design optimization via surrogate modeling and space mappingmbakr/ece718/lecture_12.pdf · select...
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Design Optimization Via Surrogate Modeling and Space Mapping
Qingsha Cheng, John W. Bandler and Koziel Slawek
presented at
Class ECE 718, Dr. Mohamed H. Bakr, McMaster UnviersityApril 26, 2010
Current Space Mapping Collaborators
Dr. M.H. Bakr (McMaster)Dr. J.W. Bandler (McMaster)Dr. Q.S. Cheng (McMaster)Dr. S. Koziel (Reykjavik University)Dr. K. Madsen (TU Denmark)Dr. N.K. Nikolova (McMaster)Dr. J.C. Rautio (Sonnet Software)Dr. J. E. Rayas-Sánchez (ITESO)Dr. Q.J. Zhang (Carleton)
The Space Mapping Concept(Bandler et al., 1994-) validation space
optimization space
mapping
prediction
surrogate update (surrogate
optimization)
(high-fidelityphysics model)
(low-fidelityphysics model)
The Space Mapping Concept(Bandler et al., 1994-)
fx
( )f fR xfine
modelcoarsemodelcx
( )c cR x
fx cx
such that( )c f=x P x
( ( )) ( )c f f f≈R P x R x
Aggressive Space Mapping Practice—Cheese-Cutting Problem(Bandler, 2002)
(2) (1) * (1)c cf fx x x x= + −
parameter extraction
prediction
initial guess
optimal coarse brick*cx
(1)fx
(1)cx
(1) *cfx x=
(2)fx
coarse model can be imaginaryactual human brain process different person may have different imaginary coarse modelspace mapping is a mathematical representation of brain process
Initializationcoarse model optimization
target solution
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
Iteration 1extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 1extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 2extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 3extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 4extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 5extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 6extracted coarse model
fine model prediction
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Iteration 7extracted coarse model
fine model predictiontarget solution
0 2 4 6 8 10 12 14 16 18 20 22 01
024
z
0 2 4 6 8 10 12 14 16 18 20 22 01
024
x
ASM: The Wedge-Cutting Illustration (Dakroury et al., 2002)
Linking Companion Coarse (Empirical) and Fine (EM) ModelsVia Space Mapping (Bandler et al., 1994-)
finemodel
coarsemodel
designparameters
responses responsesdesignparameters
JDH +=×∇ ωj
BE ωj−=×∇ρ=∇ D
ED ε=
HB μ=
0=∇ B
(low-fidelityphysics model)
(high-fidelityphysics model)
Explicit (Input) Space Mapping Concept(Bandler et al., 1994-)
used in the microwave industry (e.g., Com Dev, since 2003, for optimization of dielectric resonator filters and multiplexers)
coarsemodel
finemodel
spacemapping
designparameters responses
responses
surrogate
*( ) ( ) , f f c− →f x P x x f 0
Aggressive Space Mapping Optimization(Bandler et al., 1995)
corresponds to solving the nonlinear system of equations
equivalently, “solve”*
c c=x x
( )f =f x 0
)()()( jjj fhB −=
)()()1( jjf
jf hxx +=+
Aggressive Space Mapping Optimization (Bandler et al., 1995)
iteratively solves the nonlinear system
the quasi-Newton step h( j) in the fine space is given by
the next iterate
( +1) ( ) ( ) ( )( 1) ( ) ( )
( ) ( )
j j j jTj j j
Tj j= ++ − −f f B hB B h
h h
Aggressive Space Mapping Optimization(Bandler et al., 1995)
Broyden update
Aggressive Space Mapping Optimization(Bandler et al., 1995)
estimate the fine model Jacobian (Bakr et al., 1999)
estimate the mapping matrix
BxJxJ )()( ccff ≈
1( )T Tc c c f
−≈B J J J J
( ) ( ) *
( ) ( ) ( )
( 1) ( ) ( )
,
and
j jc c
j j j
j j jf f+
= −
= −
= +
f x x
B h fx x h
Space Mapping Design of Dielectric Resonator Multiplexers(Ismail et al., 2003, Com Dev, Canada)
10-channel output multiplexer, 140 variables, aggressive SM
Space Mapping Crashworthiness Design of Saab 93
(Redhe et al., 2001-2004, Sweden)
[type “saab space mapping” into Google]
in crashworthiness finite element design, space mapping reduces the total computing time to optimize the vehicle structure more than 50% compared to traditional optimization
when space mapping was applied to the complete FE model of the new Saab 93 Sport Sedan, intrusion into the passenger compartment area after impact was reduced by 32% with no reduction in other crashworthiness responses
US-NCAP EU-NCAP
Space Mapping Crashworthiness Design of Saab 93
Frontal Impact (Nilsson and Redhe, 2005, Sweden)
Space Mapping Crashworthiness Design of Saab 93
