Train running track optimization method, device, equipment, medium and product

Abstract

The embodiment of the invention provides a train running track optimization method and device, equipment, a medium and a product, and relates to the technical field of rail transit. The method comprises the following steps: acquiring a plurality of input data; constructing a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data; smoothing the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smooth calculation models and a plurality of smooth constraint conditions; constructing a smooth optimization model according to the plurality of smooth calculation models and the plurality of smooth constraint conditions; and according to preset test data, solving the smooth optimization model to obtain multiple pieces of target operation data. According to the method, the calculation model and the constraint condition are smoothed, a discrete or non-derivable model is converted into a continuous and derivable form, the limitation of an optimization algorithm in processing discrete and non-derivable problems is solved, and the method can find a plurality of optimal solutions, so that the running track of the train at the lowest energy consumption is determined, and the running efficiency of the train is improved. And the train energy consumption optimization efficiency is improved.

Description

Technical Field

[0001] This application relates to the technical field of rail transit, and particularly to a method, device, equipment, medium and product for optimizing the running track of a train. Background Art

[0002] With the progress of rail transit technology, the application scope of trains has been expanding day by day. However, with the popularization of trains in diverse application scenarios, the problem of high energy consumption of trains has become increasingly prominent. Therefore, how to effectively reduce the energy consumption of trains has become an urgent problem to be solved in the rail transit industry.

[0003] In the prior art, the energy of trains is mainly utilized efficiently and the energy consumption of trains is reduced by adjusting the running speeds and driving strategies of multiple trains. By dynamically adjusting the train speed and optimizing the running sequence of trains, unnecessary stagnation is avoided, thereby reducing the energy consumption of trains. The optimization of driving strategies includes the intelligent management of the running paths and schedules of trains to minimize the overall energy consumption. In this way, trains can reduce energy consumption on the premise of maintaining punctuality and safety.

[0004] However, the prior art has the problem of low efficiency in optimizing the energy consumption of trains. Due to the highly irregular nature of the running process of trains, it is difficult to effectively apply traditional optimization algorithms, because these algorithms usually rely on derivative information to determine the optimization direction and step size. The highly irregular nature of the running process of trains makes it impossible to fully utilize the tools and methods in mathematical analysis during the optimization process, resulting in problems such as high computational complexity, slow convergence speed, and difficulty in finding the global optimal solution during the determination of the optimization scheme, thereby reducing the efficiency of optimizing the energy consumption of trains. Summary of the Invention

[0005] Embodiments of this application provide a method, device, equipment, medium and product for optimizing the running track of a train to improve the efficiency of optimizing the energy consumption of trains.

[0006] In a first aspect, embodiments of this application provide a method for optimizing the running track of a train, including:

[0007] Obtain a plurality of input data;

[0008] According to the plurality of input data, construct a plurality of calculation models and a plurality of constraint conditions; wherein, the plurality of calculation models and the plurality of constraint conditions are discrete or non-differentiable;

[0009] Perform a smoothing process on the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smoothed calculation models and a plurality of smoothed constraint conditions; wherein, the plurality of smoothed calculation models and the plurality of smoothed constraint conditions are continuous and differentiable;

[0010] Construct a smooth optimization model according to the multiple smooth calculation models and the multiple smooth constraint conditions;

[0011] Solve the smooth optimization model according to the preset test data to obtain multiple target operation data; wherein, the multiple target operation data are used to represent the operation trajectories of the multiple trains when the energy consumption of the multiple trains is the lowest.

[0012] In a possible design, the multiple input data include multiple train data, multiple line data, multiple timetable data, and multiple traction power supply system data, and the multiple calculation models include an energy coupling model and a safe separation operation model. Constructing multiple calculation models and multiple constraint conditions according to the multiple input data includes:

[0013] Construct the energy coupling model according to the multiple traction power supply system data and the multiple timetable data; wherein, the energy coupling model is used to describe the energy transmission relationship between the traction power supply system that supplies energy to the multiple trains and the multiple trains;

[0014] Construct the safe separation operation model according to the multiple train data, the multiple timetable data, and a preset spacing; wherein, the safe separation operation model is used to describe the positional relationship between the multiple trains;

[0015] Construct the multiple constraint conditions according to the multiple train data, the multiple line data, the multiple timetable data, and the multiple traction power supply system data; wherein, the multiple constraint conditions are used to constrain the operation trajectories of the multiple trains and the voltage of the traction power supply system.

