Throat area shortest interval calculation method based on multi-vehicle speed curve optimization

Abstract

The invention discloses a throat area shortest vehicle sending interval calculation method based on multi-vehicle speed curve optimization, and belongs to the technical field of traffic transportation. Comprising the steps of inputting throat area line data, train performance parameters and operation schedule data; determining a train running path and dividing a running phase; establishing a train operation constraint model which comprises a differential equation, a constraint condition, a boundary condition and a linkage condition; establishing a train conflict resolution model, and constraining arrival and departure time of the two trains at the same phase point; setting a target function to minimize train operation time and interval time; and solving by utilizing a MATLAB toolbox GPOPS to obtain the minimum departure interval of the train. According to the method, the shortest train departure interval of various running paths and different train types in the throat area can be calculated, the train departure interval can be effectively reduced, the train following distance is reduced, the passing efficiency is improved, powerful technical support is provided for railway operation, and the method has important theoretical and practical values.

Description

Technical Field

[0001] The invention relates to the technical field of transportation, and in particular to a method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization. Background Art

[0002] As the core node of the railway network, the railway throat area has a decisive impact on the overall capacity of the railway network. Among them, the departure interval of trains in the throat area is the core element to measure its capacity and plays a vital role. Therefore, it is necessary to study the calculation method of reducing the departure interval of trains in the throat area, so as to reduce the following distance between train groups in the station, improve the capacity and transportation efficiency of the railway throat area, and improve the transportation service quality of passengers and goods. Summary of the invention

[0003] The purpose of the present invention is to provide a method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization, which can calculate the shortest departure interval of trains with various operating paths and different train types in the throat area, and provide a theoretical basis for improving the throughput capacity of the throat area.

[0004] To achieve the above object, the present invention provides a method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization, comprising the following steps:

[0005] S1. Input throat area line data, train performance parameters, and operation schedule data;

[0006] S2. Based on the data, develop a method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization.

[0007] Preferably, in step S2, the calculation method based on the data comprises the following steps:

[0008] S21, determining the running path of the train in the throat area according to the throat area line data and the operation timetable data;

[0009] S22, dividing the running path of the train in the throat area into a number of phases, each phase taking the start position and the end position of the section as the starting point and the end point, forming the running phase set of the train;

[0010] S23. Establishing a train operation constraint model for each phase in the operation phase set according to the train performance parameters to describe the dynamic operation behavior of the train;

[0011] S24, establishing a train conflict resolution model to constrain the arrival and departure times of two trains at the same phase point;

[0012] S25, establishing an objective function based on the train operation model and train conflict resolution model established in the above steps;

[0013] S26. Use the MATLAB toolbox GPOPS to solve the objective function and obtain the compressed train block time ladder diagram. The departure interval between the two cars at the starting point is the required shortest departure interval for the throat area trains.

[0014] Preferably, in step S23, the method for establishing the train operation constraint model is specific and includes the following steps:

[0015] S231, establishing a differential equation for the train motion in each phase;

[0016] S232, setting constraints to limit vehicle performance parameters of the train, constrain speed, and set corresponding restrictions on passenger comfort;

[0017] S233, setting boundary conditions to ensure that the running speed of the train at the start point of the first phase and the end point of the last phase is zero;

[0018] S234. Establish linkage conditions to ensure the continuity of train speed-distance trajectories and time-distance trajectories in adjacent phases.

[0019] Preferably, in step S24, a specific method for establishing a train conflict resolution model comprises the following steps:

[0020] S241. Establish constraint conditions to stipulate the shortest time interval between two train heads passing the same position;

[0021] S242, setting up constraint conditions to determine the entry time and approach time of the locomotive of the following train at a certain phase;

[0022] S243. Establish constraint conditions to determine the time when the front locomotive of the preceding train leaves a certain phase.

[0023] Therefore, the present invention adopts the above-mentioned structure to calculate the shortest departure interval in the throat area based on the optimization of multi-vehicle speed curves, which has the following beneficial effects:

[0024] The present invention provides a method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization in a throat area, and solves the shortest departure interval in the throat area by establishing a train operation constraint model and a conflict resolution model. Based on this, the train operation process is first divided into phases, and a train operation model is established for each phase to describe the dynamic operation process of the train in the phase. Constraints are set to ensure that the train operation meets its performance and speed constraints, meets the needs of passengers for travel comfort, and ensures the continuity of the trajectory between phases. Secondly, the arrival, approach, and departure times of the train group at the same phase point are constrained to resolve conflicts. Finally, on the basis of the established operation model and conflict resolution model, an objective function is established to minimize the train operation time and the interval time between the two trains. Through the optimization model, a compressed train group block time ladder diagram is obtained, thereby obtaining the shortest departure interval of the train in the throat area. In summary, the method for calculating the shortest departure interval in the throat area based on the optimization of multi-vehicle speed curves in the throat area provided by the present invention can comprehensively consider various operating paths and different train types in the throat area, accurately calculate the shortest departure interval of the train group, and significantly improve the throughput capacity of the throat area, providing strong technical support for railway operations. This invention has important practical and theoretical value for the optimized operation and train scheduling of the throat area.

