列车节能操纵理论模型与参数标定方法研究
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摘要
交通运输业是国家的基础性服务业,为社会经济的发展提供重要的支撑作用,但交通运输业也消耗了大量的能源,在能源形势日趋紧张的当今社会值得深切关注。铁路运输是最重要的交通运输方式之一,完成了全社会相当比例的运量,近年来,铁路进行了大规模的建设,在综合运输网络中的主导地位进一步加强,但随之而来的是铁路运输业的能耗日趋庞大。为有效降低占铁路能耗主体的牵引能耗,进行了列车节能运行的基础理论研究,重点研究列车节能操纵的基本原理,以期为优秀的列车节能操纵指导系统的研制和开发奠定理论基础。
本文在借鉴国内外已有研究成果的基础上,充分考虑到列车运行线路复杂多变的特性,引入连续陡坡的概念,对列车在陡坡区段的最优控制策略进行了深入的研究与探讨,主要研究内容及结论如下：
(1)根据列车运行受力分析,构建了基于机械能的列车运行理论模型,引入协态变量,基于Pontryagin极值原理,采用状态变量、协态变量和控制变量联合表达Hamiltonian函数,然后应用Karush-Kuhn-Tucker条件求得最优控制策略的必要条件,即符合列车节能运行的状态仅有四种：最大加速相位、均速相位、惰行相位和制动相位；借助协态变量满足的微分方程,分析出相位转换关系,再根据列车运行的现实环境,寻找正确的相位序列和相位转换点位置,即确定了列车的最优控制策略。
(2)列车匀速运行时,阻力所做的功最少,均速相位成为各种运行状态的纽带,依此对列车运行全程划分阶段,即启动阶段、途中运行阶段和制动阶段,把列车控制全局优化问题化解为由均速速度决定的局部优化问题。采用四阶Runge-Kutta方法来求解列车控制的微分方程,针对陡坡区段,先计算出陡坡临界点,反推出首个相位转换点的初始范围,然后利用二分法逐渐缩小搜索区间,得到了陡坡区段的最优控制策略及相应的最优轨线。随着总运行时分的增加,列车的能耗随之减少,但两者并不呈线性关系,本文算例中,当总旅程时间从2142.54s逐渐增加至2473s时,全程最优控制的能耗值从1845.01J下降至1527.23J。
(3)列车行驶在陡上坡时,速度会下降,局部的最优控制策略为均速—最大加速—均速相位序列,且最优控制的必要条件要求最大加速相位切换回均速相位时,协态变量恰等于1,据此条件可确定陡上坡区段各相位转换点的具体位置。为提高数值计算的效率,结合列车运动方程,构造陡上坡区段新的目标泛函Jp和变量μ,当列车操纵策略为最优时,Jp取极值,且μ在陡上坡区段的始末值均为零,因μ在某些坡段不发生变化,使得数值计算范围缩小而效率得到提升。列车行驶在陡下坡时,速度会上升,局部的最优控制策略为均速—惰行—均速相位序列,且惰行相位转入均速相位时,协态变量恰等于1,为提高计算效率,同样可构造出陡下坡区段的新目标泛函Jp和变量μ,当列车操纵策略为最优时,μ在陡下坡区段的始末值均为零。利用μ和协态变量θ解算最优控制策略的方法在本文中分别被称为间接法和直接法,本文算例中,间接法较直接法在陡上坡区段提高计算效率60.46%,在陡下坡区段提高计算效率95.81%
(4)天气状况不同或列车运行线路不同都会导致列车基本阻力参数变化,因此,列车的每趟旅程的基本阻力参数都需进行实时标定,以便为最优控制策略的计算提供坚实的基础条件。考虑到列车现有的信息设备,利用串口通信,获取列车运行信息的实时数据,由于列车运行线路中存在基本线路切换和长短链,公里标会出现突变,设计专门的算法来同时进行数据纠错和公里标突变识别,实时数据的误码率低至0.02%。在此基础上,通过介绍Sigma点的选取办法,建立列车运动的随机动力学模型,设计UKF(无味卡尔曼滤波)的递推算法,快速地标定出精确的基本阻力参数,以宁西线合肥东—大顾店区段的列车为测试对象,结果表明：实时参数标定器能在某较长的下坡道上,约100个时间步长内完成参数的标定,较参考值符合实际情形。
本文致力于列车节能操纵的理论和实践研究,重点研究列车节能运行的基本原理,为优秀的列车节能操纵指导系统的研制和开发奠定坚实基础,以期降低列车运行的牵引能耗,有利于铁路运输业的节能降耗。
Transport industry is the fundamental service department of China, and playing an important supportive role for the development of society and economy. But a great deal of energy are consumed meanwhile, it should be paid great attention especially when the energy shortage become more and more serious in China. Rail transportation is an important part of transport industry, and complets a large portion of traffic volume of whole society. In recent years, large-scale rail infrastructural constructions have been carried out, and rail transportation will be more dominant in integrated transport network, but energy consumption is growing increasingly come with it. For reducing the energy consumption effectively in train traction, fundamental theoritical research of train energy-efficient movement is conducted, and ultimate principles of it are stressed, in order to provide theoretical basis for the research and development of excellent guide system for train operation.