Frontal Impact (Nilsson and Redhe, 2005, Sweden)
Space Mapping Crashworthiness Design of Saab 93
(www.studyinsweden.se, 2005)
space mapping cuts calculation times by three fourths compared with traditional response surface optimization
driven straight into a steel barrierat 56 km/h
penetration of the passenger spacewas reduced by 32 percent
Implicit, Input and Output Space Mappings(Bandler et al., 2003-)
expert engineering expertise helpful in engineering expertiseknowledge helpful “tuning the surrogate” perhaps less necessary(few designable (many possibilities, (many output variables)variables) e.g., dielectric constant)
The Novice-Expert Continuum
output space mapping: a “band-aid” solution for engineers and non-engineers; the parameter extraction step does not require coarse model re-analysis; good for final touch-ups
input space mapping: an engineering approach to find and curethe root-cause of a defect; but the parameter extraction stepcan be a difficult inverse optimization problem to solvew.r.t. the coarse model
tuning space mapping (new): simulator-based expert approach
but all types of space mapping can be viewed as special casesof implicit space mapping
Space Mapping: (1) for Design Optimization, (2) for Modeling
Start
simulate fine model
select models and mapping framework
optimize coarse model
criterionsatisfied
yes
no
End
optimize surrogate(prediction)
update surrogate(match models)
Start
simulate fine model points
select models and mapping framework
generate base andtest points
End
multi-point parameter extraction
test SM-based model
interpolate responses
High-Temperature Superconducting (HTS) Filter:Modeling + Optimization
Sonnet em fine model Agilent ADS coarse model (Westinghouse, 1993) (Bandler et al., 2004)
εr
S2
S1
S3
S1L 0
L 1
L 0
L 2
L 1
L 2
L 3
S2
W
H
Coarse Model
S_ParamSP1
Step=0.02 GHzStop=4.161 GHzStart=3.901 GHzSweepVar="freq"
S-PARAMETERS
MCLINCLin5
L=L1c milS=S1c milW=W milSubst="MSub"MCLIN
CLin4
L=L2c milS=S2c milW=W milSubst="MSub"MCLIN
CLin3
L=L3c milS=S3c milW=W milSubst="MSub"MCLIN
CLin2
L=L2c milS=S2c milW=W milSubst="MSub"MCLIN
CLin1
L=L1c milS=S1c milW=W milSubst="MSub"
MSUBMSub
Rough=0 milTanD=0.00003T=0 milHu=3.9e+034 milCond=1.0E+50Mur=1Er=23.425H=20 mil
MSub
TermTerm1
Z=50 OhmNum=1
MLINTL1
Mod=KirschningL=50 milW=W milSubst="MSub"
MLINTL2
Mod=KirschningL=50.0 milW=W milSubst="MSub"
TermTerm2
Z=50 OhmNum=2
Implicit and Output SM Modeling, with Input SM: HTS Filter(Cheng and Bandler, 2006)
More Base Points for Space-Mapping-based Modeling(Bandler et al., 2001)
2n more base points located at the corner of the region of interestwith n design parameters
HTS Filter: Modeling Region of Interest(Cheng and Bandler, 2006)
parameters reference point (x0)
region 1 size (δ1)
region 2 size (δ2)
region 3 size (δ3)
region 4 size (δ4)
region 5 size (δ5)
L1 180 5 6 8 10 45
L2 200 10 11 15 20 50
L3 180 5 6 8 10 45
S1 20 2 3 3 4 5
S2 80 5 6 8 10 20
S3 80 10 11 15 20 20
HTS Filter: Implicit SM Modeling Surrogate Test Region 2
fine model (○) Rs surrogate (—)
HTS Filter: Implicit SM Modeling + Surrogate Optimization (Cheng and Bandler, 2006)
xf* = [172 207 172 20 90 84]T
Implicit Space Mapping Practice—Cheese-Cutting Problem(Bandler et al., 2004)
initial guess
prediction
verification
PE
optimal coarse brick 3
10
10
3
target volume =301
1volume =24
102.4
12.5
volume =31.5
target volume =30
volume =24
12.5
the “coarse” brick is idealized, the algorithm is non-expert
PE
verification
prediction
verification…
volume =31.512.5 3
2.52volume =31.5
11.9 volume =30.0
volume =29.711.9
error = (30−29.7)/30×100%=1%
Implicit Space Mapping Practice—Cheese-Cutting Problem(Bandler et al., 2004)
Implicit Space Mapping Optimization (Cheng et al., 2008)
fine model optimal solution
surrogate optimization
parameter extraction
1 arg min ( ( , ))k kcU+ =x R x px
arg min || ( ) ( , ) ||k k kf c= −p R x R x pp
* arg min ( ( ))fU=x R xx
Implicit Space Mapping Parameter Extraction (Cheng et al., 2008)
matching the initial surrogate (coarse model) to the fine model
surrogate shifted surrogate scaled
1p 0p 1p 0pinitialsurrogate
surrogateafter PE
finemodel initial
surrogatefinemodel
surrogateafter PE
Implicit Space Mapping Flowchart (Cheng et al., 2008)
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
filter structure (Brady, 2002)
specification|S11|<−16 dB for 3.7 GHz ≤ω≤ 4.2 GHz|S21|<−28 dB for ω≤ 3.2 GHz and ω≥ 4.7 GHz.
