TY - JOUR
AU - Zhang,, Wenlu
AB - Abstract This paper looks at the heavy-haul combined train composed of different types of locomotives and its distributed power control system with a combination of 800 MHz and TD-LTE wireless communication. It analyses some key characteristic parameters that affect the synchronism and communication of the differential wireless multi-traction synchronous control systems for heavy-haul combined trains. At the same time, in order to reduce the latency of instruction and information transfer between different types of locomotives, improve the time-limit certainty of wireless transmission and optimize the control quality of multi-traction control systems for heavy-haul combined trains, a synchronism optimization strategy based on the Markov decision process on the basis of Petri networkconstruction is proposed. Relevant experiments and tests are carried out to verify the effectiveness of the synchronism optimization of the control system, which provides a guarantee for improving the differential wireless multi-traction synchronous control system for combined trains and optimizing train control. 1. Introduction For quite a long time, China's railway transport capacity was seriously inadequate, and the contradiction between transportation capacity and volume was very prominent, restricting the development of the national economy. Since the 1980s, China has pursued the frontier of railway science and technology in the world, and has made great progress towards high-speed passenger transport and heavy-haul freight transport. In the 21st century, the development of high-speed passenger transport has accelerated the diversion between passenger and cargo transport, and the demand for heavy-haul freight transport has increased; in order to improve the traction capacity of heavy-haul trains, the wireless multi-traction running control of locomotives has become particularly important [1]. For combined trains implementing the locomotive wireless multi-traction synchronous control system, when the weight and length increase, the traction force and braking force during operation will increase, the braking wave transfer time will increase and the change of longitudinal force of heavy-haul trains will be more complicated [2–4]. At this time, for a combined train with different types of locomotives, the problems of locomotive synchronous running performance will be more prominent, and these will affect the quality of train running. Because of the inconsistency of traction drive mode (AC drive, DC drive), energy supply mode (electric locomotive, diesel locomotive), characteristic control mode (DC drive locomotive quasi-permanent speed control, AC drive locomotive quasi-permanent speed control, constant torque control mode, etc.), traction power, electrical logic line and auxiliary system, etc., it is necessary to implement different locomotives combined control on the basis of the wireless multi-traction control system. Secondly, the quality of communication is also one of the factors that affect the performance of train running, and it is desirable to combine different locomotives control with wireless broadband communication or a fusion communication solution, so as to improve the synchronization performance and further improve the running quality of trains [5–7]. Practice shows that on the basis of certain synchronism, the performance and quality optimization of heavy-haul combined trains can be realized through locomotive synchronous operation and asynchronous controls as well as macroscopic cooperative operation and different type locomotive remote wireless multi-traction. Therefore, this paper conducts a thorough research of the synchronous operation yet asynchronous control of locomotives as well as other macroscopic cooperative control questions. 2. Analysis of wireless multi-traction synchronous control and differential locomotive control strategy The different type locomotives wireless multi-traction synchronous control system for heavy-haul combined trains is a complex construction system, which is based on the wireless multi-traction synchronous control system for locomotives and serves as the dynamic system of train traction running control. It involves various intelligent subsystems with complicated logic and electrical correlation, including the traction/brake control system, locomotive auxiliary electrical system, locomotive electrical control system and locomotive safety protection control system—it is a large system which automatically adjusts itself during locomotive running. Fig. 1 shows a mode of multi-traction heavy-haul operation that uses four different types of locomotives. The wireless multi-traction synchronous control system for locomotives is not a simple single input and output system, but a complex dynamic system with multiple ins and outs. Its complexity is manifested in its heterogeneous data relationship structure, function, algorithm, determinism and integration. Therefore, one of the key problems to be solved urgently is how to combine the different type locomotives system organically to form the remote wireless multi-traction synchronous control system for locomotives and coordinate the train traction operation with it [5, 8–10]. Fig. 1. Open in new tabDownload slide Basic method of different type locomotives wireless multi-traction for heavy-haul combined trains Fig. 1. Open in new tabDownload slide Basic method of different type locomotives wireless multi-traction for heavy-haul combined trains When the combined train with mixed locomotives is in operation, the locomotive