Group train tracking operation optimization method considering communication delay

Abstract

The invention discloses a group train tracking operation optimization method considering communication delay. The method comprises the following steps: establishing a heavy haul railway train group of a'navigation-front train following 'topological structure; a multi-target optimization model is constructed according to the characteristic constraint, the speed limitation and the safety distance constraint of the vehicle; generating a random communication delay in the model, calculating a time step number corresponding to the delay, and making a control decision on the following train based on state information of a previous time step of the preceding train; and solving the running speed of the following train in the multi-objective optimization model based on a particle swarm algorithm. According to the group train tracking operation optimization method, the problems of uncertainty and dynamic response lag caused by communication delay in the tracking operation process of heavy haul railway group trains are effectively solved, the tracking error between the trains can be remarkably reduced, the speed synchronism is improved, and the tracking operation efficiency is improved. And the distance fluctuation in the acceleration and deceleration stages can be effectively reduced, so that the train distance stability is ensured.

Description

Technical Field

[0001] The present invention relates to the field of rail transit control technology, and in particular to a group train tracking operation optimization method taking communication delay into consideration, which is applicable to scenarios such as heavy-load railways, high-speed railways, and urban rail transit that require coordinated operation of multiple trains. Background Art

[0002] With the rapid development of rail transit systems, the density and speed of train operations are constantly increasing. Traditional train operation control methods can no longer meet the needs of modern rail transit systems. Especially in the scenario of multi-train coordinated operation, problems such as communication delays and inaccurate information transmission between trains may lead to reduced train operation efficiency and increased safety hazards. Most of the existing train operation optimization methods are based on idealized communication conditions, assuming that information transmission between trains is instant and accurate, ignoring the delays and uncertainties in actual communication systems.

[0003] In actual operation, communication delays between trains may be caused by a variety of factors, such as network congestion, signal interference, equipment failure, etc. These delays will cause the information received by the train control system to lag, which in turn affects the train's operation decisions. For example, when the front train suddenly slows down, the rear train may not be able to obtain information in time due to communication delays, resulting in a too close tracking distance and increased collision risk. In addition, existing train operation optimization methods usually only consider the operating efficiency of a single train, lack of overall optimization of the coordinated operation of multiple trains, and it is difficult to achieve global optimization.

[0004] The implementation of group control technology on heavy-haul railways still faces many challenges: First, the requirements of communication and control technology. Group control requires high-precision, low-latency train-to-train communication (such as T2T communication) to ensure real-time coordination of trains, while the stability and coverage of communication signals place stringent requirements on complex terrain and climatic conditions. Second, the problem of dynamic heterogeneity of trains. Heavy-haul trains are composed of different vehicle groups, with uneven distribution of traction, braking force and weight, and significant differences in dynamic characteristics, which makes the coordinated control of group trains complex and easily causes speed and vehicle spacing fluctuations, threatening transportation safety and efficiency. Third, the safety guarantee of group train control systems. While group control shortens the tracking distance between trains and improves efficiency, it also increases safety risks. Once the communication or control system fails, it is difficult for the rear vehicle to obtain the status of the front vehicle in time, which can easily cause serious rear-end collisions. It is urgent to build a strong and robust fault detection and emergency mechanism. Fourth, the balance between energy consumption and economy. The control system of group trains frequently and dynamically adjusts to adapt to the front vehicle, which increases energy consumption. In addition, the cost of technology research and development and initial deployment is high, including control system design and line reconstruction, which puts heavy pressure on the economic decision-making of operators.

[0005] Therefore, there is an urgent need for a group train tracking operation optimization method that can effectively consider communication delays to improve the safety, efficiency and reliability of train operation. Summary of the invention

[0006] The purpose of the present invention is to provide a group train tracking operation optimization method taking into account communication delay. The method is based on real-time communication information and collaborative control between trains, and optimizes factors such as train speed, position, acceleration, etc. to ensure safe spacing and efficient operation between trains.

