Passenger and freight trains collaborative driving strategy optimization method based on distributed model predictive control

Abstract

This invention discloses an optimization method for cooperative driving strategy of passenger and freight trains on shared lines based on distributed model predictive control, including the following steps: Step 1: Establish a basic train dynamics model; Step 2: Design train operation control objectives; Step 3: Design local optimization problems; Step 4: Design the DMPC algorithm for energy-saving cooperative control of passenger and freight trains on shared lines. This method designs the control objectives, constraints, and energy-saving optimization problems for both passenger and freight trains. By repeatedly solving the energy-saving optimization control problem at each step, the energy-saving speed trajectory of the train under dynamic operating conditions can be obtained online. It can simultaneously optimize and adjust the train timetable at the macro level and the train control strategy at the micro level, achieving precise control of train speed.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, specifically an online optimization method for cooperative driving strategies of passenger and freight trains on shared lines based on distributed model predictive control. Background Technology

[0002] Railway transportation is becoming increasingly important in public transportation systems due to its large capacity, low energy consumption, and high efficiency. Automatic Train Operation (ATO) systems are a key component of train control systems, enabling automatic control and adjustment of train operations, reducing driver workload, lowering operating energy consumption, and ensuring the safety and reliability of the operating system. In recent decades, numerous advanced ATO control algorithms have been developed to achieve precise, fast, and stable tracking control to cope with the ever-expanding railway network and increasing train speeds.

[0003] Before a train leaves the station, the ATO (Automatic Train Operation) system calculates a recommended speed curve for the next journey. This curve serves as a reference signal for the ATO system and determines the planned location and operating speed within a given time. It plays a crucial role in ensuring the punctuality and energy efficiency of the train's automated operation. The generation of the recommended speed curve is typically modeled as an optimization problem, solvable through various computational methods. These methods can be broadly categorized into two types: direct methods and indirect methods. Indirect methods, such as the Pontryagin maximum principle, have been widely applied to train optimal control problems. The earliest work on train optimal control based on the Pontryagin maximum principle was conducted by Ichikawa in 1968, which derived the optimal mechanisms for energy-efficient train operation on level tracks (i.e., maximum acceleration, cruise, coasting, and maximum braking). Since then, many researchers have utilized the Pontryagin maximum principle to generate optimal train driving strategies and speed curves, considering track gradient variations, arbitrary speed limits, and traction / braking constraints. One of the main challenges of these indirect methods is obtaining the transformation conditions for the optimal mechanism. In contrast, direct methods use mathematical programming algorithms to find approximate solutions to the original optimal problem. In recent years, the pseudospectral method has been widely used to solve the optimal train control problem due to its fast convergence speed and good computational accuracy. This invention proposes a novel multi-train trajectory optimization method for single-track lines, aiming to find the optimal speed curve that saves energy.

[0004] However, many methods are largely limited to fixed operating parameters, such as train drag coefficient and static speed limits, and calculate the train's reference speed curve offline. If a train's ATO system continues to operate according to the offline-determined reference curve even under train operation interference, it may cause unnecessary energy consumption and even lead to chaos on the entire line. Furthermore, to support regional economic growth and enhance the competitiveness of railways in freight transport, some railways are actively promoting mixed passenger and freight operation, with passenger and freight trains operating on the same lines. Clearly, passenger and freight trains differ significantly in their operational needs and constraints, posing challenges to traffic control and management. However, existing research on the optimal control of mixed passenger and freight trains remains very limited.

[0005] The existing technical literature [1] ([1] Li, D., Dong, X., Cao, J., Zhang, S., and Yang, L. (2022). "Energy-efficient rail transit vertical alignment optimization: Gaussian pseudospectral method." Journal of Transportation Engineering, Part A. Systems, (1), 148.) proposes a high-efficiency rail transit vertical alignment optimization model with the goal of minimizing energy consumption and running time deviation, and proposes an accurate solution method.

[0006] The existing technical literature [2] ([2] Yan, X.-H., Cai, B.-G., Ning, B., and ShangGuan, W. (2015). "Moving horizon optimization of dynamic trajectory planning for high-speed train operation." IEEE Transactions on Intelligent Transportation Systems, 17(5), 1258–1270.) proposes a rolling time-domain optimization scheme to deal with the collaborative operation planning problem of multiple high-speed trains, which optimizes the reference trajectory of multiple trains under uncertain conditions to a large extent.

