Tire parameter fitting for combined conditions based on artemisinin hybrid optimization

doi:10.3969/j.issn.1674-8484.2026.02.002

Abstract

Abstract:

A parameter identification method, named the artemisinin hybrid optimization (AHO) algorithm, was proposed with combining the artemisinin optimization (AO) algorithm and the post-processing optimization to provide a tire model foundation for vehicle control strategies. The AO algorithm conducted the global parameter identification of the tire model based on the magic formula, using the test data from 3 conditions (the pure longitudinal slip, the pure side slip, and the combined conditions involving the tire roll, the side slip, and the longitudinal slip), before performing post-processing optimization by integrating the sensitivity analysis and the parameter significance. The results show that the AHO increases the overall accuracy of the longitudinal force by 1.83%, 1.87%, and 1.71%, and that of the lateral force by 1.62%, 3.86%, and 1.80% respectively under the combined conditions, compared with the stepwise identification method, genetic algorithm, and least squares method. Therefore, the AHO algorithm improves the identification accuracy of tire mechanical models under the combined conditions.

Key words: vehicle control strategies, tire models, magic formula, combined conditions, artemisinin hybrid optimization (AHO) algorithm

CLC Number:

U463.341

DING Wenhao, WANG Fei, JIN Yanxi, ZHAO Yirui, WU Tianqi. Tire parameter fitting for combined conditions based on artemisinin hybrid optimization[J]. Journal of Automotive Safety and Energy, 2026, 17(2): 170-178.

Figures/Tables 12

References 20

[1]	董梒, 季学武, 陶书鑫, 等. 商用车电控转向系统的发展现状与趋势[J]. 汽车工程, 2024, 46(5): 816-829.
	DONG Han, JI Xuewu, TAO Shuxin, et al. Development status and trends of electronic control steering systems for commercial vehicles[J]. *Autom Engineering*, 2024, 46(5): 816-829. (in Chinese)
[2]	Ayyasamy S. A comprehensive review on advanced driver assistance system[J]. *J Soft Comput Parad*, 2022, 4(2): 69-81.
[3]	卢荡, 索艳茹, 孙宇航, 等. 基于无量纲格式的轮胎侧倾侧偏力学特性预测[J]. 吉林大学学报(工学版), 2025, 55(5): 1516-1524.
	LU Dang, SUO Yanru, SUN Yuhang, et al. Estimation of tire camber and sideslip combined mechanical characteristics based on dimensionless expression[J]. J Jilin Univ (Engi Tech Ed), 2025, 55(5): 1516-1524. (in Chinese)
[4]	张硕, 李潇, 陈轶嵩, 等. 智能车辆自适应轨迹跟踪控制方法研究[J]. 汽车安全与节能学报, 2025, 16(2): 303-314.
	ZHANG Shuo, LI Xiao, CHEN Yisong, et al. Research on adaptive trajectory tracking control method for intelligent vehicle[J]. *J Autom Safe Energ*, 2025, 16(2): 303-314. (in Chinese)
[5]	Pacejka H B, Besselink I J M. Magic formula tyre model with transient properties[J]. *Vehi Syst Dyn*, 1997, 27(S1): 234-249.
[6]	郭孔辉, 杨杰. 大侧倾角下UniTire稳态侧倾侧偏工况侧向力模型[J]. 机械工程学报, 2014, 50(8): 95-101.
	GUO Konghui, YANG Jie. Steady-state UniTire lateral force model under sideslip combined with large camber condition[J]. *J Mech Engi*, 2014, 50(8): 95-101. (in Chinese)
[7]	边伟, 龚佳慧, 文爱民, 等. 基于遗传算法的魔术公式轮胎模型参数两级辨识[J]. 重庆交通大学学报(自然科学版), 2017, 36(5): 115-120. doi: 10.3969/j.issn.1674-0696.2017.05.20
	BIAN Wei, GONG Jiahui, WEN Aimin, et al. Two levels of parameter identification of magic formula tire model based on genetic algorithm[J]. J Chongqing Jiaotong Univ (Nat Sci Ed), 2017, 36(5): 115-120. (in Chinese)
[8]	郑香美, 高兴旺, 赵志忠. 基于“魔术公式”的轮胎动力学仿真分析[J]. 机械与电子, 2012(9): 16-20.
	ZHENG Xiangmei, GAO Xingwang, ZHAO Zhizhong. Simulation analysis of tire dynamic based on “magic formula”[J]. Mech Elect, 2012(9): 16-20. (in Chinese)
[9]	Olazagoitia J L, Perez J A, Badea F. Identification of tire model parameters with artificial neural networks[J]. *Appl Sci*, 2020, 10(24): 9110.
[10]	尹珩沣, 卢荡, 闵海涛, 等. 侧倾角对轮胎转偏力学特性影响研究[J]. 汽车工程, 2025, 47(2): 342-355.
	YIN Hengfeng, LU Dang, MIN Haitao, et al. Study on the influence of inclination angle on the mechanical characteristics of tire turn-slip[J]. *Autom Engineering*, 2025, 47(2): 342-355. (in Chinese)
[11]	Pacejka H B, Besselink I J M. Tire and Vehicle Dynamics[M]. Oxford: Butterworth-Heinemann, 2012: 165-211.
[12]	Kennedy J. Swarm intelligence[M]// Handbook of Nature-Inspired and Innovative Computing: Integrating Classical Models with Emerging Technologies. Boston, MA: Springer US, 2006: 187-219.
[13]	YUAN Chong, ZHAO Dong, Heidari A A, et al. Artemisinin optimization based on malaria therapy: Algorithm and applications to medical image segmentation[J]. *Displays*, 2024, 84: 102740. doi: 10.1016/j.displa.2024.102740 URL
[14]	Beheshti Z, Shamsuddin S M H. A review of population-based meta-heuristic algorithms[J]. *Int’l J Advan Soft Comput Appl*, 2013, 5(1): 1-35.
[15]	Druckmann S, Banitt Y, Gidon A A, et al. A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data[J]. *Front Neurosci*, 2007, 1: 56.
[16]	肖前湖, 马超. 基于MATLAB遗传算法和GUI的FSAE轮胎魔术公式辨识[C]// 2021中国汽车工程学会年会论文集(8). 中国汽车工程学会, 重庆理工大学车辆工程学院, 2021: 139-144.
	XIAO Qianhu, MA Chao. Identification of FSAE tire magic formula based on MATLAB genetic algorithm and GUI[C]// Proc 2021 Ann Conf Chin Soc Autom Engi (8). Vehicle Engineering Institute, Chongqing University of Technology, 2021: 139-144. (in Chinese)
[17]	LI Yongshun, WANG Guo, MIN Yongzhi, et al. Sensitivity analysis of power quality factors on additional losses of distribution network lines based on Sobol’method[C]// 2023 7th Int’l Conf Smart Grid Smart Cities (ICSGSC). IEEE, 2023: 205-209.
[18]	毛桥. UniTire轮胎模型建模测试方法研究[D]. 长春: 吉林大学, 2024.
	MAO Qiao. Research on UniTire tire model modeling test method[D]. Changchun: Jilin University, 2024. (in Chinese)
[19]	Saltelli A, Annoni P, Azzini I, et al. Variance based sensitivity analysis of model output: Design and estimator for the total sensitivity index[J]. *Comput Phys Commun, 2010, 181*(2): 259-270.
[20]	冯哲. 基于Adams的UniTire与MF轮胎模型应用对比研究[D]. 长春: 吉林大学, 2022.
	FENG Zhe. A comparative study on the application of UniTire and MF tire models based on Adams[D]. Changchun: Jilin University, 2022. (in Chinese)