Based on the well known research achievements, the concept of continuous steep gradient is introduced due to complexity of rail line, and optimal control strategies of train movement on the steep sections are dug deeply. The main contents and results are as following:
(1) According to the mechanical anaylsis of train movement, theoretical model with general applicability is established. The adjoint variable is introduced based on the Pontryagin maximum principle, subsequently Hamiltonian function jointly expressed by state variables, adjoint variables and control variables are put forward, which contribute to the acquisition of necessary condition of optimal control strategy by applying Karush-Kuhn-Tucker conditions. There are only four phases in the train optimal movement:power, speedhold, coast and brake. With the analysis on differential equation of adjoint variable, transfer relation of phases are established, combined with the comprehension of practical environment, the exact phase sequence and phase transfer position are obtained, immediately the optimal control strategy appears obviously.
(2) When train moves uniformly, the negative work done by resistance is minimized. So the speedhold phase becomes the link between different train states. Due to this, the total journey is divided into three stages:start-up, middle and brake, thus the global optimal problem of train operation is decomposed into local optimization induced by speedhold. Afterwards, the numerical solutions of train control system are solved by the fourth order Runge-Kutta method. For steep sections, the critical identification points of steep gradient are calculated first, the initial search interval of phase switch point is determined as a result. Then bisection searching method is adopted to obtain the optimal position, consequently the optimal control strategy and corresponding trajectory is achieved. The total energy consumption has a decreasing tendency as journey time increasing, but there exists no linearity relations between them. A numerical example is given to show that the energy consumption of total journey is falling from 1845.01 Joules to 1527.23 Joules while total journey time increases from 2142.54 seconds to 2473 seconds gradually.
(3) When train moves on the uphill steep gradient, the speed of train will decline definitely, the local optimal control strategy comprise holdspeed-power-holdspeed phase sequence, and the necessary condition of optimal control asks for the adjoint variable equal to one exactly while train switching from power phase back to holdspeed phase. Based on that fact, the position of phase switching point can be determined precisely. To improve the efficiency of numerical computation, in terms of equation of train motion, the new objective functional Jρand new variableμis introduced. When the control strategy is optimal, Jρreaches the minimum and the two endpoint values ofμduring the uphill steep sections equal zero. Becauseμdoes not change within some interval, it causes computational efficiency improved. When train moves on the downhill steep gradient, the speed of train will incline, and the local optimal control strategy comprise holdspeed-coast-holdspeed phase sequence, the adjoint variable equal to one while train switching from coast phase back to holdspeed phase. Similar to uphill steep section, Jp attains its minimum and the two endpoint values ofμequal zero when the control strategy is optimal. For convenience, the method using the property of adjoint variable 6 is called "direct method" and the method usingμcalled "indirect method" throughout this study. Simulation results show that indirect method has better performance, and enhance the computational efficiency by 60.46% during uphill steep section and by 95.81% during downhill steep section.
(4) The resistance parameters of train varies with weather conditions and rail lines, thus train parameters of every journey require real time calibration in order to provide a solid basis for the calculation of optimal control strategy. Take the existing information devices into consideration, the real time information concerning with train movement are acquired through serial communication. According to the existence of the discontinuity of milestones and base line among rail lines, special algorithm is designed, which is capable of correcting data error and identifying the discontinuity simultaneously, and bit error rate is down to 0.02% consequently. In this foundation, in terms of selection method of Sigma points and stochastic dynamic model of train movement, recursive algorithm of UKF is proposed, which calibrates the resistance parameters of train instantly. Taking the trains from Hefei-Dagudian section of Ningxi line for studying object, test result shows that true value of resistance parameters are calibrated within about 100 time steps on some long downhill gradient by designed calibration device.
