Stockholm Archipelago Antenna and Current Optimization Workshop - PowerPoint PPT Presentation

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

Outline 1 Optimization Setup 2 Feeding Position Optimization 3 MOO Features 4 Optimization of Rectangular Plate 5 Steve Best’s Meander M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 2 / 26

Optimization Setup Geometry Initial Geometry ◮ 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) often chosen. PEC rectangular plate of L × L/ 2 size. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 3 / 26

Optimization Setup Geometry Reducing Geometrical Complexity ◮ Periodic holes added to reduce the complexity of the geometry on discretized level. • Number of RWG is drastically increased. • Shorts are eliminated. • Symmetry is preserved for MoM acceleration (with PEC plane). Reducing complexity of the shape to be optimized. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 4 / 26

Optimization Setup Geometry Discretization Grid ◮ Uniform grid to preserve symmetries and improve convergence. Discretized model. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 5 / 26

Optimization Setup Geometry Feedable Edges To calculate optimal feeding, not all edges have to be taken into account: ◮ Some can cause shorts. Edges to be potentially fed. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 6 / 26

Optimization Setup Geometry Pixelized Structure ✼ ✶✶ ✶✽ ✷✷ ✷✾ ✸✸ ✹✵ ✹✼ ✺✶ ✺✽ ✻✷ ✻✾ ✼✸ ✽✵ 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. Pixelization of rectangle into 80 unknowns. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 7 / 26

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

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 � H X ′ � Q = I H X ′ I � Z − 1 V Z − 1 V � = V H X ′ Z V 2 I H RI = 2 V H R Z V , (1) 2 ( Z − 1 V ) H R ( Z − 1 V ) with A Z ≡ Z − H AZ − 1 , A ∈ N × N , and since vector of excitation coefficients is full of zero except one position with V n = 1, we get optimal position as � � X ′ � � n : min diag ⊘ diag ( R Z ) (2) Z ◮ Analogously for other optimized quantities. ◮ For two feeders, only N − 1 calculations for exact optimal feeding network (?) M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 9 / 26

Feeding Position Optimization Determine Feeder’s Position – Matlab Sample Will be shown in Matlab. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 10 / 26

Feeding Position Optimization Optimization of Feeding Position Comparison 30 variable Q 25 R in Possibilities in MOO? | X in | /R in no pref. 200 ag., 1000 its. ◮ Prefer one optimized quantity. no pref. 400 ag., 1000 its. 20 Ω, V {| X in | /R in } • Which one? Why? no pref. 400 ag., 5000 its. ◮ Use GA to find the position 15 ( e.g. , 8 bits needed for min N = 256 edges). 10 • Which criterion to be used? ◮ Leave the decision which 5 criterion will be used to the GA. • Only 2 bits for 4 optimized 0 50 55 60 65 70 75 80 criteria. Ω, V { Q } min M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 11 / 26 aa.

MOO Features Used GA NSGAII for MOO Potentially: MOPSO, single-criterion GA M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 12 / 26

MOO Features What Can Be Optimized? Following criteria are always calculated and optimized only when chosen so: ◮ minimum (tuned) quality factor Q , ◮ external tuning | X in | = 2 Q ext , R in ◮ input resistance | R 0 − R in | , R 0 ◮ radiation (in)efficiency 1 − η rad , ◮ total area spanned by the structure A used . A tot Notes: ◮ Arbitrary number of criteria can be optimized (recommended: 2–4). ◮ All quantities normalized (no units). ◮ All quantities to be minimized. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 13 / 26

MOO Features Optional Features – Flood-Filling (FF) Algorithm Flood-filling implemented: 7 11 18 22 29 33 40 47 51 58 62 69 73 80 ◮ All isolated pixels are removed by FF algorithm before physics 6 17 28 39 46 57 68 79 is evaluated. 5 10 16 21 27 32 38 45 50 56 61 67 72 78 ◮ Kind of penalization. 4 15 26 37 44 55 66 77 ◮ In terms of fractional area, i.e. , 3 9 14 20 25 31 36 43 49 54 60 65 71 76 � (2 H + 1) ( H + 1) − H 2 / 2 � C/ , 2 13 24 35 42 53 64 75 • C constant, • H number of holes in 1 8 12 19 23 30 34 41 48 52 59 63 70 74 horizontal direction, • C = 4, H = 6 : 0 . 055, Gree: kept, red: removed by GA, yellow: removed by FF. H = 10 : 0 . 022 M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 14 / 26

MOO Features Optional Features – Probability Map 1 Probability map of how often were various pixels used can be displayed. 0 Statistics how often were the pixels used. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 15 / 26

Optimization of Rectangular Plate Multiobjective Optimization Tuned quality factor Q vs tuning element 30 H = 6, 500 agents, 1500 iterations cut from Q / Q ext / R in / A optimization 25 20 Ω, V {| X in | /R in } 15 Expected result (?) min 10 5 0 50 55 60 65 70 75 Ω, V { Q } min M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 16 / 26

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 {| X in | /R in } . M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 17 / 26

Optimization of Rectangular Plate Multiobjective Optimization Tuned quality factor Q vs radiation efficiency η rad – Currents Optimal current with respect to min Ω, V { Q } . Optimal current with respect to max Ω, V { η rad } . M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 18 / 26

Optimization of Rectangular Plate Multiobjective Optimization Tuned quality factor Q vs required area A 0 . 4 250 agents, 1000 iterations 6 × 3, 1040 s 8 × 4, 2397 s 10 × 5, 3860 s 0 . 3 8 × 4 ( 50 iters., 250 ags. ) Ω, V { A used /A tot } ◮ The granularity of the grid 0 . 2 causes big difference in quality factor Q . min • What about convergence? 0 . 1 0 10 2 10 3 10 4 min Ω, V { Q } M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 19 / 26

Optimization of Rectangular Plate Multiobjective Optimization Sample of 3(4)-criteria optimization 1 0 . 97 0 . 96 Area Ω, V {| R 0 − R in | /R 0 } 0 . 96 0 . 96 0 . 96 min 270 0 . 96 250 245 0 240 235 230 260 225 min Ω { Q } 220 min Ω, V {| X in | /R in } M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 20 / 26

Steve Best’s Meander Reference Example Best’s meander: ◮ slightly below resonance, ◮ ka = 0 . 3, ◮ Q = 205 . 43, ◮ | X in | /R in = 30 . 75, ◮ R in = 1 . 17 Ω. Best’s M1 meander (1595 RWGs, 800 with PEC yz symmetry). M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 21 / 26

Steve Best’s Meander Pixelized Mask To Hound Best Optimal bounds: ◮ ka = 0 . 3, ◮ min Q = 164 . 164, I ◮ min I , TM Q = 194 . 086. Prepixelized structure prepared for GA. M. ˇ Capek and L. Jel´ ınek Antenna and Current Optimization Workshop 22 / 26