[0007] To achieve the above object, the present invention provides a group train tracking operation optimization method considering communication delay, comprising the following steps:

[0008] Step 1: Establish a heavy-load railway train group with a "pilot-follower" topology structure;

[0009] Step 2: Based on the vehicle's own characteristic constraints, speed limit and safety distance constraints, a multi-objective optimization model is constructed with the goal of minimizing the speed difference between the preceding and following trains and minimizing the difference between the target distance and the actual tracking distance;

[0010] Step 3: Generate a random communication delay in the multi-objective optimization model, calculate the time step corresponding to the delay, and make a control decision based on the state information of the previous time step of the leading train by the following train;

[0011] Step 4: Solve the running speed of the following train in the multi-objective optimization model based on the particle swarm algorithm.

[0012] Furthermore, in step 2, the optimization goal is to minimize the difference between the actual distance and the target distance between the preceding train and the following train and to minimize the speed difference between the two trains; wherein:

[0013] Speed ​​difference index f v It is expressed as:

[0014] f v =(V L -V F ) 2 ;

[0015] Distance index f d It is expressed as:

[0016] f d =(s L -s F -L T -L d ) 2 ;

[0017] Among them, V L and V Fare the speeds of the preceding train and the following train respectively; s L and F are the positions of the preceding train and the following train, L T is the length of the preceding train, L d is the expected distance between the two trains.

[0018] Furthermore, in step 2, according to the constraints of the multi-objective optimization model, a mathematical model for the group train tracking operation optimization problem is established as follows:

[0019] min a J=K v ·f v +K d ·f d (1)

[0020] U min ≤u i (t)≤U max (2)

[0021]

[0022] s i-1 (t)-s i (t)-D l ≥s min (6)

[0023] In the above formulas (1)-(6), F max is the upper limit of the rear vehicle’s traction force; u i (t) is the unit train control quantity, U min is the maximum deceleration; U max is the maximum acceleration; v i is the speed of unit train i; D min is the safety spacing margin related to the train positioning error; D l is the unit train length; F max,lead is the traction force of the front vehicle, which is determined by the traction characteristic curve; S min is the minimum train spacing, safety buffer distance; a brake is the maximum deceleration under emergency braking; is the position s i The speed limit at (t).

[0024] Furthermore, in step 2, the minimum safe distance between unit trains in the group is expressed as:

[0025]

[0026] In formula (7), l acIndicates the distance traveled by the rear vehicle from the start of braking of the front vehicle to the start of braking of the rear vehicle. Its value is affected by the equipment response time, communication delay and marshaling speed. Indicates the braking distance of the following vehicle under the most unfavorable conditions; Indicates the braking distance of the front vehicle under the most favorable conditions, S m Indicates the safety protection distance between trains.

[0027] Furthermore, in step 3, the following train obtains the status information of the preceding train through the onboard equipment, and uses the information as the algorithm input to calculate the target tracking speed of the following train at the next time step according to step 4;

[0028] l ac =(t a +t delay )·v 0

[0029] Among them, t delay is the communication delay; ac Indicates the distance traveled by the rear vehicle from the start of braking of the front vehicle to the start of braking of the rear vehicle; v 0 Indicates the initial speed of the rear vehicle when braking; t a represents the inherent time difference between the braking actions of the leading and trailing vehicles, and the communication delay t delay Together, the following vehicle continues to move at a speed of V before braking. 0 The total time of driving.

[0030] Furthermore, the specific steps of step 4 are:

[0031] Step 4.1, Initialize the particle swarm: Set the total simulation time T and divide it into multiple time steps Δt, that is, t 0 , t 1 , t 2 ,…,t N , at each time step k, initialize and generate a number of particles n i , each particle represents an acceleration control strategy for that time step and is randomly initialized in the range of [-1, 1] to ensure that the particle swarm is widely distributed in the search space;

[0032] Step 4.2: Simulate the dynamic motion process of the following vehicle; for the current time step k, each particle corresponds to an acceleration control strategy a k , use the train dynamics model to calculate the position x of the following vehicle in the current time step k , speed v k and acceleration a k ; Randomly generate delay time to calculate the state of the lagging front vehicle and calculate the fitness function value;

[0033] Step 4.3, update the particle swarm state; use the standard particle swarm update formula to adjust the particle speed and position to ensure that the particle acceleration control variable is within a reasonable range;

[0034] Step 4.4, update individual optimal and global optimal solutions: During the iteration process, compare the current fitness value of each particle with the best historical fitness of the particle. If the current fitness is smaller, update the individual optimal solution pbest of the particle. Compare the individual optimal solutions of all particles. If the fitness of a particle is better than the current global optimal solution, update the global optimal solution gbest.

