基于广义多项式混沌的跨座式单轨车辆随机平稳性分析

PDF(2351 KB)

振动与冲击 ›› 2021, Vol. 40 ›› Issue (6) : 190-200.

论文

周生通1，王迪1，肖乾1，李鸿光2，张沛1

作者信息 +

Stochastic stationarity analysis of a straddle monorail vehicle using the generalized polynomial chaos method

ZHOU Shengtong1,WANG Di1,XIAO Qian1,LI Hongguang2,ZHANG Pei1

Author information +

文章历史 +

摘要

借助参数化UM(universal mechanism)仿真模型，考虑车辆载重、悬挂参数和轮轨参数的随机性，建立某型跨座式单轨车辆的随机平稳性模型。然后，在有限试验设计样本数限制下，以最佳近似精度为目标，结合低阶交互截断、最小角回归、最小二乘法和留一法交叉验证等实现广义多项式混沌（generalized polynomial chaos ,gPC）的自适应稀疏展开。分别基于拉丁超立方抽样（Latin hypercube sampling ,LHS）方法和自适应稀疏gPC方法，讨论三种速度等级下单轨车辆平稳性指标的概率分布特征和全局灵敏度。算例表明：相比LHS结果，基于gPC近似模型的随机结果更为准确可靠，尤其是在高阶统计矩方面；同一速度等级下垂向平稳性指标均值要大于横向平稳性指标均值，并且随着速度的增大各平稳性指标的离散性在减小，而75 km/h下的分布特征与正态分布的差异最为明显；车辆载重、走行轮垂向刚度、水平轮径向刚度、空气弹簧垂向阻尼是对平稳性指标方差贡献最主要的随机参数。

Abstract

With the help of the parameterized universal mechanism(UM) simulation model, the stochastic stationarity model of a straddle monorail vehicle was established considering the randomness of input variables such as vehicle load, vehicle suspension parameters, and wheel-track parameters.Then, aiming at the best approximation accuracy under the limited number of experimental design samples, the adaptive sparse expansion of generalized polynomial chaos (gPC) was realized by combinedly using the low-order interaction truncation, least angle regression, ordinary least squares, and leave-one-out cross-validation.Later, the probability distribution characteristics of the stationarity index and global sensitivity of the monorail vehicle under three speed levels were discussed based on the Latin hypercube sampling (LHS) method and adaptive sparse gPC method respectively.The results show that: compared with the LHS results, the results based on the gPC approximation model are more accurate and reliable, especially in the high-order statistical moments; at the same speed level, the mean value of the vertical stationarity index is greater than that of the lateral stationarity index, and the degree of dispersion of each stationarity index decreases with the increase of speed.The distribution characteristics of the stationarity index at 75 km/h are the most obviously different from those of normal distribution; the vehicle load, vertical stiffness of driving wheel, radial stiffness of horizontal wheel and vertical damping of air spring are the main random parameters contributing to the variance of stationarity index.

导出引用

周生通1，王迪1，肖乾1，李鸿光2，张沛1. 基于广义多项式混沌的跨座式单轨车辆随机平稳性分析[J]. 振动与冲击, 2021, 40(6): 190-200

ZHOU Shengtong1,WANG Di1,XIAO Qian1,LI Hongguang2,ZHANG Pei1. Stochastic stationarity analysis of a straddle monorail vehicle using the generalized polynomial chaos method[J]. Journal of Vibration and Shock, 2021, 40(6): 190-200

参考文献

［1］肖乾，陈光圆，李超，等.跨座式单轨列车动力学分析研究综述［J］.华东交通大学学报, 2018, 35(6): 8-12.
XIAO Qian, CHEN Guangyuan, LI Chao, et al.Research on dynamic modeling of straddle-type monorail train［J］.Journal of East China Jiaotong University, 2018, 35(6): 8-12.

