基于混合滤波最大期望算法的高速列车建模

王呈; 陈晶; 荀径; 李开成

doi:10.16383/j.aas.c190193

基于混合滤波最大期望算法的高速列车建模

doi: 10.16383/j.aas.c190193

王呈^1,,
陈晶^2,,
荀径^3,,
李开成^4,

1.
江南大学物联网工程学院无锡 214012
2.
江南大学理学院无锡 214012
3.
北京交通大学轨道交通控制与安全国家重点实验室北京 100044
4.
北京交通大学轨道交通运行控制系统国家工程研究中心北京 100044

基金项目: 国家自然科学基金(61603156, 61973137), 高速铁路基础研究联合基金(U1734210), 北京交通大学教育基金会基金(9907006519)资助

详细信息

作者简介:
王呈：江南大学物联网工程学院副教授. 2014年获得北京交通大学交通信息工程及控制专业博士学位. 主要研究方向为先进列车控制技术, 非线性系统建模与控制, 机器学习与数据挖掘. 本文通信作者. E-mail: wangc@jiangnan.edu.cn

陈晶：江南大学理学院副教授. 2013年获得江南大学控制理论与控制工程博士学位. 主要研究方向为系统辨识和过程控制. E-mail: chenjing1981929@126.com

荀径：北京交通大学轨道交通控制与安全国家重点实验室副教授. 2012年获北京交通大学交通信息工程与控制博士学位. 主要研究方向为先进列车控制方法, 轨道交通优化问题, 交通流理论, 元胞自动机和加强学习. E-mail: jxun@bjtu.edu.cn

李开成：北京交通大学轨道交通运行控制系统国家工程研究中心研究员. 主要研究方向为轨道交通列车运行控制, 智能控制技术及应用. E-mail: kchli@bjtu.edu.cn

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出版历程
- 收稿日期: 2019-03-19
- 录用日期: 2019-08-15
- 刊出日期: 2019-12-01

Hybrid Filter Based Expectation Maximization Algorithm for High-speed Train Modeling

1.
School of Internet of Things, Jiangnan University, Wuxi 214012
2.
School of Science, Jiangnan University, Wuxi 214012
3.
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044
4.
National Engineering Research Center of Rail Transportation Operation and Control System, Beijing Jiaotong University, Beijing 100044

Funds: Supported by National Natural Science Foundation of China (61603156, 61973137), the Joint Fund for Basic Research of High Speed Railway (U1734210), and Beijing Jiaotong University Education Foundation (9907006519)

摘要

摘要: 针对高速列车非线性单质点模型的特殊结构及含有隐含变量问题, 提出一种基于混合滤波的最大期望辨识方法. 借助递阶辨识理论, 将高铁列车状态空间模型分解为线性子系统模型和非线性子系统模型. 进而, 分别利用卡尔曼滤波和粒子滤波对速度和位移状态进行联合估计. 最后, 使用最大期望方法辨识高铁列车子系统模型参数, 解决了隐含变量辨识问题. 和传统方法相比, 本文所提出方法计算量小, 且具有较高的辨识精度. 仿真对比实验结果验证了该方法的有效性.
- 参数估计 /
- 卡尔曼滤波 /
- 粒子滤波 /
- 递阶辨识 /
- 最大期望算法
Abstract: For the special high-speed train model structure with hidden variables in the form of the single mass-point, a hybrid filter based expectation maximization (EM) algorithm is proposed. By employing the hierarchical identification theory, the high-speed train state-space model is decomposed into a linear subsystem and a nonlinear subsystem. Furthermore, the Kalman filter and the particle filter are provided to estimate the velocity and displacement, respectively. Finally, the parameters of subsystems are identified by using the EM algorithm. Compared to the classical methods, the proposed algorithm can produce high accuracy estimation with less computational effort. The simulation results verify the effectiveness of the algorithm.
- Parameter estimation /
- Kalman filtering /
- particle filtering /
- hierarchical identification /
- EM algorithm

HTML全文

图 1 参数误差$\tau$随$k$变化曲线

Fig. 1 Parameter estimation error $\tau$ versus $k$

下载: 全尺寸图片幻灯片

图 2 位移估计变化曲线($+$: 估计位移; $-$: 真实位移)

Fig. 2 Displacement estimation curve

下载: 全尺寸图片幻灯片

图 3 速度估计变化曲线($+$: 估计速度; $-$: 真实速度)

Fig. 3 Velocity estimation curve

下载: 全尺寸图片幻灯片

表 1 模型参数的估计(混合滤波方法)

Table 1 Parameters and their estimates (Hybrid filter)

$k$	$\bar{d}$	$\bar{d}a$	$\bar{d}b$	$\bar{d}c$	$\delta\ ({\text{%}})$
5	0.00920012	0.00491263	0.00003991	0.00000098	0.33063
8	0.00920015	0.00492316	0.00003992	0.00000098	0.37553
10	0.00920314	0.00494321	0.00003991	0.00000097	0.59953
20	0.00920287	0.00494295	0.00003987	0.00000097	0.58897
30	0.00919972	0.00483822	0.00003846	0.00000099	0.74688
真值	0.00920000	0.00490000	0.00004000	0.00000100

下载: 导出CSV

表 2 模型参数的估计(拓展的卡尔曼滤波方法)

Table 2 Parameters and their estimates (Extended Kalman filter)

$k$	$\bar{d}$	$\bar{d}a$	$\bar{d}b$	$\bar{d}c$	$\delta ({\text{%}})$
5	0.00921632	0.00548236	0.00003124	0.00000086	5.52150
8	0.00921594	0.00544469	0.00003262	0.00000089	5.19838
10	0.00921621	0.00545321	0.00003173	0.00000091	5.22873
20	0.00921845	0.00546151	0.00003292	0.00000091	5.39818
30	0.00921706	0.00545076	0.00003189	0.00000091	5.31865
真值	0.00920000	0.00490000	0.00004000	0.00000100

下载: 导出CSV

表 3 模型参数的估计(粒子滤波方法)

Table 3 Parameters and their estimates (Particle filter)

$k$	$\bar{d}$	$\bar{d}a$	$\bar{d}b$	$\bar{d}c$	$\delta\ ({\text{%}})$
5	0.00917652	0.00502136	0.00003865	0.00000096	1.14182
8	0.00919138	0.00498754	0.00003973	0.00000098	0.82781
10	0.00919141	0.00498763	0.00004016	0.00000098	0.85850
20	0.00919136	0.00501627	0.00004098	0.00000096	1.02914
30	0.00919139	0.00490032	0.00004074	0.00000097	0.94999
真值	0.00920000	0.00490000	0.00004000	0.00000100

下载: 导出CSV

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