located in the head position of the train is usually the master locomotive (master), which acts as the leading locomotive, and the rest of the locomotives are the subordinate locomotives (subordinates). Multi-traction locomotive control means that the master issues control instructions by the specific mode of communication, and the subordinates immediately react to the instruction. At the same time, subordinates send back the corresponding locomotive running conditions through the wireless channel. Combined with the current technical research results, the characteristic factor extraction and analysis of different type locomotives wireless multi-traction synchronous control mainly concerns the following three parts: Logical control is involved in running preparation conditions and running control conditions. Locomotive logic control functions mainly include traction/brake control, pantograph control, main circuit breaker control, auxiliary system control, traction direction control, locomotive automatic through phase neutral separation section passing control, compressor control, pneumatic braking and ATP interlocking, etc. Most of the information of these logical controls is expressed in the form of status quantity, that is, the control information is ‘1’ or ‘0’. The locomotive control system needs to control the locomotive function equipment and obtain the information state feedback before starting and during operation, and the execution of the relevant control command and state information also has a logical sequence. Based on the logic relation within locomotive control, the control quantity can be divided into two categories: one is the independent control quantities, the other is the quantities which include the sequential logic relation. Therefore, the logic control between different locomotives needs to be matched according to the condition of locomotive operation preparation and running control. Dynamic control of coordinated running. Dynamic synchronous running is based on the safe and smooth running of the train, and this also involves the dynamic performance of the train. From the point of view of the stability of traction operation, the dynamic running of different type locomotives remote multi-traction synchronous control mainly involves the adjustment of traction force to ensure the balance of force between train vehicles. In general, in dynamic running of the train, each subordinate receives the speed regulation instruction and traction torque instruction from the master, and then according to the running condition of the locomotive and the feedback information of the traction system, the synchronous closed loop adjustment of traction force is carried out to achieve smooth operation. The traction power control often varies between different types of locomotive, and the coordinated control can compensate for the impact caused by this difference. Remote pneumatic brake co-control. Different types of locomotives may have different pneumatic brakes: the setting mode of the target value of the train brake pipe pressure, the control of the locomotive pneumatic balanced cylinder, the action response time of the brake and especially the control command of the brake handle can all be different. In order to effectively relieve the impact of longitudinal force between vehicles during braking and speed up the train pneumatic filling and release time, it is necessary to control the brakes of each locomotive in the remote multi-traction control system. This is so that they work together to ensure that the train pipe pressure control of the rear part of the train can quickly follow the head train and achieve the goal of smooth braking. 3. The model and algorithm of different type locomotives wireless multi-traction synchronous control based on Petri Nets The locomotive wireless multi-traction synchronous control system based on Petri Nets makes the locomotives of the whole train into a whole, and it is divided into three layers according to the locomotive network and control relationship; namely, the train level, the locomotive and rolling stock level and the locomotive driving control level [5, 10]. According to the operating environment, the multi-traction combined train with four different types of locomotives is selected for distributed power traction operation. It is assumed that each locomotive adopt the compatible wireless multi-traction control system, and that the train level is mainly composed of space network made up of wireless data terminal equipment (DTE) and corresponding wireless network management. On the basis of Petri network theory and the deterministic and stochastic Petri Nets (DSPN) model, four different locomotives are regarded as a large communication network control system composed of four subnets, each of which includes location S(i)_on, S(i)_ready, S(i)_token, S(i)_tran, S(i)_recv and S(i)_end. At the same time, the transferred are T(i)_signal, T(i)_token,T(i)_empty, T(i)_ins, T(i)_tran, T(i)_recv, T(i)_restar andT(i)_force, where location S(i)_on has a constant tag number of 1, indicating that the subnet system always has real-time information sources; transfer T(i)_signal indicates that the no. i subnet system produces a packet to be sent, and the packet enters the send buffer S(i)_ready and waits for the network management token there. A token is transmitted at each network node and its time is determined, expressed in S(i)_token. When location S(i)_token receives the token, the transfer T(i)_ins is triggered, the packet enters location T(i)_tran and the transfer T(i)_tran process is performed, i.e. the