[0035] Step 4.5: Time step advancement: If the current time step k has not reached T, set the optimal acceleration As the input variable for the following vehicle to enter the next time step k+1; enter the next time step k+1 and re-execute steps 4.2-4.4 to continue to optimize the acceleration strategy of subsequent time steps;

[0036] Step 4.6: When the simulation time step reaches T or the termination condition is met, stop the algorithm; output the optimal acceleration trajectory of the entire time series Used for dynamic control of the following vehicle.

[0037] Furthermore, the simulation time step termination condition in step 4.6 is: the global optimal solution converges or reaches the maximum number of iterations of 100.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] (1) The present invention adopts a pilot-following topology structure to adapt to the operating characteristics of virtual train formations. The train obtains the real-time status of the leading train and the global goals of the pilot train, thus achieving a balance between local safety and global coordination. This structure reduces the complexity of communication and the dependence on high bandwidth, improves the robustness of the system, and simplifies the construction of collaborative optimization models and the implementation of distributed control algorithms. When dealing with uncertain interference such as communication delays and traction fluctuations, the pilot-following topology structure shows the advantages of strong formation stability and high scalability, and is suitable for complex operation scenarios of heavy-loaded freight trains.

[0040] (2) The group train tracking operation optimization method of the present invention effectively solves the uncertainty and dynamic response lag caused by communication delays during the tracking operation of heavy-duty railway group trains. It can not only significantly reduce the tracking error between trains and improve speed synchronization, but also effectively reduce the distance fluctuations in the acceleration and deceleration stages to ensure the stability of the train spacing. By introducing dynamic safety distance penalty terms and acceleration smoothness constraints, the system's anti-interference ability can be improved and the train's following performance can be optimized. The present invention not only helps to improve the safety and efficiency of train operation, but also improves the overall transportation capacity and operation stability of railway transportation in complex dynamic environments.

[0041] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following specific implementations, they are used to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention. In the accompanying drawings:

[0043] Figure 1 It is a flow chart of a group train tracking operation optimization method considering communication delay of the present invention;

[0044] Figure 2 It is a schematic diagram of train force analysis in the group train tracking operation optimization method of the present invention;

[0045] Figure 3 It is a schematic diagram of a safety braking model of a group train in the group train tracking operation optimization method of the present invention;

[0046] Figure 4 It is a flow chart of the particle swarm algorithm in the group train tracking operation optimization method of the present invention;

[0047] Figure 5 It is the speed-time (vt) and speed difference-time curve of the front and rear trains after optimization in the present invention; wherein: (a) is the speed-time (vt) curve of the front and rear trains after optimization; (b) is the speed difference-time curve of the front and rear trains after optimization;

[0048] Figure 6 It is the distance difference-time curve before and after optimization in the present invention; wherein: (a) is the distance difference-time curve before optimization, and (b) is the distance difference-time curve after optimization. DETAILED DESCRIPTION

[0049] The present invention will be described in detail below in conjunction with the various embodiments shown in the accompanying drawings, but it should be noted that these embodiments are not limitations of the present invention, and any equivalent transformations or substitutions in functions, methods, or structures made by ordinary technicians in the field based on these embodiments are all within the scope of protection of the present invention.

[0050] See also Figures 1 to 6 , an embodiment of the present invention provides a group train tracking operation optimization method considering communication delay, comprising the following steps:

[0051] Step 1: Establish a heavy-load railway train group with a "pilot-follower" topology structure;

[0052] Establishing a group train dynamics model: In order to achieve speed tracking control of group trains, establishing an accurate train dynamics model is the first prerequisite. The dynamics model of a single train is Figure 2 shown.

[0053] During the operation of a train, it is mainly affected by traction, braking force, basic resistance and additional resistance. The traction and braking force determine the acceleration or deceleration of the train, while the resistance is always opposite to the direction of the train's movement. Additional resistance includes slope resistance and curve resistance. The slope resistance is generated by the gravity component, and the curve resistance is caused by the centrifugal force of the train on the curved path.

[0054] The dynamic equation of the train during operation can be expressed as:

[0055]

[0056] Where M is the mass of the train; F traction is the train traction force, F brake is the train braking force, W(v(s)) is the air resistance, N G (s) is the additional resistance, N C (s) is the additional resistance of the curve, T and B are the traction and braking states (Boolean variables of 0 or 1).

