Heavy-load train track optimization method, device and system based on multi-mass-point model

Abstract

The invention provides a heavy-load train trajectory optimization method, device and system based on a multi-mass-point model. The method comprises the steps that a dynamic model and initial constraint conditions of a heavy-load train in the running process are constructed; according to the dynamic model and the initial constraint condition, an initial target function is constructed by taking train operation energy consumption and coupler force minimization as targets; based on the single-phase optimal control model, determining a state variable and a control variable in the train operation process; according to the state variable and the control variable, converting the initial objective function to obtain an objective function based on a single-phase optimal control model; and according to the target function and the constraint condition based on the single-phase optimal control model, determining the optimal track in the running process of the heavy haul train by using a pseudo-spectral method. The optimization problem is constructed based on the multi-mass-point model, and the train running track is optimized, so that the safety and the energy efficiency of train running are improved, and the maintenance cost is reduced.

Description

Technical Field

[0001] This article belongs to the technical field of railway transportation, and specifically relates to a heavy-haul train trajectory optimization method, device, and system based on a multi-particle model. Background Art

[0002] With the rapid development of railway transportation, heavy-haul railway transportation has become an important part of the national development strategy due to its advantages such as large capacity, high efficiency, low cost, and environmental protection. However, due to its large load and long length, heavy-haul trains generate significant coupler forces during operation, which affect the safety and maintenance cost of the trains. The traditional single-particle model has significant limitations in describing the dynamics of heavy-haul trains and cannot accurately reflect the longitudinal dynamic characteristics inside the trains.

[0003] Existing train trajectory optimization methods are mainly based on the single-particle model. Although they can optimize the train operation energy consumption to a certain extent, they cannot effectively consider the influence of coupler forces. In addition, existing optimization methods usually adopt a combination of offline optimization and online tracking. In the offline optimization process, the single-particle model is usually applied, while in online tracking, the multi-particle model is used. Such model mismatch easily leads to deviations between the optimization results and the actual operation situation. Therefore, there is an urgent need for a direct optimization method for heavy-haul train operation trajectories based on the multi-particle model that can comprehensively consider train energy consumption and coupler forces. Summary of the Invention

[0004] Aiming at the above problems of the existing technology, the purpose of this article is to provide a heavy-haul train trajectory optimization method, device, and system based on the multi-particle model, which can reduce the train operation energy consumption and coupler forces and improve the safety and energy efficiency of train operation by optimizing the train operation trajectory.

[0005] To solve the above technical problems, the specific technical solutions of this article are as follows:

[0006] On the one hand, this article provides a heavy-haul train trajectory optimization method based on the multi-particle model. The method includes:

[0007] Construct a dynamic model and initial constraint conditions of the heavy-haul train during operation;

[0008] According to the dynamic model and initial constraint conditions, and with the goal of minimizing the train operation energy consumption and coupler forces, construct an initial objective function;

[0009] Based on the single-phase optimal control model, determine the state variables and control variables during the train operation;

[0010] According to the state variables and control variables, transform the initial objective function to obtain an objective function based on the single-phase optimal control model;

[0011] Based on the objective function and constraint conditions of the single-phase optimal control model, the pseudo-spectral method is used to determine the optimal trajectory during the operation of the heavy-haul train.

[0012] Furthermore, a dynamic model and initial constraint conditions during the operation of the heavy-haul train are constructed, including:

[0013] Based on the spring-damper model composed of each carriage in the heavy-haul train, the coupler force corresponding to each carriage is determined, expressed as: f i in = k i (s i - s i+1 - L i ), i = 1, 2,..., n - 1, where f i in is the coupler force corresponding to the i-th carriage, k i is the elastic coefficient of the i-th coupler, s i is the position of the i-th vehicle, L i is the distance between the i-th carriage and the (i + 1)-th carriage when the coupler force is 0;

[0014] According to the coupler force corresponding to each carriage and the operation parameters of the heavy-haul train, a dynamic model during the operation of the heavy-haul train is constructed, expressed as:

[0015]

[0016] u i is the control force of the i-th carriage, v i is the speed of the i-th vehicle. When the i-th carriage is a freight car, i.e., the freight car can only provide braking force; when it is a locomotive, where and respectively represent the traction force and braking force of the locomotive, f i ro 、f i ra are respectively the running resistance and additional resistance of the i-th carriage. The running resistance includes rolling friction resistance and air resistance; the additional resistance includes the gradient and curvature of the train operation route;

[0017] Based on the operation parameters of the heavy-haul train, the initial constraint conditions during the operation of the heavy-haul train are determined. The initial constraint conditions include control force constraint, terminal constraint, speed constraint and safety constraint.

