Vol. 174
Latest Volume
All Volumes
PIERC 174 PIERC 173 PIERC 172 PIERC 171 PIERC 170 PIERC 169 PIERC 168 PIERC 167 PIERC 166 PIERC 165 PIERC 164 PIERC 163 PIERC 162 PIERC 161 PIERC 160 PIERC 159 PIERC 158 PIERC 157 PIERC 156 PIERC 155 PIERC 154 PIERC 153 PIERC 152 PIERC 151 PIERC 150 PIERC 149 PIERC 148 PIERC 147 PIERC 146 PIERC 145 PIERC 144 PIERC 143 PIERC 142 PIERC 141 PIERC 140 PIERC 139 PIERC 138 PIERC 137 PIERC 136 PIERC 135 PIERC 134 PIERC 133 PIERC 132 PIERC 131 PIERC 130 PIERC 129 PIERC 128 PIERC 127 PIERC 126 PIERC 125 PIERC 124 PIERC 123 PIERC 122 PIERC 121 PIERC 120 PIERC 119 PIERC 118 PIERC 117 PIERC 116 PIERC 115 PIERC 114 PIERC 113 PIERC 112 PIERC 111 PIERC 110 PIERC 109 PIERC 108 PIERC 107 PIERC 106 PIERC 105 PIERC 104 PIERC 103 PIERC 102 PIERC 101 PIERC 100 PIERC 99 PIERC 98 PIERC 97 PIERC 96 PIERC 95 PIERC 94 PIERC 93 PIERC 92 PIERC 91 PIERC 90 PIERC 89 PIERC 88 PIERC 87 PIERC 86 PIERC 85 PIERC 84 PIERC 83 PIERC 82 PIERC 81 PIERC 80 PIERC 79 PIERC 78 PIERC 77 PIERC 76 PIERC 75 PIERC 74 PIERC 73 PIERC 72 PIERC 71 PIERC 70 PIERC 69 PIERC 68 PIERC 67 PIERC 66 PIERC 65 PIERC 64 PIERC 63 PIERC 62 PIERC 61 PIERC 60 PIERC 59 PIERC 58 PIERC 57 PIERC 56 PIERC 55 PIERC 54 PIERC 53 PIERC 52 PIERC 51 PIERC 50 PIERC 49 PIERC 48 PIERC 47 PIERC 46 PIERC 45 PIERC 44 PIERC 43 PIERC 42 PIERC 41 PIERC 40 PIERC 39 PIERC 38 PIERC 37 PIERC 36 PIERC 35 PIERC 34 PIERC 33 PIERC 32 PIERC 31 PIERC 30 PIERC 29 PIERC 28 PIERC 27 PIERC 26 PIERC 25 PIERC 24 PIERC 23 PIERC 22 PIERC 21 PIERC 20 PIERC 19 PIERC 18 PIERC 17 PIERC 16 PIERC 15 PIERC 14 PIERC 13 PIERC 12 PIERC 11 PIERC 10 PIERC 9 PIERC 8 PIERC 7 PIERC 6 PIERC 5 PIERC 4 PIERC 3 PIERC 2 PIERC 1
2026-11-06
Improved LSSVR Uncertainty Quantification Method Based on Hierarchical Dimension-Reduced Sparse Grid
By
Progress In Electromagnetics Research C, Vol. 174, 110-119, 2026
Abstract
Uncertainty quantification (UQ) is an important means of characterizing how input-parameter fluctuations affect electromagnetic responses, and it provides a theoretical basis for performance prediction, reliability evaluation, and robust optimization in computational electromagnetics. For high-cost full-wave electromagnetic simulations, the least-squares support vector regression (LSSVR) surrogate model can improve the efficiency of computational electromagnetics UQ within a reasonable accuracy range because of its small-sample learning and nonlinear fitting capabilities. However, the sampling strategy directly affects the accuracy of the surrogate model. Conventional Latin hypercube sampling (LHS) allocates sampling resources equally among all dimensions, which may waste computational resources in LSSVR-based UQ. The paper proposes an LSSVR surrogate-model-based UQ method incorporating a hierarchical dimensionality reduction sparse grid strategy (LSSVR-DRSG-H) to prioritize the allocation of computational resources to highly sensitive input parameters. Validation results from a case study on human head electromagnetic exposure demonstrate that, compared with the conventional LSSVR, which achieves an MEAM of 0.8391 using 100 full-wave simulations, the proposed LSSVR-DRSG-H attains a higher MEAM of 0.8530 with only 85 full-wave simulations.
Citation
Yujia Song, Jiming Qi, Jiasheng Wang, Yuantai Niu, Jinjun Bai, and Shenghang Huo, "Improved LSSVR Uncertainty Quantification Method Based on Hierarchical Dimension-Reduced Sparse Grid," Progress In Electromagnetics Research C, Vol. 174, 110-119, 2026.
References

1. Wang, Tianhao, Quanyi Yu, Bo Li, Gang Lv, Yangyun Wu, and Shanshan Guan, "Uncertainty quantification of human electromagnetic exposure From electric vehicle wireless power transfer system," IEEE Transactions on Intelligent Transportation Systems, Vol. 24, No. 8, 8886-8896, August 2023.
doi:10.1109/tits.2023.3235807        Google Scholar

2. Manfredi, Paolo, "A hybrid polynomial chaos expansion --- Gaussian process regression method for Bayesian uncertainty quantification and sensitivity analysis," Computer Methods in Applied Mechanics and Engineering, Vol. 436, 117693, March 2025.
doi:10.1109/epeps61853.2024.10754236        Google Scholar