[0016] In a possible design, the multiple smooth calculation models include a smooth energy coupling model and a smooth safe separation operation model. The smooth processing of the multiple calculation models and the multiple constraint conditions to obtain multiple smooth calculation models and multiple smooth constraint conditions includes:

[0017] Obtain the equivalent power of the substation; wherein, the equivalent power of the substation is used to represent the electric power provided by the substation to the traction power supply system;

[0018] Construct the smooth energy coupling model according to the equivalent power of the substation and the energy coupling model;

[0019] Construct the smooth safe separation operation model according to the multiple train data and the safe separation operation model;

[0020] Perform smooth processing on the multiple constraint conditions according to the multiple train data and the multiple line data to obtain the multiple smooth constraint conditions.

[0021] In a possible design, the multiple train data includes a position function, multiple braking parameters, multiple speed limit values, and multiple control forces, and the multiple constraint conditions include a position constraint condition, a braking force constraint condition, a speed constraint condition, and a power constraint condition. Smoothing the multiple constraint conditions according to the multiple train data and the multiple line data to obtain the multiple smoothed constraint conditions includes:

[0022] Constructing a smoothed position constraint condition according to the position function, the multiple braking parameters, and the position constraint condition;

[0023] Constructing a smoothed braking force constraint condition according to the position function, the multiple braking parameters, and the braking force constraint condition;

[0024] Constructing a smoothed speed constraint condition according to the multiple speed limit values, the position function, and the speed constraint condition;

[0025] Constructing a smoothed power constraint condition according to the position function, the multiple control forces, and the power constraint condition.

[0026] In a possible design, constructing the smoothed position constraint condition according to the position function, the multiple braking parameters, and the position constraint condition includes:

[0027] Performing function fitting according to the position function to obtain a slope height function; wherein, the slope height function is used to represent the variation of the slope height of the running line of the multiple trains with position;

[0028] Calculating a smoothed slope function according to the slope height function; wherein, the smoothed slope function is used to represent the variation of the slope of the running line of the multiple trains with position;

[0029] Constructing the smoothed position constraint condition according to the smoothed slope function, the multiple braking parameters, and the position constraint condition.

[0030] In a possible design, the multiple braking parameters include the maximum traction force and the maximum braking force corresponding to the constant force area in the train control force boundary, and the maximum traction power and the maximum braking power corresponding to the constant power area. Constructing the smoothed braking force constraint condition according to the position function, the multiple braking parameters, and the braking force constraint condition includes:

[0031] Calculating a speed function according to the position function; wherein, the position function and the speed function are respectively used to represent the variation of the position and speed of the multiple trains with time;

[0032] Construct a first smooth braking force constraint according to the maximum traction force, the maximum braking force, the speed function, and the braking force constraint condition; wherein, the first smooth braking force constraint is used to limit the forces that the multiple trains can exert.

[0033] Construct a second smooth braking force constraint according to the maximum traction power, the maximum braking power, and the braking force constraint condition; wherein, the second smooth braking force constraint is used to limit the maximum power of the multiple trains.

[0034] Generate the smooth braking force constraint according to the first smooth braking force constraint and the second smooth braking force constraint.

[0035] In a second aspect, the present application provides a train operation trajectory optimization device, and the device includes:

[0036] An acquisition module, configured to acquire a plurality of input data.

[0037] A first construction module, configured to construct a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data; wherein, the plurality of calculation models and the plurality of constraint conditions are discrete or non-differentiable.

[0038] A smooth processing module, configured to perform smooth processing on the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smooth calculation models and a plurality of smooth constraint conditions; wherein, the plurality of smooth calculation models and the plurality of smooth constraint conditions are continuous and differentiable.

[0039] A second construction module, configured to construct a smooth optimization model according to the plurality of smooth calculation models and the plurality of smooth constraint conditions.

[0040] A model solving module, configured to solve the smooth optimization model according to preset test data to obtain a plurality of target operation data; wherein, the plurality of target operation data is used to represent the operation trajectories of the multiple trains when the energy consumption of the multiple trains is the lowest.

[0041] In a possible design, the plurality of input data includes a plurality of train data, a plurality of line data, a plurality of timetable data, and a plurality of traction power supply system data, the plurality of calculation models include an energy coupling model and a safe separation operation model, and the first construction module includes:

[0042] An energy coupling model construction unit, configured to construct the energy coupling model according to the plurality of traction power supply system data and the plurality of timetable data; wherein, the energy coupling model is used to describe the energy transmission relationship between the traction power supply system that supplies energy to the multiple trains and the multiple trains.

[0043] A safety separation operation model construction unit for constructing the safety separation operation model according to the multiple train data, the multiple timetable data, and a preset spacing; wherein the safety separation operation model is used to describe the positional relationship between the multiple trains;

[0044] A constraint condition construction unit for constructing the multiple constraint conditions according to the multiple train data, the multiple line data, the multiple timetable data, and the multiple traction power supply system data; wherein the multiple constraint conditions are used to constrain the running trajectories of the multiple trains and the voltage of the traction power supply system.