[0057] Step 2: Based on the vehicle's own characteristic constraints, speed limit and safety distance constraints, a multi-objective optimization model is constructed with the goal of minimizing the speed difference between the front and rear trains and the difference between the target distance and the actual tracking distance; this step analyzes and establishes a mathematical optimization model for group train tracking operation with the optimization goal of minimizing the train spacing error and speed difference, while considering the constraints such as train dynamic characteristics, maximum traction force limit, braking force limit and safety distance. Specifically:

[0058] 1. Model optimization objectives:

[0059] Based on the actual operation of heavy-haul railway group control, the optimization goal is to minimize the difference between the actual distance and the target distance between the preceding train and the following train and to minimize the speed difference between the two trains. v Expressed as: f v =(V L -V F ) 2 ; Distance index f d Expressed as: f d =(s L -s F -L T -L d ) 2 ; Among them, V L and V F are the speeds of the preceding train and the following train respectively; s L and F are the positions of the preceding train and the following train, L T is the length of the preceding train, L d is the expected distance between the two trains. The smaller the distance index, the closer the distance between the two trains is to the expected distance.

[0060] The model is based on the tracking operation optimization of two trains, assuming that the trains can be analyzed independently, without considering the complex global network interference or interaction. It focuses on the operation adjustment of two adjacent trains, so it is suitable for local optimal solutions, but may not be able to find the global optimal solution in multi-train scenarios; it is suitable for relatively simple scenarios such as tracking operation and alternating scheduling, but it is not expressive enough for complex scenarios such as dense train formation or cross scheduling. Multi-train optimization requires consideration of a wider decision space, which may cause the model to converge more slowly or fall into a local optimal solution.

[0061] 2. Model constraints:

[0062] Constraints are based on the dynamic characteristics of group trains and real-time communication requirements. They are generally designed under conditions such as maximum traction, braking force, and safe distance between trains, and meet the standards for train operation safety and efficiency. During the optimization process, the maximum acceleration limit of the train and the safety constraints of the train spacing are mainly considered to ensure that the train can follow stably in different environments, avoid collision risks, and improve the system response speed:

[0063] ① Constraints of vehicle characteristics: The traction and braking performance of the train is an inherent attribute of the train vehicle, which determines the traction and braking force that the train can provide during operation, and plays an important role in the automatic driving control of the train. Since the design of the traction and braking system of the train is complex, it is necessary to consider factors such as train resistance, weight, transmission system, and marshaling for matching design. The present invention only considers the output range of traction and braking force of the train affected by the saturation characteristics of the traction motor.

[0064] Considering the traction and braking characteristics of the unit train, the unit train control quantity needs to consider the following constraints: the traction and braking force of each unit train are subject to physical limitations, and the control system must ensure that it does not exceed the maximum capacity range when allocating control inputs. Exceeding the range may cause equipment damage or the system cannot operate normally.

[0065] ② Speed ​​limit: The train speed is limited by the maximum allowable speed of the line conditions, the ATP protection speed and the maximum safe operating speed calculated based on the train's own performance. The train speed constraint is expressed as the train speed must not exceed the maximum allowable speed under the track curvature radius and marshaling requirements. The speed of each unit train must meet the speed limit requirements caused by the line or environmental conditions (such as terrain, weather, line conditions, etc.). For each unit train, the following speed limits need to be met. The speed limit of the line may be caused by factors such as curves, ramps, and platforms. During the group train tracking process, each train needs to meet the speed limit conditions at all times, otherwise it may cause unsafe situations (such as derailment or failure to stop in time).

[0066] ③In addition, train tracking must also meet the constraints of safe distance:

[0067] Considering that the actual relative distance between unit trains should be controlled within a reasonable range, a safety constraint is added to keep the relative distance between units within a safe range. The minimum running distance is adopted. In order to avoid rear-end collisions during operation or braking, it is necessary to ensure that the minimum safe distance between adjacent trains meets certain physical conditions. The minimum distance between unit train i and its preceding train is constrained by the relative braking distance principle.