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
coarse model (“half” implementation, Brady, 2002)
MSOBND_MDSBend5
W=55 milSubst="MSub1"
MSUBMSub2
Rough=0 milTanD=0.002T=0.7 milHu=3.9e+034 milCond=1.0E+50Mur=1Er=Er1H=H1 mil
MSub
MSUBMSub3
Rough=0 milTanD=0.002T=0.7 milHu=3.9e+034 milCond=1.0E+50Mur=1Er=Er2H=H2 mil
MSub
MSUBMSub1
Rough=0 milTanD=0.002T=0.7 milHu=3.9e+034 milCond=1.0E+50Mur=1Er=ErH=H mil
MSub MLINTLc
L=Lc milW=55 milSubst="MSub1"
MLINTLb
L=Lb milW=55 milSubst="MSub1"
MSOBND_MDSBend3
W=50 milSubst="MSub1"
MCLINCLin2
L=L4 milS=S2 milW=55 milSubst="MSub3"
MCLINCLin1
L=L3 milS=S1 milW=50 milSubst="MSub2"
MLINTLa
L=La milW=40 milSubst="MSub1"
MLINTL2
L=L2 milW=40 milSubst="MSub1"
MLEFTL1
L=L1 milW=40 milSubst="MSub1"
MLINTL0
L=100.0 milW=65 milSubst="MSub1"
PortP2Num=2
CC4C=.01 pF
CC1C=.01 pF
PortP1Num=1
CC2C=.01 pF C
C3C=.01 pF
MSOBND_MDSBend4
W=55 milSubst="MSub1"
MSOBND_MDSBend1
W=40 milSubst="MSub1"
MSOBND_MDSBend2
W=50 milSubst="MSub1"
MTEETee1
W3=65 milW2=40 milW1=40 milSubst="MSub1"
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
coarse model optimization
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
fine model in Sonnet em
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
initial design
coarse model optimal (---) and fine model initial (—) desired specification (—) and the tightened specification (---)
3 3.5 4 4.5 5-70
-60
-50
-40
-30
-20
-10
0
frequency [GHz]
|S11
| and
| S21
| in
dB
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
fine model responses after 3 implicit SM iterations
desired specification (—) and the tightened specification (---)
3 3.5 4 4.5 5-60
-50
-40
-30
-20
-10
0
frequency [GHz]
|S11
| and
| S21
| in
dB
Microstrip Hairpin Filter: Implicit SM (Cheng et al., 2008)
fine model after 3 implicit SM iterations and one output SM
desired specification (—) and the tightened specification (---)
3 3.5 4 4.5 5-70
-60
-50
-40
-30
-20
-10
0
frequency [GHz]
|S11
| and
| S21
| in
dB
Implicit Space Mapping Design of Thick, Tightly CoupledConductors (Rautio, 2004, Sonnet Software)
thick, closely spaced conductorson silicon (fine model)
“space-mapping” (top) layer(coarse model)
EPCOS LTCC/Feb 04 (Rautio, 2006, Sonnet Software)
(courtesy Rautio, 2006)
SMF: A User-friendly Space Mapping Software Engine(Bandler Corp., 2006, Koziel and Bandler, 2007)
SMF: for SM-based constrained optimization,modeling and statistical analysis
to make space mapping accessible to engineersinexperienced in the art
to incorporate existing space mapping approaches in one package
implementation: a GUI based Matlab package
simulators sockets: Agilent ADS, Sonnet em,FEKO, MEFiSTo, Ansoft Maxwell, Ansoft HFSS
SMF Uses a General Space Mapping Surrogate Model
surrogate model Rs(i) at iteration i
where A(i), B(i), c(i), xp(i) and G(i) are determined using parameter
extraction
and
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( , ) ( )i i i i i i i i is c p= ⋅ ⋅ + ⋅ + + + ⋅ −R x A R B x c G x x d E x x
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( , )i i i i i i i i if c p= − ⋅ ⋅ + ⋅ +d R x A R B x c G x x
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( , )f s
i i i i i i i ip= − ⋅ + ⋅ +R RE J x J B x c G x x
( ) ( ) ( ) ( ) ( ) ( )0( , , , , )
( ) ( )
( ) ( ) ( )0
( , , , , ) arg min || ( )
( , ) ||
|| ( ) ( , ) ||
p
f s
ii i i i i kp k fk
k kc p
i k k kk pk
w
v
=
=
=
− ⋅ ⋅ + ⋅ +
+ − ⋅ + ⋅ +
∑
∑
A B c x G
R R
A B c x G R x
A R B x c G x x
J x J B x c G x x
SMF: Optimization Flowchart (Bandler Corp., 2006)
SMF: Optimization Flowsetup linking fine/coarse models
coarse model optimization
space mapping optimization
SMF Optimization of Probe-Fed Printed Double Annular Ring Antenna with Finite Ground (Zhu et al., 2006)
coarse model (FEKO) fine model (FEKO)