message packet is sent. For determining the arrival of the packet, the retransmission process is performed when the sending node does not receive the response information within a certain period of time; when the maximum retransmission number is exceeded, the transfer T(i)_force is used to force the end of the transmission. Location T(i)_recv, indicate this node is in the sending state, the other nodes execution transfer T(i)_restar is in the receiving state, the transfer T(i)_recv is executed after receiving the information packet and the information packet is returned to the multi-traction control system [5, 11–15]. The DSPN basic model of the remote wireless multi-traction system composed of four different types of locomotives based on Petri Nets is shown in Fig. 2. Fig. 2. Open in new tabDownload slide DSPN basic model of the remote wireless multi-traction system composed of four different types of locomotives based on Petri Nets Fig. 2. Open in new tabDownload slide DSPN basic model of the remote wireless multi-traction system composed of four different types of locomotives based on Petri Nets As shown in Fig. 1, by analysing the basic working process of the above model, we can see that multi-traction control is a real-time periodic process, and the system executes locomotive control according to the received command and the feedback information of each locomotive node. Therefore, for cooperative control of different types of locomotives, according to the above ideas, the system can be equivalently normalized to achieve compatibility. In order to simplify the process, the vehicle-level control system in the locomotive can be treated as an inertial environment, and the influence of lag time is neglected. In practical application, the master and subordinates adopt the polling mode when the normal non-triggered instruction is generated, and the trigger mode is used when the node needs special protection control on the locomotive. But, in any case, the node must get the network management token to be entitled to send broadcast processing. To simplify the analysis, they can be merged. The related approximate solution is carried out according to the concept of Petri Nets, and the structure of deterministic delay in different cases in this DSPN model is given to construct a model that approximates the actual system. The basic DSPN model of generalized stochastic Petri nets with deterministic delay is composed of seven element groups (P,T, A,M0,R,H andW), marked as: DSPN = (P,T,A,M0,R,H,W), where: |$P = \{ {P_1}, \cdots ,{P_m}\} $| is a set of positions; |$T = \{ {t_1}, \cdots ,{t_m}\} $| is a set of transfers, including immediate transfer, time scale transfer and deterministic time delay transfer; |$A = ({A_t} \cup {A_0}), {A_t} \subseteq (P \times T), {A_0} \subseteq (T \times P)$|⁠; |${M_0} = \{ {m_1}, \cdots ,{m_m}\} $| is the initial marked state; |$R = \{ {r_1}, \cdots ,{r_m}\} $| is a set of transfer-related trigger rates in the Petri nets; |$H \subseteq (P \times T)$| is a set of forbidden arcs; |${\rm{W}} = \{ {w_1}, \cdots ,{w_m}\} $|⁠. Typically, the position P0 enables only the unique deterministic delay transfer and satisfies the condition of M(P0) ≤ 1. And so does the wireless multi-traction DSPN model in this paper. If the generalized stochastic Petri nets model is ergodic, the steady-state probability of its mark can be solved by the matrix equation, namely formula 1: $$\begin{equation*} \left\{ {\begin{array}{@{}*{1}{c}@{}} {\pi Q = 0}\\ {\sum\limits_{t \in R({M_0})} {{\pi _t} = 1} } \end{array}} \right. \end{equation*}$$(1) Where |$\pi $| is the steady-state probability vector, |$Q$| is the transfer rate matrix and |$R({M_0})$| is the reachable state of the net. According to formula 1, the |$\pi $| value can be obtained. At this point, the steady-state performance of the generalized stochastic network can be analysed. The steady-state marker probability density function |$P\{ {\rm{A}} \}{\rm{ = }}\sum {{\pi _{t }}} $|⁠; |$t \in A$|⁠; |$A \in R({M_0})$| are the set of all the marked states that satisfy the condition, giving the mean value of the marked numbers in the location. If |$A(i,x) \in R({M_0})$| is a set of markers with |$x$| numbers in the position |${P_t}$|⁠, and the model is |$K$| bounded, the obtained mean value is |$E(m) = \sum\nolimits_{n = 1}^k {[nP\{ A(i,n)\} ]} $|⁠. For the average time delay difference caused by the approximate processing calculated by the aforementioned |${\rm{DSPN}}$| model, for the time-scale transfer which satisfies the negative exponential probability density distribution, when the time limit for deterministic transfer is set, the probability density function of the transfer is: $$\begin{equation*} f(t) = \frac{N}{d}{e^{ - N \cdot t/d}} \end{equation*}$$(2) The average delay between the number of markers in the position |${P_0}$| and the transfer of the marker to position |${P_1}$| is: $$\begin{equation*} E(t) = \sum\limits_{t = 1}^N {{E_t}(t) = d} \end{equation*}$$(3) The variance is: $$\begin{equation*} Var(t) = \sum\limits_{t = 1}^N {Va{r_t}(t) = } \frac{{{d^2}}}{N} \end{equation*}$$(4) Under extreme conditions: $$\begin{equation*} Var(t) = \mathop {\lim }\limits_{N \to \infty } \sum\limits_{t = 1}^N {Va{r_t}(t) = 0} \end{equation*}$$(5) According to references [11–15], as long as |$N$| is large enough, the position |${P_0}$| will only enable the unique deterministic delay transfer, and the model |${\rm{DSPN}}$| of approximate processing approximates the actual system. 