[0007] Existing technical literature [3] ([3] Liu, L. and Dessouky, M. (2017). “A decomposition-based hybrid heuristic algorithm for the joint passenger and freight trainscheduling problem.” Computers & Operations Research, 87, 165–182.) studies the joint scheduling problem of passenger and freight trains for complex railway networks and proposes a novel heuristic algorithm, but does not take into account energy saving and interference during train operation.

[0008] In summary, there is currently no online control algorithm for passenger and freight trains that takes into account both operational disturbances and energy-saving operation in the scenario of passenger and freight trains operating together. Summary of the Invention

[0009] Based on this, the purpose of this invention is to provide a new online control algorithm for train operation, which adopts the distributed model predictive control (DMPC) method to design an energy-saving online control algorithm for passenger and freight trains that takes into account operational disturbances.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] An optimization method for cooperative driving strategy of passenger and freight trains based on distributed model predictive control includes the following steps:

[0012] Step 1: Establish a basic train dynamics model;

[0013] Step 1.1: Passenger trains stop at all stations, while freight trains do not stop at intermediate stations. (Let Q...) t =Q p ∪Q f Q t Q represents the collection of trains. p Q represents a collection of passenger trains. f Let Q represent the set of freight trains. Then for train i∈Q t The dynamic model with position s as the independent variable is described as follows:

[0014]

[0015] Among them, v i (s) represents the speed of train i, t i s represents time, m represents position. i For the mass of train i, u i1 (s) and u i2(s) represent the traction force and braking force of train i, respectively. The maximum traction force and maximum braking force of freight trains are both greater than those of passenger trains, and the two have different traction characteristic curves. The fundamental resistance to train operation is caused by mechanical and air friction, and is generally represented by the following Davis equation:

[0016]

[0017] Among them, a i b i c i This is a non-negative coefficient determined by a specific train. Furthermore, The track resistance caused by the track gradient can be expressed as:

[0018]

[0019] Where α(s) is the inclination angle of the track at position s, and g is the acceleration due to gravity. When α(s) is small, formula (3) holds.

[0020] Due to complex environmental factors, trains are inevitably subject to external interference during operation, namely:

[0021]

[0022] Here, rand represents a set of random numbers generated using the rand function to simulate the disturbances experienced by the train during operation.

[0023] Step 1.2: Single-track railway route map as shown Figure 1 As shown, the total number of stations is M, let z m Let m = 1, 2, ..., M represent the position of station m. Then the initial position of the train is z1, and the final position is z2. M .

[0024] Step 2: Design train operation control objectives;

[0025] Step 2.1: For passenger train i∈Q p The timetable specifies the designated arrival and departure times for each train, and each train must arrive at the designated time. It leaves the initial position z1 and then runs along the orbit at a given time. Reaching the destination position z M .

[0026] therefore,

[0027]

[0028] In addition, passenger trains need to stop at intermediate stations to facilitate passenger boarding and alighting:

[0029] v i (z m )=0,m=2,3,...,M-1 (6)

[0030]

[0031]

[0032] Where z m Let m be the location of station. Let m be the actual arrival time of train i at station m. Let be the actual departure time of train i at station m. Let i be the scheduled arrival time of train i at station m. Let m be the scheduled departure time of train i at station m.

[0033] Step 2.2: Define the various constraints during train operation.

[0034] During train operation, the following constraints need to be considered: traction and braking forces, speed constraints, and train spacing constraints.

[0035]

[0036]

[0037] 0≤v i (s)V max (s) (11)

[0038] t i (s)-t i-1 (s)≥T min (12)

[0039] in, and These represent the maximum traction force and the maximum braking force, respectively. max (s) represents the speed limit of the train at position s, T min This indicates the minimum safe distance between trains.

[0040] Passenger train i∈Q p Follows constraints (5)-(12). For freight trains i∈Q f It follows the same constraints as passenger trains at the origin and destination stations, while passing directly through intermediate stations without any stops. Freight trains are subject to the same operational constraints as passenger trains, therefore, freight trains follow constraints (5), (9)-(12).

[0041] Step 2.3: Establish the control objective function for passenger trains.

[0042] For passenger trains i∈Q p The control objective is to minimize the traction energy consumption of the train as it runs between stations:

[0043]

[0044] Step 2.4: Establish the control objective function for freight trains.

[0045] For freight trains i∈Q f The control objective is to minimize the train's total running time and total traction energy consumption.

[0046]

[0047] In the formula: w if These are the weighting coefficients.

[0048] Step 3: Design a local optimization problem.

