Subway speed curve optimization method and storage medium

Abstract

The invention discloses a subway speed curve optimization method and a storage medium, and the method comprises the steps: 1, obtaining train operation basic data, including train parameters, line data and interval operation time data of a train number model to be optimized; step 2, constructing an improved dynamic planning state space based on the coasting state transition process according to the train operation basic data, so that the state space comprises coasting state points; 3, determining a state transition equation and a state transition cost of each interval, and constructing an optimal state transition path selection formula; 4, in the improved state space, dynamic planning solving is carried out through state transition, transition cost and an optimal state transition path selection formula, and a train energy-saving operation speed curve is obtained. According to the method, the state space is perfected based on the coasting state transition process, the defect that an optimized speed curve lacks an accurate coasting stage in a conventional dynamic programming algorithm state space construction mode is overcome, and the train traction energy consumption is reduced.

Description

Technical Field

[0001] The present invention relates to the field of urban rail transit, and in particular to a subway speed curve optimization method based on improved dynamic programming. Background Art

[0002] At present, rail transit has developed into an important part of the urban rail transit system with its advantages of large capacity and high speed. While urban rail transit is developing rapidly, the construction and operating costs of urban rail transit are also increasing year by year. According to the statistics of urban rail transit's electricity consumption, the energy consumption of urban rail transit system mainly includes traction energy consumption and auxiliary energy consumption, of which traction energy consumption accounts for about 60%. The huge energy consumption is a very serious problem currently facing urban rail transit. Therefore, how to effectively reduce the traction energy consumption of trains has become a task that needs to be solved urgently by various subway operating companies.

[0003] It has important practical significance. Experts and scholars at home and abroad have conducted extensive research on the optimization of train speed curves and achieved corresponding results. When studying the optimization of train speed curves, foreign scholars focused on theoretical research. Based on the theory of the maximum principle, they proposed that the most energy-saving operation plan should include four stages: "full traction, constant speed, coasting, and full braking", which laid the foundation for subsequent research by other scholars. Domestic research started late, but a lot of research has been done. Some scholars used the maximum principle for theoretical research, and some scholars used optimization algorithms such as dynamic programming to solve it. However, the solution process of the conventional dynamic programming algorithm requires the simultaneous discretization of the train position and speed. Due to the influence of the discrete accuracy, the coasting state processing is usually rough, and there is no absolute coasting condition in the speed curve, which affects the effect of energy-saving optimization. Summary of the Invention

[0004] In view of the technical defects and drawbacks in the prior art, embodiments of the present invention provide a subway speed curve optimization method and storage medium that overcome or at least partially resolve the aforementioned problems. Firstly, the method aims to accurately describe the train's coasting state, especially for ramps and speed-limited areas on complex lines, while maximizing energy savings without affecting operating time. Secondly, the method aims to optimize the scale of the improved state space. Specific solutions of the present invention are as follows:

[0005] As a first aspect of the present invention, a method for optimizing a subway speed curve is provided, the method comprising:

[0006] Step 1: Obtain basic train operation data, including train parameters, line data, and interval operation time data of the train model to be optimized;

[0007] Step 2: Based on the basic train operation data and the coasting state transition process, an improved dynamic programming state space is constructed so that the state space contains the coasting state point.

[0008] Step 3: Determine the state transition equation and state transition cost of each interval, and construct the optimal state transition path selection formula;

[0009] Step 4: In the improved state space, dynamic programming is performed through the state transfer, transfer cost and optimal state transfer path selection formula to obtain the train energy-saving operation speed curve.

[0010] Furthermore, the line data includes ramp data, curve data, speed limit data and station data; the train parameters include the train's formation mode, length, load level, maximum speed, maximum acceleration, basic resistance parameters, traction characteristic curve and braking characteristic curve.