［2］文孝霞, 杜子学, 申震, 等.单轨车辆参数对轮胎磨损的影响及优化研究［J］.机械设计与制造, 2014(9): 214-217.
WEN Xiaoxia, DU Zixue, SHEN Zhen, et al.The monorail tire parameters affect on tire wear and optimization analysis on curve driving condition［J］.Machinery Design & Manufacture, 2014(9): 214-217.

［3］赵树恩, 刘淅, 李玉玲.横向风对跨座式单轨车辆运行平稳性的影响［J］.噪声与振动控制, 2015, 35(1): 136-140.
ZHAO Shuen, LIU Xi, LI Yuling.Influence of lateral wind on the stability of straddle type monorail vehicles traveling in straight track sections［J］.Noise and Vibration Control, 2015, 35(1): 136-140.

［4］李小珍, 葛延龙, 晋智斌.跨座式单轨车辆-轨道梁耦合振动的计算分析［J］.铁道工程学报, 2018(1): 78-83.
LI Xiaozhen，GE Yanlong，JIN Zhibin.Calculation and analysis of the straddle-type monorail vehicle-track beam coupling vibration［J］.Journal of Railway Engineering Society, 2018 (1): 78-83.

［5］罗仁, 李然, 胡俊波 ,等.考虑随机参数的高速列车动力学分析［J］.机械工程学报, 2015, 51(24): 90-96.
LUO Ren, LI Ran, HU Junbo, et al.Dynamic analysis of high-speed train with stochastic parameters［J］.Journal of Mechanical Engineering, 2015, 51(24): 90-96.

［6］KASSA E, NIELSEN J C O.Stochastic analysis of dynamic interaction between train and railway turnout［J］.Vehicle System Dynamics， 2008, 46(5): 429-449.

［7］滕万秀, 罗仁, 石怀龙, 等.高寒动车组-40℃环境下动力学性能［J］.机械工程学报, 2019, 55(4):165-170.
TENG Wanxiu, LUO Ren, SHI Huailong, et al.Dynamics behaviour of high-speed train at the low temperature of -40℃ ［J］.Journal of Mechanical Engineering, 2019, 55(4): 165-170.

［8］项盼, 赵岩, 林家浩, 等.轨道不平顺激励下不确定车轨耦合系统动力分析［J］.固体力学学报, 2013, 33(增刊1): 204-210.
XIANG Pan, ZHAO Yan, LIN Jiahao, et al.The dynamic analysis for vehicle-track coupled systems with parameter uncertainties under track irregularity［J］.Chinese Journal of Solid Mechanics, 2013, 33(Sup1): 204-210.

［9］刘付山, 曾志平, 郭无极, 等.考虑轮轨非线性接触的车辆-轨道-桥梁垂向耦合系统随机振动分析［J］.振动工程学报, 2020, 33(1): 139-148.
LIU Fushan, ZENG Zhiping, GUO Wuji, et al.Random vibration analysis of vehicle-track-bridge vertical coupling system considering wheel-rail nonlinear contact［J］.Journal of Vibration Engineering, 2020, 33(1): 139-148.

［10］罗仁, 胡俊波, 王一平.考虑随机因素的高速列车动力学模拟方法及应用［J］.铁道车辆, 2016, 54(10): 1-6.
LUO Ren, HU Junbo, WANG Yiping.Dynamics simulation method and the application on high speed trains with consideration of random factors［J］.Rolling Stock, 2016, 54(10): 1-6.

［11］BIGONI D, TRUE H, ENGSIG-KARUP A P.Sensitivity analysis of the critical speed in railway vehicle dynamics［J］.Vehicle System Dynamics, 2014, 52(Sup1): 272-286.

［12］赵岩, 项盼, 张有为, 等.具有不确定参数车轨耦合系统随机振动灵敏度分析［J］.工程力学, 2013, 30(4):370-376.
ZHAO Yan, XIANG Pan, ZHANG Youwei, et al.Random vibration sensitivity analysis for coupled vehicle-track systems with parameter uncertainties［J］.Engineering Mechanics, 2013, 30(4): 370-376.