This paper makes efforts to analyze the theory and practice of train energy-efficient movement, mainly probe the mechanism of train optimal control in order to lay a solid foundation for the development of outstanding optimal guide system for train operation. Hopefully, it can promote the efficiency of train movement and reduce the energy consumption of rail transportation.
本文在借鉴国内外已有研究成果的基础上,充分考虑到列车运行线路复杂多变的特性,引入连续陡坡的概念,对列车在陡坡区段的最优控制策略进行了深入的研究与探讨,主要研究内容及结论如下：
(1)根据列车运行受力分析,构建了基于机械能的列车运行理论模型,引入协态变量,基于Pontryagin极值原理,采用状态变量、协态变量和控制变量联合表达Hamiltonian函数,然后应用Karush-Kuhn-Tucker条件求得最优控制策略的必要条件,即符合列车节能运行的状态仅有四种：最大加速相位、均速相位、惰行相位和制动相位；借助协态变量满足的微分方程,分析出相位转换关系,再根据列车运行的现实环境,寻找正确的相位序列和相位转换点位置,即确定了列车的最优控制策略。
(2)列车匀速运行时,阻力所做的功最少,均速相位成为各种运行状态的纽带,依此对列车运行全程划分阶段,即启动阶段、途中运行阶段和制动阶段,把列车控制全局优化问题化解为由均速速度决定的局部优化问题。采用四阶Runge-Kutta方法来求解列车控制的微分方程,针对陡坡区段,先计算出陡坡临界点,反推出首个相位转换点的初始范围,然后利用二分法逐渐缩小搜索区间,得到了陡坡区段的最优控制策略及相应的最优轨线。随着总运行时分的增加,列车的能耗随之减少,但两者并不呈线性关系,本文算例中,当总旅程时间从2142.54s逐渐增加至2473s时,全程最优控制的能耗值从1845.01J下降至1527.23J。
(3)列车行驶在陡上坡时,速度会下降,局部的最优控制策略为均速—最大加速—均速相位序列,且最优控制的必要条件要求最大加速相位切换回均速相位时,协态变量恰等于1,据此条件可确定陡上坡区段各相位转换点的具体位置。为提高数值计算的效率,结合列车运动方程,构造陡上坡区段新的目标泛函Jp和变量μ,当列车操纵策略为最优时,Jp取极值,且μ在陡上坡区段的始末值均为零,因μ在某些坡段不发生变化,使得数值计算范围缩小而效率得到提升。列车行驶在陡下坡时,速度会上升,局部的最优控制策略为均速—惰行—均速相位序列,且惰行相位转入均速相位时,协态变量恰等于1,为提高计算效率,同样可构造出陡下坡区段的新目标泛函Jp和变量μ,当列车操纵策略为最优时,μ在陡下坡区段的始末值均为零。利用μ和协态变量θ解算最优控制策略的方法在本文中分别被称为间接法和直接法,本文算例中,间接法较直接法在陡上坡区段提高计算效率60.46%,在陡下坡区段提高计算效率95.81%
(4)天气状况不同或列车运行线路不同都会导致列车基本阻力参数变化,因此,列车的每趟旅程的基本阻力参数都需进行实时标定,以便为最优控制策略的计算提供坚实的基础条件。考虑到列车现有的信息设备,利用串口通信,获取列车运行信息的实时数据,由于列车运行线路中存在基本线路切换和长短链,公里标会出现突变,设计专门的算法来同时进行数据纠错和公里标突变识别,实时数据的误码率低至0.02%。在此基础上,通过介绍Sigma点的选取办法,建立列车运动的随机动力学模型,设计UKF(无味卡尔曼滤波)的递推算法,快速地标定出精确的基本阻力参数,以宁西线合肥东—大顾店区段的列车为测试对象,结果表明：实时参数标定器能在某较长的下坡道上,约100个时间步长内完成参数的标定,较参考值符合实际情形。
本文致力于列车节能操纵的理论和实践研究,重点研究列车节能运行的基本原理,为优秀的列车节能操纵指导系统的研制和开发奠定坚实基础,以期降低列车运行的牵引能耗,有利于铁路运输业的节能降耗。
Transport industry is the fundamental service department of China, and playing an important supportive role for the development of society and economy. But a great deal of energy are consumed meanwhile, it should be paid great attention especially when the energy shortage become more and more serious in China. Rail transportation is an important part of transport industry, and complets a large portion of traffic volume of whole society. In recent years, large-scale rail infrastructural constructions have been carried out, and rail transportation will be more dominant in integrated transport network, but energy consumption is growing increasingly come with it. For reducing the energy consumption effectively in train traction, fundamental theoritical research of train energy-efficient movement is conducted, and ultimate principles of it are stressed, in order to provide theoretical basis for the research and development of excellent guide system for train operation.
