A Multi-Fidelity Surrogate Model for Aerodynamic Coefficients of Iced Bundle Conductors

Yang Hui; Yan Bo; Gao Yingbo; Zhang Bo; Lü Zhongbin; Liu Guanghui; Wu Xingwang; Deng Huachao

doi:10.21656/1000-0887.460131

Volume 47 Issue 9

Sep. 2026

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(9): 1159-1178

Yang Hui, Yan Bo, Gao Yingbo, Zhang Bo, Lü Zhongbin, Liu Guanghui, Wu Xingwang, Deng Huachao. A Multi-Fidelity Surrogate Model for Aerodynamic Coefficients of Iced Bundle Conductors[J]. Applied Mathematics and Mechanics, 2026, 47(9): 1159-1178. doi: 10.21656/1000-0887.460131

Citation:

PDF( 10882 KB)

A Multi-Fidelity Surrogate Model for Aerodynamic Coefficients of Iced Bundle Conductors

doi: 10.21656/1000-0887.460131

1.
College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R. China
2.
State Grid Henan Electric Power Research Institute, Zhengzhou 450052, P.R. China

Received Date: 2025-06-27
Rev Recd Date: 2025-07-30
Publish Date: 2026-09-01

Abstract

Abstract

For quad-, six-, and eight-bundle conductors with crescent-shaped ice, the air flow fields around the iced conductors under different icing and wind conditions were numerically simulated with the computational fluid dynamics, and the variations of drag, lift, and torque coefficients of each iced sub-conductor vs. the wind attack angle were obtained. With the high-fidelity data of aerodynamic coefficients measured by wind tunnel tests and the low-fidelity data by numerical simulations, a multi-fidelity surrogate model was built by means of the BP neural networks, the random forest algorithm and the feature enhancement technique, with the sub-conductor position, the ice thickness, the ice accretion angle, the wind speed, the turbulence intensity and the wind attack angle as the input, and the aerodynamic coefficients of each sub-conductor as the output. The efficiency of the surrogate model was verified through the analysis of aerodynamic stability regions based on the Den Hartog and Nigol coefficients, and through the galloping simulations of typical iced bundle conductors. By this multi-fidelity surrogate model, a software with the bundle number of conductor lines, the ice thickness, the ice accretion angle, the wind speed and the turbulence intensity as the input, and the aerodynamic coefficient vs. the wind attack angle for each iced sub-conductor as the output, was developed. This work lays a foundation for the investigation of galloping of iced transmission lines and its prevention technologies.
- iced bundled conductor,
- aerodynamic coefficient,
- machine learning,
- multi-fidelity surrogate model

(Contributed by Yan Bo, Member of the Editorial Board of AMM)

FullText(HTML)

References(39)

