Research in Engineering Optimization & Modeling Center at Reykjavik University

Slawomir Koziel

Engineering Optimization & Modeling CenterSchool of Science and Engineering

Reykjavik Universitykoziel@ru.is

presented at

Reykjavik University, March 17, 2011

Engineering Optimization & Modeling Center (EOMC)

EOMC is a research group within the School of Science and Engineering, Reykjavik University

Members: Slawomir Koziel Leifur Leifsson Stanislav Ogurtsov

Website:http://eomc.ru.is

EOMC: Background and Motivation

Contemporary engineering is more and more dependent on computer simulation

Increasing complexity of structures and systems and higher demand for accuracy make engineering design challenging due to: Lack of “design applicable” theoretical models High computational cost of accurate simulation

Simulation-driven design becomes a must for growing number of engineering fields

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[m/s]

Flow separation on the back of the conning tower.

EOMC: Research Outline

Research outline: EOMC develops efficient optimization and modeling techniques for computationally expensive real-world engineering design problems

Application areas:

Microwave/RF engineering

Aerospace design

Aeroacoustics

Hydrodynamics

Ocean science

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[m/s]

Flow separation on the back of the conning tower.

EOMC: Research Outline

Selected topics: Algorithms for rapid optimization of expensive objective functions Surrogate-based and knowledge-based techniques Tuning methodologies High-performance distributed computing Interfacing major microwave/RF CAD software packages

Selected applications: Simulation-based design of RF/microwave components and circuits Development of component models for CAD/EDA software Inverse design in electromagnetic and aerodynamics Aerodynamic and hydrodynamic optimization Multidisciplinary design and optimization  Optimization of ocean models

Simulation-Driven Microwave Design Using Surrogate Models

Traditional design methods employing EM solver in an optimization loop are impractical due to: High computational cost of EM simulation Poor analytical properties of EM-based objective functions Lack of sensitivity information or sensitivity expensive to computeSurrogate-based design replaces direct optimization by iterative re-optimization and updating of the surrogate:

Example: Design of Hairpin Filter Using Space Mapping

Fine model: Simulation time 17 hours per design!

Coarse model: Equivalent circuit – simulation time less than 0.1s

Surrogate: Coarse model composed with auxiliary transformation

S1

r

H

S2

L1

L2

La

L3L4

2LcLb

S2S1Lb

La

L4

L3

L2

L1

Term 1Z=50 Ohm

Term 2Z=50 Ohm

MTEETee1W=W mmW2=W mmW3=W mm

MLINTL1W=W mmL=L0 mm

MLOCTL5W=W mmL=1e-9 mm

MLINTL3W=W mmL=d mm

MSOBNDBend1W=W mm

MSOBNDBend2W=W mm

MLINTL4W=W mmL=L4 mm

MLOCTL8W=W mmL=1e-9 mm

MSOBNDBend3W=W mm

MSOBNDBend4W=W mm

MLINTL7W=W mmL=L5 mm

MCLINClin1W=W mmL=L2 mm

MLOCTL2W=W mmL=L1-d-W mm

MSOBNDBend7W=W mm

MSOBNDBend8W=W mm

MLINTL13W=W mmL=L5 mm

MSOBNDBend5W=W mm

MSOBNDBend6W=W mm

MLINTL10W=W mmL=L6 mm

MSOBNDBend9W=W mm

MSOBNDBend10W=W mm

MLINTL16W=W mmL=L4 mm

MLOCTL6W=W mmL=1e-9 mm

MCLINClin2W=W mmL=L3 mm MCLIN

Clin3W=W mmL=L3 mm

MCLINClin4W=W mmL=L2 mm

MLOCTL9W=W mmL=1e-9 mm

MLOCTL11W=W mmL=1e-9 mm

MLOCTL12W=W mmL=1e-9 mm

MLOCTL14W=W mmL=1e-9 mm

MLOCTL15W=W mmL=1e-9 mm

MLINTL17W=W mmL=d mm

MLOCTL18W=W mmL=L1-d-W mm

MTEETee2W=W mmW2=W mmW3=W mm

MLINTL19W=W mmL=L0 mm

Example: Design of Microstrip Hairpin Filter

Traditional design methods fail for this example

Space Mapping: Optimal design obtained after 5 EM simulations!

