基于代理模型进化的履带车辆动力学参数优化

doi:10.12382/bgxb.2022.0266

摘要/Abstract

摘要：

为解决履带车辆动力学优化过程因代理模型构建和应用的不足而导致的参数寻优精度和效率不高的问题,提出基于代理模型进化的参数优化方法,将优化迭代和代理模型动态构建相融合,来降低仿真模型调用次数和提高优化效率。根据车辆几何拓扑结构,构建考虑履带包络效应的车辆多体动力学模型;提出优化设计变量空间的3层子空间划分方法,以及具有空间聚焦、空间约简和跳出局部寻优的多级模糊聚类空间约简方法,实现设计参数在3层子空间的高效缩减。以履带车辆多体动力学模型参数优化过程为例进行应用验证。研究结果表明:在3种路况下的履带车辆多体动力学优化过程降低仿真模型调用次数最高可达85%;表征履带车辆行进特性的综合性能指标分别提升约32.4%、24.5%、20.4%。证明了新方法可有效提高动力学模型的优化效率和精度。

关键词: 履带车辆, 动力学模型, 三层设计空间, 代理模型进化, 递阶优化方法

Abstract:

To solve the problem of low precision and low efficiency in tracked vehicle dynamics optimization resulting from the weaknesses of traditional agent model construction and application, a parameter optimization method based on surrogate model evolution is proposed. It integrates the optimization iteration process with the dynamic construction process of the surrogate model to reduce the times of invoking the simulation model and hence improve the optimization efficiency. First, based on the vehicle’s geometric topology, a multi-body dynamics model considering track envelope effect is constructed. Then, the design space is divided into three-level subspaces. A multi-level fuzzy clustering space reduction method with spatial focus and spatial reduction and not bounded by local optimization is proposed to efficiently reduce the design parameters in the three-level subspaces. Finally, the application is verified by taking the parameter optimization process of the tracked vehicle’s multi-body dynamics model as an example. The results show that the multi-body dynamics optimization process of the tracked vehicle under three road conditions reduces the invoking times of simulation model by up to 85%; the comprehensive performance indexes representing tracked vehicle ride comfort and firing accuracy are increased by about 32.4%, 24.5% and 20.4%, respectively. It is proved that this method can effectively improve the efficiency and accuracy of dynamic model optimization.

Key words: tracked vehicle, dynamical model, three-layer design space, surrogate model evolution, evolutionary optimization algorithm, hierarchical optimal algorithm

中图分类号:

TG156

张发平, 张书畅, 武锴, 张云贺, 阎艳. 基于代理模型进化的履带车辆动力学参数优化[J]. 兵工学报, 2023, 44(1): 27-39.

ZHANG Faping, ZHANG Shuchang, WU Kai, ZHANG Yunhe, YAN Yan. Dynamics Parameter Optimization for Tracked Vehicle Based on Surrogate Model Evolution[J]. Acta Armamentarii, 2023, 44(1): 27-39.

图/表 16

表1 坦克多体动力学模型部件明细

Table 1 Details of tank multi-body dynamics model cemponents

序号	名称	数量	序号	名称	数量
1	车体	1	11	限位器	8
2	滑柱	2	12	扭杆弹簧	12
3	套筒	2	13	平衡肘	12
4	曲臂	2	14	炮塔	1
5	诱导轮	2	15	摇架	1
6	托带轮	6	16	前衬瓦	1
7	主动轮	2	17	后衬瓦	1
8	负重轮	12	18	身管	1
9	履带销	368	19	炮尾	1
10	履带板	184

表2 坦克多体动力学模型约束明细

Table 2 Constraint details of tank multi-body dynamics model

编号	名称	数量	编号	名称	数量
J1	固定铰	8	J15	旋转副	2
J2	间隙碰撞	8	J16	接触力	2
J3	固定铰	12	J17	旋转副	2
J4	弹簧阻尼	12	J18	接触力	6
J5	驱动力矩	2	J19	轴套力	368
J6	旋转副	2	J20	接触摩擦	184
J7	旋转副	12	J21	弹簧阻尼	4
J8	接触力	2	J22	接触力	2
J9	接触力	12	J23	固定铰	2
J10	球副	2	J24	固定铰	2
J11	移动副	2	J25	间隙碰撞	2
J12	弹簧阻尼	2	J26	间隙碰撞	2
J13	圆柱副	2	J27	固定铰	2
J14	旋转副	2

图1 坦克多体动力学模型拓扑结构图

Fig.1 Topological structure of the multi-body dynamics model

图2 D、F、H级路面左右相干三维不平度模型

Fig.2 Left-right coherent three-dimensional roughness model of class D, F and H pavements