[0049] Step 3.1: Build a distributed control framework for train trajectory optimization.

[0050] Each train is autonomously controlled and possesses the ability to perform calculations and communicate with other trains. This invention uses, for example... Figure 2 The leader-follower topology shown is used to simulate communication between passenger and freight trains on a single-track railway. Specifically, train i can only receive information from train i-1, while train 1 does not receive information from other trains. The window represents passenger trains and freight trains.

[0051] Step 3.2: Establish a local optimization problem.

[0052] An optimization problem is assigned to different types of trains. This invention employs a distributed model predictive control (DMPC) method to design a control law u for each train in equation (1). i1 (s) and u i2 (s).

[0053] The train energy-saving control problem is reduced to a general optimal control problem with train speed and time as state variables and traction and braking force as control variables. Let x i (s)=[v i (s), t i (s)] T u i (s)=[u i1 (s), u i2 (s)] T Formula (1) can be rewritten in the following compact form:

[0054]

[0055] For passenger trains, consider The problem of train optimization control within the system, including s i This is the current position of train i. For the next station n along the direction of travel i The location. In the prediction time domain. Within the k-th step, the cost function of the passenger train energy-saving control problem can be written as:

[0056]

[0057] The initial condition for the optimization problem is x i (s i ) = [v i (s i ), t i (s i ] indicates that train i is at its current position s i The speed and time. At the end of the prediction time domain, the terminal state needs to satisfy:

[0058]

[0059] in, For the next stop n i Location, For train i at the next station n i The specified arrival time, t a This represents the permissible deviation from the train's arrival time. To avoid collisions, safety constraints must be met:

[0060]

[0061] in, The predicted time series T is calculated by train i-1 in step k-1. min This represents the minimum safe time interval for train operation. In the prediction time domain... Within this context, the energy-saving control problem of the k-th passenger train can be expressed as:

[0062]

[0063] in, This indicates the maximum speed limit for passenger trains.

[0064] For freight trains, consider [s] i , z M The cost function for the optimal train control problem within the range of ] is: [Equation omitted for brevity]

[0065]

[0066] At the end of the prediction time domain, the terminal state needs to satisfy:

[0067]

[0068] In the prediction time domain [s i , z M Within this context, the energy-saving control problem for the k-th freight train is described as follows:

[0069]

[0070] in, This indicates the maximum speed limit for freight trains.

[0071] In optimization problems (21) and (24), at the current position s i Measured real-time state x i (s i ) = [v i (s i ), t i (s i The optimal control sequence in the prediction time domain can be obtained by solving problems (21) or (24). Moreover, the train only executes the first control quantity. At the next sampling time t k+1 In this approach, the optimal control problems (21) and (24) are resolved using the updated train state, and the train is only allowed to execute the first control variable. By repeatedly solving a set of optimal control problems in the rolling time domain, the online train control problem based on real-time updates of train operating state is solved.

[0072] Step 4: Design the DMPC algorithm for energy-saving collaborative control of passenger and freight trains.

[0073] Step 4.1: Each train obtains its control input by solving a local optimization problem (21) or (24) that includes information about itself and its neighbors. For details, see the DMPC algorithm:

[0074] DMPC algorithm input: the location z of each station m Real-time measurement of train i at t k The state at time [v] i (s i ), t i (s i )], where t i (s i )=t k The scheduled arrival time of each train at station m and scheduled departure time

[0075] The DMPC algorithm outputs the predicted state trajectory and the optimal control sequence in the predicted time domain.

[0076] Step 1, let k = 0, and car i measures t. k The state at time [v] i (s i ), t i , (s i Solve the local optimization problem (21) or (24) to obtain... and And update the previously stored predicted state trajectory and

[0077] Step 2: The i-car transmits its updated predicted state trajectory to the following car.

[0078] Step 3: The i-car executes the optimal control quantity.

[0079] Step 4: Let k = k + 1, then go back to step 1.

[0080] The present invention provides an optimization method for cooperative driving strategy of passenger and freight trains based on distributed model predictive control, which has the following advantages and effects compared with the prior art: (1) Control objectives, constraints and energy-saving optimization problems for passenger and freight trains are designed separately for the different operational needs of passenger and freight trains. (2) By repeatedly solving the energy-saving optimization control problem of each step of the train, the energy-saving speed trajectory of the train under dynamic operating conditions can be obtained online. (3) The proposed algorithm can simultaneously optimize and adjust the train operation diagram at the macro level and the train control strategy at the micro level, realizing precise control of train speed. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of a single-track railway line corresponding to the invention described in this invention;

[0082] Figure 2 This is a communication topology diagram corresponding to the invention's content.