[0011] Furthermore, step 2 specifically includes:

[0012] Step 201: Generate the initial state space: including setting the discrete step length, the minimum coasting speed state transition speed limit v comin , the maximum number of state points in a single stage N max and the minimum speed difference threshold dv of the state point lim , calculate the state space under uniform discretization based on discrete steps;

[0013] Step 202, coasting state transition calculation: including selecting the current stage k with a speed greater than v comin state point, calculate the coasting speed corresponding to the state point;

[0014] Step 203: Eliminate redundant state points: This includes determining the number of states in the k+1 stage. If it is greater than N max , calculate the minimum speed difference of each coasting point, if it is less than dv lim Then remove the original state points;

[0015] Step 204: determine whether the final stage has been reached. If not, enter the k+1 stage and proceed to step 202. Otherwise, complete the state space construction.

[0016] Furthermore, if the speed is lower than v comin No idle state transfer calculation is performed; if the number of states in the current stage reaches N max And the difference between the calculated coasting speed and the adjacent original state point speed is less than the threshold dv lim , then remove the original state points.

[0017] Furthermore, the calculation formula for the idle state transition is:

[0018]

[0019] Among them, v k，i is the velocity corresponding to the i-th discrete point in the k-th stage, v co_k+1，i is v in the k+1th stage k，i The corresponding coasting speed, a r_k，i is the acceleration corresponding to the running resistance only, and Δs is the position discrete interval.

[0020] Furthermore, in step 203, the minimum speed difference of each coasting point is calculated as follows:

[0021] dv k+1，j =min(|v co_k+1，j -V k+1 |)

[0022] Among them, v co_k+1，j is v in the k+1th stage k，j Corresponding coasting speed, V k+1 is the velocity point set of the k+1th stage, V k+1 ={v k+1，1 , v k+1，2 ,…,v k+1，i ,…,v k+1，I}, I is the discrete velocity number of k+1 stage, dv k+1，j v co_k+1，j The corresponding minimum speed difference.

[0023] Furthermore, in step 3, the state transfer equation is X k+1 =T(X k ,u k ), where X k is the current state, u k is the current decision, X k+1 is the next state, T is the state transfer function, the state is composed of position and speed indicators, recorded as X(s, v), which represents the current state of the train, s is the position, and v is the speed;

[0024] The state transfer calculation is based on the train dynamics model, and its kinematic equation is:

[0025]

[0026] Where M represents the mass of the train, c is the resultant force of the train, and v represents the speed of the train.

[0027] Furthermore, in step 3, the state transfer cost is the energy consumption cost and time cost during the state transfer process;

[0028] The energy consumption cost is as follows:

[0029] ek+1，i_j =u kt F t (v k，i )·Δs

[0030] Among them, v k，i is the velocity corresponding to the i-th discrete point in the k-th stage, F t (v k，i ) is the speed v k，i The train has full traction force, u kt is the traction control coefficient of the kth stage, Δs is the position discrete interval, e k+1，i-j For v k，i to v k+1，j energy consumption costs;

[0031] The time cost is specifically:

[0032]

[0033] Among them, v k+1，j is the velocity corresponding to the jth discrete point in the k+1th stage, t k+1，i-j For v k，i to v k+1，j The state transfer time cost;

[0034] Considering the train running on time constraint, adding the time cost coefficient, the total state transfer cost C k+1，i_j for:

[0035] C k+1，i-j =e k+1，i-j +λ·t k+1，i-j

[0036] Where λ is the time cost coefficient, which is used to make the optimized speed curve meet the punctuality constraint.

[0037] Furthermore, in step 3, the optimal state transition path selection formula is constructed as follows:

[0038] Define the optimal state transfer path selection formula from stage k to k+1;

[0039] J k+1，j =min(J k +C k+1，j )

[0040] Among them, J k is the cost set of the kth stage, J k ={J k，1 , J k，2 ,…,J k，i ,…,J k，I}, I is the number of discrete speeds in the k-stage; C k+1，j Each state in the kth stage is transferred to xk+1，j The set of single-step state transition costs for a state.

[0041] As a second aspect of the present invention, a computer-readable storage medium is provided, in which a computer program is stored. When the computer program is executed by a computer, the computer executes any of the above-described subway speed curve optimization methods.