［13］李双, 余衍然, 陈玲, 等.随机悬挂参数下轨道车辆平稳性的全局灵敏度分析［J］.铁道学报, 2015, 37(8): 31-37.
LI Shuang, YU Yanran, CHEN Ling, et al.Global sensitivity analysis on the ride quality of railway vehicle with stochastic suspension parameters［J］.Journal of the China Railway Society, 2015, 37(8):31-37.

［14］解欢, 杨岳, 童林军, 等.基于混合代理模型的高速轨道车辆悬挂参数多目标优化［J］.铁道科学与工程学报, 2016, 13(10): 2056-2063.
XIE Huan, YANG Yue, TONG Linjun, et al.Multi-objective optimization of the suspension parameters for high speed rail vehicle based ona hybrid surrogate model［J］.Journal of Railway Science and Engineering, 2016, 13(10): 2056-2063.

［15］东方世平. 高速列车悬挂系统参数多目标优化［D］.北京：北京交通大学, 2015.

［16］ZHOU S, WU X, LI H, et al.Critical speed analysis of flexible rotor system with stochastic uncertain parameters［J］.Journal of Vibration Engineering & Technologies, 2017, 5(4): 319-328.

［17］周生通，李鸿光，张龙，等.基于嵌入式谱随机有限元法的转子系统随机不平衡响应特性分析［J］.振动与冲击, 2016, 35(19): 45-49.
ZHOU Shengtong, LI Hongguang, ZHANG Long, et al.Stochastic unbalance response characteristics of rotor systems based on intrusive spectral stochastic finite element method［J］.Journal of Vibration and Shock, 2016, 35(19): 45-49.

［18］周生通, 祁强, 周新建, 等.轴弯曲与不平衡柔性转子共振稳态响应随机分析［J］.计算力学学报, 2020, 37(1): 20-27.
ZHOU Shengtong, QI Qiang, ZHOU Xinjian, et al.Stochastic analysis of resonance steady-state response of rotor with shaft bending and unbalance faults［J］.Chinese Journal of Computational Mechanics, 2020, 37(1): 20-27.

［19］BIGONI D, ENGSIG-KARUP A P, TRUE H.Modern uncertainty quantification methods in railroad vehicle dynamics［C］∥ Proceedings of the ASME 2013 Rail Transportation Division Fall Technical Conference.Altoona: ASME, 2013.

［20］项盼，赵岩，林家浩.复合随机振动分析的自适应回归算法［J］.应用力学学报, 2015, 32(6): 934-941.
XIANG Pan, ZHAO Yan, LIN Jiahao.An adaptive regression algorithm for double random vibration analysis［J］.Chinese Journal of Applied Mechanics, 2015, 32(6): 934-941.

［21］BLATMAN G, SUDRET B.An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis［J］.Probabilistic Engineering Mechanics, 2010, 25(2): 183-197.

［22］BLATMAN G, SUDRET B.Adaptive sparse polynomial chaos expansion based on least angle regression［J］.Journal of Computational Physics, 2011, 230(6): 2345-2367.

［23］DIAZ P, DOOSTAN A, HAMPTON J.Sparse polynomial chaos expansions via compressed sensing and D-optimal design［J］.Computer Methods in Applied Mechanics and Engineering, 2018, 336: 640-666.

［24］崔可萌.跨座式单轨交通行车舒适性影响因素研究［D］.哈尔滨：哈尔滨工业大学, 2018.

［25］SUDRET B. Global sensitivity analysis using polynomial chaos expansions［J］.Reliability Engineering & System Safety, 2008, 93(7): 964-979.

［26］MARELLI S, SUDRET B.UQLab: a framework for uncertainty quantification in MATLAB［C］∥Proceedings 2nd International Conference on Vulnerability, Risk Analysis and Management (ICVRAM 2014).Liverpool：ICVRAM，2014.