Online identification method of time-varying parameters for longitudinal dynamics model of high-speed train
-
摘要: 针对高速列车纵向动力学特性, 分析了牵引力、制动力、阻力与速度和加速度的关系; 考虑了天气和线路对高速列车运行状态造成的随机干扰, 以及机械磨损和运行环境对列车模型结构参数造成的随机影响, 建立了噪声干扰下的高速列车纵向动力学参数化状态空间模型, 利用期望极大化准则, 计算了列车模型参数的条件数学期望, 并结合粒子滤波理论估计了参数粒子下的列车状态; 基于贝叶斯后验概率理论, 建立了高速列车非线性动力学模型的时变参数辨识方法, 估计了列车的实时状态, 并在噪声与参数分布均属于高斯分布、噪声属于高斯分布与参数属于指数分布、噪声属于伽玛分布与参数属于高斯分布的3种工况下, 进行了蒙特卡洛仿真试验。仿真结果表明: 在3种工况下, 高速列车位移和速度的估计值与真实值的相对误差小于5%, 列车模型参数估计值与真实值的相对误差小于10%, 满足实际系统需求, 因此, 在高斯或伽玛噪声的干扰下, 针对给定概率分布的时变参数, 本方法均能实现系统状态的估计和模型参数的辨识。Abstract: In view of the longitudinal dynamics characteristic of high-speed train, the relationships between traction, braking force, resistance and velocity and acceleration were analyzed.The random disturbance caused by weather and route in high-speed train running condition was studied, the random effect on the structural parameters of train model caused by mechanical wearand running environment was analyzed, and a nonlinear parametric state space model was established to describe the longitudinal dynamics characteristic of high-speed train under the disturbances of noises.The conditional mathematical expectations of the model parameters were calculated by the expectation maximization (EM) algorithm, and the state of the train with particles parameters was estimated by combining the particle filter theory.The online identification method of time-varying parameters for the nonlinear dynamics model of high-speed train was set up based on the Bayesian posterior probability theory, and the real-time state of train was estimated.The parameters of Gaussian and Exponential distribution under Gaussian or Gamma noise were identified by Monte Carlo simulation.The simulation result shows that the relative errors of estimated and real speeds and displacements of high-speed train are less than 5%, and the relative errors of estimated parameters and real parameters of train model are less than 10%, which meets the actual requirement of train system.So, when the probability distributions of time-varying parameters are given, the states and model parameters of train can be identified and estimated under Gaussian or Gamma noise by the method.
-
图 4 高斯噪声和高斯分布参数下列车位移曲线
Figure 4. Displacement curves of train with Gaussian noise and Gaussian distribution parameters
图 5 高斯噪声和高斯分布参数下列车速度曲线
Figure 5. Velocity curves of train with Gaussian noise and Gaussian distribution parameters
图 6 高斯噪声下高斯分布参数辨识结果
Figure 6. Identification results of Gaussian distribution parameters under Gaussian noise
图 7 高斯噪声和指数分布参数下列车位移曲线
Figure 7. Displacement curves of train with Gaussian noise and exponential distribution parameters
图 8 高斯噪声和指数分布参数下列车速度曲线
Figure 8. Velocity curves of train with Gaussian noise and exponential distribution parameters
图 9 高斯噪声下指数分布参数的辨识结果
Figure 9. Identification results of exponential distribution parameters under Gaussian noise
图 10 伽玛噪声和高斯分布参数下CRH2型动车组的位移曲线
Figure 10. Displacement curves of CRH2with Gamma noise and Gaussian distribution parameters
图 11 伽玛噪声和高斯分布参数下CRH2型动车组的速度曲线
Figure 11. Velocity curves of CRH2with Gamma noise and Gaussian distribution parameters
图 12 伽玛噪声和高斯分布参数下CRH3型动车组位移曲线
Figure 12. Displacement curves of CRH3with Gamma noise and Gaussian distribution parameters
图 13 伽玛噪声和高斯分布参数下CRH3型动车组速度曲线
Figure 13. Velocity curves of CRH3with Gamma noise and Gaussian distribution parameters
-