[0018] Furthermore, the initial objective function is expressed by the following formula:

[0019]

[0020] Among them, is the train operation energy consumption, is the total coupler force of the couplers in all carriages, and α 1 and α 2 are weight coefficients, which are respectively used to balance the influences of energy consumption and coupler force.

[0021] Furthermore, the control force constraint is expressed as:

[0022] When the carriage is a locomotive:

[0023] When the carriage is a freight car:

[0024] The terminal constraint is expressed as:

[0025] s 1 (t 0 ) = s 0 , v i (t 0 ) = 0, i = 1, 2,..., n,

[0026] s 1 (t f ) = s 0 , v i (t f ) = 0, i = 1, 2,..., n;

[0027] The speed constraint is expressed as:

[0028]

[0029] Safety constraint:

[0030]

[0031] Furthermore, the state variables during the train operation process at least include the position and speed of each carriage, expressed as The control variables at least include the control forces received by each carriage, expressed as

[0032] as

[0033] The objective function based on the single-phase optimal control model is expressed as:

[0034]

[0035] Furthermore, according to the objective function and constraint conditions of the single-phase optimal control model, using the pseudospectral method, the optimal trajectory during the operation of the heavy-haul train is determined, including:

[0036] Perform time-domain normalization transformation on the preset operation time interval of the heavy-haul train to obtain the transformed time interval, which is expressed as: where \(t\in[t 0 ,t f \), \(\tau\in[-1, +1]\);

[0037] According to the transformed time interval, as well as the objective function and constraint conditions based on the single-phase optimal control model, determine the transformed objective function and objective constraint conditions. The transformed objective function is expressed as:

[0038] Perform grid division processing on the transformed time interval to obtain multiple grid intervals;

[0039] Within each grid interval, use the Lagrange polynomial to approximate the state variables to obtain the discretized target state variables;

[0040] According to the target state variables and the transformed objective function, determine the final objective function based on nonlinear programming;

[0041] According to the final objective function, output the optimal control sequence to obtain the optimal trajectory during the operation of the heavy-haul train.

[0042] Furthermore, the objective constraint conditions include dynamic constraints, path constraints, integral constraints, and terminal constraints,

[0043] The dynamic constraints are expressed as:

[0044]

[0045] The path constraints are expressed as:

[0046]

[0047] The integral constraints are expressed as:

[0048]

[0049] The terminal constraints are expressed as:

[0050] v(-1)=v 0 ,s(-1)=s 0 ,

[0051] v(+1)=v f ,s(+1)=s f .

[0052] Furthermore, the target state variables are expressed by the following formula:

[0053]

[0054] Among them, is the Lagrange basis function, defined as:

[0055]

[0056] The final objective function is expressed as:

[0057]

[0058] On the other hand, this paper also provides an overloaded train trajectory optimization device based on a multi-particle model. The device includes:

[0059] The first construction module is used to construct the dynamic model and initial constraint conditions of the overloaded train during operation;

[0060] The second construction module constructs an initial objective function according to the dynamic model and initial constraint conditions, with the goal of minimizing the train operation energy consumption and coupler force;

[0061] The variable determination module is used to determine the state variables and control variables during the train operation based on the single-phase optimal control model;

[0062] The objective function obtaining module is used to transform the initial objective function according to the state variables and control variables to obtain the objective function based on the single-phase optimal control model;

[0063] The optimal trajectory determination module is used to determine the optimal trajectory during the operation of the overloaded train by using the pseudospectral method according to the objective function and constraint conditions based on the single-phase optimal control model.

[0064] Finally, this paper also provides a railway transportation system, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned method is implemented.