[0068] Combined with the above analysis, the mathematical model of group train tracking operation optimization problem is established as follows:

[0069] min a J=K v ·f v +K d ·f d (1)

[0070] U min ≤u i (t)≤U max (2)

[0071]

[0072] s i-1 (t)-s i (t)-D l ≥s min (6)

[0073] In the above formulas (1)-(6), Fmax is the upper limit of the rear vehicle’s traction force; u i (t) is the unit train control quantity, U min is the maximum deceleration; U max is the maximum acceleration; v i is the speed of unit train i; D min is the safety spacing margin related to the train positioning error; D l is the unit train length; F max,lead is the traction force of the front vehicle, which is determined by the traction characteristic curve; S min is the minimum train spacing, safety buffer distance; a brak is the maximum deceleration under emergency braking; is the position s i The speed limit at (t).

[0074] like Figure 3 This is a schematic diagram of the group train safety braking model. The scenario of "the front car is the most favorable braking, and the rear car is the most unfavorable braking" is the most unfavorable scenario for group train safety braking. Based on this scenario, a group train safety braking model is established. The minimum safe distance between unit trains in the group under the most unfavorable scenario can be expressed as:

[0075]

[0076] In formula (7), l ac Indicates the distance traveled by the rear vehicle from the start of braking of the front vehicle to the start of braking of the rear vehicle. Its value is affected by the equipment response time, communication delay and marshaling speed. Indicates the braking distance of the following vehicle under the most unfavorable conditions; Indicates the braking distance of the front vehicle under the most favorable conditions, S m Indicates the safety protection distance between trains.

[0077] Step 3: Generate a random communication delay in the multi-objective optimization model, calculate the time step corresponding to the delay, and make a control decision based on the state information of the preceding train in the previous time step; the following train obtains the state information of the preceding train through the on-board equipment, and at the same time knows its own state information, which is used as the algorithm input to calculate the target tracking speed of the following train in the next time step according to step 4;

[0078] l ac =(t a +t delay )·v 0

[0079] Among them, t delay is the communication delay; ac Indicates the distance traveled by the rear vehicle from the start of braking of the front vehicle to the start of braking of the rear vehicle; v 0Indicates the initial speed of the rear vehicle when braking; t a represents the inherent time difference between the braking actions of the leading and trailing vehicles, and the communication delay t delay Together, the following vehicle continues to move at a speed of V before braking. 0 The total time of driving.

[0080] Step 4: Solve the running speed of the following train in the multi-objective optimization model based on the particle swarm algorithm; Figure 4 As shown, the specific steps are:

[0081] Step 4.1, Initialize the particle swarm: Set the total simulation time T and divide it into multiple time steps Δt, that is, t 0 , t 1 , t 2 ,…,t N , at each time step k, initialize and generate a number of particles n i , each particle represents an acceleration control strategy for that time step and is randomly initialized in the range of [-1, 1] to ensure that the particle swarm is widely distributed in the search space;

[0082] Step 4.2: Simulate the dynamic motion process of the following vehicle; for the current time step k, each particle corresponds to an acceleration control strategy a k , use the train dynamics model to calculate the position x of the following vehicle in the current time step k , speed v k and acceleration a k ; Randomly generate delay time to calculate the state of the lagging front vehicle and calculate the fitness function value;

[0083] Step 4.3, update the particle swarm state; use the standard particle swarm update formula to adjust the particle speed and position to ensure that the particle acceleration control variable is within a reasonable range;

[0084] Step 4.4, update individual optimal and global optimal solutions: During the iteration process, compare the current fitness value of each particle with the best historical fitness of the particle. If the current fitness is smaller, update the individual optimal solution pbest of the particle. Compare the individual optimal solutions of all particles. If the fitness of a particle is better than the current global optimal solution, update the global optimal solution gbest.

[0085] Step 4.5: Time step advancement: If the current time step k has not reached the total simulation time T, set the optimal acceleration As the input variable for the following vehicle to enter the next time step k+1; enter the next time step k+1 and re-execute steps 4.2-4.4 to continue to optimize the acceleration strategy of subsequent time steps;

[0086] Step 4.6: When the simulation time step reaches T or the termination condition is met (the global optimal solution converges, or the maximum number of iterations reaches 100), stop the algorithm; output the optimal acceleration trajectory of the entire time series Used for dynamic control of the following vehicle.

