Method for optimizing speed curve of high-speed train

Abstract

The invention relates to the technical field of train operation optimization, and discloses a high-speed train speed curve optimization method, which comprises the following steps: acquiring train data, line data and operation data; dividing the train journey into a plurality of sub-stages, and establishing corresponding time constraint conditions according to the speed characteristics of the mixed running train in each sub-stage; establishing a train speed curve optimization model by taking train energy consumption minimization and train operation stability maximization as dual optimization objectives; and solving the train speed curve optimization model to obtain a train speed curve optimization result. According to the method, the safety, comfort and punctuality of train operation are ensured, and the overall operation efficiency of train groups with different speed grades is remarkably improved on the core long-distance route section.

Description

Technical Field

[0001] The present invention relates to the technical field of train operation optimization, and in particular to a method for optimizing a speed curve of a high-speed train. Background Art

[0002] As the core, leading and key infrastructure in the national development strategy, high-speed railway plays an important role in the lifeline of the national economy and occupies a pivotal position in promoting the comprehensive development of the economy and society. In the operation environment of high-speed EMUs with a speed of up to 400 kilometers per hour, the line conditions show significant diversity, the train speed level has not been unified, and different track sections have set different maximum speed limits, resulting in complex scenarios where multiple speed levels of trains (such as 400km / h and 350km / h) may run in parallel in key line sections. This phenomenon puts forward more stringent requirements on the safety, punctuality and energy-saving driving strategies of individual trains. At the same time, at the level of train groups, it may also cause a decrease in overall operating efficiency and a significant increase in operating risks. The above problems have become major issues that urgently need to be explored and solved. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for optimizing the speed curve of a high-speed train, in order to achieve a global optimal solution for train operation in the three dimensions of safety, punctuality and energy saving, and to provide strong technical support for the efficient and safe operation of the high-speed railway system.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A high-speed train speed curve optimization method comprises the following steps:

[0006] Obtain train data, line data and operation data;

[0007] The train journey is divided into multiple sub-stages, and corresponding time constraints are established according to the speed characteristics of the mixed-running trains in each sub-stage;

[0008] Taking minimizing train energy consumption and maximizing train running stability as dual optimization goals, a train speed curve optimization model is established;

[0009] The train speed curve optimization model is solved to obtain the train speed curve optimization result.

[0010] Preferably, the train data retains the train weight and traction and braking performance curves;

[0011] The line data includes station locations, kilometer markers, speed limits in each section, grade changes, and curve radii;

[0012] The operating data includes departure intervals, stop duration at each station and preset running time of the interval.

[0013] Preferably, dividing the train journey into a plurality of sub-stages comprises:

[0014] According to each natural station in the timetable, the section between adjacent stations is divided into a sub-stage;

[0015] Determine whether there are one or more core segments in the divided sub-stages; if there is a single core segment, the core segment is directly divided into a new sub-stage; if there are multiple core segments, the continuous core segments are taken as a sub-stage, and the discontinuous core segments are taken as new sub-stages respectively.

[0016] Preferably, the establishing of corresponding time constraints according to the speed characteristics of the mixed-running trains in each sub-stage includes:

[0017] When the speed limit level of the core section is higher than the speed limit benchmark and there is a high-speed train following a low-speed train, a core section time constraint is imposed to allow the high-speed train to extend its running time in the core section and require the low-speed train to reduce its running time accordingly; the core section time constraint is:

[0018]

[0019] Among them, t i is the core segment running time, K i is the ratio of the core section length to the maximum train speed, Δt i for the time to increase or decrease;

[0020] When the speed limit level in the core section is higher than the speed limit benchmark and there is a low-speed train following a high-speed train, the high-speed train is allowed to run at normal speed, while the low-speed train is required to reduce its running time in the core section.