[0065] Adopting the above technical solutions, a method, device, and system for optimizing the trajectory of an overloaded train based on a multi-particle model in this paper. The method includes: constructing the dynamic model and initial constraint conditions of the overloaded train during operation; constructing an initial objective function according to the dynamic model and initial constraint conditions, with the goal of minimizing the train operation energy consumption and coupler force; determining the state variables and control variables during the train operation based on the single-phase optimal control model; transforming the initial objective function according to the state variables and control variables to obtain the objective function based on the single-phase optimal control model; determining the optimal trajectory during the operation of the overloaded train by using the pseudospectral method according to the objective function and constraint conditions based on the single-phase optimal control model. This paper constructs an optimization problem based on a multi-particle model, aiming to minimize the train operation energy consumption and coupler force, and improves the train operation safety, energy efficiency, and reduces the maintenance cost by optimizing the train operation trajectory.

[0066] In order to make the above and other objectives, features, and advantages of this article more obvious and understandable, the following provides preferred embodiments and, in conjunction with the accompanying drawings, detailed descriptions are as follows. Description of the Drawings

[0067] In order to more clearly illustrate the technical solutions in the embodiments of this article or in the prior art, the following will briefly introduce the accompanying drawings required for use in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of this article. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0068] Figure 1 Shows a schematic diagram of the steps of a heavy-haul train trajectory optimization method based on a multi-particle model provided by an embodiment of this article;

[0069] Figure 2 Shows a schematic diagram of a heavy-haul train in an embodiment of this article;

[0070] Figure 3 Shows a schematic diagram of the steps of the method provided in an embodiment of this article;

[0071] Figure 4 Shows a parameter table of HXD2 electric locomotives and C80B fully loaded freight cars in an embodiment of this article;

[0072] Figure 5(1) shows the result graph of Experiment 1 on the optimal train operation trajectory in an embodiment of this article;

[0073] Figure 5(2) shows the result graph of Experiment 2 on the optimal train operation trajectory in an embodiment of this article;

[0074] Figure 5(3) shows the optimal operation trajectory of a 20,000-ton long formation heavy-haul train on the Datong-Qinhuangdao Railway in an embodiment of this article;

[0075] Figure 6 Shows a schematic structural diagram of a heavy-haul train trajectory optimization device based on a multi-particle model provided by an embodiment of this article;

[0076] Figure 7 Shows a schematic framework diagram of the railway transportation system provided by an embodiment of this article.

[0077] Description of the Reference Signs in the Drawings:

[0078] 610, the first construction module; 620, the second construction module; 630, the variable determination module; 640, the objective function obtaining module; 650, the optimal trajectory determination module. Detailed Embodiments

[0079] The technical solutions in the embodiments of this article will be clearly and completely described below with reference to the accompanying drawings in the embodiments of this article. Obviously, the described embodiments are only a part of the embodiments of this article, rather than all the embodiments. Based on the embodiments in this article, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of this article.

[0080] It should be noted that the terms "first", "second", etc. in the specification and claims of this article and the above-mentioned accompanying drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of this article described here can be implemented in an order other than those illustrated or described here. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, device, product, or equipment that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products, or equipment.

[0081] Existing train trajectory optimization methods are mainly based on single-particle models. Although they can optimize train operation energy consumption to a certain extent, they cannot effectively consider the influence of coupler forces. In addition, existing optimization methods usually adopt a combination of offline optimization and online tracking. In the offline optimization process, a single-particle model is usually applied, while a multi-particle model is applied during online tracking. Such model mismatch easily leads to a deviation between the optimization result and the actual operation situation.

[0082] To solve the above problems, the embodiments of this article provide a heavy-haul train trajectory optimization method based on a multi-particle model, which can reduce train operation energy consumption and coupler forces and improve the safety and energy efficiency of train operation by optimizing the train operation trajectory. Figure 1 FIG. is a schematic diagram of the steps of a heavy-haul train trajectory optimization method based on a multi-particle model provided by the embodiments of this article. This specification provides method operation steps such as in the embodiments or flowcharts, but based on routine or non-creative labor, more or fewer operation steps may be included. The step order listed in the embodiments is only one way among the execution orders of numerous steps and does not represent the only execution order. When actually executed in a system or device product, it can be executed in the order shown in the embodiments or the accompanying drawings or in parallel. Specifically, as Figure 1 shown, the method may include:

[0083] S101: Construct a dynamic model and initial constraint conditions of a heavy-haul train during operation;

[0084] S102: Construct an initial objective function according to the kinetic model and initial constraint conditions, with the goal of minimizing the train operation energy consumption and coupler force;

[0085] S103: Based on the single-phase optimal control model, determine the state variables and control variables during the train operation process;

[0086] S104: According to the state variables and control variables, transform the initial objective function to obtain the objective function based on the single-phase optimal control model;

[0087] S105: According to the objective function and constraint conditions based on the single-phase optimal control model, use the pseudospectral method to determine the optimal trajectory during the operation of the heavy-haul train.

[0088] It can be understood that in the embodiments of this specification, a heavy-haul train is generally a dedicated freight car formation, a super-long and overweight freight train pulled by a double locomotive or multiple locomotives. The heavy-haul train has a large vehicle load capacity and a large number of cars coupled. Therefore, the coupler force between carriages is generally relatively large, and there will be relatively large energy consumption and safety problems during the entire freight process of the train. Therefore, controlling the trajectory during the train operation is beneficial to reducing energy consumption and improving the control safety of the train. Specifically, in this article, the heavy-haul train is regarded as a system composed of multiple mass points, where each mass point represents a carriage (locomotive or freight car), which is convenient for dynamic simulation during the train operation process and for analyzing the constraint conditions according to the set train operation conditions, obtaining an optimization problem of the objective function with the train running energy consumption and coupler force as comprehensive indicators. Then, this article uses a combination of the single-phase optimal control model and the pseudospectral method to solve this optimization problem to obtain the optimal trajectory of the heavy-haul train during the running process, thereby achieving the optimal control of the heavy-haul train and reducing energy consumption and running safety.

[0089] As Figure 2 shown, it is a schematic diagram of the operation of a heavy-haul train in this specification. As shown in the figure, it is a heavy-haul train pulled by multiple locomotives, where Locomotive is the locomotive and Wagon is the freight car.

[0090] In the embodiments of this specification, constructing the kinetic model and initial constraint conditions during the operation of the heavy-haul train includes:

[0091] Based on the spring-damper model composed of each carriage in the heavy-haul train, determine the coupler force corresponding to each carriage, expressed as:

[0092] f i in =k i (s i -s i+1 -L i ), i = 1, 2,..., n - 1, (1)

[0093] Among them, f i in is the coupler force corresponding to the i-th carbody, k i is the elastic coefficient of the i-th coupler, s i is the position of the i-th vehicle, L i is the distance between the i-th carbody and the (i + 1)-th carbody when the coupler force is 0;

[0094] According to the coupler force corresponding to each carbody and the operation parameters of the heavy-haul train, a dynamic model of the heavy-haul train during operation is constructed, expressed as:

[0095]

[0096] Among them, m i is the mass of the i-th carbody, u i is the control force of the i-th carbody, v i is the speed of the i-th vehicle. When the i-th carbody is a freight car, that is, the freight car can only provide braking force; when it is a locomotive, Among them and respectively represent the traction force and braking force of the locomotive, f i ro 、f i ra are respectively the running resistance and additional resistance of the i-th carbody. The running resistance includes rolling friction resistance and air resistance; the additional resistance includes the gradient and curvature of the train operation route;

[0097] Based on the operation parameters of the heavy-haul train, the initial constraint conditions of the heavy-haul train during operation are determined. The initial constraint conditions include control force constraint, terminal constraint, speed constraint and safety constraint.

[0098] That is to say, in this paper, the heavy-haul train is regarded as a system composed of multiple mass points, each mass point represents a carbody (locomotive or freight car), and the connection between adjacent carbodies is represented by a simplified spring-damping model. In this way, the coupler force on each coupler can be simulated according to this model and the motion parameters (elastic coefficient, position, etc.) corresponding to the carbody in the model. Then, based on the above modeling of the coupler, the dynamic model and the corresponding dynamic equation of the heavy-haul train are obtained.

[0099] Among them, the running resistance can be expressed by the following formula:

[0100]

[0101] The additional resistance can be expressed by the following formula:

[0102]

[0103] Among them, A i , B i and C i are coefficients related to rolling friction and air resistance, and are all positive values; θ i represents the ramp angle, and R i represents the radius of curvature.