References

[1]	Nigol O, Buchan P G. Conductor galloping, part Ⅱ: torsional mechanism[J]. IEEE Transactions on Power Apparatus and Systems, 1981, PAS-100 (2): 708-720. doi: 10.1109/TPAS.1981.316922
[2]	Chabart O, Lilien J L. Galloping of electrical lines in wind tunnel facilities[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1998, 74: 967-976.
[3]	李万平, 杨新祥, 张立志. 覆冰导线群的静气动力特性[J]. 空气动力学学报, 1995(4): 427-434. Li Wanping, Yang Xinxiang, Zhang Lizhi. Static aerodynamic characteristics of the galloping of bundled iced power transmission lines[J]. Acta Aerodynamica Sinica, 1995(4): 427-434. (in Chinese)
[4]	李万平. 覆冰导线群的动态气动力特性[J]. 空气动力学学报, 2000, 18(4): 413-420. Li Wanping. Dynamic aerodynamic characteristics of the galloping of bundled iced power transmission lines[J]. Acta Aerodynamica Sinica, 2000, 18(4): 413-420. (in Chinese)
[5]	李万平, 黄河, 何锃. 特大覆冰导线气动力特性测试[J]. 华中科技大学学报(自然科学版), 2001, 29(8): 84-86. Li Wanping, Huang He, He Zeng. Aerodynamic characteristics of heavily iced conductors[J]. Journal of Huaxhong University of Science and Technology, 2001, 29(8): 84-86. (in Chinese)
[6]	肖正直, 晏致涛, 李正良, 等. 八分裂输电导线结冰风洞及气动力特性试验[J]. 电网技术, 2009, 33(5): 90-94. Xiao Zhengzhi, Yan Zhitao, Li Zhengliang, et al. Wind tunnel and aerodynamic characteristics tests for ice-covering of transmission line adopting 8-bundled conductor[J]. Power System Technology, 2009, 33(5): 90-94. (in Chinese)
[7]	马文勇, 顾明, 全涌, 等. 准椭圆形覆冰导线气动力特性试验研究[J]. 同济大学学报(自然科学版), 2010, 38(10): 1409-1413. Ma Wenyong, Gu Ming, Quan Yong, et al. Testing study on aerodynamic force characteristics of quasi-oval shape iced conductor[J]. Journal of Tongji University (Natural Science), 2010, 38(10): 1409-1413. (in Chinese)
[8]	张宏雁, 严波, 周松, 等. 覆冰四分裂导线静态气动力特性试验[J]. 空气动力学学报, 2011, 29(2): 150-154. Zhang Hongyan, Yan Bo, Zhou Song, et al. Static test on aerodynamic characteristics of iced quad bundled conductors[J]. Acta Aerodynamica Sinica, 2011, 29(2): 150-154. (in Chinese)
[9]	张宏雁, 严波, 刘小会, 等. 覆冰导线气动特性及驰振风洞试验[J], 振动与冲击, 2013, 32(10): 95-99. Zhang Hongyan, Yan Bo, Liu Xiaohui, et al. Wind-tunnel tests for aerodynamic characteristics and galloping behaviors of iced conductors[J]. Journal of Vibration and Shock, 2013, 32(10): 95-99. (in Chinese)
[10]	Hu J, Yan B, Zhou S, et al. Numerical investigation on galloping of iced quad bundle conductors[J]. IEEE Transactions on Power Delivery, 2012, 27(2): 784-792. doi: 10.1109/TPWRD.2012.2185252
[11]	周林抒, 严波, 张亮, 等. 新月形覆冰八分裂导线舞动特征研究[J]. 振动与冲击, 2015, 34(18): 183-189. Zhou Linshu, Yan Bo, Zhang Liang, et al. Study on galloping behaviors of eight bundled conductors with crescent-shaped ice[J]. Journal of Vibration and Shock, 2015, 34(18): 183-189. (in Chinese)
[12]	Lou W J, Lin W, Huang M F, et al. The impact of ice thickness on the aerodynamic characteristics of crescent shape iced conductors[J]. Acta Aerodynamica Sinica, 2013, 31(5): 616-622.
[13]	Flaga A, Pistol A, Krajewski P, et al. Aerodynamic and aeroelastic wind tunnel model tests of overhead power lines in triangular configuration under different icing conditions[J]. Cold Regions Science and Technology, 2020, 170: 102919. doi: 10.1016/j.coldregions.2019.102919
[14]	Wan Z Y, Zhang D D, Li Z B, et al. A wind tunnel study on the aerodynamic characteristics of ice-accreted twin bundled conductors[J]. International Journal of Structural Stability and Dynamics, 2022, 22(7): 2250038. doi: 10.1142/S0219455422500389
[15]	Braun A L, Awruch A M. Aerodynamic and aeroelastic analysis of bundled cables by numerical simulation[J]. Journal of Sound and Vibration, 2005, 284(1/2): 51-73.
[16]	黄河, 刘建军, 李万平. 覆冰导线绕流的数值模拟[J]. 辽宁工程技术大学学报, 2004, 23(6): 767-769. Huang He, Liu Jianjun, Li Wanping. Numerical simulations of fluid around iced conductors[J]. Journal of Liaoning Technical University, 2004, 23(6): 767-769. (in Chinese)
[17]	吕翼, 楼文娟, 孙珍茂, 等. 覆冰三分裂导线气动力特性的数值模拟[J]. 浙江大学学报(工学版), 2010, 44(1): 174-179. Lü Yi, Lou Wenjuan, Sun Zhenmao, et al. Numerical simulation of aerodynamic characteristics of three bundled iced transmission lines[J]. Journal of Zhejiang University (Engineering Science), 2010, 44(1): 174-179. (in Chinese)
[18]	Ishihara T, Oka S. A numerical study of the aerodynamic characteristics of ice-accreted transmission lines[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 177: 60-68. doi: 10.1016/j.jweia.2018.04.008
