Why Space Mapping Works J.W. Bandler, Q.S. Cheng, S. Koziel, and - PowerPoint PPT Presentation

Why Space Mapping Works J.W. Bandler, Q.S. Cheng, S. Koziel, and K.Madsen Simulation Optimization Systems Research Laboratory McMaster University, www.sos.mcmaster.ca, bandler@mcmaster.ca Bandler Corporation, www.bandler.com, john@bandler.com Technical University of Denmark, www.dtu.dk, km@imm.dtu.dk presented at SURROGATE MODELLING AND SPACE MAPPING FOR ENGINEERING OPTIMIZATION (SMSMEO-06) Technical University of Denmark, Lyngby, Denmark, November 9-11, 2006

The Space Mapping Concept ( Bandler et al., 1994- ) validation space (high-fidelity mapping physics model) surrogate (surrogate update optimization) prediction (low-fidelity physics model) optimization space

Linking Companion Coarse (Empirical) and Fine (EM) Models ( Bandler et al., 1994- ) responses responses coarse design fine design parameters parameters model model ∇ × = ω + H D J j D ε = E ∇ B = � 0 ∇ × = − ω E B j ∇ D = ρ � B μ = H (high-fidelity (low-fidelity physics model) physics model)

Why Does Space Mapping Work? because space mapping is a natural mechanism for the brain to relate objects or images with other objects, images, reality, or experience “experienced” engineering designers (experts), knowingly or not, routinely employ (or have employed) space mapping to achieve complex designs with virtually no mathematics, simple everyday examples illustrate space mapping , e.g., archery, stone-throwing, cheese-cutting, log-cutting, cake-cutting, shoe-selection, . . . the following illustrations of the “cheese-cutting problem” are interpreted as if for implicit space mapping

Implicit, Input and Output Space Mappings ( Bandler et al., 2003 )

Cheese-Cutting Problem Tutorial: Input Space Mapping ( Bandler et al., 2004 ) = *(0) 10 x c 1 3 = (0) 10 x f 1 3 x = 10 c 3 c = − 2 *(1) = 12 x c 3 c = − 2 (1) = 12 x f error = 0 the “coarse” brick is idealized, the algorithm is non-expert

Space Mapping Design of Dielectric Resonator Multiplexers ( Ismail et al., 2003, Com Dev, Canada ) 10-channel output multiplexer, 140 variables, Aggressive SM

Cheese-Cutting Problem Tutorial: Implicit Space Mapping ( Bandler et al., 2004 ) *(0) = 10 x c 1 = (0) 3 x = (0) 10 x f 1 3 x = 10 c = (1) 2.4 x = *(1) 12.5 x c = (1) 12.5 x f 1 3 the “coarse” brick is idealized, the algorithm is non-expert

Cheese-Cutting Problem Tutorial: Implicit Space Mapping = *(1) 12.5 x c = (1) 12.5 x f 1 3 = *(1) 12.5 x c = (2) 2.52 x = *(2) 11.9 x c = (2) 11.9 x f 1 3 error − 30 29.7 × = 100% 30 =1%

Implicit Space Mapping Design of Thick, Tightly Coupled Conductors ( Rautio, 2004, Sonnet Software ) thick, closely spaced conductors on silicon (fine model) “space-mapping” (top) layer (coarse model)

EPCOS LTCC/Feb 04 ( Rautio, 2006, Sonnet Software ) ( courtesy Rautio, 2006 )

Cheese-Cutting Problem Tutorial: Output Space Mapping ( Bandler et al., 2004 ) = *(0) 10 x c 1 3 = (0) 10 x f 1 3 x = d = − 10 6 c 3 d = − *(1) = 6 12 x c 3 (1) = 12 x f error = 0 the “coarse” brick is idealized, the algorithm is non-expert

Space Mapping: a Glossary of Terms (parameter/input) space mapping mapping, transformation or correction of design variables (response) output space mapping 1 mapping, transformation or correction of responses response surface approximation linear/quadratic/polynomial approximation of responses w.r.t. design variables 1 advocated by John E. Dennis, Jr., Rice University 1 Alexandrov’s “high-order model management”

Space Mapping: (1) for Design Optimization, (2) for Modeling Start Start select models and select models and mapping framework mapping framework optimize coarse model generate base and test points simulate fine model simulate fine model points multi-point parameter yes criterion extraction End satisfied no test SM-based model update surrogate (match models) interpolate responses optimize surrogate (prediction) End

Implicit, Input and Output Space Mappings ( Bandler et al., 2003 )