[0104] In the embodiments of this specification, before formulating the optimization problem of the heavy-haul train operation trajectory, it is necessary to analyze the constraints suffered during the train operation. Among them, the operation parameters of the heavy-haul train can be factors such as the designed speed range of the current line of the train, the designed control forces of the locomotive and freight cars, etc. These design parameters can ensure that the vehicle can complete the transportation task as soon as possible under the condition of safety and reliability. Specifically,

[0105] The control force constraint is expressed as:

[0106] When the carriage is a locomotive:

[0107] When the carriage is a freight car:

[0108] The terminal constraint is expressed as:

[0109] s 1 (t 0 ) = s 0 , v i (t 0 ) = 0, i = 1, 2,..., n,

[0110] s 1 (t f ) = s 0 , v i (t f ) = 0, i = 1, 2,..., n;

[0111] The speed constraint is expressed as:

[0112]

[0113] Safety constraint:

[0114]

[0115] The above are the constraints during the heavy-haul train operation, and the corresponding constraint conditions for different heavy-haul trains will also be different.

[0116] Then, based on the above analysis, with the goal of minimizing the train operation energy consumption and coupler force, the following initial objective function is constructed:

[0117]

[0118] Among them, is the train operation energy consumption, is the total coupler force of the couplers in all carriages, and α 1 and α 2 are weight coefficients, which are respectively used to balance the influence of energy consumption and coupler force. The specific values of α 1 and α 2 are set according to the actual situation. For example, the weight coefficients of energy consumption and coupler force can be determined according to the climbing situation of the operation line.

[0119] In the embodiments of this specification, the state variables during the train operation process at least include the position and speed of each carriage, expressed as The control variables at least include the control force received by each carriage, expressed as

[0120] The objective function based on the single-phase optimal control model is expressed as:

[0121]

[0122] That is to say, in this article, by transforming the above optimization problem into a single-phase optimal control model, the state variables control variables integration variables initial time t 0 and the termination time t f are defined, so that the formula (3) can be re-expressed to obtain formula (4).

[0123] Of course, the optimization problem corresponding to formula (4) still satisfies the above constraints.

[0124] In the embodiments of this specification, according to the objective function and constraints of the single-phase optimal control model, using the pseudospectral method, the optimal trajectory during the operation of the heavy-haul train is determined, including:

[0125] Perform a time-domain normalization transformation on the preset operation time interval of the heavy-haul train to obtain the transformed time interval, expressed as:

[0126]

[0127] Among them, t ∈ [t 0 , t f , τ ∈ [-1, +1];

[0128] According to the transformed time interval, as well as the objective function and constraints of the single-phase optimal control model, determine the transformed objective function and objective constraint conditions. The transformed objective function is expressed as:

[0129]

[0130] Perform grid division on the converted time interval to obtain multiple grid intervals;

[0131] Within each grid interval, use Lagrange polynomials to approximate the state variables to obtain the discretized target state variables;

[0132] Determine the final objective function based on nonlinear programming according to the target state variables and the conversion objective function;

[0133] According to the final objective function, output the optimal control sequence to obtain the optimal trajectory during the operation of the heavy-haul train.

[0134] It can be understood that the pseudospectral method has an exponential convergence rate and high precision under sparse grids, and can effectively handle multi-stage train trajectory optimization problems. In this paper, the pseudospectral method (Pseudospectral Method) can be used to solve the optimization problem. Specifically, the optimization problem solving method is based on the multi-interval Legendre-Gauss-Radau collocation method (Radau Collocation Method) and is implemented in combination with the GPOPS-II software package. Specifically,

[0135] The objective function is transformed and expressed through the above single-phase optimal control model to obtain the objective function based on the single-phase optimal control model. Then, through normalization transformation of the time interval, the function based on the time series is expressed in the form based on τ, as shown in formulas (5) and (6). Of course, the constraint conditions also need to be adjusted accordingly. Among them, the objective constraint conditions include dynamic constraints, path constraints, integral constraints, and terminal constraints.

