volume | PIER Journals

Abstract

In recent years, uncertainty analysis methods have become a research hotspot in the field of Electromagnetic Compatibility (EMC), and non-intrusive uncertainty analysis methods are widely used in the field of EMC due to their advantages such as easy solver generalization and easy programming. The proposal of Bayesian optimization-based uncertainty analysis method further enhances the competitiveness of non-intrusive uncertainty analysis methods in solving complex EMC simulation problems. However, in traditional Bayesian optimization-based uncertainty analysis methods, Latin hypercube sampling strategy is used to construct the initial Gaussian process model, which lacks adaptive adjustment capability, and the quality of the initial Gaussian process model has a significant impact on the efficiency of subsequent calculations and the accuracy of the final results. This defect limits the computational efficiency and accuracy of Bayesian optimization methods in uncertainty analysis applications. In response to this issue, this paper proposes an active sampling strategy based on the Stochastic Reduced Order Model (SROM) method. This strategy improves the fitness function used by the SROM method in clustering to enhance the representativeness of the training set to the sampling space. By using this active sampling strategy instead of Latin hypercube sampling strategy, a higher quality initial Gaussian process model can be constructed, and the accuracy of Bayesian optimization method uncertainty analysis calculation is improved in the example, verifying the effectiveness of the proposed initial sampling point selection improvement strategy.

1. Manfredi, Paolo, Dries Vande Ginste, Igor S. Stievano, Daniël De Zutter, and Flavio G. Canavero, "Stochastic transmission line analysis via polynomial chaos methods: An overview," IEEE Electromagnetic Compatibility Magazine, Vol. 6, No. 3, 77-84, Nov. 2017.

2. Zhang, Yin, Cheng Liao, Rui Huan, Yuping Shang, and Haijing Zhou, "Analysis of nonuniform transmission lines with a perturbation technique in time domain," IEEE Transactions on Electromagnetic Compatibility, Vol. 62, No. 2, 542-548, Apr. 2020.

3. Zhang, Zheng, Tarek A. El-Moselhy, Ibrahim M. Elfadel, and Luca Daniel, "Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 32, No. 10, 1533-1545, Oct. 2013.

4. Manfredi, Paolo, Dries Vande Ginste, Daniël De Zutter, and Flavio G. Canavero, "On the passivity of polynomial chaos-based augmented models for stochastic circuits," IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 60, No. 11, 2998-3007, Nov. 2013.

5. Pignari, Sergio A., Giordano Spadacini, and Flavia Grassi, "Modeling field-to-wire coupling in random bundles of wires," IEEE Electromagnetic Compatibility Magazine, Vol. 6, No. 3, 85-90, Nov. 2017.

6. Wang, Tianhao, Yinhan Gao, Le Gao, Chang-Ying Liu, Juxian Wang, and Zhanyang An, "Statistical analysis of crosstalk for automotive wiring harness via polynomial chaos method," Journal of the Balkan Tribological Association, Vol. 22, No. 2, 1503-1517, 2016.

7. Fei, Zhouxiang, Yi Huang, Jiafeng Zhou, and Qian Xu, "Uncertainty quantification of crosstalk using stochastic reduced order models," IEEE Transactions on Electromagnetic Compatibility, Vol. 59, No. 1, 228-239, 2017.

8. Ren, Ziyan, Jiangang Ma, Yanli Qi, Dianhai Zhang, and Chang-Seop Koh, "Managing uncertainties of permanent magnet synchronous machine by adaptive Kriging assisted weight index Monte Carlo simulation method," IEEE Transactions on Energy Conversion, Vol. 35, No. 4, 2162-2169, 2020.

9. Xie, Haiyan, John F. Dawson, Jiexiong Yan, Andy C. Marvin, and Martin P. Robinson, "Numerical and analytical analysis of stochastic electromagnetic fields coupling to a printed circuit board trace," IEEE Transactions on Electromagnetic Compatibility, Vol. 62, No. 4, 1128-1135, Aug. 2020.

10. Teckentrup, A. L., P. Jantsch, C. G. Webster, and M. Gunzburger, "A multilevel stochastic collocation method for partial differential equations with random input data," SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, No. 1, 1046-1074, 2015.

11. Bai, Jinjun, Bing Hu, and Alistair Duffy, "Uncertainty analysis for EMC simulation based on Bayesian optimization," IEEE Transactions on Electromagnetic Compatibility, Vol. 67, No. 2, 587-597, Apr. 2025.

12. Greenhill, Stewart, Santu Rana, Sunil Gupta, Pratibha Vellanki, and Svetha Venkatesh, "Bayesian optimization for adaptive experimental design: A review," IEEE Access, Vol. 8, 13937-13948, Jan. 2020.

13. Lindauer, Marius, Katharina Eggensperger, Matthias Feurer, André Biedenkapp, Difan Deng, Carolin Benjamins, Tim Ruhkopf, René Sass, and Frank Hutter, "SMAC3: A versatile Bayesian optimization package for hyperparameter optimization," Journal of Machine Learning Research, Vol. 23, No. 54, 1-9, 2022.

14. Candelieri, Antonio, Andrea Ponti, and Francesco Archetti, "Fair and green hyperparameter optimization via multi-objective and multiple information source Bayesian optimization," Machine Learning, Vol. 113, No. 5, 2701-2731, 2024.

15. Olsson, A., G. Sandberg, and O. Dahlblom, "On Latin hypercube sampling for structural reliability analysis," Structural Safety, Vol. 25, No. 1, 47-68, Jan. 2003.

16. Bai, Jinjun, Jingchao Sun, and Ning Wang, "Convergence determination of EMC uncertainty simulation based on the improved mean equivalent area method," Applied Computational Electromagnetics Society Journal (ACES), Vol. 36, No. 11, 1446-1452, Dec. 2021.

17. COMSOL Multiphysics. Lightning-Induced Voltage of a Wire in an Airplane. [Online], Available: https://cn.comsol.com/model/lightning-induced-voltage-of-a-wire-in-an-airplane-110121.

Dr. Jinjun Bai

Dr. Xiangrui Ji

Dr. Qing Liu

Dr. Yujia Song

Dr. Zhongjiu Zheng