[1] SONG Qi, SONG Yong-duan, TANG Tao, et al. Computationally inexpensive tracking control of high-speed trains with traction/braking saturation[J]. IEEE Transactions on Intelligent Transportation Systems, 2011, 12 (4): 1116-1125. doi: 10.1109/TITS.2011.2143409 [2] SONG Qi, SONG Yong-duan. Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures[J]. IEEE Transactions on Neural Networks, 2011, 22 (12): 2250-2261. doi: 10.1109/TNN.2011.2175451 [3] 衷路生, 李兵, 龚锦红, 等. 高速列车非线性模型的极大似然辨识[J]. 自动化学报, 2014, 40 (12): 2950-2958. https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO201412028.htmZHONG Lu-sheng, LI Bing, GONG Jin-hong, et al. Maximum likelihood identification of nonlinear models for high speed trains[J]. ACTA Automatic Sinica, 2014, 40 (12): 2950-2958. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO201412028.htm [4] 杨国伟, 魏宇杰, 赵桂林, 等. 高速列车的关键力学问题[J]. 力学进展, 2015, 45 (1): 217-460. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201500007.htmYANG Guo-wei, WEI Yu-jie, ZHAO Gui-lin, et al. Research progress on the mechanics of high speed rails[J]. Advances In Mechanics, 2015, 45 (1): 217-460. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201500007.htm [5] 丁建明, 林建辉, 王晗, 等. 基于边缘粒子滤波的高速列车性能参数估计方法[J]. 交通运输工程学报, 2014, 14 (3): 52-57. doi: 10.3969/j.issn.1671-1637.2014.03.011DING Jian-ming, LIN Jian-hui, WANG Han, et al. Performance parameter estimation method of high-speed train based on Rao-Blackwellised particle filter[J]. Journal of traffic and Transportation Engineering, 2014, 14 (3): 52-57. (in Chinese). doi: 10.3969/j.issn.1671-1637.2014.03.011 [6] 韩鹏, 张卫华, 李艳, 等. 轮对磨损与轮径差对高速列车动力学性能的影响[J]. 交通运输工程学报, 2013, 13 (6): 47-83. doi: 10.3969/j.issn.1671-1637.2013.06.007HAN Peng, ZHNAG Wei-hua, LI Yan, et al. Influence of wheelset wear and wheel radius difference on dynamics performances of high-speed train[J]. Journal of traffic and Transportation Engineering, 2013, 13 (6): 47-83. (in Chinese). doi: 10.3969/j.issn.1671-1637.2013.06.007 [7] 陈哲明, 曾京. 牵引电机转子振动对高速列车动力学性能的影响[J]. 交通运输工程学报, 2011, 28 (1): 238-244. http://transport.chd.edu.cn/article/id/201306007CHEN Zhe-ming, CENG Jing. Effect of rotor vibration of Traction motor on dynamic behavior of high speed train[J]. Journal of traffic and Transportation Engineering, 2011, 28 (1): 238-244. (in Chinese). http://transport.chd.edu.cn/article/id/201306007 [8] DING Feng, LIU P X, LIU Guang-jun. Multiinnovation least-squares identification for system modeling[J]. IEEETransactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2010, 40 (3): 767-778. doi: 10.1109/TSMCB.2009.2028871 [9] KIM Y, MALLICK R, BHOWMICK S, et al. Nonlinear system identification of large-scale smart pavement systems[J]. Expert Systems with Applications, 2013, 40 (9): 3551-3560. doi: 10.1016/j.eswa.2012.12.062 [10] DING F, CHEN Tong-wen. Identiflcation of Hammerstein nonlinear ARMAX systems[J]. Automatica, 2005, 41 (9): 1479-1489. doi: 10.1016/j.automatica.2005.03.026 [11] 郭红戈, 谢克明. 动车组列车制动系统的Hammerstein模型及其参数辨识方法[J]. 铁道学报, 2014, 36 (4): 48-53. doi: 10.3969/j.issn.1001-8360.2014.04.009GUO Hong-ge, XIE Ke-ming. Hammerstein model and parameters identification of EMU braking system[J]. Journal of the China Railway Society, 2014, 36 (4): 48-53. (in Chinese). doi: 10.3969/j.issn.1001-8360.2014.04.009 [12] 陈德旺, 唐涛, 郜春海, 等. 城轨列车在车站停车误差估计模型与在线学习算法的研究[J]. 中国铁道科学, 2010, 31 (6): 122-127. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201006023.htmCHEN De-wang, TANG Tao, GAO Chun-hai, et al. Research on the error estimation models and online learning algorithms for train station parking in urban rail transit[J]. China Railway Science, 2010, 31 (6): 122-127. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201006023.htm [13] 于振宇, 陈德旺. 城轨列车制动模型及参数辨识[J]. 铁道学报, 2011, 33(10): 37-40. doi: 10.3969/j.issn.1001-8360.2011.10.007YU Zhen-yu, CHEN De-wang, Modeling and system identification of the braking system of urban rail vehicles[J]. Journal of the China Railway Society, 2011, 33(10): 37-40. (in Chinese) doi: 10.3969/j.issn.1001-8360.2011.10.007 [14] 郜春海, 陈德旺. 基于模型选择和优化技术的自动驾驶制动模型辨识研究[J]. 铁道学报, 2011, 33 (10): 57-60. doi: 10.3969/j.issn.1001-8360.2011.10.011GAO Chun-hai, CHEN De-wang. Study on ATO braking model identification based on model selection and optimization techniques[J]. Journal of the China Railway Society, 2011, 33 (10): 57-60. (in Chinese). doi: 10.3969/j.issn.1001-8360.2011.10.011 [15] 王呈. 列车自动驾驶控制模型参数辨识及其应用[D]. 北京: 北京交通大学, 2014.WANG Cheng. Parameter identification and its application in automatic train operation control[D]. Beijing: Beijing Jiaotong University, 2014. (in Chinese). [16] Zhang J, Ding G F, Zhou Y S, et al. Identification of key design parameters of high-speed train for optimal design[J]. The International Journal of Advanced Manufacturing Technology, 2014, 73 (1): 251-265. [17] WANG D Q. Least squares-based recursive and iterative estimation for output error moving average systems using data filtering[J]. IET Control Theory and Applications, 2011, 5 (14): 1648-1657. doi: 10.1049/iet-cta.2010.0416 [18] XIE Li, YANG Hui-zhong, DING Feng. Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering[J]. Mathematical and Computer Modelling: An International Journal, 2011, 54 (1/2): 315-324. [19] CHOU M, XIA X, KAYSER C. Modelling and model validation of heavy-haul trains equipped with electronically controlled pneumatic brake systems[J]. Control Engineering Practice, 2007, 15 (4): 501-509. doi: 10.1016/j.conengprac.2006.09.006 [20] 衷路生, 李兵, 龚锦红, 等. 高速动车组多质点模型的极大似然辨识[J]. 计算机仿真, 2016, 33 (1): 181-187. doi: 10.3969/j.issn.1006-9348.2016.01.039ZHONG Lu-sheng, LI Bing, GONG Jin-hong, et al. Maximum likelihood identification of multiple point model for high-speed electrical multiple units[J]. Computer Simulation, 2016, 33 (1): 181-187. (in Chinese). doi: 10.3969/j.issn.1006-9348.2016.01.039 [21] 杨辉, 张坤鹏, 王昕. 高速动车组多模型切换主动容错预测控制[J]. 控制理论与应用, 2012, 29 (9): 1211-1214. https://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201209018.htmYANG Hui, ZHANG Kun-peng, WANG Xin. Multi-model switching predictive control with active fault tolerance for high-speed train[J]. Control Theory and Applications, 2012, 29 (9): 1211-1214. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201209018.htm [22] ANDRIEU C, DOUCET A, TADIC V. On-line parameter estimation in generalstate-space models[C]//IEEE. The 44th Conference on Decision and Control. New York: IEEE, 2006: 332-337. [23] SHAWASH J, SELVIAH D R. Real-time nonlinear parameter estimation using the Levenberg-Marquardt algorithm on field programmable gate arrays[J]. IEEE Transactions on Industrial Electronics, 2013, 60 (1): 170-176. doi: 10.1109/TIE.2012.2183833 [24] ALTMANN Y, PEREYRA M, MCLAUGHLIN S. Bayesian nonlinear hyperspectral unmixing with spatial residual component analysis[J]. IEEE Transactions on Computational Imaging, 2015, 1 (3): 174-185. doi: 10.1109/TCI.2015.2481603 [25] LINDSTEN F. An efficient stochastic approximation EMalgorithm using conditional particle filters[C]//IEEE. 2013IEEE International Conference on Acoustics, Speech and Signal Processing. New York: IEEE, 2013: 6274-6278. -
下载:
点击查看大图
计量
- 文章访问数: 638
- HTML全文浏览量: 125
- PDF下载量: 612
- 被引次数: 0
