复合工况下轮胎非线性力学特性的分段仿射辨识

doi:10.3969/j.issn.1674-8484.2022.01.006

汽车安全与节能学报 ›› 2022, Vol. 13 ›› Issue (1): 70-77.DOI: 10.3969/j.issn.1674-8484.2022.01.006

复合工况下轮胎非线性力学特性的分段仿射辨识

王玉麟(), 胡伟伟, 孙晓强()

江苏大学汽车工程研究院,镇江212013,中国

收稿日期:2021-06-12 修回日期:2021-11-16 出版日期:2022-03-31 发布日期:2021-04-02
通讯作者: 孙晓强
作者简介:*孙晓强,副教授。E-mail：sxq@ujs.edu.cn。
王玉麟(1997–),男(汉族),江苏,硕士研究生。E-mail:1124018443@qq.com。
基金资助:
国家自然科学基金资助项目(52072161, U20A20331);汽车安全与节能国家重点实验室开放课题(KF2016)

Piecewise affine identification of the tire nonlinear mechanical properties under combined conditions

WANG Yulin(), HU Weiwei, SUN Xiaoqiang()

Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China

Received:2021-06-12 Revised:2021-11-16 Online:2022-03-31 Published:2021-04-02
Contact: SUN Xiaoqiang

摘要/Abstract

摘要：

为实现复合工况下轮胎非线性力学特性的准确模拟,提出了一种基于分段仿射（PWA）辨识的数学建模方法。采用基于Gauss混合模型的统计数据聚类方法进行轮胎力学特性试验数据聚类,将原始试验数据划分为若干个子集;基于最小二乘算法进行仿射子模型参数估计;结合改进的近似支持向量机算法完成相邻仿射子模型间分界面系数矩阵的求解;将辨识模型仿真结果与原始试验数据进行对比,验证辨识精度。结果表明：所辨识的轮胎分段仿射模型能够很好地拟合复合工况下轮胎纵向力及侧向力与其影响因素间的非线性关系,模型拟合精度高于93%。

关键词: 轮胎, 非线性力学特性, 复合工况, 分段仿射（PWA）辨识, 精度验证

Abstract:

A mathematical modeling approach was proposed based on piecewise affine (PWA) identification for accurately approximating the nonlinear characteristics of the tire mechanical properties under longitudinal and lateral combined driving conditions. The statistical data clustering method based on Gaussian mixture model was used to conduct the data clustering, thus the original experimental data of the tire mechanical properties can be divided into several subsets. The parameter estimation of the affine submodel was achieved based on least square algorithm. the hyperplane coefficient matrices between adjacent affine sub-models were calculated by using the modified proximal support vector machine method. To verify the accuracy of the identified model, the comparison between the model simulation data and the experimental data was conducted. The results show that the PWA identified tire model can well approximate the nonlinear relationship between the tire longitudinal force and lateral force and their influencing factors under combined conditions, and the overall fitting accuracy of the model is more than 93%.

Key words: tire, nonlinear mechanical properties, combined conditions, piecewise affine (PWA) identification, accuracy verification

中图分类号:

U463.33

王玉麟, 胡伟伟, 孙晓强. 复合工况下轮胎非线性力学特性的分段仿射辨识[J]. 汽车安全与节能学报, 2022, 13(1): 70-77.

WANG Yulin, HU Weiwei, SUN Xiaoqiang. Piecewise affine identification of the tire nonlinear mechanical properties under combined conditions[J]. Journal of Automotive Safety and Energy, 2022, 13(1): 70-77.

图/表 11

参考文献 21

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轮胎垂向载荷, F_z	8.06 kN
轮胎侧偏角, α	-10°~10°
轮胎纵向滑移率, λ	-1.0~0.5
路面附着因数, μ	0.34

轮胎垂向载荷, F_z	8.06 kN
轮胎侧偏角, α	-10°~10°
轮胎纵向滑移率, λ	-1.0~0.5
路面附着因数, μ	0.34

轮胎纵向力			轮胎侧向力
θ_i_-1	θ_i_-2	θ_i_-3	θ_i_-1	θ_i_-2	θ_i_-3
-177.8	14 936	-1 713	-70.97	-4 239	1 820
112.2	-163	-3 266	-87.82	154.6	124
-82.1	-804	3 283	-14.83	-3 887	-2 338
175.1	13 775	1 784	-66.3	-630	-773
-0.58	-2 513	3 614	-86.8	-2 316	-1 285
30.3	-1 533	-3 332	-340.0	-141.4	8.5
-12.2	37 666	46.5	-56.0	586	476
120.8	170	3 292	-165.3	2 686	981
-191.0	9 411	2 267	-48.9	4 741	2 012
-34.0	-986	-3 088	-81.9	3 309	-1 680
-11.9	-536	-2 686
-119.1	-111	-3 346
-193.7	16 750	-1 590
11.7	-607	-2 746

轮胎纵向力			轮胎侧向力
θ_i_-1	θ_i_-2	θ_i_-3	θ_i_-1	θ_i_-2	θ_i_-3
-177.8	14 936	-1 713	-70.97	-4 239	1 820
112.2	-163	-3 266	-87.82	154.6	124
-82.1	-804	3 283	-14.83	-3 887	-2 338
175.1	13 775	1 784	-66.3	-630	-773
-0.58	-2 513	3 614	-86.8	-2 316	-1 285
30.3	-1 533	-3 332	-340.0	-141.4	8.5
-12.2	37 666	46.5	-56.0	586	476
120.8	170	3 292	-165.3	2 686	981
-191.0	9 411	2 267	-48.9	4 741	2 012
-34.0	-986	-3 088	-81.9	3 309	-1 680
-11.9	-536	-2 686
-119.1	-111	-3 346
-193.7	16 750	-1 590
11.7	-607	-2 746

复合工况下轮胎非线性力学特性的分段仿射辨识

Piecewise affine identification of the tire nonlinear mechanical properties under combined conditions

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