[0021] Preferably, the train speed curve optimization model is established with the dual optimization goals of minimizing train energy consumption and maximizing train running smoothness, including:

[0022] Taking minimizing train energy consumption and maximizing train running stability as dual optimization goals, an objective function is established;

[0023] Equality constraints are established based on the law of conservation of energy, basic train resistance model, additional line resistance model, and traction and braking force calculation model;

[0024] Establish inequality constraints based on line speed limit, train traction and braking force characteristics, electrical phase separation constraints, and force change rate constraints;

[0025] Establish boundary constraints based on kinetic energy, traction and braking forces, and auxiliary variable constraints;

[0026] A train speed curve optimization model is constructed based on the objective function and equality constraints, inequality constraints and boundary constraints.

[0027] Preferably, the objective function is:

[0028]

[0029] Among them, J is the objective function, N is the number of subintervals, η t is the vehicle electromechanical efficiency under traction condition, α is the utilization rate of regenerative braking energy, η d is the vehicle electromechanical efficiency under braking conditions, Δs is the step size of a single sub-interval, ω k is a continuous variable, F e,k is the difference between the traction force and the braking force in the kth subinterval, and min is the minimum value function.

[0030] Preferably, the equality constraint is:

[0031] E k =a k-1 E k-1 +b k-1 F e,k +c k-1

[0032]

[0033] Among them, E k is the instantaneous kinetic energy of the train when it reaches the kth sub-interval, F e,k is the difference between the traction force and the braking force in the kth subinterval, t k is the total time to travel to the kth subinterval, M is the total mass of the train, Δs is the step size of a single subinterval, a w0 and c w0 is the fitted unit basic resistance coefficient, g is the acceleration of gravity, γ is the train rotation coefficient, M is the total mass of the train, W j (s) is the slope value at position s, Δs k is the length of the kth subinterval.

[0034] Preferably, the inequality constraint is:

[0035] F e,min (E k )≤F e,k ≤F e,max (E k )

[0036] ΔF min≤F e,k -F e,k-1 ≤ΔF max

[0037] F e,k -ω k ≤0

[0038]

[0039] Among them, F e,min (E k ), F e,max (E k ) are the maximum traction and maximum braking force that the train can exert in the kth subinterval when the kinetic energy is E due to the constraints of traction and braking characteristics, ΔF min is the lower limit of the difference between the traction force and the braking force in adjacent sub-intervals, ΔF max is the upper limit of the difference between the traction force and the braking force in adjacent sub-intervals, F e,k is the difference between the traction force and the braking force in the kth subinterval, ω k is a continuous variable, T k _ is the target time for the train to pass the kth sub-stage, ò is the set error, k p,i With k q,i are the starting position number and the ending position number of the kth subinterval, respectively, t k is the actual time it takes for the train to pass through the kth sub-interval.

[0040] Preferably, the boundary constraint is:

[0041] 0≤E k ≤E pro,k

[0042] -F d,max ≤F e,k ≤F t,max

[0043] F e,j =0,j∈N e

[0044] -ω k ≤0

[0045] Among them, E k is the instantaneous kinetic energy of the train when it reaches the kth sub-interval, E pro,k is the maximum kinetic energy value obtained according to the line speed limit in the kth sub-interval, F d,max is the maximum braking force of the train, F t,max is the maximum traction force of the train, F e,j is the difference between the train traction and braking force in the jth core section, N eis the sub-interval number set containing the electrical phase, ω k is a continuous variable.

[0046] Preferably, solving the train speed curve optimization model includes:

[0047] The augmented Lagrangian function method is used to add time equality constraints and strong nonlinear inequality constraints such as the difference between traction and braking force in subintervals into the objective function, and a linear constraint matrix is ​​constructed for simple linear equality constraints, inequality constraints and boundary constraints.

