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Space Mapping for Engineering Design and Optimization

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Space Mapping for Engineering Design and Optimization Powered By Docstoc
					Research in Engineering Optimization &
Modeling Center at Reykjavik University

                  Slawomir Koziel

        Engineering Optimization & Modeling Center
             School of Science and Engineering
                   Reykjavik University
                        koziel@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




                                                Flow separation on the
                                                back of the conning
                                                tower.
                                      V
                                    [m/s]
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
                                                      Flow separation on the
                                                      back of the conning
                                                      tower.
                                             V
                                           [m/s]




  Ocean science
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 compute
Surrogate-based design replaces direct optimization by iterative re-optimization and
updating of the surrogate:
Example: Design of Hairpin Filter Using Space Mapping
                                                                                                                      S1       La
                                                                                                    S2       Lb
Fine model: Simulation time                                     S1        Lb     S2        2Lc                                                                          L2
                                                       La
17 hours per design!                                                                                                                                                       L1
                                                                                                                                           L3
                              L2                                                                                         L4
                                                                     L3               L4
                                                                                                                                                                                   H
                                   L1

                                                     r

Coarse model: Equivalent                    MSOBND TL4
                                                      MLIN
                                                               MSOBND
                                                               Bend2
                                                                         MLOC
                                                                                          MSOBND TL10
                                                                                          Bend5
                                                                                                    MLIN
                                                                                                              MSOBND
                                                                                                    W=W mm Bend6
                                                                                                                                         MSOBND TL16
                                                                                                                                         Bend9
                                                                                                                                                    MLIN
                                                                                                                                                             MSOBND
                                                                                                                                                    W=W mm Bend10

circuit – simulation time
                                            Bend1     W=W mm             TL6              W=W mm L=L6 mm W=W mm MLOC                     W=W mm L=L4 mm W=W mm
                                            W=W mm L=L4 mm W=W mm W=W mm                                               TL12
                                                                         L=1e-9 mm                                     W=W mm
                               Term 1                                          MLOC                                    L=1e-9 mm                                        Term 2
                                                                                                                                                       MLIN
                               Z=50 Ohm                                        TL8                                            MLOC                                      Z=50 Ohm

less than 0.1s                 MLIN
                                                  MLIN
                                                  TL3
                                                  W=W mm
                                                                               W=W mm
                                                                               L=1e-9 mm
                                                                                                MCLIN
                                                                                                Clin2
                                                                                                W=W mm
                                                                                                                              TL14
                                                                                                                              W=W mm
                                                                                                                              L=1e-9 mm
                                                                                                                                               MCLIN
                                                                                                                                               Clin4
                                                                                                                                               W=W mm
                                                                                                                                                       TL17
                                                                                                                                                       W=W mm
                                                                                                                                                       L=d mm
                                                                                                                                                                        MLIN
                               TL1                                       MCLIN                                         MCLIN                                            TL19
                                                  L=d mm                 Clin1                  L=L3 mm                                        L=L2 mm
                               W=W mm                                                                                  Clin3                                            W=W mm
                               L=L0 mm                                   W=W mm                                        W=W mm                                           L=L0 mm
                                                                                                       MLOC                                    MLOC
                                                                         L=L2 mm                                       L=L3 mm
                                                                                                       TL11                                    TL15
                                                           MLOC
                                                           TL5                                  MLOC W=W mm                                    W=W mm
                                      MTEE                                                      TL9    L=1e-9 mm                               L=1e-9 mm
                                                           W=W mm                                                                                                 MTEE
                                      Tee1                                                      W=W mm
                                                           L=1e-9 mm                                                                                              Tee2
                                      W=W mm                                                    L=1e-9 mm
                                                  MLOC                                                                                                MLOC        W=W mm
                                      W2=W mm
                                                  TL2              MSOBND MLIN         MSOBND                    MSOBND MLIN          MSOBND          TL18        W2=W mm
                                      W3=W mm
                                                  W=W mm           Bend3     TL7       Bend4                     Bend7      TL13      Bend8           W=W mm      W3=W mm
                                                  L=L1-d-W mm      W=W mm W=W mm W=W mm                          W=W mm W=W mm W=W mm                 L=L1-d-W mm
                                                                             L=L5 mm                                        L=L5 mm




Surrogate: Coarse model composed with auxiliary transformation
            Example: Design of Microstrip Hairpin Filter
            Traditional design methods fail for this example
            Space Mapping: Optimal design obtained after 5 EM simulations!

