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Stockholm Archipelago Antenna and Current OptimizationWorkshop
Notes
Miloslav Capek Lukas Jelınek
Department of Electromagnetic FieldCTU in Prague, Czech [email protected]
Stockholm, September 6–9, 2017
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 1 / 26
Outline
1 Optimization Setup2 Feeding Position Optimization3 MOO Features4 Optimization of Rectangular Plate5 Steve Best’s Meander
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 2 / 26
Optimization Setup
GeometryInitial Geometry
PEC rectangular plate of L× L/2 size.
I According our agreement, initialstructure Ω of L× L/2dimensions (i.e., b = 1/2) hasbeen chosen,
I ka = 0.3 (since Best) andka = 0.5 (since other papers)often chosen.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 3 / 26
Optimization Setup
GeometryReducing Geometrical Complexity
Reducing complexity of the shape to be optimized.
I Periodic holes added to reducethe complexity of the geometryon discretized level.
• Number of RWG is drasticallyincreased.
• Shorts are eliminated.• Symmetry is preserved for
MoM acceleration (with PECplane).
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 4 / 26
Optimization Setup
GeometryDiscretization Grid
Discretized model.
I Uniform grid to preservesymmetries and improveconvergence.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 5 / 26
Optimization Setup
GeometryFeedable Edges
Edges to be potentially fed.
To calculate optimal feeding, not alledges have to be taken into account:
I Some can cause shorts.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 6 / 26
Optimization Setup
GeometryPixelized Structure
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Pixelization of rectangle into 80 unknowns.
To compress the optimizationproblem, map from RWG to GA“pixels” is done:
I pixel enabled (1) = all RWGedges present,
I pixel disabled (0) = all RWGedges removed.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 7 / 26
Optimization Setup
GeometryOptimized Structures and Their Reduction
H Holes Grid RWGs RWGs (reduced) Feedable edges GA pixels
6 6× 3 14× 7 564 423 103 80
8 8× 4 18× 9 945 689 169 130
10 10× 5 22× 11 1419 1019 192 192
Comparison of optimized structures.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 8 / 26
Feeding Position Optimization
Determination of Optimal Feeding Position
I For one feeder, the optimal placement with respect to a given quantity can befound directly (no heuristics)!
Example: minimum quality factor Q
Q =IHX′I
2IHRI=
(Z−1V
)HX′
(Z−1V
)2 (Z−1V)HR (Z−1V)
=VHX′ZV
2VHRZV, (1)
with AZ ≡ Z−HAZ−1, A ∈ N× N, and since vector of excitation coefficients is fullof zero except one position with Vn = 1, we get optimal position as
n : min
diag(X′Z
) diag (RZ)
(2)
I Analogously for other optimized quantities.
I For two feeders, only N − 1 calculations for exact optimal feeding network (?)
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 9 / 26
Feeding Position Optimization
Determine Feeder’s Position – Matlab Sample
Will be shown in Matlab.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 10 / 26
Feeding Position Optimization
Optimization of Feeding PositionComparison
50 55 60 65 70 75 800
5
10
15
20
25
30
minΩ,V
Q
min
Ω,V
|X
in|/R
in
variableQRin|Xin| /Rinno pref. 200 ag., 1000 its.no pref. 400 ag., 1000 its.no pref. 400 ag., 5000 its.
aa.
Possibilities in MOO?
I Prefer one optimized quantity.
• Which one? Why?
I Use GA to find the position(e.g., 8 bits needed forN = 256 edges).
• Which criterion to be used?
I Leave the decision whichcriterion will be used to the GA.
• Only 2 bits for 4 optimizedcriteria.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 11 / 26
MOO Features
Used GA
NSGAII for MOOPotentially: MOPSO, single-criterion GA
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 12 / 26
MOO Features
What Can Be Optimized?
Following criteria are always calculated and optimized only when chosen so:
I minimum (tuned) quality factor Q,
I external tuning|Xin|Rin
= 2Qext,
I input resistance|R0 −Rin|
R0,
I radiation (in)efficiency 1− ηrad,
I total area spanned by the structureAused
Atot.
Notes:
I Arbitrary number of criteria can be optimized (recommended: 2–4).
I All quantities normalized (no units).
I All quantities to be minimized.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 13 / 26
MOO Features
Optional Features – Flood-Filling (FF) Algorithm
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Gree: kept, red: removed by GA, yellow: removed by FF.
Flood-filling implemented:
I All isolated pixels are removedby FF algorithm before physicsis evaluated.
I Kind of penalization.
I In terms of fractional area, i.e.,C/
((2H + 1) (H + 1)−H2/2
),
• C constant,• H number of holes in
horizontal direction,• C = 4, H = 6 : 0.055,H = 10 : 0.022
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 14 / 26
MOO Features
Optional Features – Probability Map
1
0Statistics how often were the pixels used.
Probability map of how often werevarious pixels used can be displayed.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 15 / 26
Optimization of Rectangular Plate
Multiobjective OptimizationTuned quality factor Q vs tuning element
50 55 60 65 70 750
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25
30
minΩ,V
Q
min
Ω,V
|X
in|/R
in
H = 6, 500 agents, 1500 iterationscut from Q/Qext/Rin/A optimization
Expected result (?)
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 16 / 26
Optimization of Rectangular Plate
Multiobjective OptimizationTuned quality factor Q vs tuning element – Currents
Optimal current with respect to minΩ,VQ. Optimal current with respect to min
Ω,V|Xin| /Rin.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 17 / 26
Optimization of Rectangular Plate
Multiobjective OptimizationTuned quality factor Q vs radiation efficiency ηrad – Currents
Optimal current with respect to minΩ,VQ. Optimal current with respect to max
Ω,Vηrad.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 18 / 26
Optimization of Rectangular Plate
Multiobjective OptimizationTuned quality factor Q vs required area A
102 103 1040
0.1
0.2
0.3
0.4
minΩ,VQ
min
Ω,VA
used/A
tot
250 agents, 1000 iterations6× 3, 1040 s8× 4, 2397 s10× 5, 3860 s8× 4 (50 iters., 250 ags.)
I The granularity of the gridcauses big difference in qualityfactor Q.
• What about convergence?
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 19 / 26
Optimization of Rectangular Plate
Multiobjective OptimizationSample of 3(4)-criteria optimization
260
270
2202252302352402452500.96
0.96
0.96
0.96
0.96
0.97
minΩQ
minΩ,V|Xin| /Rin
min
Ω,V|R
0−R
in|/R
0
0
1
Area
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 20 / 26
Steve Best’s Meander
Reference Example
Best’s M1 meander (1595 RWGs, 800 with PEC yz symmetry).
Best’s meander:
I slightly below resonance,
I ka = 0.3,
I Q = 205.43,
I |Xin| /Rin = 30.75,
I Rin = 1.17 Ω.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 21 / 26
Steve Best’s Meander
Pixelized Mask To Hound Best
Prepixelized structure prepared for GA.
Optimal bounds:
I ka = 0.3,
I minIQ = 164.164,
I minI,TM
Q = 194.086.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 22 / 26
Steve Best’s Meander
Optimization ResultsBest’s meander made with the paremetrization
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M. Capek and L. Jelınek Antenna and Current Optimization Workshop 23 / 26
Steve Best’s Meander
Optimization Results
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 24 / 26
Steve Best’s Meander
Optimization ResultsExample of Sub-Optimal Current
aaa. aaa.
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 25 / 26
Questions?
For complete PDF presentation see capek.elmag.org
Miloslav [email protected]
September 7, 2017, v0.2
M. Capek and L. Jelınek Antenna and Current Optimization Workshop 26 / 26