Based on the well known research achievements, the concept of continuous steep gradient is introduced due to complexity of rail line, and optimal control strategies of train movement on the steep sections are dug deeply. The main contents and results are as following:
(1) According to the mechanical anaylsis of train movement, theoretical model with general applicability is established. The adjoint variable is introduced based on the Pontryagin maximum principle, subsequently Hamiltonian function jointly expressed by state variables, adjoint variables and control variables are put forward, which contribute to the acquisition of necessary condition of optimal control strategy by applying Karush-Kuhn-Tucker conditions. There are only four phases in the train optimal movement:power, speedhold, coast and brake. With the analysis on differential equation of adjoint variable, transfer relation of phases are established, combined with the comprehension of practical environment, the exact phase sequence and phase transfer position are obtained, immediately the optimal control strategy appears obviously.
(2) When train moves uniformly, the negative work done by resistance is minimized. So the speedhold phase becomes the link between different train states. Due to this, the total journey is divided into three stages:start-up, middle and brake, thus the global optimal problem of train operation is decomposed into local optimization induced by speedhold. Afterwards, the numerical solutions of train control system are solved by the fourth order Runge-Kutta method. For steep sections, the critical identification points of steep gradient are calculated first, the initial search interval of phase switch point is determined as a result. Then bisection searching method is adopted to obtain the optimal position, consequently the optimal control strategy and corresponding trajectory is achieved. The total energy consumption has a decreasing tendency as journey time increasing, but there exists no linearity relations between them. A numerical example is given to show that the energy consumption of total journey is falling from 1845.01 Joules to 1527.23 Joules while total journey time increases from 2142.54 seconds to 2473 seconds gradually.
(3) When train moves on the uphill steep gradient, the speed of train will decline definitely, the local optimal control strategy comprise holdspeed-power-holdspeed phase sequence, and the necessary condition of optimal control asks for the adjoint variable equal to one exactly while train switching from power phase back to holdspeed phase. Based on that fact, the position of phase switching point can be determined precisely. To improve the efficiency of numerical computation, in terms of equation of train motion, the new objective functional Jρand new variableμis introduced. When the control strategy is optimal, Jρreaches the minimum and the two endpoint values ofμduring the uphill steep sections equal zero. Becauseμdoes not change within some interval, it causes computational efficiency improved. When train moves on the downhill steep gradient, the speed of train will incline, and the local optimal control strategy comprise holdspeed-coast-holdspeed phase sequence, the adjoint variable equal to one while train switching from coast phase back to holdspeed phase. Similar to uphill steep section, Jp attains its minimum and the two endpoint values ofμequal zero when the control strategy is optimal. For convenience, the method using the property of adjoint variable 6 is called "direct method" and the method usingμcalled "indirect method" throughout this study. Simulation results show that indirect method has better performance, and enhance the computational efficiency by 60.46% during uphill steep section and by 95.81% during downhill steep section.
(4) The resistance parameters of train varies with weather conditions and rail lines, thus train parameters of every journey require real time calibration in order to provide a solid basis for the calculation of optimal control strategy. Take the existing information devices into consideration, the real time information concerning with train movement are acquired through serial communication. According to the existence of the discontinuity of milestones and base line among rail lines, special algorithm is designed, which is capable of correcting data error and identifying the discontinuity simultaneously, and bit error rate is down to 0.02% consequently. In this foundation, in terms of selection method of Sigma points and stochastic dynamic model of train movement, recursive algorithm of UKF is proposed, which calibrates the resistance parameters of train instantly. Taking the trains from Hefei-Dagudian section of Ningxi line for studying object, test result shows that true value of resistance parameters are calibrated within about 100 time steps on some long downhill gradient by designed calibration device.
This paper makes efforts to analyze the theory and practice of train energy-efficient movement, mainly probe the mechanism of train optimal control in order to lay a solid foundation for the development of outstanding optimal guide system for train operation. Hopefully, it can promote the efficiency of train movement and reduce the energy consumption of rail transportation.
引文
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