                           0                                                                                              0

                          -10                                                                                            -10




                                                                                               | S11| and | S21| in dB
| S11| and | S21| in dB




                          -20                                                                                            -20

                          -30                                                                                            -30

                          -40                                                                                            -40

                          -50                                                                                            -50

                          -60                                                                                            -60
                             3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4   4.6   4.8   5.0                                3.0    3.2   3.4   3.6   3.8   4.0   4.2   4.4   4.6   4.8   5.0
                                                     frequency (GHz)                                                                                 frequency (GHz)

                          Initial responses and design specifications                                                             Responses of the optimized filter
Invasive Methods: Simulation-Based Tuning
                                                                            fine model                                              co-calibrated ports
Tuning SM constructs the surrogate
by replacing designable sub-sections                             design                                                                   responses
                                                               parameters
of the structure with suitable
circuit-based components
                                                                                                                                          responses
                                                             embedded
Example: Microstrip filter                                tuning element
                                                                                                     tuning model
with co-calibrated ports
                                                                              2                                                 2

and its tuning model                                                   4                5                            8               9                   2
                                                      MLOC                              11                           14                    MLIN
                                                      W=W                                         MACLIN                                   W=W




                                                                                  15




                                                                                                                           17
                                                                                                  W1=W         MLIN                        L=L2-L3/2-2
                                                      L=L1-L2-L3/2-2
                                                                                                               W=W1
                               L2                                                      MLIN       W2=W1
                                                                                                               L=L4-0.4
                                                                                       W=W1       S=S2
                                                                                                  L=L3-0.4 MCLIN
                                                                                       L=L4-0.4
                                                                                                           W=W1
W                                   2    Output                                                            S=S1




                                                                                  20




                                                                                                                           22
                                                                                                           L=L3/2-0.2
                                                                                        23                            26
                                         S2                                                                       30
                          L4                                                            27
                                                                                              MCLIN   MGAP
                 g




                                                                                  31




                                                                                                                           33
                               S1                                                             W=W1    W=W1
            W1                                                                                S=S1    S=g
                                                                                       MLIN L=L3/2-0.2 MACLIN MLIN
                                                                                       W=W1            W1=W     W=W1
                     L3                                                                L=L4-0.4        W2=W1 L=L4-0.4
                                                                                                       S=S2

                                                                                  36




                                                                                                                           38
                                        S2                                                             L=L3-0.4
                                                                                         39                       42

Input   1                                         1                    44               45                           48              49
                                                        MLIN                                                                               MLOC
                                                        W=W                                                                                W=W
                                                        L=L2-L3/2-2                                                                        L=L1-L2-L3/2-2
                     L1
   Example: Box-Section Chebyshev Microstrip Bandpass Filter
   Filter structure with places                                                                                    Tuning model:
   for inserting the tuning ports:                                                                                                                                 Lt5                             Lt4

                          S1                                                                    S1                                                                                  Lt5     Lt4
        Input                                                                                         Output                                                          28 27 26 25 24 23 22
                                                                                                                                                                    1                     21
        1                                                                                                  2
                                                                                                                                                                                                            Lt3
                                                                                                                                                                    2                             20
                                            S2                              S2                                        Term 1
                                                                                                                                                                    3                             19
                                                                  W                                                   Z=50 Ohm
                                                                                                                                   Term 2                                            S28P
                                                                                                                                                                    4                             18
                                                     25 26        27 28                                                            Z=50 Ohm   Ct1                                    SNP1
                                                                                                                                                                    5                             17
                                                     L5
                                                                                                                                                                    6                             16                        Ct2
                L1    3
                      4
                               5
                               6
                                                                                            7
                                                                                            8
                                                                                                 9
                                                                                                 10
                                                                                                                                                                                                          Ct2
                                                             19
                                                                   L3                                                                         Lt1                   7                            15
                                                             20
                                   L2      11
                                           12
                                                13
                                                14
                                                                          15
                                                                          16
                                                                               17
                                                                               18
                                                                                                                                                                         8     9   10 11 12 13 14 Ref             Lt2

