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

doi:10.3969/j.issn.1674-8484.2022.01.006

Abstract

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

CLC Number:

U463.33

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.

Figures/Tables 11

References 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