参数	纯纵滑工况(纵向力)	纯侧偏工况(侧向力)
形状因子	PCX1	PCY1
峰值因子	PDX1、PDX2、PDX3	PDY1、PDY2、PDY3
曲率因子	PEX1、PEX2、PEX3、PEX4	PEY1、PEY2、PEY3、PEY4
刚度因子	PKX1、PKX2、PKX3	PKY1、PKY2、PKY3
曲线水平偏移因子	PHX1、PHX2	PHY1、PHY2、PHY3
曲线垂直偏移因子	PVX1、PVX2	PVY1、PVY2、PVY3、PVY4

参数	纯纵滑工况(纵向力)	纯侧偏工况(侧向力)
形状因子	PCX1	PCY1
峰值因子	PDX1、PDX2、PDX3	PDY1、PDY2、PDY3
曲率因子	PEX1、PEX2、PEX3、PEX4	PEY1、PEY2、PEY3、PEY4
刚度因子	PKX1、PKX2、PKX3	PKY1、PKY2、PKY3
曲线水平偏移因子	PHX1、PHX2	PHY1、PHY2、PHY3
曲线垂直偏移因子	PVX1、PVX2	PVY1、PVY2、PVY3、PVY4

参数	纵向力权函数的辨识参数	侧向力权函数的辨识参数
刚度因子	RBX1、RBX2	RBY1、RBY2、RBY3
形状因子	RCX1	RCY1
曲率因子	REX1、REX2	REY1、REY2
水平偏移因子	RHX1	RHY1、RHY2
垂直偏移因子	-	RVY1、RVY2、RVY3、 RVY4、RVY5、RVY6

参数	纵向力权函数的辨识参数	侧向力权函数的辨识参数
刚度因子	RBX1、RBX2	RBY1、RBY2、RBY3
形状因子	RCX1	RCY1
曲率因子	REX1、REX2	REY1、REY2
水平偏移因子	RHX1	RHY1、RHY2
垂直偏移因子	-	RVY1、RVY2、RVY3、 RVY4、RVY5、RVY6

工况	SA / (°)	IA / (°)	F_z / kN	κ / %
纯侧偏	-12~12	0, 2, 4	1.13, 0.89, 0.67, 0.22	0
纯纵滑	-6, -3, 0	0, 2, 4	1.13, 0.89, 0.67, 0.22	-20~20
复合	-6, -3, 0	0, 2, 4	1.13, 0.89, 0.67, 0.22	-20~20