                                                                                    L4                                                              Ct1


                                   21 22                     W1                     23 24
                                                                                                                                                             Ct1                   Ct1      Ct2           Ct2
                                                W                                   W            W                                                                       Lt1                      Lt2



                     Coarse (- - -) and fine model ()                                                                             Fine model response after
                      response at the initial design                                                                                 one (!) TSM iteration
            0                                                                                                               0
        -10                                                                                                                -10
        -20                                                                                                                -20
|S21|




                                                                                                                   |S21|




        -30                                                                                                                -30
        -40                                                                                                                -40
        -50                                                                                                                -50
          1.8                        2                2.2    2.4    2.6                                 2.8    3             1.8         2                2.2    2.4    2.6                              2.8            3
                                                       Frequency [GHz]                                                                                     Frequency [GHz]
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 wing
can take up to several days on a typical workstation.
            High-                                       Low-speed
            speed

                        Shock
                                            Mach contours and streamlines
          Mach contours
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.
       1.5                                                                                                         1.4
                                            Initial               0.6                                 Initial      1.3
                                                                                                                   1.2
                                            Optimized                                                              1.1
         1                                                        0.4                                              1.0
                                                                                                                   0.9




                                                            z/c
              Target                     Initial                  0.2
                                                                                                                   0.8
                                                                                                                   0.7
       0.5                                                                                                         0.6
                                                                                                                   0.5
 -Cp




                                                                                                                   0.4
                                                                  0.0
                                                                                                                   0.3
                                                                                                                   0.2
         0                                                              0.0   0.2   0.4
                                                                                          x/c
                                                                                                0.6    0.8   1.0
                                                                                                                   0.1

                                                                                                                   1.4
       -0.5                                                   0.6                           Optimized              1.3
                                                                                                                   1.2
                                                                                                                   1.1
                                                              0.4                                                  1.0
                                                                                                                   0.9
        -1
          0   0.2      0.4         0.6     0.8          1   z/c                                                    0.8
                                                                                                                   0.7
                             x/c                              0.2
                                                                                                                   0.6
  Surrogate-based optimization gives 92% in                                                                        0.5
                                                                                                                   0.4
                                                              0.0
  CPU cost compared to direct optimization.                                                                        0.3
                                                                                                                   0.2
                                                                        0.0   0.2   0.4         0.6    0.8   1.0
                                                                                          x/c                      0.1
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 Rs(i ) ( x )  A( x ) Rc ( 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 solution
u* – result of direct Rf optimization
ud – result of direct Rc optimization
ud – 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 System
                            Tuning Model
                                                                                  Lt3
                                                                                                                                    Ct

SMF implements:
                                                                                                                                                             Ct
                                                                                                           Lt2                               Lt1
                                                                                        26 25 24 23 22 21
                                                                             1




 Major SBO algorithms
                                                                             2                                                 20

                                                                             3                                                 19
                                                        Lt3                                           S26P
                                                                             4                                                 18
                                                                                                      SNP1                                        Lt3
                                     Term 1                                  5                                                 17
                                     Z=50 Ohm
                                                                             6                                                 16



  and modeling schemes
                                                         Lt3                                                                                      Lt3
                                                                             7                                 15
                                                                                 8       9       10 11 12 13 14 Ref

                                            Term 2




 Sockets for major EM/
                                            Z=50 Ohm
                                                                                                                                Lt3

                                                                                                                    Lt2
                                                                   Ct            Lt1             Ct


                           Calibration Model
  circuit simulators
                                                                                                           MACLIN                         MACLIN
                                                                                                           Clin2                          Clin3
                                                                             C                             W1=0.5 mm                      W1=0.5 mm
                                                                  MACLIN     C1
                                                                  Clin1                                    W2=0.25 mm C                   W2=0.25 mm       MLOC
                                                                             C=Ct pF                       S=S mm                         S=S mm
                                                                  W1=0.5 mm                                           C2                                   TL17




