Low-Cost Surrogate Modeling of Miniaturized Microwave Components Using Nested Kriging
Keywords:design optimization, microwave design, miniaturized structures, nested kriging, surrogate modeling
In the paper, a recently reported nested kriging methodology is employed for modeling of miniaturized microwave components. The approach is based on identifying the parameter space region that contains high-quality designs, and, subsequently, rendering the surrogate in this subset. The results obtained for a miniaturized unequal-power-split rat-race coupler and a compact three-section impedance transformer demonstrate reliability of the method even for highly-dimensional parameter spaces, as well as its superiority over conventional modeling methods.
J. Zhang, C. Zhang, F. Feng, W. Zhang, J. Ma, and Q. J. Zhang, “Polynomial chaos-based approach to yield-driven EM optimization,” IEEE Trans. Microw. Theory Tech., vol. 66, no. 7, pp. 3186-3199, 2018.
W. Liu, W. Na, L. Zhu, J. Ma, and Q. J. Zhang, “A Wiener-type dynamic neural network approach to the modeling of nonlinear microwave devices,” IEEE Trans. Microwave Theory Tech., vol. 65, no. 6, pp. 2043-2062, 2017. 1 2 3 4 l1 l2 l3 w1 w d w d1 (a) lk.1 lk.2 wk.1 wk.2 wk.0 (c) (d) (b) (e) Fig. 2. Verification test cases: (a) microstrip rat-race coupler (RRC) , (b) allocation of the reference designs for the RRC, (c) compact cell (CMRC), (d) CMRC-based miniaturized three-section impedance transformer, and (e) allocation of the reference designs for the transformer. Fig. 3. Responses of the compact RRC of Fig. 2 (a) at the selected test designs for N = 800: EM model (—), nested kriging surrogate (o). Fig. 4. Responses of the impedance transformer of Fig. 2 (d) at the selected test designs for N = 800: EM model (—), nested kriging surrogate (o). TABLE I. MODELING RESULTS FOR RRC AND TRANSFORMER Number of Training Samples Relative RMS Error for Compact RRC Relative RMS Error for Impedance Transformer Conventional Kriging Model Nested Kriging Model [This Work] Conventional Kriging Model Nested Kriging Model [This Work] 50 25.7% 6.9% 49.1% 17.3% 100 17.9% 5.7% 31.1% 13.9% 200 13.5% 3.8% 25.9% 10.3% 400 9.9% 3.5% 20.4% 7.4% 800 8.0% 3.1% 15.7% 6.1%
D. I. L. de Villiers, I. Couckuyt, and T. Dhaene, “Multi-objective Optimization of Reflector Antennas using Kriging and Probability of Improvement,” Int. Symp. Ant. Prop., pp. 985-986, San Diego, USA, 2017.
S. Koziel and A. Bekasiewicz, “Accurate Simulation-driven Modeling and Design Optimization of Compact Microwave Structures,” Int. Microwave Symp., San Francisco, CA, 2016, pp. 1-3.
S. Koziel and A. T. Sigurðsson, “Performance-driven modeling of compact couplers in restricted domains,” Int. J. RF Microwave CAE, vol. 28, no. 6, 2018.
S. Koziel and A. Pietrenko-Dabrowska, “Performance-based nested surrogate modeling of antenna input characteristics,” IEEE Trans. Ant. Prop., vol. 67, no. 5, pp. 2904-2912, 2019.