[0042] The present invention has the following beneficial effects:

[0043] The present invention realizes the optimization of the running curve for train safety, punctuality, comfort and energy saving. The present invention improves the state space based on the coasting state transfer process, overcomes the disadvantage that the speed curve optimized by the conventional dynamic programming algorithm state space construction method lacks an accurate coasting stage, and further reduces the train traction energy consumption. At the same time, by introducing the minimum coasting speed limit v comin , speed difference threshold dv lim and the maximum number of state points N max , while ensuring energy-saving effects, the number of state points is significantly reduced and the state space construction process is optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic flow chart of a subway speed curve optimization method based on improved dynamic programming provided by an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of the improved dynamic programming state space construction process provided by an embodiment of the present invention;

[0046] Figure 3 A schematic diagram of an improved dynamic programming solution provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. The terms used in this specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0049] refer to Figure 1FIG. 1 is a flow chart of a subway speed curve optimization method based on improved dynamic programming provided by an embodiment of the present invention, wherein the method includes:

[0050] Step 1: Obtain basic train operation data, including train parameters, line data, and interval operation time data of the train model to be optimized;

[0051] Step 2: Based on the basic train operation data and the coasting state transition process, an improved dynamic programming state space is constructed so that the state space contains the coasting state point.

[0052] Step 3: Determine the state transition equation and state transition cost of each interval, and construct the optimal state transition path selection formula;

[0053] Step 4: In the improved state space, dynamic programming is performed through the state transfer, transfer cost and optimal state transfer path selection formula to obtain the train energy-saving operation speed curve.

[0054] The present invention realizes the optimization of the train's operating curve for safety, punctuality, comfort and energy saving. The present invention improves the state space based on the coasting state transfer process, overcomes the disadvantage that the speed curve optimized under the conventional dynamic programming algorithm state space construction method lacks an accurate coasting stage, and reduces the train's traction energy consumption.

[0055] In some embodiments, in step 1, the line data includes ramp data, curve data, speed limit data and station data, and the train parameters include the train's formation mode, length, load level, maximum speed, maximum acceleration, basic resistance parameters, traction characteristic curve and braking characteristic curve, etc.

[0056] See also Figure 2 As shown, in some embodiments, step 2 specifically includes:

[0057] Step 201: Generate the initial state space: including setting the discrete step length, the minimum coasting speed state transition speed limit v comin , the maximum number of state points in a single stage N max and the minimum speed difference threshold dv of the state point lim , calculate the state space under uniform discretization based on discrete steps;

[0058] Step 202, coasting state transition calculation: including selecting the current stage k with a speed greater than v comin state point, calculate the coasting speed corresponding to the state point;

[0059] Step 203: Eliminate redundant state points: This includes determining the number of states in the k+1 stage. If it is greater than N max , calculate the minimum speed difference of each coasting point, if it is less than dv limThen remove the original state points;

[0060] Step 204: determine whether the final stage has been reached. If not, enter the k+1 stage and proceed to step 202. Otherwise, complete the state space construction.

[0061] The minimum coasting speed state transition speed limit v in step 201 is comin Meaning: If the speed is lower than v comin The coasting state transfer calculation is not performed; the minimum speed difference threshold dv of the state point lim Meaning: If the number of states in the current stage reaches N max And the difference between the calculated coasting speed and the adjacent original state point speed is less than the threshold dv lim , then remove the original state points.

[0062] In some embodiments, in step 202, the idle state transition calculation formula is:

[0063]

[0064] Among them, v k，i is the velocity corresponding to the i-th discrete point in the k-th stage, v co_k+1，i is v in the k+1th stage k，i The corresponding coasting speed, a r_k，i is the acceleration corresponding to the running resistance only, and Δs is the position discrete interval.

[0065] In some embodiments, in step 203, the minimum speed difference of each coasting point is calculated as follows:

[0066] dv k+1，j =min(|v co_k+1，j -V k+1 |)

[0067] Among them, v co_k+1，j is v in the k+1th stage k，j Corresponding coasting speed, V k+1 is the velocity point set of the k+1th stage, V k+1 ={v k+1，1 , v k+1，2 ,…,v k+1，i ,…,v k+1，I}, I is the discrete velocity number of k+1 stage, dv k+1，j v co_k+1，j The corresponding minimum speed difference.