4. Control synchronization performance and the effect of wireless communication The premise of running heavy-haul combined trains is to guarantee their safe running quality by certain means, among which the most important is to ensure balanced traction force (i.e. that longitudinal force is as small as possible) and excellent braking performance. This requires that combined trains have good coordinated running, i.e. good synchronization performance between the locomotives, especially between different types of locomotives with different traction characteristics and control modes. There are many advantages of locomotive wireless multi-traction control, but there is no denying the limitation of wireless communication and its impact on multi-traction synchonous control. First of all, it is necessary to clarify and define the connotation and definition of locomotive multi-traction synchronism [5, 8, 16]. Ideally, it can be assumed that the multi-traction control and information transmission between locomotives are seamless. But this is not the case in reality: wireless communication has a decisive impact on control synchronization, and its synchronization requirements are different for different modes of wireless multi-traction control (e.g. for zero-distance multi-traction locomotives and remote wireless multi-traction locomotives). Therefore, according to the previous research and practice, the synchronization of locomotive wireless reconnection is defined as: under the premise of ensured safety and quality of train running, the control data and the associated data information of each locomotive in the multi-traction system or combined train have the consistency and integrity of the information within a specific time limit, and the coordinated operation of each locomotive can be consistent in the macroscopic level. The main functions of multi-traction control include: (1) locomotive traction/brake synchronous control; (2) real-time wireless transmission of locomotive data; (3) fault diagnosis and safety guidance; (4) train running control optimization. To some extent, each locomotive in the combined train can be formed into a large closed-loop control system, as shown in Fig. 2. However, in order to ensure the robustness of the system in a certain range of conditions, the synchronization time delay, certainty and stability of the system are the key factors, which are strongly related to the method of wireless communication. The wireless communication methods applied in the field of railway multi-traction operation include: 800 MHz radio communication, 400 kHz catenary induction communication, TD-LTE broadband communication and so on [5, 8, 17–22]. Using wireless communication can achieve the purpose of remote control, but due to interference it is difficult for the wireless mode to achieve real-time, safe and reliable communication to meet the requirements of synchronous control. Therefore, the synchronization of wireless multi-traction is closely related to the method and processing of wireless communication. The composition of the different type locomotives multi-traction synchronous control system based on wireless communication is shown in Fig. 3. Fig. 3. Open in new tabDownload slide Composition of different type locomotives multi-traction synchronous control system based on wireless communication Fig. 3. Open in new tabDownload slide Composition of different type locomotives multi-traction synchronous control system based on wireless communication Suppose the ideal system synchronization function is A and the actual system synchronization function is B, then the difference between the two is |$J = A - B$|⁠. In the construction of the actual system, we need to achieve the minimum value of |$J$|⁠. In practice, for wireless multi-traction control, if the ground base station is not used, considering the situation of weak field, signal relay between multiple locomotives is necessary. In addition, radio stations that use radio to send and receive signals cannot carry out continuous transmission work, since they require a certain time interval. Therefore, it is also necessary to pay attention to the adverse effect of air wireless communication network management on locomotive synchronization. The 800 MHz wireless communication routing management mode is shown in Fig. 4. Fig. 4. Open in new tabDownload slide 800 MHz wireless communication routing management mode (1∼6 are possible communication links) Fig. 4. Open in new tabDownload slide 800 MHz wireless communication routing management mode (1∼6 are possible communication links) Based on practice, in order to ensure the real-time capabilty, time-bound certainty and stability of multi-traction control, the normal distribution of synchronous time delay of the data of the remote multi-traction control system should be limited to within about 3 seconds [23]. In the course of train operation, the wireless communication between locomotives is a discrete process, and state correlation between the front and rear is not guaranteed; indeed, it is uncertain from one state to the next, i.e. factors such as terrain and tunnel can cause a change in the communication state and result in communication relay forwarding or periodic retransmission. When the state of the current system is known and the synchronism of each multi-traction locomotive meets the requirements, the synchronization performance of the transferred state of the system cannot be determined because of the impact of such factors as the external environment at the front of the train. But according to the prediction, the probability distribution followed by the next transition state is known and independent of the historical process of the previous time of the system. According to the above characteristics, in order to determine the law of the state transfer of wireless transmission communication routing for each locomotive in Fig. 4, it can be treated as a Markov process, and the multi-traction synchronization decision making can be carried out based on the Markov process [5, 8, 24–27]. 