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Stockholm Archipelago Antenna and Current Optimization Workshop Notes Miloslav Capek Luk a s Jel nek Department of Electromagnetic Field CTU in Prague, Czech Republic miloslav.capek@fel.cvut.cz Stockholm, September 69, 2017

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SLIDE 1

Stockholm Archipelago Antenna and Current Optimization Workshop

Notes Miloslav ˇ Capek Luk´ aˇ s Jel´ ınek

Department of Electromagnetic Field CTU in Prague, Czech Republic miloslav.capek@fel.cvut.cz

Stockholm, September 6–9, 2017

  • M. ˇ

Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 1 / 26

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SLIDE 2

Outline

1 Optimization Setup 2 Feeding Position Optimization 3 MOO Features 4 Optimization of Rectangular Plate 5 Steve Best’s Meander

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 2 / 26

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SLIDE 3

Optimization Setup

Geometry

Initial Geometry

PEC rectangular plate of L × L/2 size.

◮ According our agreement, initial structure Ω of L × L/2 dimensions (i.e., b = 1/2) has been chosen, ◮ ka = 0.3 (since Best) and ka = 0.5 (since other papers)

  • ften chosen.
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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 3 / 26

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SLIDE 4

Optimization Setup

Geometry

Reducing Geometrical Complexity

Reducing complexity of the shape to be optimized.

◮ Periodic holes added to reduce the complexity of the geometry

  • n discretized level.
  • Number of RWG is drastically

increased.

  • Shorts are eliminated.
  • Symmetry is preserved for

MoM acceleration (with PEC plane).

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 4 / 26

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SLIDE 5

Optimization Setup

Geometry

Discretization Grid

Discretized model.

◮ Uniform grid to preserve symmetries and improve convergence.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 5 / 26

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SLIDE 6

Optimization Setup

Geometry

Feedable Edges

Edges to be potentially fed.

To calculate optimal feeding, not all edges have to be taken into account: ◮ Some can cause shorts.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 6 / 26

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SLIDE 7

Optimization Setup

Geometry

Pixelized Structure ✶ ✷ ✸ ✹ ✺ ✻ ✼ ✽ ✾ ✶✵ ✶✶ ✶✷ ✶✸ ✶✹ ✶✺ ✶✻ ✶✼ ✶✽ ✶✾ ✷✵ ✷✶ ✷✷ ✷✸ ✷✹ ✷✺ ✷✻ ✷✼ ✷✽ ✷✾ ✸✵ ✸✶ ✸✷ ✸✸ ✸✹ ✸✺ ✸✻ ✸✼ ✸✽ ✸✾ ✹✵ ✹✶ ✹✷ ✹✸ ✹✹ ✹✺ ✹✻ ✹✼ ✹✽ ✹✾ ✺✵ ✺✶ ✺✷ ✺✸ ✺✹ ✺✺ ✺✻ ✺✼ ✺✽ ✺✾ ✻✵ ✻✶ ✻✷ ✻✸ ✻✹ ✻✺ ✻✻ ✻✼ ✻✽ ✻✾ ✼✵ ✼✶ ✼✷ ✼✸ ✼✹ ✼✺ ✼✻ ✼✼ ✼✽ ✼✾ ✽✵

Pixelization of rectangle into 80 unknowns.

To compress the optimization problem, map from RWG to GA “pixels” is done: ◮ pixel enabled (1) = all RWG edges present, ◮ pixel disabled (0) = all RWG edges removed.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 7 / 26

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SLIDE 8

Optimization Setup

Geometry

Optimized 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.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 8 / 26

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SLIDE 9

Feeding Position Optimization

Determination of Optimal Feeding Position

◮ For one feeder, the optimal placement with respect to a given quantity can be found directly (no heuristics)! Example: minimum quality factor Q Q = IHX′I 2IHRI =

  • Z−1V

H X′ Z−1V

  • 2 (Z−1V)H R (Z−1V)

= VHX′

ZV

2VHRZV, (1) with AZ ≡ Z−HAZ−1, A ∈ N × N, and since vector of excitation coefficients is full

  • f zero except one position with Vn = 1, we get optimal position as

n : min

  • diag
  • X′

Z

  • ⊘ diag (RZ)
  • (2)

◮ Analogously for other optimized quantities. ◮ For two feeders, only N − 1 calculations for exact optimal feeding network (?)

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 9 / 26

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SLIDE 10

Feeding Position Optimization

Determine Feeder’s Position – Matlab Sample

Will be shown in Matlab.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 10 / 26

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SLIDE 11

Feeding Position Optimization

Optimization of Feeding Position

Comparison

50 55 60 65 70 75 80 5 10 15 20 25 30 min

Ω,V {Q}

min

Ω,V {|Xin| /Rin}

variable Q Rin |Xin| /Rin no pref. 200 ag., 1000 its. no pref. 400 ag., 1000 its. no pref. 400 ag., 5000 its.

aa.

