Online identification method of time-varying parameters for longitudinal dynamics model of high-speed train
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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.
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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
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