4.1 Markov process analysis of synchronism of multi-traction control Taking 800 MHz communication as an example, according to the characteristics of multi-locomotive communication, in order to determine the law of routing state transfer of wireless transmission communication in Fig. 4, it can be regarded as a Markov process, and the related synchronous decision making can be carried out based on the Markov process, i.e. (i) the probability distribution of system state at t + 1 is only related to the state at t, independent of the state before t; (ii) the state transfer from t to t + 1 is independent of the value of t. By definition, the Markov chain [24] is a sequence of random variables S1,S2,S3…. The range of these variables, that is, the set of possible values for all of them, is called the state space. The value of the St is the state at t. If the conditional probability distribution of the past state for St+1 is only a function of the St, then the Markov property identity is: $$\begin{equation*} P({S_{t = 1}} = s|{S_0},{S_1},{S_2}, \cdot \cdot \cdot ,{S_t}) = P({S_{t + 1}} = s|{S_t}) \end{equation*}$$(6) If the time interval between two successive transfers is assumed to be constant 1 (i.e. the communication characteristic period), and the system is limited, there are N states marked with number 1-N. If the system is in state i at t, the probability that the system is in state j at t+1 is pij: $$\begin{equation*} P = {[{p_{ij}}]_{N \times N }} \end{equation*}$$(7) At any decision-making moment, after state i taking action (control) |$\alpha \in A(i)$|⁠, there are two outcomes: (i) The action gains related benefits |$r(i,\alpha ) $|⁠; (ii) The state of the system at the next moment of actionis determined by the probability distribution |$p( \bullet |i,\alpha ) = 1$|⁠. |$r(i,\alpha ) $| is defined as the immediate real-time value function of |$i \in S$| and |$\alpha \in A(i)$|⁠. Access to |$r(i,\alpha ) $| isn't important in the relevant action cycle; just knowing the expected value after the action is enough. Actually, considering the one-time benefit at the next action moment, and the cumulative benefit that lasts until the next stage, and the random benefit which is transferred to the next stage, it is assumed that the state j of dependence on the next action moment, namely |$r(i,\alpha ,j)$|⁠, the expected benefits of the action |$\alpha $| are therefore: $$\begin{equation*} r(i,\alpha )\underline{\underline {{\rm{def}}}} \sum\limits_j {r(i,\alpha ,j)p(j|i,\alpha )} \end{equation*}$$(8) Assuming that in the above Markov process, the corresponding benefits can be obtained when it move from state i to state j at any time, denoted as |${r_{ij}}$|⁠, i.e. the synchronization performance expectation matrix. The efficiency vector is used to represent the synchronism of the system. In order to overcome the influence of the relevant characteristic parameters, especially the weak field, the data sent by the relevant locomotive is transmitted in the space and the multi-point receiving and sending state is transferred to the corresponding locomotive for receiving. For the expectation benefit vector, there may be a state of superior synchronization performance or a state of poor synchronization performance. Conversely, if there is a state of superior efficiency, there must be a corresponding Markov chain. Due to the possible existence of states with different levels of performance, it is necessary to make relevant decisions to select a state with a superior synchronization performance for control. At a certain state, making a different decision can change the corresponding state transition matrix and synchronism matrix, which results in the problem of finding the optimal decision by dynamic stochastic process of the system. Here, the Markov decision process is used to solve the problem. 4.2 The Markov decision process on wireless communication routing The Markov decision process can be used to optimize the wireless transmission synchronization strategy in order to improve the synchronization performance of multi-traction control, achieve safe and reliable running, reduce the delay of multi-point transmission and retransmission of data, as well as compensating for the impact on efficiency of wireless communication routing and relaying in the space by the aforementioned main characteristic parameters. Using the Markov strategy, the commonly used indexes include: (i) limited stage index; (ii) discount index; (iii) average index. For different categories of indexes, different concepts of policy optimality can be established. Due to the time-limited nature of the communication characteristic period, in order to avoid excessive wireless communication routing relay forwarding, we choose to establish a Markov dynamic decision process model with limited stages. According to the state observed at each moment, we select one action from the available action set to make the decision. The next (future) state of the system is stochastic, according to the newly observed state, then new decision is made, and this is repeated accordingly. The decision-making process uses the Markov decision five-element group |$\{ T,S,A(i),P( \bullet |i,\alpha ),$|⁠,|$r(i,\alpha )\} $| where, |$T = \{ 0,1,2,$||$ ... \, ,N - 1\} ,0 < N < \infty $| is the decision time set; S is the set of all possible states; A (i) is the set of actions (measures, controls) available to the system at state i; |$\alpha $| for an action, |$\alpha \in {\rm A}(i)$|⁠; |$P( \bullet |i,\alpha )$| give the probability law of transferring, |$P(j|i,\alpha )$| indicating that the current state is i, selecting the probability rate of action |$\alpha $| to the next decision time transferring to the state j; and |$r(i,\alpha )$| for the benefit function, which depends on the current system state and selected actions, independent of past history. Under the Markov strategy, for each |$i \in S$|⁠, there are deterministic decision rules or decision functions |$f(i) \in A(i)$|⁠, and the whole f is marked as F. A system decision-making model is established as follows (E defined as a set of communication links): (i) Decision-making time |$T = \{ 0,1,2, ... \, ,h\} $|⁠; for four locomotives, |$h = 4$|⁠; (ii) The possible state |$S = V = [0,1,2, ... \, ,|V|]$|⁠, i.e. the state contained in a node; (iii) Possible action set: $$\begin{equation*} A(i) = {d_{ij}} \end{equation*}$$ Where |${d_{ij}} \in E$|⁠, the action set of a state is all the communication links that it represents in Fig. 4. (iv) Benefits $$\begin{equation*} {r_k}(i,\alpha ) = {r_k}(i,{d_{ij}}) = b_{ij}^w \end{equation*}$$ Where, |${b_{ij}}$| for the delay of the link |${d_{ij}}$|⁠, which is the deterministic factor of the communication link, the adjusted unit of |${b_{ij}}$| makes |${b_{ij}} > 1$|⁠. |$w \ge 1$| is the weight index of delay; the greater the|$w$|the higher the real-time requirement; (v) Probability of transfer: $$\begin{equation*} {P_k}({j^{\prime}}|i,{d_{ij}}) = \left\{ {\begin{array}{@{}*{1}{l}@{}} {1 - p({d_{ij}}),}\\ {p({d_{ij}}),}\\ {0,} \end{array}\begin{array}{@{}*{1}{l}@{}} {j^{\prime} = j}\\ {j^{\prime} = next \to N}\\ {j^{\prime} = other} \end{array}} \right. \end{equation*}$$(9) where, |$i,j,j^{\prime} \in S,{d_{ij}} \in E,k \in [0,h]$| |$p({d_{ij}})$| is the transfer probability of the link |${d_{ij}}$|⁠. In summary, a sequence of decision functions |$\pi = ({f_0},{f_1},{f_2}, \cdot \cdot \cdot ),{f_t} \in F,t \in N$|⁠, where ft is the Markov decision of wireless communication routing at decision time t. 4.3 The Markov strategy algorithm of different type locomotives wireless multi-traction synchronous control Combined with Fig. 4 and the above analysis, the Markov strategy algorithm of different type locomotives wireless multi-traction synchronous control is formed. According to the state of the system at decision time t and the action selected, they are stochastic variables which depend on the strategy |$\pi $|⁠. The sum of the expected benefits of synchronization performance from time t to time N |$u_t^\pi ({h_t})$| is defined as: $$\begin{equation*} u_t^\pi ({h_t}) = {E_\pi }\bigg\{ \sum\limits_{\pi = t}^{N - 1} {{R_n}} (\pi ) + {R_N}({i_N})|{h_t},{Y_t} = {i_t}\bigg\} \end{equation*}$$(10) Among them, |${E_\pi }$| is the expectation factor, ht, it, π, Rn(π) and the above are in consistent meaning, |${R_N}({i_N}) = r({i_N},{\alpha _N})$|⁠. ht is a trajectory |${h_t} = ({i_0},{\alpha _0},{i_1},{\alpha _1}, \cdot \cdot \cdot ,{i_{t - 1}},{\alpha _{t - 1}},{i_t}),t \ge 0$| from time 0 to time t. For every |$i \in S$|⁠, |${V_N}(i,\pi ) = u_0^\pi (i)$|⁠, and the optimal equation is: $$\begin{equation*} {u_t}({h_t}) \!= \!\!\mathop {\sup }\limits_{\alpha \in {\rm A}({i_t})} \!\!\bigg\{ {r_t}({i_t},\!\alpha )\! + \!\sum\limits_{j \in S} {{p_t}} (j|({i_t},\!\alpha )){u_{t + 1}}({h_t},\!\alpha ,\!\!j)\!\bigg\} \end{equation*}$$(11) Add boundary conditions to t = N: $$\begin{equation*} {\rm{Of}\,\,\, {which}}.\;{u_N}({h_N}) = {r_N}({i_N}) \end{equation*}$$(12) The related algorithm steps are as follows: Step 1: Make t = N and for every |${i_N} \in S$|⁠, |$u_N^*({i_N}) = {r_N}({i_N})$|⁠. Step 2: If t = 0, then |$\pi = (f_1^*,f_2^*, \cdot \cdot \cdot ,f_{N - 1}^*)$| is the optimal Markov strategy, and |$V_N^*(i) = u_0^*(i)$| is the optimal value function, algorithm stops. Otherwise, after the order |$t - 1 \Rightarrow t$|⁠, go to step 3. Step 3: For every |${i_t} \in S$|⁠, calculate $$\begin{equation*} u_t^*({i_t}) = \mathop {\max }\limits_{\alpha \in A(i)} \{ {r_t}({i_t},\alpha ) + \sum\limits_{j \in S} {{p_t}(j|{i_t},\alpha )} u_{t = 1}^*(j)\} \end{equation*}$$ and mark the collection $$\begin{equation*} A_t^*({i_t}) = \mathop {\arg \max }\limits_{\alpha \in A(i)} \{ {r_t}({i_t},\alpha ) + \sum\limits_{j \in S} {{p_t}(j|{i_t},\alpha )} u_{t = 1}^*(j)\} \end{equation*}$$ and take arbitrary determination|$f_t^*({i_t}) \in A_t^*({i_t})$|⁠, so as to define the decision rules |$f_t^*({i_t})$| at time t. Step 4: Return to Step 2. 5. Testing and experiment verification In order to test and verify the synchronism of the wireless remote multi-traction synchronous control system for different type locomotives, the constructed wireless multi-traction system includes: wireless data transmission; synchronous multi-traction control; human–machine dialogue and display; braking system and interface; and traction system electrical interface (main circuit, auxiliary circuit, control circuit interface, etc.). 