Data Modeling of Multi-Axle Special Vehicles and Lateral Dynamics Applications

doi:10.12382/bgxb.2022.0811

Abstract

Abstract:

The dynamic model of multi-axle special vehicles has strong nonlinearity. The modeling method based on physical laws requires precise model parameters and complex mathematical equations to reflect the characteristics of vehicle dynamics. In the absence of accurate prior physical parameter information of the vehicle and dynamic function relationship, to improve the fidelity of vehicle dynamics modeling, a data modeling method based on neural networks is proposed for the lateral dynamic behavior of a five-axle special vehicle. At the same time, it is used as an input to predict the state of the next moment, and the recursive update of data modeling is realized; for the closed-loop network model, a training strategy is designed for the closed-loop structure, and intermediate variables are introduced into the network model, so that the network still maintains the closed-loop structure during the training phase; the network module adopts a combination of Gate Recurrent Unit (GRU) and Full Neural Networks (FNN); the data set is generated by the TruckSim simulation model that has been verified by real vehicles. The results show that it is difficult for physical modeling to accurately predict vehicle state information without accurate prior vehicle information, and the data model has better fidelity. The closed-loop training method can make the network with a closed-loop structure have better fidelity. The maximum absolute errors of the prediction of lateral velocity and yaw velocity are only 0.079km/h and 0.342°/s; compared with the results of open-loop training, the maximum errors are reduced by 58.40% and 49.48%.

Key words: multi-axle special vehicle, lateral dynamics, data modeling, neural network

CLC Number:

TJ301

CHEN Jianwei, YU Chuanqiang, LIU Zhihao, TANG Shengjin, ZHANG Zhihao, SHU Hongbin. Data Modeling of Multi-Axle Special Vehicles and Lateral Dynamics Applications[J]. Acta Armamentarii, 2023, 44(1): 165-175.

Figures/Tables 28

Fig.1 Single track model

Fig.2 Update process of the physical model

Fig.3 Closed-loop network model

Table 1 GRU module parameters

超参数	数值
GRU层数	1
输出层维度	150
输入序列长度	1

Table 2 FNN module parameters

超参数	数值
FNN层数	2
第1层维度	150×150
第1层激活函数	Tanh激活函数
第2层维度	150×2
第2层激活函数	无

Fig.4 Experimental platform

Fig.5 Experimental path

Fig.6 Experimental longitudinal velocity

Fig.7 The experimental steering wheel angle

Fig.8 Lateral acceleration verification

Fig.9 Yaw rate verification

Table 3 Trucksim model error

工况	均方根误差	最大误差
侧向加速度/g	0.0023	0.0735
横摆角速度/(°·s^-1)	0.0359	3.6006

Table 4 Trucksim simulated vehicle parameters

参数	数值
簧载质量m_s/kg	50200
转向系传动比τ	24.6
绕z轴转动惯量I_z/(kg·m²)	734251
绕侧倾轴转动惯量I_x/(kg·m²)	230700
质心高度h_c/m	1.4
轮胎半径r_w/m	0.55
悬架等效侧倾刚度K_s/(N·m/rad)	2000000
悬架等效阻尼系数C_s/(N·m·s/rad)	120000

Fig.10 Driving path in dataset

Fig.11 Longitudinal velocity in Dataset

Fig.12 RMSprop optimizer update strategy

Fig.13 Dynamic update strategy of global learning rate

Fig.14 Training in closed structure

Fig.15 Comparison of loss function changes

Fig.16 Comparison of lateral velocity prediction results

Fig.17 Absolute value error of lateral velocity

Table 5 Statistical analysis of lateral velocity

模型	标准差	最大值/ (km·h^-1)	平均值/ (km·h^-1)
线性化横向模型	0.035	0.233	0.061
开环训练模型	0.012	0.103	0.017
闭环训练模型	0.007	0.079	0.006

Fig.18 Relative error analysis of lateral velocity

Fig.19 Comparison of lateral velocity prediction results

Fig.20 Absolute value error of lateral velocity

Table 6 Statistical analysis of yaw rate error

模型	标准差	最大值/ ((°)·s^-1)	平均值/ ((°)·s^-1)
线性化横向模型	0.283	0.885	0.514
开环训练	0.073	0.677	0.144
闭环训练	0.041	0.342	0.056