[0048] The present invention has the following beneficial effects:

[0049] By optimizing the train speed curve, the present invention not only ensures the safety, comfort and punctuality of train operation, but also significantly improves the overall operating efficiency of train groups of different speed levels on the core long-distance line section. This optimization strategy effectively solves the risk of collision caused by too close distance between trains and the waste of line resources caused by too far distance between trains, providing strong support for the efficient and safe operation of the high-speed railway system. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A schematic diagram of a flow chart of a high-speed train speed curve optimization method;

[0051] Figure 2 Schematic diagram of train itinerary division. DETAILED DESCRIPTION

[0052] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0053] At present, the global online optimization of train operation has been revealed to be a highly comprehensive and complex system problem, and its solution depends on the accurate equivalent characterization of the temporal and spatial gradient characteristics of parameters, efficient high-dimensional order reduction technology and reasonable system decoupling strategy. Based on this, the present invention innovatively proposes a high-speed train speed curve optimization method, aiming to achieve a comprehensive improvement in the safety, punctuality and comfort of train operation, and significantly reduce the energy consumption during train traction. The strategy also focuses on optimizing the overall operating efficiency of the train group in the core line section, and promotes efficient collaboration and smooth operation between trains through refined scheduling and coordinated control. More importantly, the present invention significantly accelerates the speed of solving optimization problems, providing solid technical support for the online optimization of train speed curves.

[0054] like Figure 1 As shown, a high-speed train speed curve optimization method provided by an embodiment of the present invention includes the following steps S1 to S4:

[0055] S1. Obtain train data, line data and operation data;

[0056] In an optional embodiment of the present invention, the train data retains the train weight and traction and braking performance curves;

[0057] The line data includes station locations, kilometer markers, speed limits in each section, grade changes, and curve radii;

[0058] The operating data includes departure intervals, stop duration at each station and preset running time of the interval.

[0059] In this embodiment, data initialization and collection are performed through step S1. First, a series of basic data are comprehensively acquired and initialized, covering the basic physical properties of the train (such as vehicle weight, detailed traction and braking performance curves), the specific geometry and operating conditions of the line (including station locations, kilometer marks, speed limits for each section, slope changes, curve radius, etc.), and key information of the operating timetable (departure intervals, stop times at each station, preset operating time of the interval, etc.).

[0060] S2, dividing the train journey into multiple sub-stages, and establishing corresponding time constraints according to the speed characteristics of the mixed-running trains in each sub-stage;

[0061] In an optional embodiment of the present invention, dividing the train journey into a plurality of sub-stages comprises:

[0062] According to each natural station in the timetable, the section between adjacent stations is divided into a sub-stage;

[0063] Determine whether there are one or more core segments in the divided sub-stages; if there is a single core segment, the core segment is directly divided into a new sub-stage; if there are multiple core segments, the continuous core segments are taken as a sub-stage, and the discontinuous core segments are taken as new sub-stages respectively.

[0064] The establishing of corresponding time constraints according to the speed characteristics of mixed-running trains in each sub-stage includes:

[0065] When the speed limit level of the core section is high and there are high-speed trains following low-speed trains, the core section time constraint is imposed to allow high-speed trains to extend their running time in the core section and require low-speed trains to reduce their running time accordingly; the core section time constraint is:

[0066]

[0067] Among them, t i is the core segment running time, K i is the ratio of the core section length to the maximum train speed, Δt i for the time to increase or decrease;

[0068] When the speed limit level in the core section is high and there are low-speed trains following high-speed trains, high-speed trains are allowed to run at normal speed, while low-speed trains are required to reduce their operating time in the core section.

[0069] In this embodiment, the itinerary is divided and the time constraint is set in step S2. The whole train journey is divided into several sub-stages, and the corresponding time constraint conditions are set according to the characteristics of each speed level, so as to ensure that trains of different speed levels can run independently and without interfering with each other in the same line section, thereby ensuring operation safety and efficiency.

[0070] This embodiment first performs a detailed division of sub-stages. According to the natural station division in the timetable, the train journey is equally divided into N sub-intervals according to adjacent stations, and each sub-interval is used as a sub-stage. This is the first division. If there are one or more core segments in a sub-stage in the first division, a second division is performed. If there is a single core segment, it is directly divided into a new sub-stage; if there are multiple core segments, it is determined whether the sub-stages are continuous. If they are continuous, they are regarded as one core segment. If the core segments are not continuous, different core segments become new sub-stages.