[0025] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A flow chart of a method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization provided by the present invention;

[0027] Figure 2 A schematic diagram of a scenario of a method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization provided by the present invention;

[0028] Figure 3 A schematic diagram of a train block time ladder diagram after compression of different line combinations provided by the present invention. DETAILED DESCRIPTION

[0029] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0030] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0031] Example

[0032] like Figure 1 As shown, the present invention provides a method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization, comprising the following steps:

[0033] S1. Input throat area line data, train performance parameters, and operation schedule data;

[0034] S2. Based on the data, develop a method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization. The specific calculation method is as follows:

[0035] S21, calculate the train group in the throat area according to the input throat area line data, train performance parameters and operation timetable data The shortest departure interval time h (r,l),(r',l') , where r is the path of the train in the throat area, l is the type of train, and the train in the train group and train can be expressed as

[0036] S22, using the entry and exit positions of each section as the dividing points, divide the railway hub into i phases, where Phase The starting position of Phase The end position of

[0037] S23. Build a train In phase The operation constraint model within is as follows:

[0038]

[0039]

[0040] Where: Indicates the phase The train set, is a set of adjacent phases. Equation (1-2) is the differential equation of train motion, which is used to describe the dynamic operation behavior of the train in the section. and speed limits is a function of distance, so the equation uses distance s as the independent variable and introduces It is used to eliminate the influence of the train running direction. Constraints (3-6) are respectively for train The vehicle performance parameters, speed limit and passenger comfort are set accordingly. Equation (7) is used as a boundary condition to ensure that the train Initial velocity and terminal velocity The linkage conditions (8-9) ensure that the speed-distance trajectory and time-distance trajectory of each train are continuous.

[0041] S24. Build a model for the train With train At the same phase point The arrival and departure times are constrained to resolve the conflict. The specific model is as follows:

[0042]

[0043]

[0044] Constraint (10) is used to constrain the train With train The shortest interval time to pass through position s, where Represents the forward train The time when the front of the vehicle leaves position s, Representatives follow the train The time when the front of the vehicle approaches position s, t min It is equal to the sum of the preceding train clearing time and the route unlocking time.

[0045] Constraints (11-16) are used to determine the following train The front of the vehicle is entering the phase Time and close phase Time The constraints (11-12) are used to ensure that the two variables are constant values ​​in each phase. Constraint (13) is used to detect the train Enter Phase The position of If the train The running direction is down but On the contrary, if the train is running in the upward direction, Constraint (14) ensures The value is equal to the train Passing location Constraint (15) is used to calculate The value of , M in the constraint is a large positive number.

[0046] Constraints (16-18) are used to calculate the forward train The front of the vehicle leaves the phase Time The constraint (16) is used to ensure The value of is constant in each phase. Constraint (17) is used to express the train Leaving stage Location If the train The running direction is down but On the contrary, if the running direction is upward, Constraint (18) is used to ensure The value is equal to the train The vehicle head passes the position time.

[0047] S25. Based on the train operation model and train conflict resolution model established in the above steps, an objective function is established. The objective function (19) consists of two parts, which aims to minimize the train departure interval while reducing the overall running time of the train set. The first item is used to minimize the running time of the train, and the second item is used to minimize the train interval time.

[0048]

[0049] S26. Use the GPOPS program in MATLAB to solve and obtain the train operation block time ladder diagram after the two trains are compressed. Figure 2 As shown, the section block time diagrams of the two trains are fully compressed on the basis of non-overlap.

[0050] like Figure 3 As shown in the figure, based on the compressed train operation block time ladder diagram, the departure interval of the two trains at the starting point is the shortest departure interval time h in the throat area. (r,l),(r',l') .

[0051] Therefore, the present invention adopts the above-mentioned throat area shortest departure interval calculation method based on multi-vehicle speed curve optimization, takes throat area line data, train performance data, and operation schedule data as input, establishes a throat area shortest departure interval calculation model based on multi-vehicle speed curve optimization, and uses MATLAB toolbox GPOPS to solve the shortest departure interval of throat area trains under different vehicle types and multiple station train running paths. The present invention can effectively reduce the departure interval in the throat area, reduce the train following distance in the railway throat area, and improve the passing efficiency in the throat area, which has very important theoretical and practical value.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for calculating the shortest departure interval in a throat area based on multi-vehicle speed curve optimization, characterized in that: The following steps are involved: S1. Input throat area line data, train performance parameters, and operation schedule data; S2. Based on the data, develop a method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization.

2. The method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization according to claim 1 is characterized by: In step S2, the calculation method based on the data includes the following steps: S21, determining the running path of the train in the throat area according to the throat area line data and the operation timetable data; S22, dividing the running path of the train in the throat area into a number of phases, each phase taking the start position and the end position of the section as the starting point and the end point, forming the running phase set of the train; S23. Establishing a train operation constraint model for each phase in the operation phase set according to the train performance parameters to describe the dynamic operation behavior of the train; S24, establishing a train conflict resolution model to constrain the arrival and departure times of two trains at the same phase point; S25, establishing an objective function based on the train operation model and train conflict resolution model established in the above steps; S26. Use the MATLAB toolbox GPOPS to solve the objective function and obtain the compressed train block time ladder diagram. The departure interval between the two cars at the starting point is the required shortest departure interval for the throat area trains.

3. The method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization according to claim 2 is characterized by: In step S23, the method for establishing the train operation constraint model is specific and includes the following steps: S231, establishing a differential equation for the train motion in each phase; S232, setting constraints to limit vehicle performance parameters of the train, constrain speed, and set corresponding restrictions on passenger comfort; S233, setting boundary conditions to ensure that the running speed of the train at the start point of the first phase and the end point of the last phase is zero; S234. Establish linkage conditions to ensure the continuity of train speed-distance trajectories and time-distance trajectories in adjacent phases. The method for calculating the shortest departure interval in the throat area based on multi-vehicle speed curve optimization according to claim 2 is characterized in that: In step S24, a specific method for establishing a train conflict resolution model includes the following steps: S241. Establish constraint conditions to stipulate the shortest time interval between two train heads passing the same position; S242, setting up constraint conditions to determine the entry time and approach time of the locomotive of the following train at a certain phase; S243. Establish constraint conditions to determine the time when the front locomotive of the preceding train leaves a certain phase.

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