Fig.21 Relative error analysis of yaw rate

Table A-1 Linearized lateral dynamics model parameters

参数	数值
整车质量m/kg	50200
1轴至质心距离L₁/m	5.7
2轴至质心距离L₂/m	3.2
3轴至质心距离L₃/m	1.1
4轴至质心距离L₄/m	3.4
5轴至质心距离L₅/m	5.9
绕z轴转动惯量I_z/(kg·m²)	734251
传动比η	28
各轴轮胎侧偏刚度C/(N·rad^-1)	300000
时间间隔T/s	0.01

References 21

[1]	陈慧岩, 陈舒平, 龚建伟. 智能汽车横向控制方法研究综述[J]. 兵工学报, 2017, 38(6):1203-1214. doi: 10.3969/j.issn.1000-1093.2017.06.021
	CHEN H Y, CHEN S P, GONG J W. A review on the research of lateral control for intelligent vehicles[J]. Acta Armamentarii, 2017, 38(6):1203-1214. (in Chinese)
[2]	张超朋, 刘庆霄, 董昊天, 等. 无人驾驶履带车辆机电联合制动的协调控制[J]. 兵工学报, 2022, 43(11):2727-2737.
	ZHANG Z C, LIU Q X, DONG H T, et al. Coordinated control of electric-mechanical combined braking system for unmanned tracked vehicles[J]. Acta Armamentarii, 43(11):2727-2737. (in Chinese)
[3]	李春明, 吴维, 郭智蔷, 等. 履带车辆纵向与垂向耦合动力学模型及功率特性[J]. 兵工学报, 2021, 42(3):449-458. doi: 10.3969/j.issn.1000-1093.2021.03.001
	LI C M, WU W, GUO Z Q, et al. Longitudinal and vertical coupled dynamic model and power characteristics of tracked vehicle[J]. Acta Armamentarii, 2021, 42(3):449-458. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.03.001
[4]	王博洋, 关海杰, 龚建伟, 等. 面向异构履带车辆的统一运动规划方法[J]. 兵工学报, 2022, 43(2):241-251.
	WANG B Y, GUAN H J, GONG J W, et al. Unified motion planning method for heterogeneous tracked vehicles[J]. Acta Armamentarii, 2022, 43(2):241-251. (in Chinese) doi: 10.3969/j.issn.1000-1093.2022.02.001
[5]	刘志浩, 高钦和, 刘准, 等. 重载轮胎面内刚柔耦合动力学建模及振动传递特性分析[J]. 兵工学报, 2018, 39(2):224-233. doi: 10.3969/j.issn.1000-1093.2018.02.003
	LIU Z H, GAO Q H, LIU Z, et al. In-plane rigid-elastic coupling dynamic modeling and vibration response prediction of heavy duty radial tire[J]. Acta Armamentarii, 2018, 39(2):224-233. (in Chinese)
[6]	陈鼎, 侯亮, 祝青园, 等. 考虑轮胎几何与胎压因素的轮地相互作用力模型及其参数辨识[J]. 机械工程学报, 2020, 56(2):174-183. doi: 10.3901/JME.2020.02.174
	CHEN D, HOU L, ZHU Q Y, et al. Tire-ground interaction force model and its parameter identification considering tire geometry and pressure[J]. Journal of Mechanical Engineering, 2020, 56(2):174-183. (in Chinese) doi: 10.3901/JME.2020.02.174
[7]	许男, 周健锋, 郭孔辉, 等. 胎压载荷耦合效应下复合工况UniTire轮胎模型[J]. 机械工程学报, 2020, 56(16):193-203. doi: 10.3901/JME.2020.16.193
	XU N, ZHOU J F, GUO K H, et al, UniTire model under combined slip conditions with the coupling effect of inflation pressure and vertical load[J]. Journal of Mechanical Engineering, 2020, 56(16):193-203. (in Chinese) doi: 10.3901/JME.2020.16.193
[8]	王珍, 项昌乐, 刘辉, 等. 基于集中-分布参数模型的车辆机电传动系统动力学响应及影响规律[J]. 兵工学报, 2021, 42(10):2145-2158. doi: 10.3969/j.issn.1000-1093.2021.10.010
	WANG Z, XIANG C L, LIU H, et al. Dynamics response and influence factors of electromechanical transmission system based on lumped-distributed parameter model[J]. Acta Armamentarii, 2021, 42(10):2145-2158. (in Chinese)
[9]	李睿, 项昌乐, 王超, 等. 自动驾驶履带车辆鲁棒自适应轨迹跟踪控制方法[J]. 兵工学报, 2021, 42(6):1128-1137. doi: 10.3969/j.issn.1000-1093.2021.06.002