[0068] In some embodiments, the state transition equation is X k+1 =T(X k ,u k ), where Xk is the current state, u k is the current decision, X k+1 is the next state, T is the state transfer function, the state is composed of position and speed indicators, recorded as X(s, v), which represents the current state of the train, s is the position, and v is the speed;

[0069] The above equation means that once the state X k and decision making k (X k ) is determined, the state of the next stage can be expressed by the above formula. If the initial state and a set of strategies {u1(x1), u2(x2), ..., u N (x N )}, the state of the entire system process can be calculated based on the above state transfer equation.

[0070] The state transfer calculation is based on the train dynamics model, and its kinematic equation is:

[0071]

[0072] Where M represents the mass of the train, c is the resultant force of the train, and v represents the speed of the train.

[0073] The state transfer cost is the energy consumption cost and time cost during the state transfer process;

[0074] The energy consumption cost is as follows:

[0075] e k+1，i-j =u kt F t (v k，i )·Δs

[0076] Among them, v k，i is the velocity corresponding to the i-th discrete point in the k-th stage, F t (v k，i ) is the speed v k，i The train has full traction force, u kt is the traction control coefficient of the kth stage, Δs is the position discrete interval, e k+1，i-j For v k，i to v k+1，j energy consumption costs;

[0077] The time cost is specifically:

[0078]

[0079] Among them, v k+1，j is the velocity corresponding to the jth discrete point in the k+1th stage, t k+1，i-j For v k，i to vk+1，j The state transfer time cost;

[0080] Considering the train running on time constraint, adding the time cost coefficient, the total state transfer cost C k+1，i_j for:

[0081] C k+1i-j =e k+1，i-j +λ·t k+1，i-j

[0082] Where λ is the time cost coefficient, which is used to make the optimized speed curve meet the punctuality constraint.

[0083] Define the optimal state transfer path selection formula from stage k to k+1;

[0084] J k+1，j =min(J k +C k+1，j )

[0085] Among them, J k is the cost set of the kth stage, J k ={J k，1 , J k，2 ,…,J k，i ,…,J k，I}, I is the number of discrete speeds in the k-stage; C k+1，j Each state in the kth stage is transferred to x k+1，j The set of single-step state transition costs for a state.

[0086] By using the optimal state transfer path selection formula, the improved state space, state transfer and transfer cost, dynamic programming can be performed to obtain the optimal state transfer route and the interval running time. Figure 3 shown.

[0087] Among them, the energy-saving train speed curve is obtained by performing dynamic programming solution through state transfer, transfer cost and optimal state transfer path selection formula, including:

[0088] Initialization: Set the initial state (e.g. the train starts from the starting point and the speed is 0) and set the initial cost to 0;

[0089] Calculate stage by stage: for each stage (position point), traverse all possible states (improved state space);

[0090] For each state, try to transition from all possible states in the previous stage and calculate the transition cost;

[0091] Update the minimum cumulative cost of the current state and record the optimal transfer path.

[0092] Termination condition: When reaching the end point, find the final state that minimizes the total cost.

[0093] Backtracking path: trace back from the end point to the starting point, extract the optimal state transfer path, and form a complete speed curve.

[0094] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program. When the computer program is executed by a computer, the computer executes any of the above-described subway speed curve optimization methods.

[0095] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0096] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0097] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0098] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1A step that specifies a function in one or more boxes.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A subway speed curve optimization method, characterized in that: The method comprises: Step 1: Obtain basic train operation data, including train parameters, line data, and interval operation time data of the train model to be optimized; Step 2: Based on the basic train operation data and the coasting state transition process, an improved dynamic programming state space is constructed so that the state space contains the coasting state point. Step 3: Determine the state transition equation and state transition cost of each interval, and construct the optimal state transition path selection formula; Step 4: In the improved state space, dynamic programming is performed through the state transfer, transfer cost and optimal state transfer path selection formula to obtain the train energy-saving operation speed curve.

2. The subway speed curve optimization method according to claim 1, characterized in that: In step 1, the line data includes ramp data, curve data, speed limit data and station data; the train parameters include the train's formation mode, length, load level, maximum speed, maximum acceleration, basic resistance parameters, traction characteristic curve and braking characteristic curve.

