Meta-Modeling With OptiY - Design Space Visualization for Electromagnetic Applications in CST Studio Suite

Transcription

1 Meta-Modeling With OptiY - Design Space Visualization for Electromagnetic Applications in CST Studio Suite The-Quan OptiY e.k. Germany CST European User Group Meeting 19 th -1 th April 010 in Darmstadt Folie 1/16

2 1. Ojective. Theoretical Basics Gaussian Process Outline Visualization of the Adaptive Gaussian Process 3. Practical EM Eample Waveguide Hyrid Junction Design Space of Reflection and Transmission Folie /16

3 Ojective Design Space Visualization Knowledge aout the relationship: Design Parameters Product Characteristics Reliaility, Safety and Quality Engineering Reduce development, manufacturing cost and failure Increasing lifetime Reduce service after sale Current Solutions Full Factorial Design (Parameter Sweep) o n design parameters with k tunale values Characteristics o n k numer of model calculations required meta model: F = y() o High computing effort o Infeasile for large model (one run takes some hours) Other Methods for Design of Eperiment (DOE) o Less numer of model calculations o Inaccurate Folie 3/16 Parameter

4 Gaussian Process Polynomial f() of p th order for gloal adaptation Stochastic process Z() for local adaptation... ) ( f Y p p = p p ) (... 1 Z p n np n n n n Correlation Function R() Multivariate Gaussian distriution (normal distriution) Interpolation etween calculated points = = n k j i k j i w R 1 ) ( ), ( Folie 4/16 Interactions etween individual parameters

5 Visualization of the Adaptive Gaussian Process Y = ( X 5) 15 e ( X 1.5) 5 Original Test Function Folie 5/15

6 Approimation Loops Start: 6 Sampling Points Loop 1 Response Surface Epected Improvement EI 95% Confidence Interval Ma. Uncertainty Ma. Epected Improvement New Sampling Points Ma. Uncertainty Ma. Epected Improvement Kamusella / Folie 6/13

7 Approimation Loops Loop Required numer of model calculations depends on: Numer of design parameters Degree of response nonlinearity Correlation etween design parameters Loop 3: Automatic Stop Ma. Uncertainty New Sampling Points New Sampling Points Ma. Epected Improvement Kamusella / Folie 7/13

8 Waveguide Hyrid Junction Design Space Hole Length 16 4 mm Hole Width mm Gap 13 5 mm Disk High mm Disk Radius mm Product Characteristics: Transmission and Reflection at the operating point 8 GHz ased on transient simulation in CST Studio Suite Folie 8/16

9 Design Space Visualization: D Section Diagrams Folie 9/16

10 Design Space Visualization: 3D Graphics Reflection Transmission Difference Folie 10/16

11 Gloal Nonlinear and Quantitative Sensitivity Analysis Design Parameter Importance Design Parameter Interactions Folie 11/16

12 Proailistic Simulation (Yield Analysis) Design Optimization Design goal: minimize the reflection S11 to get the optimal design point in the design space (Tale: optimal design parameters with manufacturing tolerances) Design Roustness Tolerances of design parameters cause variaility of the reflection and transmission: quality and reliaility in series manufacturing Input Distriutions Output Distriutions Folie 1/16

13 Roust Design Optimization Nominal Design Taguchi Quality Loss Function: L = Cost*(Variance (Mean Target Value) ) Quality loss of Transmission S31,S41 Target Value = 0 (e.g. S31 = S41), Cost = 1 Roust Design Minimizing i i i the quality loss function for the transmission Nominal Design L = 1.3E-3 Roust Design L =.6 E-7 Folie 13/16

14 Code-Eport of Surrogate Model for System Simulation Automatic Code-Eport in C, Modelica or Matla Fast surrogate model for total system simulation (e.g. Matla/Simulink, Circuit-Simulator) Development of controller or circuit in case of co- simulation with electromagnetic applications Folie 14/19

15 Conclusion Meta-Modeling is a process to win the mathematical relationship etween design parameters and product characteristics ased on the adaptive response surface methodology. The numer of required model calculations is less. Therefore, it is applicale for large product models with running time of hours. The meta-model model can e used for improvement of the design under real conditions related to quality and reliaility. It can e also eported to surrogate model in the case of system simulation We apply on the waveguide hyrid junction in CST Studio Suite. The roust design process has een demonstrated Folie 15/16