5.1 Traction and electric braking running of locomotives of the same type The tested locomotives are Shenhua SS4B0127, SS4B0128, SS4B0129 and SS4B0130, which are equipped with a wireless multi-traction synchronous control system and adopt the ‘800 MHz + 400 kHz’ wireless communication mode. The traction load is 10 000 tons. The train marshalling form is as shown in Fig. 5. Fig. 5. Open in new tabDownload slide The test of a 10 000-ton combined train adopting 800 MHz + 400 kHz and based on wireless multi-traction synchronous control of the same type of locomotive: (a) Marshalling mode of 10 000-ton combined train based on distributed dynamic traction of the same type of locomotive; (b) Tested traction operating conditions; (c) Tested electric braking conditions; (d) Response time distribution of SSB0129 locomotive traction instructions operation interval, Yanjiata-Shenchinan; (e) Response time distribution of SS4B0129 locomotive braking instructions operation interval, Yanjiata-Shenchinan Fig. 5. Open in new tabDownload slide The test of a 10 000-ton combined train adopting 800 MHz + 400 kHz and based on wireless multi-traction synchronous control of the same type of locomotive: (a) Marshalling mode of 10 000-ton combined train based on distributed dynamic traction of the same type of locomotive; (b) Tested traction operating conditions; (c) Tested electric braking conditions; (d) Response time distribution of SSB0129 locomotive traction instructions operation interval, Yanjiata-Shenchinan; (e) Response time distribution of SS4B0129 locomotive braking instructions operation interval, Yanjiata-Shenchinan Fig. 6. Open in new tabDownload slide Test of 10 000-ton combined train adopting 800 MHz + 400 kHz and based on differential wireless multi-traction synchronous control: (a) The marshalling mode of 10 000-ton combined train based on distributed power traction of different types of locomotive; (b) Test formation: 2 + 2 traction mode; (c) Traction running data obtained from Bombardier MITRAC system; (d) Test formation: display of 2 + 2 traction mode in the drive cab; (e) Test formation: display of 2 + 2 electric brake mode in the drive cab Fig. 6. Open in new tabDownload slide Test of 10 000-ton combined train adopting 800 MHz + 400 kHz and based on differential wireless multi-traction synchronous control: (a) The marshalling mode of 10 000-ton combined train based on distributed power traction of different types of locomotive; (b) Test formation: 2 + 2 traction mode; (c) Traction running data obtained from Bombardier MITRAC system; (d) Test formation: display of 2 + 2 traction mode in the drive cab; (e) Test formation: display of 2 + 2 electric brake mode in the drive cab The test results show that the four homotypic master-slave locomotives distributed in different locations of heavy-haul combined trains can cooperate in synchronous traction/electric braking operation control. Although there are follow-up differences, the synchronization is good, with an average delay of communication cycle of about 2.5 s, and the train operation is relatively stable. 5.2 Traction and electric braking operation of different types of locomotives In the traction test of a mixed marshalling heavy-haul train consisting of Shenhua HXD27002 locomotive + SS4B0092 locomotive + 58 C80 type freight vehicles + HXD27001 locomotive + SS4B0091 locomotive + 58 C80 type freight vehicles (traction weight 11 600 t), as shown in Fig. 6, HXD27001 and HXD27002 locomotives adopt AC-DC-AC drive traction system, and the TCMS system and traction system are systems produced jointly by Bombardier and its Chinese joint venture company. A different type locomotives wireless multi-traction synchronization control system is installed in the test locomotives, and the strategy optimization of the Markov algorithm is introduced into the remote multi-traction control based on Petri Nets. The delay time of the locomotive traction and braking system in the middle of the train in response to the instruction change of the master is tested to judge its synchronization performance. The wireless transmission mode adopts ‘800 MHz + 400 kHz’ wireless communication system. 5.3 The running of the multi-traction for locomotives with different traction power and different communication modes The wireless multi-traction synchronous control system based on 4G technology ‘TD-LTE + 800 MHz’ and applying the method proposed in this paper mostly uses the TD-LTE Shenhua railway network, and it can switch to 800 MHz radio communication mode in occasional network failures. The system successfully realized the running of 25 000 t wireless multi-traction heavy-haul combined trains with a 30 t axle weight. Train marshalling: 1 Shenhua HX1 AC 12-axis electric locomotive + 15 000 t freight vehicle (KM96 type) + 1 Shenhua HX1 AC 8-axis electric locomotive + 10 000 t freight vehicle (KM96 type); among them, the HXD1 locomotive adopts the Chinese AC-DC-AC traction system and TCMS system, as shown in Fig. 7. Fig. 7. Open in new tabDownload slide Test of 25 000-ton combined train with ‘TD-LTE 800 MHz’ based on differential wireless multi-traction synchronous control of different types of locomotives: (a) Based on ‘TD-LTE + 800 MHz' mode different locomotive wireless reconnection traction; (b) Cooperative response time distribution of multi-traction operation Fig. 7. Open in new tabDownload slide Test of 25 000-ton combined train with ‘TD-LTE 800 MHz’ based on differential wireless multi-traction synchronous control of different types of locomotives: (a) Based on ‘TD-LTE + 800 MHz' mode different locomotive wireless reconnection traction; (b) Cooperative response time distribution of multi-traction operation From the test data, it can be seen that in the dynamic process of differential wireless multi-traction running, synchronous control delay is within the required range, which provides the basis for the guarantee of synchronous control performance. Secondly, using broadband communication, the average time delay is reduced from the average 2.5 s of the 800 MHz communication mode to about 566 ms, which is more suitable for differential wireless multi-traction control. 