	LI R, XIANG C L, WANG C, et al. Robust adaptive trajectory tracking control approach for autonomous[J]. Tracked Vehicles[J]. Acta Armamentarii, 2021, 42(6): 1128-1137. (in Chinese)
[10]	郭弘明, 席军强, 陈慧岩, 等. 电驱动无人履带车辆线控机电联合制动技术研究[J]. 兵工学报, 2019, 40(6):1130-1136. doi: 10.3969/j.issn.1000-1093.2019.06.002
	GUO H M, XI J Q, CHEN H Y, et al. Research on wire-controlled electro-mechanical combined braking technology for electric drive unmanned tracked vehicles[J]. Acta Armamentarii, 2019, 40(6):1130-1136. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.06.002
[11]	邹渊, 张彬, 张旭东, 等. 基于归一化优势函数的强化学习混合动力履带车辆能量管理[J]. 兵工学报, 2021, 42(10):2159-2169.
	ZOU Y, ZHANG B, ZHANG X D, et al. Energy management of hybrid tracked vehicle based on reinforcement learning with normalized advantage function[J]. Acta Armamentarii, 2021, 42(10):2159-2169. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.10.011
[12]	王博洋, 龚建伟, 张瑞增, 等. 基于真实驾驶数据的运动基元提取与再生成[J]. 机械工程学报, 2020, 56(16):155-165. doi: 10.3901/JME.2020.16.155
	WANG B Y, GONG J W, ZHANG R Z, et al. Motion primitives extraction and regeneration based on real driving data[J]. Journal of Mechanical Engineering, 2020, 56(16):155-165. (in Chinese) doi: 10.3901/JME.2020.16.155
[13]	江昕炜, 陈龙, 华一丁, 等. 基于改进型ELM的熟练驾驶员行车轨迹拟合方法研究[J]. 汽车工程, 2021, 43(11):1620-1630.
	JIANG X W, CHEN L, HUA Y D, et al. Research on skilled driver’s trajectory fitting based on improved ELM[J]. Automotive Engineering, 2021, 43(11):1620-1630. (in Chinese)
[14]	PAN Y J, NIE X B, LI Z X, et al. Data-driven vehicle modeling of longitudinal dynamics based on a multibody model and deep neural networks[J]. Measurement, 2021, 180:109541. doi: 10.1016/j.measurement.2021.109541 URL
[15]	DA LIO M, BORTOLUZZI D, ROSATI PAPINIG P. Modelling longitudinal vehicle dynamics with neural networks[J]. Vehicle System Dynamics, 2019, 58: 1-19. doi: 10.1080/00423114.2018.1564834 URL
[16]	RUTHERFORD S J, COLE D J. Modelling nonlinear vehicle dynamics with neural networks[J]. International Journal of Vehicle Design, 2010, 53: 260-287. doi: 10.1504/IJVD.2010.034101 URL
[17]	CAO X U, LI H Y, LIU C X, et al. Vehicle longitudinal and lateral dynamics modeling by deep neural network[C]//Proceedings of 2021 IEEE International Conference on Real-time Computing and Robotics. Xining, China: RCAR, 2021:7-13.
[18]	HERMANSDORFER L, TRAUTH R, BETZ J, et al. End-to-end Neural network for vehicle dynamics modeling[C]//Proceedings of the 2020 6th IEEE Congress on Information Science and Technology. Agadir-Essaouira, Morocco: CIST, 2020:407-412.
[19]	WALACH J. Data normalization and scaling: consequences for the analysis in omics sciences[J]. Comprehensive Analytical Chemistry, 2018, 82:165-196.
[20]	WEN M, XU Y X, ZHENG Y L, et al. Sparse deep neural networks using L-1, L-infinity-weight normalization[J]. Statistica Sinica, 2021, 31(3):1397-1414.
[21]	XU D P, ZHANG S D, ZHANG H S, et al. Convergence of the RMSProp deep learning method with penalty for nonconvex optimization[J]. Neural Networks, 2021, 139:17-23. doi: 10.1016/j.neunet.2021.02.011 pmid: 33662649