[0136] The dynamic constraint is expressed as:

[0137]

[0138] The path constraint is expressed as:

[0139]

[0140] The integral constraint is expressed as:

[0141]

[0142] The terminal constraint is expressed as:

[0143] v(-1) = v 0 , s(-1) = s 0 ,

[0144] v(+1) = vf , s(+1) = s f . (10)

[0145] Then, divide the time interval τ ∈ [-1, +1] into K grid intervals [T k-1 , T k , k = 1, ..., K, and the grid points satisfy -1 = T 0 < T 1 < T 2 <... < T K = T f = +1. Optionally, the number of grid intervals can be set according to the actual situation, that is, the division accuracy of the grid intervals can correspond to the specific solution accuracy, which is not limited in the embodiments of this specification.

[0146] Within each grid interval k, the state variable x (k) (τ) is approximated by a Lagrange polynomial:

[0147]

[0148] where is the Lagrange basis function, defined as:

[0149]

[0150] Through the above discretization process, the continuous-time optimal control problem is transformed into a nonlinear programming (NLP) problem, and the objective function is finally transformed into:

[0151]

[0152] By converting the continuous-time optimal control problem into a nonlinear programming problem, and solving the optimal trajectory for the nonlinear final objective function, that is, formula (13). Specifically, within each time interval, combined with the objective constraint conditions, the control variables are randomly selected to determine the optimal control variables within that time interval, and in this way, the optimal control sequence of the transportation line is selected repeatedly in each time interval. In another embodiment, a guess number threshold can also be set. In each guess step, combined with the objective constraint conditions, the control variables of each time interval are randomly selected to obtain a control variable sequence, and the consumption value (i.e., energy consumption and coupler force) corresponding to this guess step is calculated through the above objective function. When the guess number reaches the threshold, the optimal control variable sequence is selected from all the guess numbers, and the control force curve, speed curve of the heavy-haul train during driving, and the coupler force curve corresponding to each carriage can be obtained, so that on the basis of ensuring the driving safety of the train, the energy consumption of the train transporting goods can be effectively reduced.

[0153] In one embodiment of this specification, a method for optimizing the trajectory of a heavy-haul train based on a multi-particle model is also provided. As Figure 3 shown, it is a schematic diagram of a step of the method, and the specific process is as follows:

[0154] Step 1: Initialize the train parameters, constraint conditions, and optimization objectives.

[0155] Step 2: Construct the dynamic equation of the multi-particle heavy-haul train.

[0156] Step 3: Transform the optimization problem into a single-phase optimal control model.

[0157] Step 4: Discretize the optimization problem using the pseudospectral method.

[0158] Step 5: Use a nonlinear optimization algorithm to solve the discretized NLP problem.

[0159] Step 6: Output the optimal control sequence and the train operation trajectory.

[0160] Among them, the implementation process of each step is as shown in the above embodiment, and will not be elaborated here.

[0161] Exemplarily, based on the above-provided method, this article also judges the reliability and advantages of the technical solution adopted in this article by using experiments. Specifically:

[0162] Step 1: Simulation scenario setting

[0163] The experiments in this case were all carried out in MATLAB using the optimization solver GPOPS-II on a laptop with a 13th-generation Intel CPU i9-13900H and an RTX 4060 GPU.

[0164] Three experiments were set in this case. The first two experiments were intended for simple simulation. The selected line was the Datong-Qinhuangdao Railway scaled by 100 times. The first experiment was to simulate a heavy-haul train pulled by a single locomotive, which was a HXD2 locomotive pulling 3 fully loaded C80B wagons; the second experiment simulated a heavy-haul train pulled by multiple locomotives, which was two HXD2 locomotives pulling 6 fully loaded C80B wagons; the third experiment applied the original line of the Datong-Qinhuangdao Railway and the formation mode of 20,000-ton heavy-haul trains, mainly consisting of a HXD2 locomotive pulling 108 fully loaded C80B wagons, and then followed by another HXD2 locomotive also pulling 108 fully loaded C80B wagons.

[0165] The parameters of the HXD2 electric locomotive and the fully loaded C80B wagon selected in the case are as shown in the appendix Figure 4 shown.