[0045] In a possible design, the multiple smooth calculation models include a smooth energy coupling model and a smooth safety separation operation model, and the smooth processing module includes:

[0046] An equivalent power acquisition unit for acquiring the substation equivalent power; wherein the substation equivalent power is used to represent the electric power provided by the substation to the traction power supply system;

[0047] A smooth energy coupling model construction unit for constructing the smooth energy coupling model according to the substation equivalent power and the energy coupling model;

[0048] A smooth safety separation operation model construction unit for constructing the smooth safety separation operation model according to the multiple train data and the safety separation operation model;

[0049] A constraint condition smooth processing unit for performing smooth processing on the multiple constraint conditions according to the multiple train data and the multiple line data to obtain the multiple smooth constraint conditions.

[0050] In a possible design, the multiple train data includes a position function, multiple braking parameters, multiple speed limit values, and multiple control forces, the multiple constraint conditions include a position constraint condition, a braking force constraint condition, a speed constraint condition, and a power constraint condition, and the constraint condition smooth processing unit includes:

[0051] A smooth position constraint condition construction device for constructing a smooth position constraint condition according to the position function, the multiple braking parameters, and the position constraint condition;

[0052] A smooth braking force constraint condition construction device for constructing a smooth braking force constraint condition according to the position function, the multiple braking parameters, and the braking force constraint condition;

[0053] A smooth speed constraint condition construction device for constructing a smooth speed constraint condition according to the multiple speed limit values, the position function, and the speed constraint condition;

[0054] A smooth power constraint condition constructing device is used to construct a smooth power constraint condition according to the position function, the multiple control forces, and the power constraint condition.

[0055] In a possible design, the smooth position constraint condition constructing device includes:

[0056] A slope height function fitting component is used to perform function fitting according to the position function to obtain a slope height function; wherein, the slope height function is used to represent the change of the slope height of the running lines of the multiple trains with position.

[0057] A smooth slope function calculating component is used to calculate a smooth slope function according to the slope height function; wherein, the smooth slope function is used to represent the change of the slope of the running lines of the multiple trains with position.

[0058] A smooth position constraint condition constructing component is used to construct the smooth position constraint condition according to the smooth slope function, the multiple braking parameters, and the position constraint condition.

[0059] In a possible design, the multiple braking parameters include the maximum traction force and the maximum braking force corresponding to the constant force area in the train control force boundary, and the maximum traction power and the maximum braking power corresponding to the constant power area. The smooth braking force constraint condition constructing device includes:

[0060] A speed function calculating component is used to calculate a speed function according to the position function; wherein, the position function and the speed function are respectively used to represent the change of the positions and speeds of the multiple trains with time.

[0061] A first smooth braking force constraint condition constructing component is used to construct a first smooth braking force constraint condition according to the maximum traction force, the maximum braking force, and the braking force constraint condition; wherein, the first smooth braking force constraint condition is used to limit the forces that the multiple trains can exert.

[0062] A second smooth braking force constraint condition constructing component is used to construct a second smooth braking force constraint condition according to the maximum traction power, the maximum braking power, the speed function, and the braking force constraint condition; wherein, the second smooth braking force constraint condition is used to limit the maximum power of the multiple trains.

[0063] A smooth braking force constraint condition generating component is used to generate the smooth braking force constraint condition according to the first smooth braking force constraint condition and the second smooth braking force constraint condition.

[0064] In a third aspect, the present application provides an electronic device, including: a processor, and a memory communicatively connected to the processor;

[0065] The memory stores computer-executable instructions;

[0066] When the processor executes the computer-executable instructions stored in the memory, it is used to implement the train operation trajectory optimization method described in any item of the first aspect.

[0067] In a fourth aspect, the present application provides a computer-readable storage medium storing computer-executable instructions, which when executed by a processor, are used to implement the train operation trajectory optimization method described in any item of the first aspect.

[0068] In a fifth aspect, the present application provides a computer program product including a computer program, which when executed by a processor, is used to implement the train operation trajectory optimization method described in any item of the first aspect.

[0069] A train operation trajectory optimization method, device, equipment, medium and product provided by the present application, the method includes: obtaining a plurality of input data; constructing a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data; performing smoothing processing on the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smoothed calculation models and a plurality of smoothed constraint conditions; constructing a smoothed optimization model according to the plurality of smoothed calculation models and the plurality of smoothed constraint conditions; solving the smoothed optimization model according to preset test data to obtain a plurality of target operation data. The train operation trajectory optimization method of the present application performs smoothing processing on the calculation model and the constraint conditions, and converts the originally discrete or non-differentiable model into a continuous and differentiable form. This process solves the limitations of traditional optimization algorithms in dealing with irregularity and non-differentiability problems, enabling the optimization process to make full use of tools and methods in mathematical analysis. By constructing a smoothed optimization model and solving it using test data, this method can effectively find multiple optimal solutions, thereby determining the train operation trajectory under the condition of the lowest energy consumption. This method improves the efficiency of train energy consumption optimization. Description of the Drawings

[0070] The drawings here are incorporated into the description and form a part of this description, showing embodiments consistent with the present application, and are used together with the description to explain the principles of the present application.