[0087] Example

[0088] A heavy-duty railway trunk line (starting station A - final station B) is selected as a case line to verify the effect of the model and algorithm. Consider the scenario of two trains tracking optimization on a track with a total length of 2000 meters. The two trains depart at the same time from the initial position (with a spacing of 200 meters). The specific assumptions and driving rules are as follows:

[0089] Each train has a mass of 5,000 tons and a maximum operating speed of 20 m / s. The train's power system is capable of providing 1 m / s during the acceleration phase. 2 During the braking phase, the train can accelerate at a maximum speed of 1m / s 2 During the algorithm optimization process, the time step is 0.1 second.

[0090] The train's travel process is divided into three main stages: acceleration stage, constant speed travel stage and braking stage.

[0091] During the acceleration phase, the front vehicle starts from a stationary state and accelerates at 1m / s 2 The acceleration gradually increases until it reaches the maximum speed of 20m / s. When the speed of the front car has not yet reached the maximum speed, its acceleration is maintained at 1m / s 2 , until the speed reaches 20m / s. When the speed of the leading vehicle reaches the maximum value of 20m / s, the train enters the uniform speed stage and maintains a constant speed until the braking requirements are met. When the train reaches the braking starting point, the train enters the deceleration stage. Specifically, when the displacement of the leading vehicle reaches or exceeds 1800 meters, the leading vehicle activates the braking mechanism and starts to accelerate at a maximum speed of 1m / s 2 The following train (the rear train) also starts the deceleration mechanism when the displacement reaches 1,600 meters, and brakes at the same deceleration to ensure that the train can stop safely, and maintain a safe distance between trains through timely deceleration to avoid collision or other safety hazards.

[0092] Table 1 Parameters

[0093]

[0094] In the research related to vehicle-to-vehicle communication, communication delay is usually affected by many factors, such as the distance between trains, interference from the surrounding environment, performance of communication equipment, etc. Taking these factors and the complex situation of actual operation into consideration, this embodiment determines a representative delay range of 0.2s-0.4s to simulate different delay scenarios that may occur in practice, so as to comprehensively evaluate the performance of the method of the present invention in reducing communication delay interference.

[0095] The results of optimizing communication delay interference using this model and algorithm are as follows:

[0096] ① The algorithm is programmed in MATLAB and runs on a machine with a processor of R7-8845HS@3.8GHz, 32.0GB of RAM, and a 64-bit operating system. According to the optimized distance difference-time curve, the overall tracking distance difference is maintained between 200 meters and 204 meters, and the fluctuation range is significantly reduced. In the acceleration and deceleration stages, the tracking distance curve is smoother and the deviation converges rapidly. In the uniform speed stage (20-100 seconds), the tracking distance is maintained at 203-204 meters, and the error is significantly reduced.

[0097] ② The average tracking distance of the optimized system is closer to the target distance (200 meters), the error is reduced, the accuracy is improved, and the optimization strategy can significantly reduce the distance deviation in the dynamic stage, improving the stable tracking performance between trains. The mean square value of the distance error after optimization is reduced by 1.70%, the response of the rear vehicle to the front vehicle during dynamic tracking is more rapid and effective, and the distance fluctuation of the system during the acceleration and deceleration stages is significantly reduced. The mean square value of the speed error after optimization is reduced by 60.74%, and the impact of communication delay on speed synchronization is greatly reduced. The rear vehicle can quickly adapt to the speed changes of the front vehicle to ensure operational stability.

[0098] Table 2 Comparison of optimization effects

[0099]

[0100] Table 3 Algorithm performance before and after optimization

[0101]

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A group train tracking operation optimization method considering communication delay, characterized in that: The following steps are involved: Step 1: Establish a heavy-load railway train group with a "pilot-follower" topology structure; Step 2: Based on the vehicle's own characteristic constraints, speed limit and safety distance constraints, a multi-objective optimization model is constructed with the goal of minimizing the speed difference between the preceding and following trains and minimizing the difference between the target distance and the actual tracking distance; Step 3: Generate a random communication delay in the multi-objective optimization model, calculate the time step corresponding to the delay, and make a control decision based on the state information of the previous time step of the leading train by the following train; Step 4: Solve the running speed of the following train in the multi-objective optimization model based on the particle swarm algorithm.