[0071] like Figure 2 As shown in the figure, the division of sub-stages is firstly based on the inter-station travel (such as AC station) to form basic sub-stages (such as AB section, BC section). Then, for the core section shared by trains of different speed levels in the long route (such as DE section), this section can be used as a new sub-stage. This method effectively captures the impact of speed differences on line utilization and provides a more detailed spatial resolution for subsequent optimization.

[0072] This embodiment then performs a detailed setting of the time constraints. When setting the time constraints, this embodiment strictly follows the time constraints between stations specified in the timetable to ensure that the actual time between stations such as the AB section and the BC section is strictly observed. For virtual station sections (such as the DE section), this embodiment performs differentiated processing based on the speed characteristics of mixed-running trains:

[0073] (1) When the speed limit level in the core section is high (such as 400 km / h), and there is a high-speed train (such as train A, 400 km / h) following a low-speed train (such as train B, 350 km / h), in order to improve the overall operation efficiency, we impose a section time constraint, allowing train A to extend its operating time appropriately in this section, while requiring train B to reduce its operating time accordingly. The specific rules for this adjustment are as follows:

[0074]

[0075] Among them, g(x) is the setting function, K i is the ratio of the core section length to the maximum speed of the train, S road is the core segment length, V limit_road This is the speed limit level in the core section.

[0076] Then the time constraint of each train in a core section is:

[0077]

[0078] Ensure that the adjusted time allocation is consistent with physical limitations and promotes efficient operation of the vehicle group.

[0079] (2) On the contrary, if the speed limit level in the core section is still high, but low-speed train B follows high-speed train A, then train A is allowed to run at normal speed, and train B is required to further shorten its running time in this section to reduce the impact on the subsequent high-speed train operation and maintain the efficiency and smoothness of the overall line.

[0080] S3. Taking the minimization of train energy consumption and maximization of train running stability as the dual optimization goals, a train speed curve optimization model is established;

[0081] In an optional embodiment of the present invention, the train speed curve optimization model is established with the dual optimization objectives of minimizing train energy consumption and maximizing train running stability, including:

[0082] Taking minimizing train energy consumption and maximizing train running stability as dual optimization goals, an objective function is established;

[0083] Equality constraints are established based on the law of conservation of energy, basic train resistance model, additional line resistance model, and traction and braking force calculation model;

[0084] Establish inequality constraints based on line speed limit, train traction and braking force characteristics, electrical phase separation constraints, and force change rate constraints;

[0085] Establish boundary constraints based on kinetic energy, traction and braking forces, and auxiliary variable constraints;

[0086] A train speed curve optimization model is constructed based on the objective function and equality constraints, inequality constraints and boundary constraints.

[0087] This embodiment constructs the model through step S3. With the dual optimization goals of minimizing train energy consumption and maximizing running stability, the corresponding objective function is constructed. At the same time, the internal mechanisms of various operating constraints are deeply analyzed, and an accurate mechanism model is established to fully reflect these constraints.

[0088] Based on the train traction calculation model, the train operation must satisfy the following train kinematic equations:

[0089]

[0090] Where v is velocity, s is displacement, and F t (v) is the train traction force, F d (v) is the train braking force, W(s,v) is the total resistance of the train, γ is the rotation coefficient, M is the total weight of the train, and t is the running time.

