , Limited Pitching , Limited Rolling
Application 2: Altitude Insensitivity
20 30 40 500
5
10
15
20
Flyi
ng h
eigh
t [nm
]
Disk radius [mm]
Initial Optimum
20 30 40 50200
250
300
350
Pitc
h an
gle
[ra
d]
Disk radius [mm]
Initial Optimum
20 30 40 50-15
-10
-5
0
5
10
15
Rol
l ang
le [
rad]
Disk radius [mm]
Initial Optimum
3838
Applications
iteration number : 17iteration number : 17total function calls : 221total function calls : 221
Application 2: Optimization Results
0 5 10 15 20-2
-1
0
1 G1 G2 G3 G4 G5 G6
Con
stra
int v
alue
Iteration number0 5 10 15 20
0
10
20
30
40
50
Cos
t val
ue
Iteration number
HOME
3939
Applications
Design PathRoad
Design Requirements
4040
Applications
ABS Controller FRT On Switch ValueABS Controller FRT Off Switch ValueABS Controller RR On Switch ValueABS Controller RR Off Switch Value
Brake Actuator Gain LR & RR
ABS Controller Switch Threshold
Application 3: Simulink Model (Including CarSim S-Function)
Simulink Model
4141
Applications
Initial/Operating Conditions (CarSim)
Application 3: CarSim Model
CarSim GUI
4242
Applications
4343
Applications
Simulink + CarSim
Application 3: Integration
Design under Uncertainty
Uncertainty Analysis
Sequential Approximate Opt.
Optimization
Approximation
Design of Experiment
Parametric StudyFRAMAX
4444
Applications
Multiobjective Problem•Weight Factor(Station) : 0.75•Weight Factor(Yaw) : 0.25
Optimum
Initial
Application 3: Pareto Optimum (1)
Station(m) vs. Time(s) Yaw(deg) vs. Time(s)
4545
Applications
Multiobjective Problem•Weight Factor(Station) : 0.5•Weight Factor(Yaw) : 0.5
Optimum
Initial
Application 3: Pareto Optimum (2)
Station(m) vs. Time(s) Yaw(deg) vs. Time(s)
4646
Applications
Multiobjective Problem•Weight Factor(Station) : 0.25•Weight Factor(Yaw) : 0.75
Optimum
Initial
Application 3: Pareto Optimum (3)
Station(m) vs. Time(s) Yaw(deg) vs. Time(s)
4747
Applications
Pareto Set
0
100
200
300
400500
600
700
150 160 170 180 190 200 210
Station
Squ
are
Sum
of Y
aw
Weighting Ratio(Staion/SquareSumYaw=0.75/0.25)
Weighting Ratio(Staion/SquareSumYaw=0.5/0.5)
Weighting Ratio(Staion/SquareSumYaw=0.25/0.75)
Application 3: Pareto Optimum Set
Pareto Optimum Set
HOME
48
Applications
Maximize Average Torque
Torque ripple
Maximum Current Phase
aveT
%20ripT
A6maxI
Switching on Angle
Switching off Angle
Rotor Pole Arc
on
off
r
Design of a Switched Reluctance Motor
Application 4: SRM (Switched Reluctance Motor)
49
Applications
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Angle (deg.)
Ave
rage
Tor
que
(N-m
)
75.0
80.0
85.0
90.0
95.0
100.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0Angle (deg.)
Tor
que
Rip
ple
(%)
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0Angle (deg.)
Max
imum
Cur
rent
Pha
se (A
)
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
45.0 47.0 49.0 51.0 53.0 55.0 57.0 59.0
Angle (deg.)
Ave
rage
Tor
que
(N-m
)
45.0
55.0
65.0
75.0
85.0
95.0
105.0
45.0 47.0 49.0 51.0 53.0 55.0 57.0 59.0Angle (deg.)
Tor
que
Rip
ple
(%)
4.00
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
45.0 47.0 49.0 51.0 53.0 55.0 57.0 59.0Angle (deg.)
Max
imum
Cur
rent
Pha
se (A
)
Switching on Angle Switching off Angle
Parameter Studies of Switching On/Off Angles
Application 4: SRM (Switched Reluctance Motor)
50
Applications
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6 7 8 9Iteration
Ave
rage
Tor
que
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
0 1 2 3 4 5 6 7 8 9Iteration
Max
imum
Con
stra
int V
iola
tion
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50 60 70 80 90
Rotation Angle (deg.)
Tor
que
(N-m
)
Initial DesignOptimum Design
Initial
Optimum
on off r aveT ripT maxI
22.4 55.7 38.0 0.30 19.98 4.91
25.2 45.1 30.0 0.17 98.60 4.02
Optimization Results
Application 4: SRM (Switched Reluctance Motor)
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51
Applications
14 inch
Minimize the vertical acceleration at the CG of the hull
wheel travels during jounce(6)
equally distributed static forces for the wheels(6)
track tension(1)
charging pressures of the 3rd and 4th HSU’s(2)
static track tension
charging pressures of the 1st, 2nd, 5th and 6th
HSU’s
length of gas chambers
pre-load for Belleville springs
choking flow rate
inner diameter of orifice
Objective
Constraints (15) Design Variables (9)
Application 5: Tracked Vehicle
52
Applications
Is the acceleration a nosy function ?
• Gradient based optimization algorithm may cannot be converged.• Function based approximate optimization algorithm should be used.
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time
Ver
tical
Acc
eler
atio
n (m
/s^2
)
Noise ?
Noisy Cost Function
Application 5: Tracked Vehicle
53
Applications
Optimization Result - Acceleration
Application 5: Tracked Vehicle
54
Applications
Optimization Result – Wheel Travel
Application 5: Tracked Vehicle
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55
Applications
1
z' z y'
y
1t
2t3t
1SV
2SV
Hz
Application 6: Automotive Body Structure
56
Applications
Optimization Results Convergence History
2.98415E-31.37259E+313
3.49547E-31.37245E+312
2.53623E-31.37371E+36.22981E-31.37171E+311
3.77472E-31.37340E+39.90981E-31.37084E+310
1.19377E-21.37201E+31.54264E-21.36953E+39
4.39808E-21.36701E+32.15811E-21.36823E+38
5.50377E-21.36875E+32.94570E-21.36642E+37
2.27294E-21.37600E+33.80981E-21.36567E+36
1.61079E-21.38161E+35.48596E-21.36501E+35
2.35630E-21.38227E+36.08585E-21.36717E+34
3.69611E-21.38771E+38.19064E-21.36478E+33
3.78596E-21.38829E+36.29008E-21.37034E+32
4.30770E-21.38883E+34.30770E-21.38883E+31
Max.Violation
Objective function
Max.Violation
Objective function
TPCATDQAIT
16 kg 15 kg
Application 6: Automotive Body Structure
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CAE-Based Design Optimization
Dong-Hoon Choi
Director, the Center of Innovative Design Optimization Technology (iDOT)Professor, School of Mechanical Engineering
Hanyang University, Seoul, Korea
September 1, 2006