High-Temperature Superconducting (HTS) Filter: Modeling + Optimization Sonnet em fine model Agilent ADS coarse model ( Westinghouse, 1993 ) ( Bandler et al., 2004 ) S L 0 S Coarse Model 2 1 L 1 L 2 S-PARAMETERS S 3 S_Param MLIN L 3 Term SP1 TL2 SweepVar="freq" Term2 Subst="MSub" Num=2 Start=3.901 GHz MCLIN W=W mil Stop=4.161 GHz Z=50 Ohm L 2 CLin5 L=50.0 mil H Step=0.02 GHz Subst="MSub" MCLIN Mod=Kirschning W=W mil CLin4 S=S1c mil L 1 Subst="MSub" MCLIN L=L1c mil W=W mil CLin3 S=S2c mil MSub Subst="MSub" MCLIN L 0 L=L2c mil W=W mil CLin2 MSUB Term S=S3c mil W Subst="MSub" MSub Term1 MLIN MCLIN L=L3c mil W=W mil H=20 mil ε r Num=1 TL1 CLin1 S=S2c mil Er=23.425 Z=50 Ohm Subst="MSub" Subst="MSub" L=L2c mil Mur=1 W=W mil W=W mil Cond=1.0E+50 L=50 mil S=S1c mil Hu=3.9e+034 mil Mod=Kirschning L=L1c mil T=0 mil TanD=0.00003 Rough=0 mil S S 1 2

Implicit and Output SM Modeling, with Input SM: HTS Filter ( Cheng and Bandler, 2006 )

More Base Points for SM-based Modeling ( Bandler et al., 2001 ) 2 n more base points located at the corner of the region of interest with n design parameters

HTS Filter: Modeling Region of Interest ( Cheng and Bandler, 2006 ) reference region 1 region 2 region 3 region 4 region 5 parameters point ( x 0 ) size ( δ 1 ) size ( δ 2 ) size ( δ 3 ) size ( δ 4 ) size ( δ 5 ) 180 5 6 8 10 45 L 1 200 10 11 15 20 50 L 2 180 5 6 8 10 45 L 3 20 2 3 3 4 5 S 1 80 5 6 8 10 20 S 2 80 10 11 15 20 20 S 3

HTS Filter: Implicit SM Modeling Surrogate Test Region 2 fine model ( ○ ) R s surrogate (—)

HTS Filter: Implicit SM Modeling + Surrogate Optimization ( Cheng and Bandler, 2006 ) x f * = [172 207 172 20 90 84] T

SMF: User-friendly Space Mapping Software Engine ( Bandler Corp., 2006 ) SMF: for SM-based constrained optimization, modeling and statistical analysis to make space mapping accessible to engineers inexperienced in the art to incorporate existing space mapping approaches in one package implementation: a GUI based Matlab package

SMF: Optimization Flowchart ( Bandler Corp., 2006 )

SMF Optimization of Probe-Fed Printed Double Annular Ring Antenna with Finite Ground ( Zhu et al., 2006 ) coarse model (FEKO) fine model (FEKO)

The Tuning Space Mapping Concept ∇× = H ω + D J j D ε = E ∇ B = � 0 ∇× E =− j ω B ∇ D = ρ � B μ = H tuning-augmented fine-model iterate (physically-based, fine-model surrogate with internal tuning ports)

Tuning Methodology ( Rautio, 2005, Sonnet Software ) circled ports are tuning ports: in series with inductors in shunt with capacitors ( courtesy Rautio, 2006 )

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

Port Tuned Combline Filter ( Swanson, 2006, M/A-COM ) P2 two-port EM model P8 P2 P7 P6 P5 P4 P3 eight-port EM model P1 ( courtesy Swanson, 2006 ) P1

Port Tuned Combline Filter ( Swanson, 2006, M/A-COM ) tune for equal ripple response C C C C6 C5 C4 S_Param or extract coupling C=.470 pF C=.2349 pF C=.2292 pF SP1 Start=2 GHz coefficients and external Q’s Stop=2.28 GHz Step=.0002 GHz TLSC TL1 Term Z=100000 Ohm Term1 Term E=90 Num=1 Term2 F=2.14 GHz Z=50 Ohm Num=2 Z=50 Ohm C C C C1 C2 C3 ( courtesy Swanson, 2006 ) C=.470 pF C=.2349 pF C=.2292 pF S8P SNP1 File="D:\Projects\Dan\PowerWave\Agilent\test5c\test5c.s8p"

Recent Space Mapping Applications 1 “multifidelity optimization” (MFO) algorithm ( Castro et al., 2005 ) optimization in electromagnetics ( Echeverria et al., 2005 ) space mapping and defect correction ( Echeverria and Hemker, 2005 ) modeling thermally active components in new buildings ( Pedersen et al., 2005 ) design of electromagnetic actuators ( Encica et al., 2005 )

Recent Space Mapping Applications 2 fast automated design of waveguide filters ( Ros et al., 2005 ) linear inverse SM algorithm to design linear and nonlinear RF and microwave circuits ( Rayas-Sánchez et al., 2005 ) optimization of planar coupled-resonator microwave filters ( Amari et al., 2006 ) response surface space mapping for electromagnetic optimization ( Dorica and Giannacopoulos, 2006 ) multifidelity optimization with variable dimensional hierarchical models ( Robinson et al., 2006 )

Space Mapping Applications 3: 2006 IEEE IMS Int. Microwave Symposium Workshop on Microwave Component Design Using Space Mapping Technology RF design closure—companion modeling and tuning methods ( J.C. Rautio, Sonnet Software, Inc., USA ) optimization of engineering designs ( S. Koziel, McMaster University, Canada ) more efficient EM simulation and optimization using port tuning ( D. Swanson, M/A-COM, USA ) ANN based microwave component modeling ( Q.J. Zhang, Carleton University, Canada )