SMF Optimization of Probe-Fed Printed Double Annular Ring Antenna with Finite Ground (Zhu et al., 2006)
εr
W1
W2
W0
L1
HL2
W1
L0
L0
|S21| ≤ 0.05 for 9.3 GHz ≤ ω ≤ 10.7 GHz|S21| ≥ 0.9 for ω ≤ 8 GHz and ω ≥ 12 GHz
Bandstop Microstrip Filter Example (Bandler et al., 2000)
fine model (Sonnet em)
coarse model (Agilent ADS)
design specs:
TLINTL2
F=10 GHzE=Ec0Z=Z0 Ohm
TLOCTL10
F=10 GHzE=Ec1Z=Z1 Ohm
Ref
TLOCTL8
F=10 GHzE=Ec1Z=Z1 Ohm
Ref
TLOCTL9
F=10 GHzE=Ec2Z=Z2 Ohm
Ref
TLINTL4
F=10 GHzE=Ec0Z=Z0 Ohm
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
SMF Bandstop Microstrip Filter Optimization: Starting Point
SMF Bandstop Microstrip Filter Optimization: Solution
Tuning Space Mapping (TSM): Type 0 Embedding(Koziel et al., 2009)
surrogate based on the auxiliary fine model (fine model with internal tuning ports); it is an expert approach
Tuning Space Mapping (TSM): Type 1 Embedding(Cheng et al., 2009)
surrogate based on the auxiliary fine model (fine model with internal tuning ports); it is an expert approach
Tuning Space Mapping (TSM): Type 1 and Type 0 Embedding (Cheng et al., 2009)
surrogate based on the auxiliary fine model (fine model with internal tuning ports); it is an expert approach
Tuning Space Mapping Flowchart
Classical Space Mapping Tuning Space Mapping (Bandler et al., 2004) (Koziel et al., 2008)
circled ports are tuning ports:in series with inductorsin shunt with capacitors
Tuning Methodology (Rautio, 2005, Sonnet Software)
(courtesy Rautio, 2006)
Motorola LTCC Quad Band Receiver(Rautio, 2006, Sonnet Software)
(courtesy Rautio, 2006)
Tuning Space Mapping Optimization of HTS Filter (Type 0)(Koziel, Meng, Bandler, Bakr, and Cheng, 2009)
fine model (Westinghouse, 1993) tuning model in ADSwith added tuning ports with circuit components(Sonnet em)
L 0L 1
L 0
L 2
L 1
L 2
L 3
W1
34
56
78
910
1112
1314
1516
1718
1920
2122
2
LL1
1
2
3
4
5
6 7 8 9 10 11 12
17
16
15
14
13
22 21 20 19 18
Ref
Term 1Z=50 Ohm
Term 2Z=50 Ohm S22P
SNP1
C1 C1
LL2
C2 C2
LL3
C3 C3
LL2
C2 C2
LL1
C1 C1
Tuning Space Mapping Optimization of HTS Filter (Type 0)(Koziel, Meng, Bandler, Bakr, and Cheng, 2009)
calibration model = coarse model + tuning elements
calibration goal: translate the “tuned” tuning parameter valuesto physical design parameter values
Tuning Space Mapping Optimization of HTS Filter (Type 0)(Koziel, Meng, Bandler, Bakr, and Cheng, 2009)
initial fine model response (—) final fine model responseoptimized tuning model (---) after two TSM iterations
responses from Sonnet em and Agilent ADS
3.95 4 4.05 4.1 4.150
0.2
0.4
0.6
0.8
1
frequency [GHz]
|S21
|
3.95 4 4.05 4.1 4.150
0.2
0.4
0.6
0.8
1
frequency [GHz]
|S21
|
Open-loop Ring Resonator Bandpass Filter (Koziel et al., 2008)
design parameters x = [L1 L2 L3 L4 S1 S2 g]T mmspecifications|S21| ≥ −3 dB for 2.8 GHz ≤ ω ≤ 3.2 GHz|S21| ≤ −20 dB for 1.5 GHz ≤ ω ≤ 2.5 GHz|S21| ≤ −20 dB for 3.5 GHz ≤ ω ≤ 4.5 GHz
Open-loop Ring Resonator Bandpass Filter (Type 1 and Type 0)(Cheng et al., 2010)
Sonnet em model with internal (co-calibrated) ports
Open-loop Ring Resonator Bandpass Filter (Type 1 and Type 0)(Cheng et al., 2010)
Sonnet em model with internal (co-calibrated) ports
Open-loop Ring Resonator Bandpass Filter (Type 1 and Type 0) (Cheng et al., 2010)
initial responses: tuning model (—), fine model (○),fine model with co-calibrated ports (---)
2.0 2.5 3.0 3.5 4.01.5 4.5
-40
-30
-20
-10
-50
0
frequency [GHz]
|S21
|
Open-loop Ring Resonator Bandpass Filter (Type 1 and Type 0) (Cheng et al., 2010)
responses after two iterations: the tuning model (—),corresponding fine model (○)
2.0 2.5 3.0 3.5 4.01.5 4.5
-40
-30
-20
-10
-50
0
frequency [GHz]
|S21
|
Space-Mapping-Based Interpolation (Koziel et al., 2006)
assumption: the fine model isavailable on a structured grid