3. Huo, Shenghang, Yujia Song, Alistair Duffy, and Jinjun Bai, "Uncertainty quantification of human electromagnetic exposure from mobile phone antenna based on migration co-kriging," IEEE Transactions on Antennas and Propagation, Vol. 73, No. 11, 9203-9212, November 2025.
doi:10.1109/tap.2025.3590080        Google Scholar

4. Hu, Runze, Vikass Monebhurrun, Ryutaro Himeno, Hideo Yokota, and Fumie Costen, "A general framework for building surrogate models for uncertainty quantification in computational electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 70, No. 2, 1402-1414, February 2022.
doi:10.1109/tap.2021.3111333        Google Scholar

5. Klink, Dieter, Petrie Meyer, and Werner Steyn, "Efficient yield estimation of multiband patch antennas using NLPLS-based PCE," IEEE Transactions on Antennas and Propagation, Vol. 70, No. 8, 7037-7045, August 2022.
doi:10.1109/tap.2021.3138496        Google Scholar

6. Biondi, Alessandro, Dries Vande Ginste, Daniel De Zutter, Paolo Manfredi, and Flavio G. Canavero, "Variability analysis of interconnects terminated by general nonlinear loads," IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 3, No. 7, 1244-1251, July 2013.
doi:10.1109/tcpmt.2013.2259896        Google Scholar

7. Shen, Jianxiang, Heng Yang, and Ji Chen, "Analysis of electrical property variations for composite medium using a stochastic collocation method," IEEE Transactions on Electromagnetic Compatibility, Vol. 54, No. 2, 272-279, April 2012.
doi:10.1109/temc.2011.2163073        Google Scholar

8. Bai, Jinjun, Gang Zhang, Di Wang, Alistair P. Duffy, and Lixin Wang, "Performance comparison of the SGM and the SCM in EMC simulation," IEEE Transactions on Electromagnetic Compatibility, Vol. 58, No. 6, 1739-1746, December 2016.
doi:10.1109/temc.2016.2588580        Google Scholar

9. Bai, Jinjun, Gang Zhang, Alistair P. Duffy, and Lixin Wang, "Dimension-reduced sparse grid strategy for a stochastic collocation method in EMC software," IEEE Transactions on Electromagnetic Compatibility, Vol. 60, No. 1, 218-224, February 2018.
doi:10.1109/temc.2017.2699691        Google Scholar

10. He, Jiachuan, Steven A. Mattis, Troy D. Butler, and Clint N. Dawson, "Data-driven uncertainty quantification for predictive flow and transport modeling using support vector machines," Computational Geosciences, Vol. 23, No. 4, 631-645, August 2018.
doi:10.1007/s10596-018-9762-4        Google Scholar

11. Bhattacharyya, Biswarup, "Uncertainty quantification of dynamical systems by a POD-Kriging surrogate model," Journal of Computational Science, Vol. 60, 101602, April 2022.
doi:10.1016/j.jocs.2022.101602        Google Scholar

12. Trinchero, Riccardo, Mourad Larbi, Hakki M. Torun, Flavio G. Canavero, and Madhavan Swaminathan, "Machine learning and uncertainty quantification for surrogate models of integrated devices with a large number of parameters," IEEE Access, Vol. 7, 4056-4066, 2019.
doi:10.1109/access.2018.2888903        Google Scholar

13. Bai, Jinjun, Shenghang Huo, Alistair Duffy, and Bing Hu, "Improvement of nonembedded EMC uncertainty analysis methods based on data fusion technique," IEEE Transactions on Electromagnetic Compatibility, Vol. 66, No. 6, 1999-2009, December 2024.
doi:10.1109/temc.2024.3447784        Google Scholar

14. Lagouanelle, Paul, Fabio Freschi, and Lionel Pichon, "Adaptive sampling for fast and accurate metamodel-based sensitivity analysis of complex electromagnetic problems," IEEE Transactions on Electromagnetic Compatibility, Vol. 65, No. 6, 1820-1828, December 2023.
doi:10.1109/temc.2023.3320285        Google Scholar

15. Rehme, Michael F., Fabian Franzelin, and Dirk Pflüger, "B-splines on sparse grids for surrogates in uncertainty quantification," Reliability Engineering & System Safety, Vol. 209, 107430, May 2021.
doi:10.1016/j.ress.2021.107430        Google Scholar

16. Farcaş, Ionuţ-Gabriel, Gabriele Merlo, and Frank Jenko, "A general framework for quantifying uncertainty at scale," Communications Engineering, Vol. 1, No. 1, 43, December 2022.
doi:10.1038/s44172-022-00045-0        Google Scholar

17. "IEC/IEEE international standard --- Measurement procedure for the assessment of specific absorption rate of human exposure to radio frequency fields from hand-held and body-mounted wireless communication devices --- Part 1528: Human models, instrumentation, and procedures (frequency range of 4 MHz to 10 GHz)," IEC/IEEE International Standard, 2020.
doi:10.1109/ieeestd.2020.9231298

18. "IEEE recommended practice for determining the peak spatial-average specific absorption rate (SAR) in the human head from wireless communications devices: Measurement techniques," IEEE Recommended Practice, 2013.
doi:10.1109/ieeestd.2013.6589093

19. Moghnieh, Hawraa, Mohammad Rammal, Rabih Barakeh, and Elias Rachid, "Analysis of human head interaction in handset antennas using ground plane corrugation," IEEE Access, Vol. 12, 151834-151845, 2024.
doi:10.1109/access.2024.3476368        Google Scholar

20. Bai, Jinjun, Lixin Wang, Di Wang, Alistair P. Duffy, and Gang Zhang, "Validity evaluation of the uncertain EMC simulation results," IEEE Transactions on Electromagnetic Compatibility, Vol. 59, No. 3, 797-804, June 2017.
doi:10.1109/temc.2016.2621182        Google Scholar