[0091] First, the standard form of the optimization problem is established, including the objective function and constraints, which can be expressed as:

[0092]

[0093] Among them, variable x=[E,F e ,w], respectively representing the kinetic energy, the difference between traction and braking force, and auxiliary variables. The objective function includes the train energy consumption index E and the stability index: the rate of change of force dF, which can be calculated by the following formula:

[0094]

[0095] Among them, J is the objective function, N is the number of sub-intervals, η t is the vehicle electromechanical efficiency under traction condition, α is the utilization rate of regenerative braking energy, η d is the vehicle electromechanical efficiency under braking conditions, Δs is the step length of a single core section, ω k is a continuous variable, F e,k is the difference between the traction force and the braking force in the kth subinterval, and min is the minimum value function.

[0096] Constraints include equality constraints, inequality constraints, and boundary constraints.

[0097] The equality constraints are: based on the law of conservation of energy, the basic resistance model of the train, the additional resistance model of the line, and the traction / braking force calculation model, and the expression is:

[0098] E k =a k-1 Ek-1 +b k-1 F e,k +c k-1

[0099]

[0100] Among them, E k is the instantaneous kinetic energy of the train when it reaches the kth sub-interval, F e,k is the difference between the traction force and the braking force in the kth subinterval, t k is the total time to travel to the kth subinterval, M is the total mass of the train, Δs is the step size of a single subinterval, a w0 and c w0 is the fitted unit basic resistance coefficient, g is the acceleration of gravity, γ is the train rotation coefficient, M is the total mass of the train, W j (s) is the slope value at position s, Δs k is the length of the kth subinterval.

[0101] The inequality constraints include: line speed limit, train traction / braking force characteristics, electrical phase separation constraints, and force change rate constraints, and their set form is as follows:

[0102] F e,min (E k )≤F e,k ≤F e,max (E k )

[0103] ΔF min ≤F e,k -F e,k-1 ≤ΔF max

[0104] F e,k -ω k ≤0

[0105]

[0106] Among them, F e,min (E k ), F e,max (E k ) are the maximum traction and maximum braking force that the train can exert in the kth subinterval when the kinetic energy is E due to the constraints of traction and braking characteristics, ΔF min is the lower limit of the difference between the traction force and the braking force in adjacent sub-intervals, ΔF max is the upper limit of the difference between the traction force and the braking force in adjacent sub-intervals, F e,k is the difference between the traction force and the braking force in the kth subinterval, ω k is a continuous variable, T k_ is the target time for the train to pass the kth sub-stage, ò is the set error, k p,i With k q,i are the starting position number and the ending position number of the kth subinterval, respectively, t k is the actual time it takes for the train to pass through the kth sub-interval.

[0107] Boundary constraints include: based on kinetic energy, traction / braking force, and auxiliary variable constraints, and their set form is as follows:

[0108] 0≤E k ≤E pro,k

[0109] -F d,max ≤F e,k ≤F t,max

[0110] F e,j =0,j∈N e

[0111] -ω k ≤0

[0112] Among them, E k is the instantaneous kinetic energy of the train when it reaches the kth sub-interval, E pro,k is the maximum kinetic energy value obtained according to the line speed limit in the kth sub-interval, F d,max is the maximum braking force of the train, F t,max is the maximum traction force of the train, F e,j is the difference between the train traction and braking force in the jth sub-interval, N e is the sub-interval number set containing the electrical phase, ω k is a continuous variable.

[0113] S4. Solve the train speed curve optimization model to obtain the train speed curve optimization result.

[0114] In an optional embodiment of the present invention, the present embodiment can perform model reconstruction in step S4. The augmented Lagrangian function method is used to cleverly simplify the complex mechanism model, and some complex strong nonlinear constraints are directly integrated into the objective function. For the remaining linear constraints, the original mechanism model is converted into a mathematical model that is easy to solve by constructing an efficient matrix form.

[0115] After writing the problem in the standard form of the optimization algorithm, this embodiment uses the augmented Lagrangian function method to simplify the above model, selectively adds high-dimensional nonlinear constraints (time equality constraints and inequality constraints about Fek) to the objective function, and then obtains an equivalent model in which the objective function is nonlinear and the constraints are linear, and the relevant solver is called for solution. In the above equivalent order reduction, the relevant mathematical theory guarantees the optimality of the solution of the equivalent model, and the equivalent transformation also reduces the dimension of the optimization problem variable, which greatly speeds up the solution efficiency.