define an interpolated fine model as
where snapping function s(.) is defined as
( 1) ( 1)
( ) ( 1) ( ) ( 1)
( ) ( ( ))
( ) ( ( ))
i if f
i i i is s
s
s
+ +
+ +
= +
+ −
R x R x
R x R x
arg min || ||,( ) : || || min || ||Xf f
f Xs X
∈= − ≠∈
⎧ ⎫= ∈ − = − ∧ ∀⎨ ⎬⎩ ⎭z
y z x y xzx x x x z x x y≺
x(4)
x(1)
s(x(3))
s(x(1))
x(2)
s(x(2))
x(3)
s(x(4))
Response-Corrected Tuning Space Mapping Algorithm(Cheng et al., 2010)
the response-corrected tuning model at optimum x*
s is a function that snaps a point to the nearest fine model grid point
* * * *( ) ( , ) ( ( )) ( ( ), )s s p f s ps s= + −R x R x x R x R x x
Yield Analysis and Yield Optimization (Bandler and Chen, 1988)
manufactured outcome
for each outcome, an acceptance index is defined
Yield Y at the nominal point x
, 1, 2, ,k k k N= + =x x Δx …
1, if ( ) 0( )
0, if ( ) 0
kpk
a kp
HI
H⎧ ≤⎪= ⎨ >⎪⎩
xx
x
∑=
≈N
k
kaI
NY
1)(1)( xx
Yield Analysis and Yield Optimization (Bandler and Chen, 1988)
the optimal yield
where
∑∈
=Kk
kk
Y H )(minarg 1* xxx α
{ }0)(1 >= kHkK x
(0)1
1 , 1,2, ,( )k k
k NH
α = = …+Δx x
Yield Analysis and Yield Optimization (Cheng et al., 2010)
Step 1 Use tuning space mapping to obtain a nominal optimal design. A tuning model or surrogate is also obtained.
Step 2 Snap the optimal design to the nearest on-grid fine model point.
Step 3 Simulate the snapped design (EM fine model).Step 4 Calculate the response difference between the fine model and
the surrogate at the nearest on-grid point.Step 5 Add the response difference to the surrogate to form a new
surrogate: the response corrected surrogate.Step 6 Perform yield analysis and yield optimization on the
response-corrected surrogate.Step 7 Compare this response to that of the fine model.
Second-order Tapped-line Microstrip Filter (Type 1)
Second-order Tapped-line Microstrip Filter (Type 1)
tuning model (—), fine model (○),response corrected surrogate (—)
yield analysis (500 trials)
3.5 4.0 4.5 5.0 5.5 6.0 6.53.0 7.0
-20
-10
-30
0
frequency [GHz]
|S21
|
3.5 4.0 4.5 5.0 5.5 6.0 6.53.0 7.0
-20
-10
-30
0
frequency [GHz]
|S21
|
Yield= 55.600%
|S21
|
|S21
|
Open-loop Ring Resonator Bandpass Filter (Type 1) (Cheng et al., 2010)
Open-loop Ring Resonator Bandpass Filter (Type 1)(Cheng et al., 2010)
tuning model (—), fine model (○),response corrected surrogate (—)
2.0 2.5 3.0 3.5 4.01.5 4.5
-40
-30
-20
-10
-50
0
frequency [GHz]
|S21
||S
21|
Open-loop Ring Resonator Bandpass Filter (Type 1)(Cheng et al., 2010)
response corrected surrogate before yield optimization
response corrected surrogate after yield optimization
2.0 2.5 3.0 3.5 4.01.5 4.5
-40
-30
-20
-10
-50
0
frequency [GHz]
|S21
|
Yield = 28.400%
2.0 2.5 3.0 3.5 4.01.5 4.5
-40
-30
-20
-10
-50
0
frequency [GHz]
|S21
|
Yield = 71.200%
|S21
|
|S21
|
Open-loop Ring Resonator Bandpass Filter (Type 1) (Cheng et al., 2010)
response corrected surrogate at design center (—)and final validation on a finer grid (○)
2.0 2.5 3.0 3.5 4.01.5 4.5
-40
-30
-20
-10
-50
0
frequency [GHz]
|S21
| |S21
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Space Mapping: a Glossary of Terms
space mapping transformation, link, adjustment,correction, shift (in parameters or responses);“internal” fine-tuning transformation
coarse model simplification or convenient representation,companion to the fine model,auxiliary representation, cheap model,“idealized” model
fine model accurate representation of system considered,device under test, component to be optimized, expensive model, an optimization process
Space Mapping: a Glossary of Terms
surrogate model, approximation or representation to be used, or to act, in place of, or as a (temporary)substitute for, the system under consideration
(updated) surrogate mapped or enhanced coarse model,corrected coarse model,tuning-parameter-augmented fine-model iterate