 Internal scripting
                                                                  W2=0.25 mm                               L=Lt1 mm   C=Ct pF             L=L1/2 mm        W=0.25 mm
                                                     MLIN         S=S mm                                                                                   L=1E-9 mm
                                                     TL3          L=L1/2 mm                                                                                 MLOC
                                                     W=0.25 mm
                                                                                                                                                            TL18
                                                     L=2*Lt3 mm
                                                                                                                                                            W=0.25 mm
                                     MLIN
                                                                                                                                                            L=1E-9 mm
                                     TL2                          MLIN                    MLIN                   MLIN            MLIN                 MLIN
                                                 MTEE
                                     W=0.25 mm                    TL4                     TL5                    TL6             TL7                  TL8
                             MLIN                Tee1
                                     L=L3 mm                                                                                                          W=0.5 mm MLIN


  language
                                                 W1=0.25 mm       W=0.25 mm               W=0.5 mm               W=0.5 mm        W=0.5 mm
                             TL1                                                                                                                      L=L3 mm TL16
                                                 W2=0.5 mm        L=L3 mm                 L=L2 mm                L=Lt2 mm        L=Lt3 mm
                             W=0.25 mm                                                                                                                         W=0.25 mm
                             L=3 mm              W3=0.25 mm                                                                     MTEE                           L=3 mm
                                                                                                                                Tee2
                                     MLIN                                                                                       W1=0.25 mm




 Distributed computing
                                     TL9                                                                                        W2=0.5 mm
                                     W=0.5 mm        MLIN         MLIN                 MLIN                      MLIN           W3=0.25 mm            MLIN
                                     L=L3 mm         TL10         TL11                 TL12                      TL13                                 TL15
                                                     W=0.5 mm     W=0.5 mm             W=0.5 mm                  W=0.25 mm                            W=0.25 mm
                                     MLOC            L=Lt3 mm     L=Lt2 mm             L=L2 mm                   L=L3 mm                              L=L3 mm
                          Term 1     TL7                                                                                                                          Term 2
                                     W=0.25 mm                                                                                                                    Z=50 Ohm
                          Z=50 Ohm                                                                                         MLIN
                                     L=1E-9 mm                                                                  MACLIN     TL14



  capabilities
                                                                                                                Clin6      W=0.25 mm
                                MLOC
                                TL7
                                W=0.25 mm MACLIN     C             MACLIN
                                                                                                                W1=0.5 mm L=2*Lt3 mm
                                                                                                                W2=0.25 mm                                                                                                                    Tuning Model   Calibration
                                                     C3                                         C               S=S mm
                                L=1E-9 mm Clin4                    Clin5
                                          W1=0.5 mm C=Ct pF
                                          W2=0.25 mm
                                                                   W1=0.5 mm
                                                                   W2=0.25 mm
                                                                                                C4
                                                                                                C=Ct pF
                                                                                                                L=L1/2 mm
                                                                                                                                                                                                                                              Optimization
                                          S=S mm                   S=S mm
                                          L=L1/2 mm                L=Lt1 mm



                           Fine Model
                                                     Input                                       S                                       Output
                                                                             L3                       L1

                                                                                                      L3
                                                                                                                                                                  SMF Script
                                                                                                      L3
                                                                                                                                                                       SO var $x0
                                                                                                                                                                       EVAL_RF $Rf0 $x0

                                                                                       L2                                                                              % evaluation of the "cut" model
                                                                                                                                                                       SET_MODEL fine db cut_fine_model
                                                                                                              S                                                        EVAL_RF $Rfc0 $x0


                           “Cut” Fine Model                                                                                                                            % finding initial values of the tuning variables
                                                                                                                                                                       SET_MODEL coarse db tuning_model
                                                                                                                                                                       SET_OPT_TYPE lsquare
                                                     Input                                       S                                       Output                        SET_SPECS_TARGET $Rfc0
                                                 1                                        8 10                                                    2                    LOAD_SO_SETUP $lsquare_so_setup
                                                                                 L3       7 9         L1                                                               SO var $xt0
                                                                                 5 6                    11 12
                                                                        4
                                                                                                                                                                       % optimization of the tuning model; optimal response stored in Rtopt
                                                                                                                          13
                                                                        3                             L3                  14
                                                                                                                                                                       SET_MODEL fine db fine_dummy
                                                                                                                                                                       SET_MODEL coarse db tuning_model
                                                                        26                                                                                             LOAD_SO_SETUP $tuning_so_setup
                                                                        25                            L3                  15
                                                                                                                          16                                           SO var $xt1
                                                                                        24 23                    18 17                                                 EVAL_RS $Rt_opt $xt1
                                                                                                      22 19
                                                                                       L2             21 20


                                                                                                                S
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

				
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