Bodycentric wireless communication Wearable Electronics Local Optimization Zbynk
Body-centric wireless communication Wearable Electronics: Local Optimization Zbyněk Raida raida@vut. cz Vytvořeno za podpory projektu OP VVV Moderní a otevřené studium techniky CZ. 02. 2. 69/0. 0/16_015/0002430
Recap § Modeling body-centric systems: - closed-form approximate expressions - numerical models § Approximate models: - layered phantoms - simplified physical approximations § Numerical models: - voxel phantoms - full-wave models of EM components raida@vut. cz 2
Contents § Optimization of electromagnetic structures: - initial simplified design - varying state variables to meet objectives § Local optimization: - steepest descent - (quasi) Newton methods § Efficient technical optimization raida@vut. cz 3
Description of EM structures § Properties: two-port network scattering parameters § Dimensions: ~ wavelength influence on properties raida@feec. vutbr. cz 4
Scattering parameters raida@feec. vutbr. cz 5
Scattering parameters raida@feec. vutbr. cz 6
HF two-port network filter § Impedance discontinuities forward and backward waves: - Pass-band: constructive interferences - Stop-band: destructive ones raida@feec. vutbr. cz 7
HF two-port network antenna § Currents on patches radiated waves - Main lobe: constructive interference - Nulls: destructive ones raida@feec. vutbr. cz 8
Objectives § For frequencies f 1, f 2, … , f. N - Min. input reflections S 11(x, f) - Max. gain G(x, f) impedance matching transmission attenuation gain raida@feec. vutbr. cz 9
Local minimization § Optimality conditions, 1 st order raida@feec. vutbr. cz 10
Local minimization § Testing: Rosenbrock function raida@feec. vutbr. cz 11
Local minimization § Steepest descent gradient raida@feec. vutbr. cz 12
Local minimization § Steepest descent X 1(1, 1) = rb( [x(1, 1) + h/2; x(2, 1)]); X 1(2, 1) = rb( [x(1, 1) - h/2; x(2, 1)]); X 2(1, 1) = rb( [x(1, 1); x(2, 1) + h/2]); X 2(2, 1) = rb( [x(1, 1); x(2, 1) - h/2]); g(1, 1) = (X 1(1, 1) - X 1(2, 1)) / h; g(2, 1) = (X 2(1, 1) - X 2(2, 1)) / h; x = x - alpha*g; raida@feec. vutbr. cz 13
Local minimization § Newton method Hessian raida@feec. vutbr. cz 14
Local minimization § Newton method raida@feec. vutbr. cz 15
Local minimization § Quasi-Newton method § Newton: curvature of the objective function described by Hessian G(x) § Quasi-Newton: explicitly expressed Hessian not needed to approximate curvature raida@feec. vutbr. cz 16
Quasi-Newton method § Expanding gradient by Taylor’s series searching step § Curvature of F(xk) along sk § Hessian Gk approximated by the estimate Bk; B 0 = E (~ the steepest descent) raida@feec. vutbr. cz 17
Quasi-Newton method § Estimated Hessian updated iteratively update matrix column vectors § Considering quasi-Newton condition raida@feec. vutbr. cz 18
Quasi-Newton method § The vector u in direction yk – Bk sk § The update expression raida@feec. vutbr. cz 19
Quasi-Newton method § Requesting symmetry § Only the first derivative needed raida@feec. vutbr. cz 20
Local minimization § Other quasi-Newton methods www. wikipedia. org raida@feec. vutbr. cz 21
Engineering approach § Filter characteristics surrogate model: raida@feec. vutbr. cz 22
Engineering approach § Low-pass prototype raida@feec. vutbr. cz 23
Engineering approach § Surrogate model optimization raida@feec. vutbr. cz 24
Engineering approach § Full-wave model optimization VęeobecnýVęeobecnýVęeobecnýVęeobecnýVęeobecnýVęeobecný -Vęeobecný d. B(S(21)) d. B(S(11)) -Vęeobecný -Vęeobecný raida@feec. vutbr. cz 25
Engineering approach § Measurement Vęeobecný Vęeobecný Vęeobecný -Vęeobecný -Vęeobecný db: Trc 1_S 11 db: Trc 2_S 21 raida@feec. vutbr. cz 26
Complex cavity filters § Tuning space mapping WOLANSKY, D. , KADLEC, R. Coaxial filters optimization using tuning space mapping in CST Studio, Radioengineering, 2011, vol. 20, no. 1, p. 289 -294. raida@feec. vutbr. cz 27
Complex cavity filters WOLANSKY, D. , KADLEC, R. Coaxial filters optimization using tuning space mapping in CST Studio, Radioengineering, 2011, vol. 20, no. 1, p. 289 -294. 28
Further CPU-time reduction § Feasible space raida@feec. vutbr. cz 29
Constrained optimization with respect to raida@feec. vutbr. cz 30
Further CPU-time reduction § Reducing the number of state variables raida@feec. vutbr. cz 31
Summary § Objective function: - requirements on technical parameters - depending on state variables § Searching minims of objective function - steepest descent: steepness by gradient - Newton method: curvature by Hessian - quasi-Newton: Hessian evaluated iteratively raida@vut. cz 32
Summary § CPU-time moderate optimization: - surrogate models (tuning space mapping) - constraints - selection of state variables raida@vut. cz 33
- Slides: 33