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.83.0 5.0

-50

-40

-30

-20

-10

-60

0

frequency (GHz)

|S11

| an

d |S

21|

in d

B

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.83.0 5.0

-50

-40

-30

-20

-10

-60

0

frequency (GHz)

|S11

| an

d |S

21|

in d

BInitial responses and design specifications Responses of the optimized filter

Invasive Methods: Simulation-Based Tuning

Tuning SM constructs the surrogate by replacing designable sub-sections of the structure with suitable circuit-based components

Example: Microstrip filterwith co-calibrated portsand its tuning model

responses

design parameters

responses

fine model

tuning model

embedded tuning element

co-calibrated ports

L2

S2

W1

L3

S2

L1

W Output

Input

L4

S1

2

1

g

MACLINW1=W W2=W1 S=S2 L=L3-0.4

24 8

48

27 30

23 26

3115

20 223836

MLINW=W1 L=L4-0.4

MGAPW=W1 S=g

MCLINW=W1 S=S1 L=L3/2-0.2

MCLINW=W1 S=S1 L=L3/2-0.2

MACLINW1=W W2=W1 S=S2 L=L3-0.4

1733

MLINW=W1 L=L4-0.4

MLINW=W1 L=L4-0.4

MLINW=W1 L=L4-0.4

MLOCW=W L=L1-L2-L3/2-2

MLINW=W L=L2-L3/2-2

MLINW=W L=L2-L3/2-2

441MLOCW=W L=L1-L2-L3/2-2

14

5

11

45

39 42

2 2

9

49

Example: Box-Section Chebyshev Microstrip Bandpass Filter

Filter structure with places Tuning model: for inserting the tuning ports:

Coarse (- - -) and fine model () Fine model response after response at the initial design one (!) TSM iteration

L3

Input Output

W1

L4

S2

S1

S2

L5

L1

L2

W

W

WW

1

34

56

1112

1314

1516

1718

78

91019

20

21 22 23 24

25 26 27 28

2

S1

1

2

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21

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28 27 26 25 24 23 22

8 9 10 11 12 13 14 Ref

S28PSNP1

Term 2Z=50 Ohm

Term 1Z=50 Ohm

Lt1

Ct1

Ct1

Ct1 Ct1 Ct2 Ct2

Ct2

Ct2

Lt1 Lt2

Lt2

Lt3

Lt4

Lt4Lt5

Lt5

1.8 2 2.2 2.4 2.6 2.8 3-50

-40

-30

-20

-10

0

Frequency [GHz]

| S21

|

1.8 2 2.2 2.4 2.6 2.8 3-50

-40

-30

-20

-10

0

Frequency [GHz]

| S21

|

Aerodynamic Design Optimization

Design wing shapes which provide the right combination of lift and drag.

CFD models are essential design tools.

CFD models are accurate but can be extremely computationally heavy.

A simulation of steady flow past a wingcan take up to several days on a typical workstation.

Shock

High-speed

Mach contoursMach contours and streamlines

Low-speed

Example: Inverse design of 2D airfoil sections

Objective: Match a given pressure distribution by design of airfoil shape.

Fine model: RANS equations with Spalart-Allmaras turbulence model.

Coarse model: Same as fine, but with coarse grid and relaxed convergence criteria.

Surrogate-based optimization gives 92% in CPU cost compared to direct optimization.

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

1.5

x/c

-Cp

InitialOptimized

x/c

z/c

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.61.41.31.21.11.00.90.80.70.60.50.40.30.20.1

x/c

z/c

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.61.41.31.21.11.00.90.80.70.60.50.40.30.20.1

InitialTarget

Initial

Optimized

Optimization of Ocean Models

Task: Calibration of the ocean model (model response: concentration of various components, e.g., zooplankton, versus time)

Rf: high-resolution time-domain simulation (integration using small time steps)Rc: low-resolution time-domain simulation (integration using larger time steps)

The surrogate: response-corrected low-fidelity model ( ) ( ) ( ) ( )is cR x A x R x

Optimization of Ocean Models

Multiplicative correction is suitable to create a surrogate model in this case:

High-fidelity model response at:ud – target; u0 – initial solutionu* – result of direct Rf optimizationud – result of direct Rc optimizationud – result of surrogate-based optimization

Surrogate-based optimization gives 84% savings in computational cost compared to direct Rf optimization (60 versus 375 high-fidelity model evaluations)

Surrogate-Based Modeling and Optimization Software

SMF system: in-house GUI-based Matlab toolbox (over 120000 code lines) for surrogate-based optimization.

