Adaptive Identification of Time-varying Environmental Parameters in Train Dynamics Model
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摘要: 考虑列车制动性能与制动距离对列车安全的重要影响, 分析了列车运行的动力学特性, 构建了列车离散化制动模型,并针对影响列车制动性能的关键参数 — 钢轨粘着系数难以直接观测、随钢轨环境变化的特点, 提出基于滑动窗口与最大期望理论的轮轨粘着系数在线辨识算法. 首先, 依据数据特征确定滑动窗口位置与窗口尺寸; 然后, 构造列车动力学模型参数的条件数学期望, 并结合粒子滤波与粒子平滑算法以及贝叶斯理论, 估计预设模型参数下的列车运行状态; 在此基础上, 分析粘着系数的后验概率, 并极大化条件数学期望对模型参数预设进行优化更新, 进而实现模型真实参数的逐步逼近. 最后, 考虑雪地、隧道等场景下的粘着系数变化, 对本文方法进行了仿真验证, 并数值分析了粘着系数对制动距离的影响. 仿真结果表明本文算法可快速、准确地对粘着系数进行实时辨识, 掌握轮轨间实时粘着状态.Abstract: Considering the braking performance and distance on train safety, the dynamic characteristics of train are analyzed, and the discrete braking model is constructed. Aiming at the pivotal rail-wheel adhesion coefficient, which is difficult to be observed directly and varies with rail environment, an online identification of adhesion coefficient based on sliding window and expectation maximization is proposed. Firstly, the position and size of window are set up. Then, the conditional expectation about the parametric train dynamic model is constructed, and the train running state under the preset parameters is estimated by the particle filter, particle smoothing and Bayesian theory. On this basis, the posterior probability of the adhesion coefficient is analyzed, and the conditional expectation is maximized to optimize and update the model parameters, so that the real parameters can be approached step by step. Finally, considering the change of adhesion coefficient in snow, tunnel and other scenes, the method is simulated and validated, and the influence of adhesion coefficient on braking distance is analyzed numerically. The simulation results show that the adhesion coefficient can be identified quickly and accurately, and the real-time adhesion state can be grasped in real time.
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Key words:
- Adhesion coefficient /
- braking model /
- expectation maximization /
- sliding window /
- parameter estimation
1) 收稿日期 2019-03-20 录用日期 2019-09-09 Manuscript received March 20, 2019; accepted September 9, 2019 国家重点研发计划 (2018YFB1201500), 国家自然科学基金 (61873201, 61773313), 北京市自然科学基金 (4192046) 资助 Supported by National Key Research and Development Program of China (2018YFB1201500), National Natural Science Foundation of China (61873201, 61773313), and Beijing Municipal Natural Science Foundation (4192046) 本文责任编委 吕宜生 Recommended by Associate Editor LV Yi-Sheng 1. 西安理工大学 西安 710048, 中国 2. 北京交通大学 北京 100044, 中国 3. 日本大学 船桥 274-8501, 日本 1. Xi'an University of Technology, Xi'an 710048, China 2. Bei2) jing Jiaotong University, Beijing 100044, China 3. Nihon University, Fun-abashi 274-8501, Japan -
图 2 制动速度 − 轮轨粘着系数
Fig. 2 Braking speed and adhesion coefficient ofwheel-rail from external rail to tunnel rail
图 4 平道 − 隧道粘着系数实时估计
Fig. 4 Real-time estimation of adhesion coefficient from external rail to tunnel rail
图 10 列车平道 − 隧道制动速度与制动距离
Fig. 10 Braking speed and distance of train fromexternal rail to tunnel rail
图 11 列车平道 − 隧道制动速度与制动时间
Fig. 11 Train braking speed and braking time fromexternal rail to tunnel rail
图 12 轮轨隧道 − 平道粘着系数
Fig. 12 Adhesion coefficient of wheel-rail from tunnel rail to external rail
图 14 隧道 − 平道粘着系数实时估计
Fig. 14 Real-time estimation of adhesion coefficient from tunnel rail to external rail
图 20 列车隧道 − 平道制动速度与制动距离
Fig. 20 Braking speed and distance of train fromtunnel rail to external rail
图 21 列车隧道 − 平道制动速度与制动时间
Fig. 21 Braking speed and braking time of train from tunnel rail to external rail
表 1 CRH3紧急制动主要参数特性
Table 1 Main emergency braking parameters of CRH3
参数名称 参数特性 列车总重量 (t) 536 最高运行速度 (km/h) 350 持续运行速度 (km/h) 300 制动缸直径 (mm) 203 制动缸空气压力 (kPa) 410 传动效率 0.85 制动倍率 2.55 制动盘摩擦系数 0.28 制动盘平均摩擦半径 (mm) 297.6 车轮滚动圆半径 (mm) 460 
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表 2 粘着系数实时估计结果对比
Table 2 Comparison of real-time estimation results of adhesion coefficient
本文方法 EKF 初值 估计误差 相对误差 (%) 估计误差 相对误差 (%) 0.00 $\pm $0.0017 2.0907 $\pm $0.0129 13.7828 0.03 $\pm $0.0011 1.3984 $\pm $0.0078 9.9778 0.05 $\pm $0.0009 1.2802 $\pm $0.0081 10.7114 0.09 $\pm $0.0016 2.1527 $\pm $0.0079 10.1600 0.12 $\pm $0.0023 2.4306 $\pm $0.0137 15.5428 平均值 $\pm $0.0015 1.8705 $\pm $0.0101 12.0350
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表 3 粘着系数实时估计结果对比
Table 3 Comparison of real-time estimation results of adhesion coefficient
本文方法 EKF 初值 估计误差 相对误差 (%) 估计误差 相对误差 (%) 0.00 $\pm $0.0011 1.2338 $\pm $0.0117 13.8956 0.03 $\pm $0.0012 1.4101 $\pm $0.0120 14.4391 0.05 $\pm $0.0017 2.0780 $\pm $0.0095 11.4757 0.09 $\pm $0.0021 2.5633 $\pm $0.0096 11.4356 0.12 $\pm $0.0015 1.7995 $\pm $0.0121 14.3814 平均值 $\pm $0.0015 1.8169 $\pm $0.0110 13.1255
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