[0116] By introducing the slack variable e, the equivalent form of the optimization problem can be obtained as follows:

[0117]

[0118] x is the optimization variable, x T is the transpose of variable x, variable x=[E,F e ,w], respectively represent the kinetic energy, the difference between traction and braking force, and auxiliary variables, H is the coefficient matrix of the quadratic term of the objective function, f T is the coefficient vector of the first-order term, c i (x) is the set of equality constraints, i is a positive integer, ε is the number of equality constraints, c j (x) is the set of inequality constraints, j is a positive integer, I is the number of inequality constraints, l b is the lower limit of the optimization variable, u b is the upper limit of the optimization variable, e j To convert inequality constraints into slack variables for equality constraints.

[0119] Keeping simple upper and lower limit constraints, the Lagrangian function is constructed as follows:

[0120]

[0121] Among them, λ i is the Lagrange multiplier of the equality constraint, μ j is the Lagrange multiplier for the inequality constraints, and both are required to be non-negative

[0122] The quadratic penalty function is constructed as follows:

[0123]

[0124] The required augmented Lagrangian function is as follows:

[0125]

[0126] Among them, σ is the penalty factor,

[0127] Finally, according to the optimality theory of convex optimization problems, we know that:

[0128]

[0129] Substituting it into the augmented Lagrangian function can eliminate e, further reduce the dimension of the problem, and improve the solution efficiency. At the same time, the constraint violation degree of the kth iteration can be obtained as shown in the following formula:

[0130]

[0131] Among them, x k+1 is the solution for the kth iteration.

[0132] For the remaining linear constraints, a matrix mathematical model is constructed. The equality constraint matrix is ​​constructed as follows:

[0133] A eq x=b eq

[0134]

[0135] A eq is the coefficient matrix of the equality constraint, b eq is the vector of values ​​on the right side of the equation, Refers to a matrix of N rows and 3N columns consisting of rational numbers. Refers to a matrix of N rows and 1 column consisting of rational numbers, specifically:

[0136] A eq =[A eq1 A eq2 A eq3 ]

[0137]

[0138] b eq =[c0+a0E0c1…c N-1 ] T

[0139] A eq1 is the coefficient matrix of the first equality constraint, A eq2 is the coefficient matrix of the second equality constraint, A eq3 is the coefficient matrix of the third equality constraint

[0140] The inequality constraint matrix is ​​constructed as follows:

[0141] Ax≤b

[0142]

[0143] A is the coefficient matrix of the equality constraint, b is the vector of the right-hand side values ​​of the inequality, Refers to a matrix of 3N rows and 3N columns consisting of rational numbers. Refers to a matrix of 3N rows and 1 column consisting of rational numbers, specifically:

[0144] A=[A1;A2;A3]

[0145]

[0146]

[0147] A1 is the coefficient matrix of the first inequality constraint, A2 is the coefficient matrix of the second inequality constraint, and A3 is the coefficient matrix of the third inequality constraint.

[0148] The boundary constraint matrix is ​​constructed as follows:

[0149] lb≤x≤ub

[0150]

[0151] Specifically, they are:

[0152]

[0153] At this point, all linear constraint matrices have been constructed.

[0154] In an optional embodiment of the present invention, this embodiment can perform solution strategy and iterative optimization in step S4. Set reasonable initial guess values ​​and key algorithm parameters, then input the constructed objective function and constraint coefficient matrix into the casadi solver, and iterate through the relevant algorithm until a solution set that satisfies all constraints and optimizes the optimization target is obtained.

[0155] In this embodiment, the variable initial point x0=[0] is first selected within the constraints, Initialize the multiplier ε 0 , penalty factor ξ0>0, agreement violation constant μ>0, precision constant η>0, and constants 0<α≤β≤1 and ρ>1, the above parameters can be selected as any value, as long as they meet the constraints. Let And k=0.