图3 坦克整车多体动力学RecurDyn模型

Fig.3 Tank multi-body dynamics RecurDyn model

图4 优化变量位置示意图

Fig.4 Schematic diagram of optimized variable location

图5 坦克参数优化过程的框架结构

Fig.5 Schematic diagram of tank parameter optimization process

图6 D级路面初始代理模型

Fig.6 Initial surrogate model of grade D pavement

图7 某次迭代过程中三层子空间示意图

Fig.7 Schematic diagram of three-layer subspaces in an iterative process

图8 基于二次聚类确定过渡区间流程图

Fig.8 Flow chart of determining transition intervals based on quadratic clustering

图9 坦克参数优化总体技术流程

Fig.9 Overall technical process of tank parameter optimization

图10 D级路面谱优化收敛曲线

Fig.10 Convergence curve of spectrum optimization of grade D pavement

表1 优化过程中算法及仿真模型参数设置

Table 1 Algorithm and simulation model parameter setting

算法参数					仿真参数
最大迭代次数	最大样本数量	初始样本数量	ADAM前进步长	ADAM前进次数	仿真时间/s	仿真步长/ms	行驶速度/(km·h^-1)
50	200	60	0.2	200	30	1	0~35

表2 基于代理模型进化优化算法的10次单路面优化(悬挂系统参数优化目标函数值)

Table 2 10 times single road optimization based on agent model evolutionary optimization algorithm (objective function value of suspension parameter optimization)

试验序号	D级路面				F级路面				H级路面
试验序号	初始值	优化值	变化率/%	样本量	初始值	优化值	变化率/%	样本量	初始值	优化值	变化率/%	样本量
1	1.9702	1.2846	34.8	108	3.5912	2.6439	26.6	96	6.7523	5.3154	21.3	97
2		1.3141	33.3	107		2.7344	24.0	103		5.3352	21.0	105
3		1.2986	34.1	93		2.7228	24.4	92		5.4238	19.6	108
4		1.3307	32.5	103		2.7534	23.5	96		5.3320	21.0	104
5		1.3530	31.3	96		2.7500	23.6	91		5.3330	21.0	95
6		1.2999	34.0	102		2.7611	23.3	102		5.4115	19.8	109
7		1.4339	27.2	91		2.6871	25.4	98		5.3647	20.5	101
8		1.3344	32.3	108		2.7478	23.7	110		5.4135	19.8	98
9		1.3292	32.5	95		2.7274	24.2	95		5.4278	19.6	99
10		1.2939	34.3	101		2.7034	24.9	104		5.4029	20.0	93

表3 3种路面下的最优参数组合

Table 3 Optimal parameter combination for each grade of pavement

路面	$k t 1$ /(N·m^-1)	$k t 2$ /(N·m^-1)	$k t 3$ /(N·m^-1)	$c t 1$ /(N·(m·s^-1)^-1)	$c t 2$ /(N·(m·s^-1)^-1)	$c t 3$ /(N·(m·s^-1)^-1)
初始值	1.000×10⁶	1.000×10⁶	1.000×10⁶	1.000×10⁴	1.000×10⁴	1.000×10⁴
D级	5.413×10⁶	5.017×10⁶	5.830×10⁶	4.262×10⁴	4.353×10⁴	5.882×10⁴
F级	6.473×10⁶	6.417×10⁶	1.757×10⁷	1.088×10⁵	1.854×10⁵	6.869×10⁴
H级	1.175×10⁷	1.582×10⁷	1.365×10⁷	9.846×10⁴	1.338×10⁵	1.460×10⁵

表3 3种路面下的最优参数组合

Table 3 Optimal parameter combination for each grade of pavement

路面	$k t 1$ /(N·m^-1)	$k t 2$ /(N·m^-1)	$k t 3$ /(N·m^-1)	$c t 1$ /(N·(m·s^-1)^-1)	$c t 2$ /(N·(m·s^-1)^-1)	$c t 3$ /(N·(m·s^-1)^-1)
初始值	1.000×10⁶	1.000×10⁶	1.000×10⁶	1.000×10⁴	1.000×10⁴	1.000×10⁴
D级	5.413×10⁶	5.017×10⁶	5.830×10⁶	4.262×10⁴	4.353×10⁴	5.882×10⁴
F级	6.473×10⁶	6.417×10⁶	1.757×10⁷	1.088×10⁵	1.854×10⁵	6.869×10⁴
H级	1.175×10⁷	1.582×10⁷	1.365×10⁷	9.846×10⁴	1.338×10⁵	1.460×10⁵

图11 H级路面下优化前后功率谱密度对比

Fig.11 Comparison of power spectral densities before and after optimization for H grades of pavement

