Design Optimization Via Surrogate Modeling and Space Mapping · Design Optimization Via Surrogate Modeling and Space Mapping Qingsha Cheng, John W. Bandler and Koziel Slawek presented

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


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

z

0 2 4 6 8 10 12 14 16 18 20 22 01

024

x




0 2 4 6 8 10 12 14 16 18 20 22 01

024

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0 2 4 6 8 10 12 14 16 18 20 22 01

024

x




0 2 4 6 8 10 12 14 16 18 20 22 01

024

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0 2 4 6 8 10 12 14 16 18 20 22 01

024

x




0 2 4 6 8 10 12 14 16 18 20 22 01

024

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0 2 4 6 8 10 12 14 16 18 20 22 01

024

x




0 2 4 6 8 10 12 14 16 18 20 22 01

024

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0 2 4 6 8 10 12 14 16 18 20 22 01

024

x




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



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


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


Broyden update


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


Frontal Impact (Nilsson and Redhe, 2005, Sweden)


Frontal Impact (Nilsson and Redhe, 2005, Sweden)


(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


CLin3


CLin2


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


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.


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


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


MSOBND_MDSBend1


MSOBND_MDSBend2


MTEETee1

W3=65 milW2=40 milW1=40 milSubst="MSub1"


coarse model optimization


fine model in Sonnet em


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


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


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


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


Ref

TLOCTL8


Ref

TLOCTL9


Ref

TLINTL4


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)


Tuning Space Mapping (TSM): Type 1 and Type 0 Embedding (Cheng et al., 2009)


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)


Motorola LTCC Quad Band Receiver(Rautio, 2006, Sonnet Software)


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


calibration model = coarse model + tuning elements

calibration goal: translate the “tuned” tuning parameter valuesto physical design parameter values


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

|

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


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


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


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


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


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


(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)


fine model simulation


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

2

3

4

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


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


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


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


21

S_ParamSP1


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


S-PARAMETERS

cake_fine_modelcake_fine_model1

1 2

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=50 OhmNum=2

VARVAR1x=120 opt{ unconst }

EqnVar


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


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


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


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


21

S_ParamSP1


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)

Documents

Design Optimization Via Surrogate Modeling and Space Mapping · Design Optimization Via Surrogate Modeling and Space Mapping Qingsha Cheng, John W. Bandler and Koziel Slawek presented