[0166] The maximum tractive effort and braking force of the HXD2 type electric locomotive (both in kN, with the speed unit being km / h) are as follows:

[0167]

[0168] Step 2: Simulation and case analysis;

[0169] The numerical simulation results of this case show that, in order to more intuitively present the reduction in coupler force and energy consumption, two performance indicators, namely and E, are defined, and the formulas are as follows:

[0170]

[0171] The numerical simulation results of this case are shown in the attached drawings. Among them, Fig. 5(1) and Fig. 5(2) are the first and second experimental result diagrams. After comparison with the results obtained by the single-mass point method, the multi-mass point method proposed by the present invention can reduce the average energy consumption E and the average coupler force by 6.56% and 11.88% respectively. Fig. 5(3) shows the optimal trajectory of the actual simulation of the operation of a 20,000-ton heavy-haul train on the Datong-Qinhuangdao Railway. The figures shown in Fig. 5 respectively include a speed curve, a control force curve, and a coupler force curve.

[0172] Based on the method provided above, the embodiments of this specification further provide a heavy-haul train trajectory optimization device based on a multi-mass point model, as Figure 6 shown. The device includes:

[0173] A first construction module 610, configured to construct a dynamic model and initial constraint conditions during the operation of the heavy-haul train;

[0174] A second construction module 620, configured to construct an initial objective function according to the dynamic model and initial constraint conditions, with the goal of minimizing the train operation energy consumption and coupler force;

[0175] A variable determination module 630, configured to determine the state variables and control variables during the train operation based on a single-phase optimal control model;

[0176] An objective function obtaining module 640, configured to transform the initial objective function according to the state variables and control variables to obtain an objective function based on a single-phase optimal control model;

[0177] An optimal trajectory determination module 650, configured to determine the optimal trajectory during the operation of the heavy-haul train by using the pseudospectral method according to the objective function and constraint conditions based on a single-phase optimal control model.

[0178] The technical effects achieved by the above device are the same as those achieved by the above method, and the embodiments of this specification will not elaborate.

[0179] This embodiment provides a railway transportation system, and its internal structure diagram can be as Figure 7 shown. The railway transportation system includes a processor, a memory, and a network interface connected through a system bus. Among them, the processor of the railway transportation system is used to provide computing and control capabilities. The memory of the railway transportation system includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the railway transportation system is used to communicate with an external terminal through a network connection.

[0180] Those skilled in the art can understand that Figure 7 the structure shown in

[0181] is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the railway transportation system to which the solution of this application is applied. The specific railway transportation system may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0182] In one embodiment, a railway transportation system is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0183] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0184] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memory can include Read-Only Memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc. The databases involved in the embodiments provided in the present application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in the present application can be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., without limitation.

[0185] It should also be understood that in the embodiments herein, the term "and / or" is merely a description of the association relationship of associated objects, indicating that three relationships can exist. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in this article generally represents an "or" relationship between the associated objects before and after.

[0186] Those of ordinary skill in the art can realize that the units and algorithm steps of the examples described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of this article.

[0187] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0188] In the several embodiments provided in this article, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of units is only a logical function division, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed couplings, direct couplings, or communication connections to each other can be indirect couplings or communication connections through some interfaces, devices, or units, and can also be electrical, mechanical, or other forms of connection.

[0189] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiments in this article.

[0190] Specific embodiments are used in this article to elaborate on the principles and implementation manners of this article. The descriptions of the above embodiments are only used to help understand the method and its core idea of this article; at the same time, for those of ordinary skill in the art, based on the idea of this article, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this article.

Claims

1. A heavy-load train trajectory optimization method based on a multi-mass point model, characterized in that: Methods include: Construct the dynamic model and initial constraints of heavy-load trains during operation; According to the dynamic model and initial constraints, the initial objective function is constructed with the goal of minimizing the train running energy consumption and the coupler force; Based on the single-phase optimal control model, determine the state variables and control variables during train operation; According to the state variables and the control variables, the initial objective function is transformed to obtain the objective function based on the single-phase optimal control model; According to the objective function and constraints based on the single-phase optimal control model, the optimal trajectory of the heavy-load train during operation is determined using the pseudo-spectral method.