参考文献 28

[1]	毛明, 张亚峰, 杜甫, 等. 高机动履带车辆行驶系统中的5个科学技术问题[J]. 兵工学报, 2015, 36(8):172-181.
	MAO M, ZHANG Y F, DU F, et al. Five scientific and technological problems on running system of high mobility tracked vehicle[J]. Acta Armamentarii, 2015, 36(8):172-181. (in Chinese)
[2]	刘飞飞, 芮筱亭, 于龙海, 等. 考虑身管柔性的坦克行进间发射动力学研究[J]. 振动与冲击, 2016, 35(2): 58-63.
	LIU F F, RUI X T, YU L H, et al. Influence of barrels’ flexibility on the launch dynamics of tank during marching fire[J]. Journal of Vibration and Shock, 2016, 35(2): 58-63. (in Chinese)
[3]	汪国胜, 药凌宇, 魏来生, 等. 某型坦克底盘线振动对行进间射击精度影响机理研究[J]. 兵工学报, 2016, 37(3):160-165.
	WANG G S, YAO L Y, WEI L S, et al. Research on the influence of linear vibration of a tank chassis on on-the-move shooting accuracy[J]. Acta Armamentarii, 2016, 37(3):160-165. (in Chinese)
[4]	韩宝坤, 李晓雷, 孙逢春. 履带车辆动力学仿真技术的发展与展望[J]. 兵工学报, 2003, 4(2):246-249.
	HAN B K, LI X L, SUN F C. Present state and future outlook of the simulation of tracked vehicles[J]. Acta Armamentarii, 2003, 4(2):246-249. (in Chinese)
[5]	戎保, 芮筱亭, 王国平, 等. 多体系统动力学研究进展[J]. 振动与冲击, 2011, 30(7):178-187.
	RONG B, RUI X T, WANG G P, et al. Developments of studies on multibody system dynamics[J]. Journal of Vibration and Shock, 2011, 30(7): 178-187. (in Chinese)
[6]	陈宇, 杨国来, 付羽翀, 等. 高速机动条件下坦克行进间火炮非线性振动动力学研究[J]. 兵工学报, 2019, 40(7):1339-1348. doi: 10.3969/j.issn.1000-1093.2019.07.002
	CHEN Y, YANG G L, FU Y C, et al. Dynamic simulation on nonlinear vibration of marching tank gun under high mobility conditions[J]. Acta Armamentarii, 2019, 40(7):1339-1348. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.07.002
[7]	王钦龙, 王红岩, 芮强. 基于多目标遗传算法的高速履带车辆动力学模型参数修正研究[J]. 兵工学报, 2016, 37(6):969-978. doi: 10.3969/j.issn.1000-1093.2016.06.002
	WANG Q L, WANG H Y, RUI Q. Research on parameter updating of high mobility tracked vehicle dynamic model based on multi-objective genetic algorithm[J]. Acta Armamentarii, 2016, 37(6): 969-978. (in Chinese)
[8]	王钦龙, 王红岩, 芮强. 基于近似模型和模式搜索法的履带车辆多体动力学模型参数修正研究[J]. 科学技术与工程, 2016, 16(33): 46-53.
	WANG Q L, WANG H Y, RUI Q. Research on parameters updating for tracked vehicle multibody dynamic model based on approximation model and pattern search method[J]. Science Technology and Engineering, 2016, 16(33): 46-53. (in Chinese)
[9]	张扬, 张维刚, 马桃, 等. 基于全局敏感性分析和动态代理模型的复杂非线性系统优化设计方法[J]. 机械工程学报, 2015, 51(4): 126-131. doi: 10.3901/JME.2015.04.126
	ZHANG Y, ZHANG W G, MA T, et al. Optimization design method of non-linear complex system based on global sensitivity analysis and dynamic moetamodel[J]. Journal of Mechanical Engineering, 2015, 51(4):126-131. (in Chinese) doi: 10.3901/JME.2015.04.126
[10]	LI R, XU P, PENG Y, et al. Scaled tests and numerical simulations of rail vehicle collisions for various train sets[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2016, 230(6):1590-1600. doi: 10.1177/0954409715605126 URL
[11]	张剑. 基于代理模型技术的高速列车性能参数设计及优化[D]. 成都: 西南交通大学, 2015.
	ZHANG J. Design and optimization of high-speed train performance parameters based on surrogate model technology[D]. Chengdu: Southwest Jiaotong University, 2015. (in Chinese)
[12]	TAHHERI M, AHMADIAN M. Machine learning from computer simulations with applications in rail vehicle dynamics[J]. Vehicle System Dynamics, 2016, 54(5):653-666. (in Chinese) doi: 10.1080/00423114.2016.1150497 URL
[13]	JONES D R. A Taxonomy of global optimization methods based on response surfaces[J]. Journal of Global Optimization, 2001, 21(4):345-383. doi: 10.1023/A:1012771025575 URL