surrogate model alternative expression for surrogate
target response a response the fine model should achieve,(usually) the optimal response of an idealized“coarse” model, an enhanced coarse model,or surrogate
Space Mapping: a Glossary of Terms
surrogate update rebuilding of a coarse- or ideal-model-basedsurrogate using, e.g., parameter extraction;supply new fine-model data to a surrogate
surrogate prediction of the next fine model;optimization “internal” fine tuning of a
tuning-parameter-augmentedfine-model iterate (tuning model)
parameter extraction aligning a coarse model or surrogatewith the corresponding fine model
Space Mapping: a Glossary of Terms
companion model coarselow fidelity/resolution coarsehigh fidelity/resolution fineempirical coarsesimplified physics coarsephysics-based coarse or finephysically expressive coarsedevice under test fineelectromagnetic fine or coarsesimulation model fine or coarsecomputational fine or coarsetuning model coarse (fine model data)
+ tuning elementscalibration model coarse + tuning elements
Space Mapping: a Glossary of Terms
tuning-parameter- surrogateaugmented fine-modeliterate (with internaltuning ports)i.e., “tuning model”
optimization process design of fine model
optimization space (design) optimization parametersfor coarse or surrogate models
validation space design optimization parametersfor the fine model
Space Mapping: a Glossary of Terms
neuro implies use of artificial neural networks
implicit space mapping space mapping using preassigned,alternative, or other accessibleparameters
“not” space mapping (usually) an expert’s algorithm,where the underlying space mappingconcept may not be obvious,or not admitted
parameter transformation space mapping
Space Mapping: a Glossary of Terms
(parameter/input) space mapping mapping, transformation orcorrection of design variables
(response) output space mapping1 mapping, transformation orcorrection of responses
response surface approximation linear/quadratic/polynomial approximation of responsesw.r.t. design variables
1advocated by John E. Dennis, Jr., Rice University1Alexandrov’s “high-order model management”
Space Mapping—Cake-Cutting Illustration (Cheng and Bandler, 2006)
Vc x(0)+ cc c(0)
c(0)
-5
0
5
-5
0
50
1
2
3
4
5
131.03°
-5
0
5
-5
0
50
1
2
3
4
5
120°
-5
0
5
-5
0
50
1
2
3
4
5
131.03°
Vc x c(0)
x x(1)
c(0)
…
-5
0
5
-5
0
50
1
2
3
4
5
120°
-5
0
5
-5
0
50
1
2
3
4
5
120°
c
Vf x(1)
x(0)
x(1)
Vf x(0)
c(0)
Implicit, Input and Output Space Mappings in Agilent ADS: Four ADS Schematics (Cheng and Bandler, 2006)
coarse model optimization
fine model simulation
parameter extraction
surrogate re-optimization
-5
0
5
-5
0
50
1
2
3
4
5
Cake-Cutting Problem(Cheng and Bandler, 2006)
use space mapping to find the optimal angle x of a cutsuch that the volume of each slice is equal, in this case, V/3
xºVf1
Vf2Vf3
-5 -4 -3 -2 -1 0 1 2 3 4 50
1
2
3
4
5
ADS Implementation of Cake-Cutting Problem: Fine Model(Cheng and Bandler, 2006)
PortP1Num=1
VARVAR2
R3 =( Vall-Rf-Rf)/VallR2 = Rf/VallR1 = Rf/Vall
EqnVarVAR
VAR1
Vall = pi * r^2 * hch = 2Rf = r**2*hmid*thita/2-r**2*hmid*sin(thita)/3 + r**2*h*thita/2hc = 3thita = x/180*pihmid = 1r = 5
EqnVar
PortP2Num=2S2P_Eqn
S2P1
Z[2]=Z[1]=S[2,2]=S[2,1]=S[1,2]=S[1,1]=if freq equals 1GHz then R1 elseif freq equals 2 GHz then R2 else R3 endif
1GHz: Vf12GHz: Vf23GHz: Vf3
-5
0
5
-5
0
50
1
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5
Proposed Coarse Model Using Only the Shift c(Cheng and Bandler, 2006)
volume Vc = [V/3 V/3 V/3] implies z + c = 120initially c = 0
zº
Vc3Vc2
Vc1
-5 -4 -3 -2 -1 0 1 2 3 4 50
1
2
3
4
5
ADS Implementation of Cake-Cutting Problem: Coarse Model (Cheng and Bandler, 2006)
PortP2Num=2
PortP1Num=1
VARVAR1