Possibilities in MOO? ◮ Prefer one optimized quantity.

  • Which one? Why?

◮ Use GA to find the position (e.g., 8 bits needed for N = 256 edges).

  • Which criterion to be used?

◮ Leave the decision which criterion will be used to the GA.

  • Only 2 bits for 4 optimized

criteria.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 11 / 26

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SLIDE 12

MOO Features

Used GA

NSGAII for MOO Potentially: MOPSO, single-criterion GA

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 12 / 26

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SLIDE 13

MOO Features

What Can Be Optimized?

Following criteria are always calculated and optimized only when chosen so: ◮ minimum (tuned) quality factor Q, ◮ external tuning |Xin| Rin = 2Qext, ◮ input resistance |R0 − Rin| R0 , ◮ radiation (in)efficiency 1 − ηrad, ◮ total area spanned by the structure Aused Atot . Notes: ◮ Arbitrary number of criteria can be optimized (recommended: 2–4). ◮ All quantities normalized (no units). ◮ All quantities to be minimized.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 13 / 26

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SLIDE 14

MOO Features

Optional Features – Flood-Filling (FF) Algorithm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Gree: kept, red: removed by GA, yellow: removed by FF.

Flood-filling implemented: ◮ All isolated pixels are removed by FF algorithm before physics is evaluated. ◮ Kind of penalization. ◮ 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

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 14 / 26

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SLIDE 15

MOO Features

Optional Features – Probability Map

1

Statistics how often were the pixels used.

Probability map of how often were various pixels used can be displayed.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 15 / 26

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SLIDE 16

Optimization of Rectangular Plate

Multiobjective Optimization

Tuned quality factor Q vs tuning element

50 55 60 65 70 75 5 10 15 20 25 30 min

Ω,V {Q}

min

Ω,V {|Xin| /Rin}

H = 6, 500 agents, 1500 iterations cut from Q/Qext/Rin/A optimization

Expected result (?)

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 16 / 26

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SLIDE 17

Optimization of Rectangular Plate

Multiobjective Optimization

Tuned quality factor Q vs tuning element – Currents

Optimal current with respect to min

Ω,V {Q}.

Optimal current with respect to min

Ω,V {|Xin| /Rin}.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 17 / 26

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SLIDE 18

Optimization of Rectangular Plate

Multiobjective Optimization

Tuned quality factor Q vs radiation efficiency ηrad – Currents

Optimal current with respect to min

Ω,V {Q}.

Optimal current with respect to max

Ω,V {ηrad}.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 18 / 26

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SLIDE 19

Optimization of Rectangular Plate

Multiobjective Optimization

Tuned quality factor Q vs required area A

102 103 104 0.1 0.2 0.3 0.4 min

Ω,V {Q}

min

Ω,V {Aused/Atot}

250 agents, 1000 iterations 6 × 3, 1040 s 8 × 4, 2397 s 10 × 5, 3860 s 8 × 4 (50 iters., 250 ags.)

◮ The granularity of the grid causes big difference in quality factor Q.

  • What about convergence?
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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 19 / 26

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SLIDE 20

Optimization of Rectangular Plate

Multiobjective Optimization

Sample of 3(4)-criteria optimization

260 270 220 225 230 235 240 245 250 0.96 0.96 0.96 0.96 0.96 0.97 min

Ω {Q}

min

Ω,V {|Xin| /Rin}

min

Ω,V {|R0 − Rin| /R0}

1 Area

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 20 / 26

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SLIDE 21

Steve Best’s Meander

Reference Example

Best’s M1 meander (1595 RWGs, 800 with PEC yz symmetry).

Best’s meander: ◮ slightly below resonance, ◮ ka = 0.3, ◮ Q = 205.43, ◮ |Xin| /Rin = 30.75, ◮ Rin = 1.17 Ω.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 21 / 26

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SLIDE 22

Steve Best’s Meander

Pixelized Mask To Hound Best

Prepixelized structure prepared for GA.

Optimal bounds: ◮ ka = 0.3, ◮ min

I

Q = 164.164, ◮ min

I,TM Q = 194.086.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 22 / 26

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SLIDE 23

Steve Best’s Meander

Optimization Results

Best’s meander made with the paremetrization

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 23 / 26

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SLIDE 24

Steve Best’s Meander

Optimization Results

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 24 / 26

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SLIDE 25

Steve Best’s Meander

Optimization Results

Example of Sub-Optimal Current

aaa. aaa.

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 25 / 26

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SLIDE 26

Questions?

For complete PDF presentation see

capek.elmag.org

Miloslav ˇ Capek miloslav.capek@fel.cvut.cz September 7, 2017, v0.2

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Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 26 / 26