[14]	JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4):455-492. doi: 10.1023/A:1008306431147 URL
[15]	VIANA F, HAFTKA R T, WATSON L T. Efficient global optimization algorithm assisted by multiple surrogate techniques[J]. Journal of Global Optimization, 2013, 56(2):669-689. doi: 10.1007/s10898-012-9892-5 URL
[16]	ALEXANDROV N M, DENNIS J E, LEWIS R M, et al. A trust-region framework for managing the use of approximation models in optimization[J]. Structural Optimization, 1998, 15(1):16-23. doi: 10.1007/BF01197433 URL
[17]	CHENG G, WANG G F. Trust region based MPS method for global optimization of high dimensional design problems[C]//Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference. Honolulu, HI, US: AIAA, 2012.
[18]	WANG G G, DDONG Z, AITCHISON P. Adaptive response surface method-a global optimization scheme for approximation-based design problems[J]. Engineering Optimization, 2001, 33(6):707-733. doi: 10.1080/03052150108940940 URL
[19]	马伟标, 王红岩, 王良曦, 等. 基于径向基函数响应面的履带车辆悬挂系统参数优化方法[J]. 兵工学报, 2011, 32(9):1053-1058.
	MA W B, WANG H Y, WANG L X, et al. Suspension parameter optimization based on radial basis function response surface method[J]. Acta Armamentarii, 2011, 32(9):1053-1058. (in Chinese)
[20]	卞美卉, 张洋, 杜志岐. 履带车辆履带预张紧力对平顺性的影响与仿真[J]. 车辆与动力技术, 2019(1):34-37.
	BIAN M H, ZHANG Y, DU Z Q. Influence of track pretension on ride comfort of tracked vehicle[J]. Vehicle & Power Technology, 2019(1):34-37. (in Chinese)
[21]	任宏斌, 陈思忠, 吴志成, 等. 车辆左右车轮路面不平度的时域再现研究[J]. 北京理工大学学报, 2013, 33(3):257-306.
	REN H B, CHEN S Z, WU Z C, et al. Time domain excitation model of random road profile for left and right wheels[J]. Transactions of Beijing Institute of Technology, 2013, 33(3):257-306. (in Chinese)
[22]	刘朋科, 周柏承, 李娜. 基于Kriging模型的行进间坦克结构参数不确定性分析及炮口响应优化[J]. 机械工程师, 2021(9):87-92.
	LIU P K, ZHOU B C, LI N. Analysis on structural parameters uncertainty of moving tank and optimization of muzzle response based on kriging model[J]. Mechanical Engineering, 2021(9):87-92. (in Chinese)
[23]	陈宇, 杨国来, 谢润, 等. 某坦克行进间射击炮口振动优化与分析[J]. 弹道学报, 2016, 28(4):86-89.
	CHEN Y, YANG G L, XIE R, et al. Optimization and analysis of muzzle vibration for tank firing on the move[J]. Journal of Ballistics, 2016, 28(4):86-89. (in Chinese)
[24]	KRISHNAMURTHY T. Response surface approximation with augmented and compactly supported radial basis functions[C]// Proceedings of the 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.Reston,VA,US:AIAA, 2003: 1748.
[25]	张永志, 董俊慧. 基于模糊C均值聚类的模糊RBF神经网络预测焊接接头力学性能建模[J]. 机械工程学报, 2014, 50(12):58-64.
	ZHANG Y Z, DONG J H. Modeling fuzzy RBF neural network to predict of mechanical properties of welding joints based on fuzzy C-means cluster[J]. Journal of Mechanical Engineering, 2014, 50(12): 58-64. (in Chinese)
[26]	张袅娜, 丁海涛, 于海芳, 等. 基于核主元约简与半监督核模糊聚类的车辆行驶工况判别[J]. 机械工程学报, 2015, 51(2):96-102. doi: 10.3901/JME.2015.02.096
	ZHANG N N, DING H T, YU H F, et al. Driving cycle distinguishing based on the kernel principal component and semi-supervised kernel fuzzy C means clustering algorithm[J]. Journal of Mechanical Engineering, 2015, 51(2): 96-102. (in Chinese) doi: 10.3901/JME.2015.02.096
[27]	KINGMA D P, BA J. Adam: a method for stochastic optimization[J]. arXiv preprint arXiv:1412.6980, 2014.
[28]	BLOMQVIST K, KASKI S, HEINONEN M. Deep convolutional Gaussian processes[C]// Proceedings of Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Cham, Germany:Springer, 2019: 582-597.