5.4 Dynamic performance test of heavy-haul combined train based on wireless multi-traction cooperative control system for different type locomotives Heavy-haul combined train running tests on the Shuohuang Line include the traction of 216 C80 freight vehicles marshalling trains by the mode ‘1 SH8 + 1 SH8 + controllable train tailing’, the traction of 232 C80 freight vehicles marshalling trains by the mode ‘1 SH8 + 1 SH8 + controllable train tailing’ and the traction of 232 C80 freight vehicles marshalling trains by the mode ‘1 SH12 +1 SH8 + controllable train tailing’, so as to test the longitudinal force of the above trains running on the Shenchi South-Suning North Section of the Shenhua Railway Line (including 19 occurrences of cyclic pneumatic braking). SH12 and SH8 are based on the Shenhua improved type of HXD1, the heavy-haul AC-DC-AC traction electric locomotive, adopting the wireless multi-traction cooperative control system for drfferent type locomotives and based on the communication mode of ‘TD-LTE Shenhua railway network + 800 MHz’. The main test data is shown in Fig. 8. Fig. 8. Open in new tabDownload slide Longitudinal force test of three kinds of 20 000-ton trains adopting the differential wireless multi-traction synchronous control system: (a) Comparison diagram of the maximum coupler force on the freight vehicles of three kinds of 20 000-ton marshalling train in cyclic braking; (b) Comparison diagram of the maximum coupler force on the middle part of the subordinate locomotive of three kinds of 20 000-ton marshalling train in cyclic braking Fig. 8. Open in new tabDownload slide Longitudinal force test of three kinds of 20 000-ton trains adopting the differential wireless multi-traction synchronous control system: (a) Comparison diagram of the maximum coupler force on the freight vehicles of three kinds of 20 000-ton marshalling train in cyclic braking; (b) Comparison diagram of the maximum coupler force on the middle part of the subordinate locomotive of three kinds of 20 000-ton marshalling train in cyclic braking The average value of the maximum coupler force of the cyclic pneumatic brake was 1021 kN (1162 kN, 1100 kN). In the running and stopping test, after the train had stopped by decompressing for 100 kPa at a −11.4‰ downhill slope, the train added the decompression amount to the full service brake. After the release, there were six vehicles’ sections with more than 1000 kN of pulling coupler force and the maximum 1748 kN of pulling coupler force in the whole course (freight vehicle 135 after 70 s release). From the test data, it can be seen that the maximum coupler force of the test vehicles occured at position 107 and position 109, i.e. 12 times adjacent to a slave, mainly after the release, and the longitudinal force was relatively small when release occurred on a gentle slope. Of the 19 occurrences of cyclic pneumatic brake release speed regulation, there were eight that featured a coupler force greater than 1000 kN in the central couplers of the slaves. 6. Conclusions The synchronous control mode and wireless transmission mode are the key factors affecting the synchronism of the different type locomotives wireless multi-traction control system. The more determinate the time limit of transmission, and the higher the real time, the better the synchronism of the system. At the same time, the introduction of the Markov process analysis and strategy optimization can promote the synchronism optimization of the system. The better the synergy of the differential multi-traction control system, the better its synchronism. From the test results, the response time of the slave is mostly within 3 seconds and the average period is 2.5 seconds for the wireless multi-traction synchronous control system relying mainly on the 800 MHz communication mode. Using the TD-LTE communication mode, the average delay is 566 ms, and the cooperative control of each locomotive is better, which is comparable to GE's LOCOTROL system used by Daqin Locomotives, and can meet the basic requirements of long heavy-haul train traction running. The different type locomotives wireless multi-traction control system enables the synchronous operation and asynchronous control of the heavy-haul combined train. The test data shows that it can guarantee the train running, but the longitudinal force of the train still has a high peak value, especially after the pneumatic brake of the train is released, and it is located in the middle to rear part of the first group of the heavy-haul combined train. From the test results and the problems found in the test, the phenomena of data frame loss and multiple retransmission in wireless communication affect synchronization performance. In summary, the wireless communication system needs further analysis and improvement. At the same time, the experiment shows that the longitudinal dynamic performance of heavy-haul combined trains needs further optimization and improvement. 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TI - Analysis of the different locomotive wireless multi-traction synchronous control systems for heavy-haul combined trains and their performance
JF - Transportation Safety and Open Environment
DO - 10.1093/tse/tdaa025
DA - 2020-10-27
UR - https://www.deepdyve.com/lp/oxford-university-press/analysis-of-the-different-locomotive-wireless-multi-traction-rvgyANuKKn
SP - 202
EP - 215
VL - 2
IS - 3
DP - DeepDyve
ER -