Vall = pi * r^2 * hcRc = hc * r**2*thita/2hc = 3thita = x/180*pir = 5
EqnVar VAR
VAR2
R3 =( Vall-Rc-Rc)/VallR2 = Rc/VallR1 = Rc/Vall
EqnVar
S2P_EqnS2P1
Z[2]=Z[1]=S[2,2]=S[2,1]=S[1,2]=S[1,1]=if freq equals 1GHz then R1 elseif freq equals 2 GHz then R2 else R3 endif
1GHz: Vc12GHz: Vc23GHz: Vc3
ADS Implementation of Cake-Cutting Problem: Initial Solution(Cheng and Bandler, 2006)
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.81.0 3.0
0.32
0.34
0.36
0.38
0.30
0.40
freq, GHz
mag
(S(1
,1))
freq1.000GHz2.000GHz3.000GHz
mag(S(1,1))0.3030.3030.395
Vf1Vf2Vf3
ADS Implementation of Cake-Cutting Problem: Third Iteration(Cheng and Bandler, 2006)
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.81.0 3.0
0.33320
0.33325
0.33330
0.33335
0.33340
0.33315
0.33345
freq, GHz
mag
(S(1
,1))
freq1.000GHz2.000GHz3.000GHz
mag(S(1,1))0.3330.3330.333
VARmappingX= 129.80972100829 opt{ unconst}
EqnVar
Vf1Vf2Vf3
EqnMeas
EqnMeas
EqnMeas
OptimOptim1
SaveCurrentEF=noUseAllGoals=yesUseAllOptVars=yes
SaveAllIterations=noSaveNominal=yesUpdateDataset=yesSaveOptimVars=noSaveGoals=yesSaveSolns=yesSeed= SetBestValues=yesNormalizeGoals=noFinalAnalysis="None"StatusLevel=4DesiredError=0.0MaxIters=25ErrorForm=MMOptimType=Minimax
OPTIM
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
VARVAR1x=120 opt{ unconst }
EqnVar
cake_coarse_modelcake_coarse1
21
Goalcoarse_optimal
RangeMax[1]=3 GHzRangeMin[1]=1 GHzRangeVar[1]="freq"Weight=Max=0Min=SimInstanceName="SP1"Expr="mag(S11)"
GOALTermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
Coarse Model Optimization (Cheng and Bandler, 2006)
exporting designparameterx valueto a file
frequency sweep
coarse model
specification optimization algorithm
Fine Model Simulation (Cheng and Bandler, 2006)
VARVAR1x=X
EqnVar
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
cake_fine_modelcake_fine_model1
1 2
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
fine model
frequency sweep
design parameter
Parameter Extraction (Cheng and Bandler, 2006)
VARVAR1c=0 opt{ unconst }
EqnVar
Goalfine_coarse_match_goal
RangeMax[1]=1.5 GHzRangeMin[1]=0.5 GHzRangeVar[1]="freq"Weight=Max=0Min=SimInstanceName="SP1"Expr="abs(mag(S33)-mag(S11))"
GOAL
EqnMeas
cake_coarse_modelcake_coarse1
21
EqnMeas
EqnMeas
VARVAR2x=X+c
EqnVar
Optimfine_coarse_match1
SaveCurrentEF=noGoalName[1]="fine_coarse_match_goal"OptVar[1]="c"
SaveAllIterations=noSaveNominal=yesUpdateDataset=yesSaveOptimVars=noSaveGoals=yesSaveSolns=yesSeed=SetBestValues=yesNormalizeGoals=noFinalAnalysis="None"StatusLevel=4DesiredError=0.0MaxIters=1000ErrorForm=L2OptimType=Quasi-Newton
OPTIM
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
TermTerm4
Z=50 OhmNum=4
TermTerm3
Z=50 OhmNum=3 S2P
SNP1File="C:\shasha\Research\ADS_SM_Framework_prj\data\cake_02_fine_simulation.ds"
21
Ref
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
exporting mapping parametervaluesto a file
fine model
coarse model
frequency sweep
matching goal
optimization algorithm
Surrogate Re-optimization (Cheng and Bandler, 2006)
Optimcoarse_opt
Sav eCurrentEF=noGoalName[1]="coarse_optimal"OptVar[1]="X"
Sav eAllIterations=y esSav eNominal=y esUpdateDataset=y esSav eOptimVars=y esSav eGoals=y esSav eSolns=y esSeed= SetBestValues=y esNormalizeGoals=y esFinalAnaly sis="None"StatusLev el=4DesiredError=-100MaxIters=1000ErrorForm=MMOptimTy pe=Minimax
OPTIM
Goalcoarse_optimal
RangeMax[1]=3 GHzRangeMin[1]=1 GHzRangeVar[1]="f req"Weight=Max=0Min=SimInstanceName="SP1"Expr="mag(S11)"
GOAL EqnMeas
EqnMeas
EqnMeas
VARVAR2x=X+c
EqnVar
VARVAR1X= 120 opt{ unconst }
EqnVar
cake_coarse_modelcake_coarse1
21
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
exporting parameters
coarse modelfrequency
sweep
specificationoptimization algorithm
mapping
ADS Space Mapping Implementation Automation Diagram(Cheng and Bandler, 2006)