SMF implements: Major SBO algorithms and modeling schemes Sockets for major EM/ circuit simulators Internal scripting language Distributed computing capabilities

1

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5

6

7

20

19

18

17

16

15

26 25 24 23 22 21

8 9 10 11 12 13 14 Ref

S26PSNP1

Term 2Z=50 Ohm

Term 1Z=50 Ohm

Ct CtLt1

Lt1

Lt3

Lt2

Ct Ct

Lt3

Lt3

Lt3

Lt3

Lt2

Lt3

L1L3

L2

Input OutputS

L3

L3

S

43

2625

1314

1516

24 23

11 12

87

109

2221

1920

1 2

5 6

18 17

SO var $x0EVAL_RF $Rf0 $x0

% evaluation of the "cut" modelSET_MODEL fine db cut_fine_modelEVAL_RF $Rfc0 $x0

% finding initial values of the tuning variablesSET_MODEL coarse db tuning_modelSET_OPT_TYPE lsquareSET_SPECS_TARGET $Rfc0LOAD_SO_SETUP $lsquare_so_setupSO var $xt0

% optimization of the tuning model; optimal response stored in RtoptSET_MODEL fine db fine_dummySET_MODEL coarse db tuning_modelLOAD_SO_SETUP $tuning_so_setupSO var $xt1EVAL_RS $Rt_opt $xt1

SMF System

L1L3

L2

Input OutputS

L3

L3

S

Tuning Model

Term 1Z=50 Ohm

Term 2Z=50 Ohm

MLOCTL17W=0.25 mmL=1E-9 mm

MLOCTL18W=0.25 mmL=1E-9 mm

MLOCTL7W=0.25 mmL=1E-9 mm

MLOCTL7W=0.25 mmL=1E-9 mm

CC3C=Ct pF

CC4C=Ct pF

CC1C=Ct pF

CC2C=Ct pF

MLINTL16W=0.25 mmL=3 mm

MLINTL1W=0.25 mmL=3 mm

MLINTL3W=0.25 mmL=2*Lt3 mm

MLINTL2W=0.25 mmL=L3 mm

MLINTL4W=0.25 mmL=L3 mm

MLINTL5W=0.5 mmL=L2 mm

MLINTL6W=0.5 mmL=Lt2 mm

MLINTL7W=0.5 mmL=Lt3 mm

MLINTL10W=0.5 mmL=Lt3 mm

MLINTL11W=0.5 mmL=Lt2 mm

MLINTL12W=0.5 mmL=L2 mm

MLINTL13W=0.25 mmL=L3 mm

MLINTL14W=0.25 mmL=2*Lt3 mm

MLINTL15W=0.25 mmL=L3 mm

MLINTL8W=0.5 mmL=L3 mm

MLINTL9W=0.5 mmL=L3 mm

MACLINClin1W1=0.5 mmW2=0.25 mmS=S mmL=L1/2 mm

MACLINClin2W1=0.5 mmW2=0.25 mmS=S mmL=Lt1 mm

MACLINClin3W1=0.5 mmW2=0.25 mmS=S mmL=L1/2 mm

MACLINClin6W1=0.5 mmW2=0.25 mmS=S mmL=L1/2 mm

MACLINClin5W1=0.5 mmW2=0.25 mmS=S mmL=Lt1 mm

MACLINClin4W1=0.5 mmW2=0.25 mmS=S mmL=L1/2 mm

MTEETee1W1=0.25 mmW2=0.5 mmW3=0.25 mm MTEE

Tee2W1=0.25 mmW2=0.5 mmW3=0.25 mm

Calibration Model

Fine Model

“Cut” Fine Model

SMF Script

Tuning Model Optimization

Calibration

EOMC: International Collaboration

Collaborating institutions: McMaster University (Canada) Stanford University (USA) Technical University of Denmark ITESO (Mexico) Carleton University (Canada) Gent University (Belgium) Christian Albrechts University (Germany) University of Pretoria (South Africa) North Carolina State University (USA) National Physical Laboratory (UK) Gdansk University of Technology (Poland) Sonnet Software Ltd. (USA) Computer Simulation Technology AG (Germany)

Research Opportunities with EOMC

EOMC offers a number of research projects for students pursuing Masters/PhD degrees in Electrical or Mechanical Engineering

Example projects in Electrical Engineering: Surrogate-based optimization techniques for computer-aided microwave design Simulation-based tuning for microwave design optimization Design of antennas for personal communication using surrogate models

Example projects in Mechanical Engineering: Efficient aerodynamic shape optimization using physics-based models Development of flapping-wing unmanned air vehicles

All the projects involve numerical simulations using both EM solvers and circuit simulators (Electrical Engineering projects) and computational-fluid dynamics solvers (Mechanical Engineering projects), Matlab programming, as well as working with various optimization and modeling techniques