[0083] Figure 3 The following are train parameter information diagrams for specific implementation methods: (1) CRH3 train parameter information; (2) HXD1 electric locomotive parameter information;

[0084] Figure 4 A train position trajectory diagram for a specific implementation method;

[0085] Figure 5 This is a diagram showing the actual train speed trajectory for a specific implementation method. Detailed Implementation

[0086] The present invention will now be further described in conjunction with implementation examples and accompanying drawings:

[0087] A method for optimizing cooperative driving strategies for passenger and freight trains on shared lines based on distributed model predictive control, specifically including:

[0088] Step 1: Simulation Scene Setup

[0089] The experiments in this case were all conducted in MATLAB using the optimization solver GPOPS-II on a laptop with a 1.90GHz AMD CPU and 16GB of RAM.

[0090] Assume there are four stations on the line, with a distance of 30 kilometers between each station. The line operates three passenger trains and one freight train. For passenger trains, the stipulated travel time between stations is 700 seconds, with a stipulated stop time of 120 seconds. For freight trains, the stipulated travel time between the originating and terminating stations is 3170 seconds. (Standard arrival time...) Allowable floating value t a Set to 30 seconds. The maximum operating speed for passenger trains is 55 m / s, and the maximum operating speed for freight trains is 45 m / s. The safe time interval T min Set to 240s, weighting coefficient w if Set to 1×10 7 .

[0091] The case study uses a CRH3 train and an HXD1 electric locomotive for simulation, and the freight car used in the simulation is a C... 80 CRH3 type freight car. The parameter information for the CRH3 type train and freight train is as follows: Figure 3 As shown in Table (1) and Table (2).

[0092] The maximum traction and braking forces of the CRH3 EMU are (both in kN):

[0093]

[0094] The maximum traction and braking forces of the HXD1 electric locomotive are (both in kN):

[0095]

[0096] Step 2: Simulation and Case Analysis;

[0097] This invention provides a numerical example to demonstrate the effectiveness and energy efficiency of the proposed DMPC-based online control algorithm for passenger and freight trains, solving the problem of online train control considering operational disturbances. The simulation results obtained from the example are as follows: Figure 4-5 As shown. Figure 4 This diagram shows the location and trajectory of three passenger trains and one freight train. Figure 5 This shows the actual operating speed trajectories of three passenger trains and one freight train. From... Figure 5 It can be seen that operational disturbances cause fluctuations in the speed curves of passenger and freight trains. The average solution time for each step is 0.39s, which is less than the sampling time period of 1.2s, thus enabling online train control.

Claims

1. An optimization method for cooperative driving strategy of passenger and freight trains on shared lines based on distributed model predictive control, characterized in that, Includes the following steps Step 1: Establish a basic train dynamics model; Step 1.1: Passenger trains stop at all stations, while freight trains do not stop at intermediate stations; make ,in Indicates a collection of trains. Indicates the assembly of passenger trains. Let this be a set of freight trains; then for each train... By location The dynamic model with independent variables is described as follows: （1） in, For train speed, For time, For location, For train quality and They represent trains The traction and braking forces of freight trains are greater than those of passenger trains, and the two have different traction characteristic curves. The fundamental resistance to train operation, caused by mechanical and air friction, is represented by the following Davis equation: （2） in, The non-negative coefficient is determined by the specific train; furthermore, The track resistance caused by the track gradient is expressed as: （3） in, For the track in position The angle of inclination at that point For gravitational acceleration; when When the value is small, formula (3) holds true; Due to complex environmental factors, trains are inevitably subject to external interference during operation, namely: （4） in, This represents a set of random numbers generated using the rand function to simulate the disturbances experienced by the train during operation. Step 1.2: In a single-track railway route map, the total number of stations is M. Let... Indicates station If the position is such that the initial position of the train is... The finish line is ; Step 2: Design train operation control objectives; Establish the control objective function for passenger trains; For passenger trains The control objective is to minimize the traction energy consumption of the train as it runs between stations: （5） Establish the control objective function for freight trains; For freight trains The control objective is to minimize the train's total running time and total traction energy consumption. （6） In the formula: These are the weighting coefficients; Step 3: Design a local optimization problem; In the prediction time domain within, no. The energy-saving control problem of passenger trains is described as follows: （7） in, This indicates the maximum speed limit for passenger trains; In the prediction time domain within, no. The energy-saving control problem of freight trains is described as follows: （8） in, This indicates the maximum speed limit for freight trains; In optimization problems (7) and (8), at the current position Measured real-time status The optimal control sequence in the prediction time domain can be obtained by solving problem (7) or (8). Moreover, the train only executes the first control quantity. ; at the next sampling time In this process, the optimal control problems (7) and (8) are re-solved using the updated train state, and the train is only allowed to execute the first control variable; by repeatedly solving a set of optimal control problems in the rolling time domain, the online control problem of train based on real-time updates of train running state is solved. Step 4: Design the DMPC algorithm for energy-saving collaborative control of passenger and freight trains on the same line; Step 4.1: Each train obtains its control input by solving a local optimization problem (7) or (8) that includes information about itself and its neighbors, and this is achieved through the DMPC algorithm.