AEL batch simulation program
AEL function save parametervalues to a file:writepara2d
AEL function to load parametervalues from a file: read_equation_from_file
ADS component to load response:SNP
VARVAR1x=X
EqnVar
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
cake_fine_modelcake_fine_model1
1 2
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
VARVAR1x=120 opt{ unconst }
EqnVar
cake_coarse_modelcake_coarse1
21
Goalcoarse_optimal
RangeMax[1]=3 GHzRangeMin[1]=1 GHzRangeVar[1]="freq"Weight=Max=0Min=SimInstanceName="SP1"Expr="mag(S11)"
GOAL
EqnMeas
EqnMeas
EqnMeas
OptimOptim1
SaveCurrentEF=noUseAllGoals=yesUseAllOptVars=yes
SaveAllIterations=noSaveNominal=yesUpdateDataset=yesSaveOptimVars=noSaveGoals=yesSaveSolns=yesSeed= SetBestValues=yesNormalizeGoals=noFinalAnalys is="None"StatusLevel=4DesiredError=0.0MaxIters=25ErrorForm=MMOptimType=Minimax
OPTIM
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
VARVAR1c=0 opt{ unconst }
EqnVar
Goalfine_coarse_match_goal
RangeMax[1]=1.5 GHzRangeMin[1]=0.5 GHzRangeVar[1]="freq"Weight=Max=0Min=SimInstanceName="SP1"Expr="abs(mag(S33)-mag(S11))"
GOAL
EqnMeas
cake_coarse_modelcake_coarse1
21
EqnMeas
EqnMeas
VARVAR2x=X+c
EqnVar
Optimfine_coarse_match1
SaveCurrentEF=noGoalName[1]="fine_coarse_match_goal"OptVar[1]="c"
SaveAllIterations=noSaveNominal=yesUpdateDataset=yesSaveOptimVars=noSaveGoals=yesSaveSolns=yesSeed=SetBestValues=yesNormalizeGoals=noFinalAnalysis="None"StatusLevel=4DesiredError=0.0MaxIters=1000ErrorForm=L2OptimType=Quasi-Newton
OPTIM
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
TermTerm4
Z=50 OhmNum=4
TermTerm3
Z=50 OhmNum=3 S2P
SNP1File="C:\shasha\Research\ADS_SM_Framework_prj\data\cake_02_fine_simulation.ds"
21
Re f
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
Optimcoarse_opt
Sav eCurrentEF=noGoalName[1]="coarse_optimal"OptVar[1]="X"
Sav eAllIterations=y esSav eNominal=y esUpdateDataset=y esSav eOptimVars=y esSav eGoals=y esSav eSolns=y esSeed= SetBestValues=y esNormalizeGoals=y esFinalAnaly sis="None"StatusLev el=4DesiredError=-100MaxIters=1000ErrorForm=MMOptimTy pe=Minimax
OPTIM
Goalcoarse_optimal
RangeMax[1]=3 GHzRangeMin[1]=1 GHzRangeVar[1]="f req"Weight=Max=0Min=SimInstanceName="SP1"Expr="mag(S11)"
GOAL EqnMeas
EqnMeas
EqnMeas
VARVAR2x=X+c
EqnVar
VARVAR1X= 120 opt{ unconst }
EqnVar
cake_coarse_modelcake_coarse1
21
S_ParamSP1
Step=1.0 GHzStop=3.0 GHzStart=1.0 GHz
S-PARAMETERS
TermTerm1
Z=50 OhmNum=1
TermTerm2
Z=50 OhmNum=2
User Instructions (Cheng and Bandler, 2006)
load our AEL functions
create the four schematics using the template, replacing the coarse and fine models, frequency sweep and variables
edit the list file to specify the folder and design names
click Load Queue to load the sequence
click Start Batch Simulation to run
ADS SM Implementation: Start(Cheng and Bandler, 2006)
click Start Batch Simulation
ADS SM Implementation of Two-section ImpedanceTransformer (Cheng and Bandler, 2006)
fine model
coarse model
RL=10Ω
L1 L2
Z in C1 C2 C3
RL=10Ω Zin
L1 L2
Z1 Z2
ADS SM Implementation of Two-section ImpedanceTransformer Using c and d, and Obtained in Four Iterations(Cheng and Bandler, 2006)
0.6 0.8 1.0 1.2 1.40.4 1.6
0.1
0.2
0.3
0.4
0.0
0.5
freq, GHz
|S11
|
Eqn m=max(mag(S(1,1))) m0.456
Spec_Err-0.044
Eqn Spec_Err=m-0.5
Space Mapping Technology: Our Current Work
new SM frameworks, SM modeling, SM optimization, software, convergence proofs, . . . (with S. Koziel, Reykjavik University)
antennas, metamaterials, microwaves, inverse problems, electromagnetic modeling and design (with M. Bakr and N. Nikolova, McMaster)
methodologies for electronic device and component modelenhancement (with Q.J. Zhang, Carleton University)
tuning space mapping and its applications (with J.C. Rautio, Sonnet Software)