[0156] In this embodiment, the sorted objective function and constraint coefficient matrix are then passed into the Casadi solver.

[0157] This embodiment then starts iterative solving, and the logical steps are as follows:

[0158] 1. Initialize each parameter, take x0 as the initial point, and solve Get the accuracy condition met

[0159] ||L ξk (x,ε k )|| 2 ≤η k The solution x k+1 ;

[0160] 2. Determine x k+1 Is the agreement violation degree of less than the agreement violation degree at the kth iteration? If so, the approximate solution x is obtained. k+1 , stop the iteration; otherwise, Update the multiplier, but keep the penalty factor unchanged, and reduce the problem solving error and constraint violation,

[0161]

[0162] 3. If x k+1 If the precision condition is not met, the multiplier remains unchanged, but σ is used k+1 =ρσ k Update the penalty factor and use Adjust the subproblem sum error and violation, and continue iterating.

[0163] 4. Determine whether the number of iterations has been exceeded. If exceeded, stop iteration and output the result.

[0164] 5. If the number of iterations has not been exceeded, continue iterating.

[0165] The overall process is to determine the strategy of adjusting the multiplier and penalty factor based on the accuracy of the solution process and whether the constraints are met, until an approximate solution is finally reached and the iteration is terminated.

[0166] Finally, the optimal solution that meets the accuracy requirements is iterated.

[0167] While working to reduce train traction energy consumption, the present invention optimizes the train speed curve, not only ensuring the safety, comfort and punctuality of train operation, but also significantly improving the overall operating efficiency of train groups of different speed levels on the core long-distance line sections. This optimization strategy effectively solves the risk of collision caused by too close distance between trains and the waste of line resources caused by too far distance between trains, providing strong support for the efficient and safe operation of the high-speed railway system.

[0168] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks 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 processes in the flowchart and / or block diagram. 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.

[0169] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate 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 A function specified in one or more boxes.

[0170] 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 instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0171] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0172] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A high-speed train speed curve optimization method, characterized in that: The following steps are involved: Obtain train data, line data and operation data; The train journey is divided into multiple sub-stages, and corresponding time constraints are established according to the speed characteristics of the mixed-running trains in each sub-stage; Taking minimizing train energy consumption and maximizing train running stability as dual optimization goals, a train speed curve optimization model is established; The train speed curve optimization model is solved to obtain the train speed curve optimization result.

2. A high-speed train speed curve optimization method according to claim 1, characterized in that: The train data retains the train weight and traction and braking performance curves; The line data includes station locations, kilometer markers, speed limits in each section, grade changes, and curve radii; The operating data includes departure intervals, stop duration at each station and preset running time of the interval.

3. A high-speed train speed curve optimization method according to claim 1, characterized in that: The train journey is divided into a plurality of sub-stages, including: According to each natural station in the timetable, the section between adjacent stations is divided into a sub-stage; Determine whether there are one or more core segments in the divided sub-stages; if there is a single core segment, the core segment is directly divided into a new sub-stage; if there are multiple core segments, the continuous core segments are taken as a sub-stage, and the discontinuous core segments are taken as new sub-stages respectively.

4. A high-speed train speed curve optimization method according to claim 1, characterized in that: The establishing of corresponding time constraints according to the speed characteristics of mixed-running trains in each sub-stage includes: When the speed limit level of the core section is higher than the speed limit benchmark and there is a high-speed train following a low-speed train, a core section time constraint is imposed to allow the high-speed train to extend its running time in the core section and require the low-speed train to reduce its running time accordingly; the core section time constraint is: Among them, t i is the core segment running time, K i is the ratio of the core section length to the maximum train speed, Δt i for the time to increase or decrease; When the speed limit level in the core section is higher than the speed limit benchmark and there is a low-speed train following a high-speed train, the high-speed train is allowed to run at normal speed, while the low-speed train is required to reduce its running time in the core section.