[19]	蔡萌琦, 严波, 吕欣, 等. 覆冰四分裂导线空气动力系数数值模拟[J]. 振动与冲击, 2013, 32(5): 132-137. Cai Mengqi, Yan Bo, Lü Xin, et al. Numerical investigation on aerodynamic coefficients of iced quad bundle conductor[J]. Journal of Vibration and Shock, 2013, 32(5): 132-137. (in Chinese)
[20]	Cai M Q, Yan B, Lu X, et al. Numerical simulation of aerodynamic coefficients of iced-quad bundle conductors[J]. IEEE Transactions on Power Delivery, 2015, 30(4): 1669-1676. doi: 10.1109/TPWRD.2015.2417890
[21]	张瑾, 祝贺. 峡谷、垭口地貌下导线流固耦合风偏振动分析[J]. 应用数学和力学, 2020, 41(7): 735-747. Zhang Jin, Zhu He. Fluid-structure coupling wind-induced vibration analysis of transmission lines across 2 close hills[J]. Applied Mathematics and Mechanics, 2020, 41(7): 735-747. (in Chinese)
[22]	Liao S K, Zhang Y, Chen X, et al. Research on aerodynamic characteristics of crescent iced conductor based on S-A finite element turbulence model[J]. Energies, 2022, 15(20): 7753. doi: 10.3390/en15207753
[23]	Zhao G F, Li Q Y, Li X, et al. Aerodynamic and vibration characteristics of iced power transmission conductors in a nonuniform wind field based on unsteady theory[J]. Energies, 2025, 18(3): 459. doi: 10.3390/en18030459
[24]	Huang G Z, Yan B, Mou Z Y, et al. Surrogate model for torsional behavior of bundle conductors and its application[J]. IEEE Transactions on Power Delivery, 2022, 37(1): 67-75. doi: 10.1109/TPWRD.2021.3053341
[25]	Huang G Z, Wu G N, Guo Y J, et al. Risk assessment models of power transmission lines undergoing heavy ice at mountain zones based on numerical model and machine learning[J]. Journal of Cleaner Production, 2023, 415: 137623. doi: 10.1016/j.jclepro.2023.137623
[26]	Mou Z Y, Yan B, Yang H X, et al. Prediction model for aerodynamic coefficients of iced quad bundle conductors based on machine learning method[J]. Royal Society Open Science, 2021, 8(10): 210568. doi: 10.1098/rsos.210568
[27]	Liang J H, Cai M Q, Wang Q Y, et al. Aerodynamic characteristics analysis of iced conductor based on BP neural network[J]. Buildings, 2023, 13(1): 64.
[28]	Chen S R, Bao X M, Lou W J, et al. Prediction of aerodynamic coefficients of iced conductors based on composite image and convolutional neural network[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2023, 238: 105430. doi: 10.1016/j.jweia.2023.105430
[29]	Han Z H, Görtz S. Hierarchical Kriging model for variable-fidelity surrogate modeling[J]. AIAA Journal, 2012, 50(9): 1885-1896. doi: 10.2514/1.J051354
[30]	Kang S, Lee K. Rapid estimation of the aerodynamic coefficients of a missilevia co-Kriging[J]. Journal of the Korean Society for Aeronautical & Space Sciences, 2020, 48(1): 13-21.
[31]	Alexandrov N M, Lewis R M, Gumbert C R, et al. Approximation and model management in aerodynamic optimization with variable-fidelity models[J]. Journal of Aircraft, 2001, 38(6): 1093-1101. doi: 10.2514/2.2877
[32]	刘佳, 杨克巍, 姜江, 等. 基于多保真度代理模型的装备系统参数估计方法[J]. 系统工程与电子技术, 2021, 43(1): 130-137. Liu Jia, Yang Kewei, Jiang Jiang, et al. Parameter estimation method of equipment system based on multi-fidelity surrogate model[J]. Systems Engineering and Electronics, 2021, 43(1): 130-137. (in Chinese)
[33]	王雨桐, 罗骁, 刘红阳, 等. 基于多保真深度神经网络的超声速客机声爆预测[J]. 航空学报, 2025, 46(20): 67-87. Wang Yutong, Luo Xiao, Liu Hongyang, et al. Sonic boom prediction of supersonic passenger aircraft based on multi-fidelity deep neural network[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(20): 67-87. (in Chinese)
[34]	Guo M W, Manzoni A, Amendt M, et al. Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 389: 114378. doi: 10.1016/j.cma.2021.114378
[35]	Zhou L S, Yan B, Zhang L, et al. Study on galloping behavior of iced eight bundle conductor transmission lines[J]. Journal of Sound and Vibration, 2016, 362: 85-110. doi: 10.1016/j.jsv.2015.09.046
[36]	Rumelhart D E, Hinton G E, Williams R J. Learning representations by back-propagating errors[J]. Nature, 1986, 323(6088): 533-536. doi: 10.1038/323533a0
[37]	Breiman L. Random forests[J]. Machine Learning, 2001, 45(1): 5-32. doi: 10.1023/A:1010933404324
[38]	Geurts P, Ernst D, Wehenkel L. Extremely randomized trees[J]. Machine Learning, 2006, 63(1): 3-42. doi: 10.1007/s10994-006-6226-1
[39]	刘小会, 严波, 张宏雁, 等. 覆冰导线舞动非线性数值模拟方法[J]. 应用数学和力学, 2009, 30(4): 457-468. http://www.applmathmech.cn/article/id/1222 Liu Xiaohui, Yan Bo, Zhang Hongyan, et al. Nonlinear numerical simulation method for galloping of iced conductor[J]. Applied Mathematics and Mechanics, 2009, 30(4): 457-468. (in Chinese) http://www.applmathmech.cn/article/id/1222