3. The subway speed curve optimization method according to claim 1, characterized in that: Step 2 specifically includes: Step 201: Generate the initial state space: including setting the discrete step length, the minimum coasting speed state transition speed limit v comin , the maximum number of state points in a single stage N max and the minimum speed difference threshold dv of the state point lim , calculate the state space under uniform discretization based on discrete steps; Step 202, coasting state transition calculation: including selecting the current stage k with a speed greater than v comin state point, calculate the coasting speed corresponding to the state point; Step 203: Eliminate redundant state points: This includes determining the number of states in the k+1 stage. If it is greater than N max , calculate the minimum speed difference of each coasting point, if it is less than dv lim Then remove the original state points; Step 204: determine whether the final stage has been reached. If not, enter the k+1 stage and proceed to step 202. Otherwise, complete the state space construction.

4. The subway speed curve optimization method according to claim 3, characterized in that: If the speed is lower than v comin No idle state transfer calculation is performed; if the number of states in the current stage reaches N max And the difference between the calculated coasting speed and the adjacent original state point speed is less than the threshold dv lim , then remove the original state points.

5. The subway speed curve optimization method according to claim 3, characterized in that: In step 202, the calculation formula for the idle state transition is: Among them, v k,i is the velocity corresponding to the i-th discrete point in the k-th stage, v co_k+1,i is v in the k+1th stage k,i The corresponding coasting speed, a r_k,i is the acceleration corresponding to the running resistance only, and Δs is the position discrete interval.

6. The subway speed curve optimization method according to claim 3, characterized in that: In step 203, the minimum speed difference of each coasting point is calculated as follows: dv k+1,j =min(|v co_k+1,j -V k+1 |) Among them, v co_k+1,j is v in the k+1th stage k,j Corresponding coasting speed, V k+1 is the velocity point set of the k+1th stage, V k+1 ={v k+1,1 ,v k+1,2 ,…,v k+1,i ,…,v k+1,I }, I is the discrete velocity number of k+1 stage, dv k+1，j v co_k+1,j The corresponding minimum speed difference.

7. The subway speed curve optimization method according to claim 1, characterized in that: In step 3, the state transfer equation is X k+1 =T(X k ,u k ), where X k is the current state, u k is the current decision, X k+1 is the next state, T is the state transfer function, the state is composed of position and speed indicators, recorded as X(s,v), which represents the current state of the train, s is the position, and v is the speed; The state transfer calculation is based on the train dynamics model, and its kinematic equation is: Where M represents the mass of the train, c is the resultant force of the train, and v represents the speed of the train.

8. The subway speed curve optimization method according to claim 1, characterized in that: In step 3, the state transfer cost is the energy consumption cost and time cost during the state transfer process; The energy consumption cost is as follows: yes k+1，i-j =you kt F t (v k，i )·Δs Among them, v k，i is the velocity corresponding to the i-th discrete point in the k-th stage, F t (v k，i ) is the speed v k，i The train has full traction force, u kt is the traction control coefficient of the kth stage, Δs is the position discrete interval, e k+1，i-j For v k，i to v k+1，j energy consumption costs; The time cost is specifically: Among them, v k+1，j is the velocity corresponding to the jth discrete point in the k+1th stage, t k+1，i-j For v k，i to v k+1，j The state transfer time cost; Considering the train running on time constraint, adding the time cost coefficient, the total state transfer cost C k+1,i_j for: C k+1,i-j =e k+1,j-j +λ·t k+1,i-j Where λ is the time cost coefficient, which is used to make the optimized speed curve meet the punctuality constraint.

9. The subway speed curve optimization method according to claim 1, characterized in that: In step 3, the optimal state transfer path selection formula is constructed as follows: Define the optimal state transfer path selection formula from stage k to k+1; I k+1，j =min(J k +C k+1,j ) Among them, J k is the cost set of the kth stage, J k ={J k,1 ,J k,2 ,…,J k,i ,…,J k,I }, I is the number of discrete speeds in the k-stage; C k+1,j Each state in the kth stage is transferred to x k+1,j The set of single-step state transition costs for a state.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a computer, the computer executes the subway speed curve optimization method according to any one of claims 1 to 9.

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