5. A high-speed train speed curve optimization method according to claim 1, characterized in that: The train speed curve optimization model is established with the dual optimization goals of minimizing train energy consumption and maximizing train running smoothness, including: Taking minimizing train energy consumption and maximizing train running stability as dual optimization goals, an objective function is established; Equality constraints are established based on the law of conservation of energy, basic train resistance model, additional line resistance model, and traction and braking force calculation model; Establish inequality constraints based on line speed limit, train traction and braking force characteristics, electrical phase separation constraints, and force change rate constraints; Establish boundary constraints based on kinetic energy, traction and braking forces, and auxiliary variable constraints; A train speed curve optimization model is constructed based on the objective function and equality constraints, inequality constraints and boundary constraints.

6. A high-speed train speed curve optimization method according to claim 5, characterized in that: The objective function is: Among them, J is the objective function, N is the number of sub-intervals, η t is the vehicle electromechanical efficiency under traction condition, α is the utilization rate of regenerative braking energy, η d is the vehicle electromechanical efficiency under braking conditions, Δs is the step size of a single sub-interval, ω k is a continuous variable, F e,k is the difference between the traction force and the braking force in the kth subinterval, and min is the minimum value function.

7. A high-speed train speed curve optimization method according to claim 5, characterized in that: The equality constraints are: E k =a k-1 E k-1 +b k-1 F e,k +c k-1 Among them, E k is the instantaneous kinetic energy of the train when it reaches the kth sub-interval, F e,k is the difference between the traction force and the braking force in the kth subinterval, t k is the total time to travel to the kth subinterval, M is the total mass of the train, Δs is the step length of a single core section, a w0 and c w0 is the fitted unit basic resistance coefficient, g is the acceleration of gravity, γ is the train rotation coefficient, M is the total mass of the train, W j (s) is the slope value at position s, Δs k is the length of the kth subinterval.

8. A high-speed train speed curve optimization method according to claim 5, characterized in that: The inequality constraints are: F e,min (AND k )≤F e,k ≤F e,max (AND k ) ΔF min ≤F e,k -F e,k-1 ≤ΔF max F e,k -oh k ≤0 Among them, F e,min (E k ), F e,max (E k ) are the maximum traction and maximum braking force that the train can exert in the kth subinterval when the kinetic energy is E due to the constraints of traction and braking characteristics, ΔF min is the lower limit of the difference between the traction force and the braking force in adjacent sub-intervals, ΔF max is the upper limit of the difference between the traction and braking forces in adjacent core sections, F e,k is the difference between the traction force and the braking force in the kth subinterval, ω k is a continuous variable, T k _ is the target time for the train to pass through the kth sub-interval, ò is the set error, k p,i With k q,i are the starting position number and the ending position number of the kth subinterval, respectively, t k is the actual time it takes for the train to pass through the kth sub-interval.

9. A high-speed train speed curve optimization method according to claim 5, characterized in that: The boundary constraints are: 0≤E k ≤E pro,k -F d,max ≤F e,k ≤F t,max F e,j =0,j∈N e -oh k ≤0 Among them, E k is the instantaneous kinetic energy of the train when it reaches the kth sub-interval, E pro,k is the maximum kinetic energy value obtained according to the line speed limit in the kth sub-interval, F d,max is the maximum braking force of the train, F t,max is the maximum traction force of the train, F e,j is the difference between the train traction and braking force in the jth sub-interval, N e is the sub-interval number set containing the electrical phase, ω k is a continuous variable.

10. A high-speed train speed curve optimization method according to claim 1, characterized in that: The solving of the train speed curve optimization model comprises: The augmented Lagrangian function method is used to add time equality constraints and strong nonlinear inequality constraints such as the difference between traction and braking force in the core section into the objective function, and a linear constraint matrix is ​​constructed for the remaining simple linear equality constraints, inequality constraints and boundary constraints.

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