2. The group train tracking operation optimization method according to claim 1, characterized in that: In step 2, the optimization goal is to minimize the difference between the actual distance and the target distance between the preceding train and the following train and to minimize the speed difference between the two trains; wherein: Speed ​​difference index f v It is expressed as: f v =(V L -V F ) 2 ; Distance index f d It is expressed as: f d =(s L -s F -L T -L d ) 2 ; Among them, V L and V F are the speeds of the preceding train and the following train respectively; s L and F are the positions of the preceding train and the following train, L T is the length of the preceding train, L d is the expected distance between the two trains.

3. The group train tracking operation optimization method according to claim 1, characterized in that: In step 2, according to the constraints of the multi-objective optimization model, a mathematical model for the group train tracking operation optimization problem is established as follows: min a J=K v ·f v +K d ·f d (1) U min ≤u i (t)≤U max (2) s i-1 (t)-s i (t)-D l ≥s min (6) In the above formulas (1)-(6), F max is the upper limit of the rear vehicle’s traction force; u i (t) is the control quantity of the unit train, u min is the maximum deceleration; u max is the maximum acceleration; v i is the speed of unit train i; S min is the safety spacing margin related to the train positioning error; D l is the unit train length; F max,lead is the traction force of the front vehicle, which is determined by the traction characteristic curve; S min is the minimum train spacing, safety buffer distance; a brake is the maximum deceleration under emergency braking; is the position s i The speed limit at (t).

4. The group train tracking operation optimization method according to claim 1, characterized in that: In step 2, the minimum safe distance between unit trains in the group is expressed as: In formula (7), l ac Indicates the distance traveled by the rear vehicle from the start of braking of the front vehicle to the start of braking of the rear vehicle. Its value is affected by the equipment response time, communication delay and marshaling speed. Indicates the braking distance of the following vehicle under the most unfavorable conditions; Indicates the braking distance of the front vehicle under the most favorable conditions, S m Indicates the safety protection distance between trains.

5. The group train tracking operation optimization method according to claim 1, characterized in that: In step 3, the following train obtains the status information of the preceding train through the onboard equipment, and uses the information as the algorithm input to calculate the target tracking speed of the following train in the next time step according to step 4; l ac =(t a +t delay )·v0 Among them, t delay is the communication delay; ac represents the distance traveled by the rear vehicle from the start of braking to the start of braking of the rear vehicle; v0 represents the initial speed of the rear vehicle when braking; t a represents the inherent time difference between the braking actions of the leading and trailing vehicles, and the communication delay t delay Together they constitute the total time that the following vehicle continues to travel at v0 before braking.

6. The group train tracking operation optimization method according to claim 1, characterized in that: The specific steps of step 4 are: Step 4.1, Initialize the particle swarm: Set the total simulation time T and divide it into multiple time steps Δt, i.e., t0, t1, t2, …, t N , at each time step k, initialize and generate a number of particles n i , each particle represents an acceleration control strategy for that time step and is randomly initialized in the range of [-1, 1] to ensure that the particle swarm is widely distributed in the search space; Step 4.2: Simulate the dynamic motion process of the following vehicle; for the current time step k, each particle corresponds to an acceleration control strategy a k , use the train dynamics model to calculate the position x of the following vehicle in the current time step k , speed v k and acceleration a k ; Randomly generate delay time to calculate the state of the lagging front vehicle and calculate the fitness function value; Step 4.3, update the particle swarm state; use the standard particle swarm update formula to adjust the particle speed and position to ensure that the particle acceleration control variable is within a reasonable range; Step 4.4, update individual optimal and global optimal solutions: During the iteration process, compare the current fitness value of each particle with the best historical fitness of the particle. If the current fitness is smaller, update the individual optimal solution pbest of the particle. Compare the individual optimal solutions of all particles. If the fitness of a particle is better than the current global optimal solution, update the global optimal solution gbest. Step 4.5: Time step advancement: If the current time step k has not reached T, set the optimal acceleration As the input variable for the following vehicle to enter the next time step k+1; Enter the next time step k+1 and re-execute steps 4.2-4.4 to continue optimizing the acceleration strategy for subsequent time steps; Step 4.6: When the simulation time step reaches T or the termination condition is met, stop the algorithm; output the optimal acceleration trajectory of the entire time series for dynamic control of the following vehicle.

7. The group train tracking operation optimization method according to claim 6, characterized in that: The simulation time step termination condition in step 4.6 is: the global optimal solution converges, or the maximum number of iterations 100 is reached.

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