Research On Theoretical Model Of Train Energy-efficient Movement And Mothod Of Train Parameters Calibration

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.