2. The method for optimizing cooperative driving strategy of passenger and freight trains based on distributed model predictive control according to claim 1, characterized in that, The input to the DMPC algorithm: the location of each station. Real-time train measurement exist state of time ,in Each train at the station The stipulated arrival time and scheduled departure time ; DMPC algorithm output: predicted state trajectory and optimal control sequence in the predicted time domain; Step 1, let , Vehicle measurement state of time Solve the local optimization problem (7) or (8) to obtain and And update the previously stored predicted state trajectory. and ; Step 2, The vehicle transmits its updated predicted state trajectory to the following vehicle; Step 3 The vehicle executes the optimal control quantity ; Step 4, let Proceed to step 1.

3. The method for optimizing cooperative driving strategy of passenger and freight trains based on distributed model predictive control according to claim 1, characterized in that, Step 2 also includes the following: Step 2.1: For passenger trains The timetable specifies the designated arrival and departure times for each train, and each train must arrive at the designated time. Leave the initial position Then it runs along the orbit, at a given time Reach the finish line ;therefore, （9） In addition, passenger trains need to stop at intermediate stations to facilitate passenger boarding and alighting: （10） （11） （12） in For the station Location, For train At the station The actual arrival time For train At the station The actual departure time For train At the station The scheduled arrival time For train At the station The designated departure time; Step 2.2: Define the various constraints during train operation; During train operation, the following constraints need to be considered: traction and braking forces, speed constraints, and train spacing constraints. （13） （14） （15） （16） in, and These are the maximum traction force and the maximum braking force, respectively. For the train in position The speed limit at that location, Indicates the minimum safe time interval for train operation; Passenger trains Follow constraints (9)-(16); for freight trains It follows the same constraints as passenger trains at the origin and destination stations, and passes directly through intermediate stations without making any stops; freight trains are subject to the same operating constraints as passenger trains, and therefore follow constraints (9), (13)-(16).

4. The method for optimizing cooperative driving strategy of passenger and freight trains based on distributed model predictive control according to claim 1, characterized in that, Step 3 also includes: Step 3.1: Build a distributed control framework for train trajectory optimization; Each train is autonomously controlled and possesses the ability to compute and communicate with other trains; a leader-follower topology is used to simulate communication between passenger and freight trains on a single-track railway; specifically, the trains... Only can receive signals from trains Train i receives information from other trains, while train i does not receive information from other trains; where windows represent passenger trains and freight trains. Step 3.2: Establish a local optimization problem; An optimization problem is assigned to each type of train; the distributed model predictive control (DMPC) method will be used to design the control law for each train in equation (1). and ; The train energy-saving control problem is reduced to a general optimal control problem with train speed and time as state variables and traction and braking force as control variables; let Formula (1) can be rewritten in the following compact form: （17） For passenger trains, consider The problem of train optimization control within the system, including For train Current location For the next station along the direction of travel Location; in the prediction time domain within, no. The cost function for the energy-saving control problem of passenger trains can be written as: （18） The initial conditions for the optimization problem are: , indicating train At the current location The speed and time; at the end of the prediction time domain, the terminal state needs to satisfy: （19） in, For the next stop Location, For train At the next stop The scheduled arrival time This represents the permissible deviation from the train's arrival time; to avoid collisions, safety constraints must be met: （20） in, It is a train exist The predicted time series obtained by step calculation, Indicates the minimum safe time interval for train operation; For freight trains, consider The optimal train control problem within the system, the first The cost function for the energy-saving control problem of pedestrian trains is: （21） At the end of the prediction time domain, the terminal state needs to satisfy: （22）。

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