2. The method according to claim 1, characterized in that Construct the dynamic model and initial constraints of the heavy-load train during operation, including: Based on the spring damping model of each carriage in the heavy-load train, the coupler force corresponding to each carriage is determined and expressed as: f i in =k i (s i -s i+1 -L i ),i=1,2,...,n-1,where f i in is the coupling force corresponding to the i-th carriage, k i is the elastic coefficient of the i-th coupler, s i is the position of the i-th vehicle, L i is the distance between the i-th car and the i+1-th car when the coupler force is 0; According to the coupler force corresponding to each carriage and the operating parameters of the heavy-load train, the dynamic model of the heavy-load train during operation is constructed, which is expressed as: Among them, m i is the mass of the i-th carriage, u i is the control force of the i-th carriage, v i is the speed of the i-th vehicle. When the i-th carriage is a truck, That is, a freight car can only provide braking force; when it is a locomotive, in and Respectively represent the traction and braking force of the locomotive, f i ro 、f i ra are the running resistance and additional resistance of the i-th carriage respectively. The running resistance includes rolling friction resistance and air resistance; the additional resistance includes the slope and curvature of the train running route; Based on the operating parameters of the heavy-load train, the initial constraints of the heavy-load train during operation are determined. The initial constraints include control force constraints, terminal constraints, speed constraints and safety constraints.

3. The method according to claim 1, characterized in that The initial objective function is expressed by the following formula: in, is the train running energy consumption, is the sum of the coupler forces of all the couplers in the carriages, α1 and α2 are weight coefficients, which are used to balance the influence of energy consumption and coupler force respectively.

4. The method according to claim 2, characterized in that The control force constraint is expressed as: When the carriage is a locomotive: When the carriage is a truck: The terminal constraint is expressed as: s1(t0)=s0,v i (t0)=0,i=1,2,...,n, s1(t f )=s0,v i (t f )=0,i=1,2,...,n; The speed constraint is expressed as: Security constraints:

5. The method according to claim 1, characterized in that The state variables during train operation include at least the position and speed of each carriage, expressed as The control variables include at least the control force on each car, expressed as The objective function based on the single-phase optimal control model is expressed as: Among them, the integral variable Initial time t0 and end time t f .

6. The method according to claim 1, characterized in that According to the objective function and constraints based on the single-phase optimal control model, the optimal trajectory of the heavy-load train during operation is determined using the pseudo-spectral method, including: The preset running time interval of the heavy-load train is normalized in the time domain to obtain the converted time interval, which is expressed as: where t∈[t0,t f ], τ∈[-1,+1]; According to the converted time interval, as well as the objective function and constraint conditions based on the single-phase optimal control model, the conversion objective function and objective constraint conditions are determined. The conversion objective function is expressed as: Performing grid division processing on the converted time interval to obtain multiple grid intervals; In each grid interval, the state variables are approximated using Lagrange polynomials to obtain the discretized target state variables. According to the target state variables and the conversion objective function, the final objective function based on nonlinear programming is determined; According to the final objective function, the optimal control sequence is output to obtain the optimal trajectory of the heavy-load train during operation.

7. The method according to claim 6, characterized in that The target constraints include dynamic constraints, path constraints, integral constraints and terminal constraints. The dynamic constraints are expressed as: The path constraint is expressed as: The integral constraint is expressed as: The terminal constraint is expressed as: v(-1)=v0,s(-1)=s0, v(+1)=v f ,s(+1)=s f 。 8. The method according to claim 1, characterized in that The target state variable is expressed by the following formula: in, is the Lagrange basis function, defined as: The final objective function is expressed as:

9. A heavy-load train trajectory optimization device based on a multi-particle model, characterized in that: The device includes: The first building module is used to build a dynamic model and initial constraints of the heavy-load train during operation; The second building module builds the initial objective function based on the dynamic model and initial constraints, with the goal of minimizing the train operation energy consumption and coupler force; A variable determination module, used to determine the state variables and control variables during the train operation process based on the single-phase optimal control model; An objective function obtaining module is used to convert the initial objective function according to the state variables and the control variables to obtain the objective function based on the single-phase optimal control model; The optimal trajectory determination module is used to determine the optimal trajectory of the heavy-load train during operation according to the objective function and constraints based on the single-phase optimal control model using the pseudo-spectral method.

10. A railway transportation system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When a processor executes the computer program, the method according to any one of claims 1 to 8 is implemented.

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