[0071] Figure 1 It is a schematic diagram of the application scenario of the train operation trajectory optimization method provided by the embodiment of the present application;

[0072] Figure 2 It is a schematic flowchart of the train operation trajectory optimization method provided by the embodiment of the present application;

[0073] Figure 3It is the equivalent circuit model diagram of the multi-train traction power supply system provided by the embodiments of the present application;

[0074] Figure 4 It is the schematic diagram of the minimum allowable safety distance between adjacent trains provided by the embodiments of the present application;

[0075] Figure 5 It is the structural schematic diagram of the train operation trajectory optimization device provided by the embodiments of the present application;

[0076] Figure 6 It is the hardware structure schematic diagram of the electronic device provided by the embodiments of the present application.

[0077] Through the above-mentioned drawings, the clear embodiments of the present application have been shown, and there will be more detailed descriptions hereinafter. These drawings and text descriptions are not intended to limit the scope of the concept of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by referring to specific embodiments. Detailed implementation manners

[0078] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all the implementation manners consistent with the present application. On the contrary, they are merely examples of the devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0079] In the embodiments of the present application, terms such as "first" and "second" are used to distinguish the same items or similar items with basically the same functions and roles. Those skilled in the art can understand that the terms "first" and "second" do not limit the quantity and execution order, and the terms "first" and "second" do not necessarily mean different. It should be noted that in the embodiments of the present application, words such as "exemplary" or "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Exactly speaking, using words such as "exemplary" or "for example" aims to present relevant concepts in a specific manner. In the embodiments of the present application, "at least one" means one or more, and "a plurality" means two or more.

[0080] It should be noted that in the embodiments of the present application, "when...", can refer to the instant when a certain situation occurs, or can refer to a period of time after a certain situation occurs. The embodiments of the present application do not make specific limitations in this regard. In addition, a train operation trajectory optimization method, device, equipment, medium and product provided by the embodiments of the present application are only examples, and a train operation trajectory optimization method, device, equipment, medium and product may also include more or less content.

[0081] To facilitate a clear description of the technical solutions of the embodiments of the present application, the following briefly introduces some terms and technologies involved in the embodiments of the present application:

[0082] Constraint condition: It refers to the rules or limiting conditions used to restrict variables or system behavior in an optimization problem or system design. These conditions can be mathematical expressions or logical rules that specify the value range of variables or the relationships between variables.

[0083] Smoothing processing: It is a mathematical method aimed at converting discrete or discontinuous functions or data into a continuous and differentiable form. This processing usually involves using interpolation, fitting or other numerical methods to make the originally possibly abrupt or irregular curve smooth, so as to facilitate differential and optimization analysis.

[0084] Traction power supply system: It refers to the infrastructure system that provides electrical energy for electrically driven trains. It usually includes substations, catenaries, feeder lines and related control equipment. The substation is responsible for converting high-voltage electricity into a voltage level suitable for trains, and then transmitting the electricity to the train through the catenary.

[0085] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. On the contrary, they are only examples of devices and methods consistent with some aspects of the present invention as detailed in the appended claims.

[0086] The technical solutions of the present invention will be described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present invention will be described below with reference to the drawings.

[0087] To clearly understand the technical solution of this application, the solutions of the prior art will be introduced in detail first. In the prior art, the running speeds and driving strategies of multiple trains are adjusted to achieve efficient energy utilization. By dynamically adjusting the train speeds and optimizing the running sequences of the trains, unnecessary stops are avoided, thereby reducing the energy consumption of the trains. The optimization of the driving strategy includes the intelligent management of the train running routes and timetables to minimize the overall energy consumption. In this way, the trains can reduce the energy consumption on the premise of maintaining punctuality and safety.

[0088] However, there is a problem of low optimization efficiency of train energy consumption in the prior art. Due to the highly irregular nature of the train operation process, it is difficult to effectively apply traditional optimization algorithms because these algorithms usually rely on derivative information to determine the optimization direction and step size. The highly irregular nature of the train operation process makes it impossible to fully utilize the tools and methods in mathematical analysis during the optimization process, resulting in problems such as high computational complexity, slow convergence speed, and difficulty in finding the global optimal solution during the determination of the optimization solution, thereby reducing the optimization efficiency of train energy consumption.

[0089] Therefore, aiming at the problem of low optimization efficiency of train energy consumption in the prior art, it is found in the research that to solve this problem, the irregularity of the train operation process can be optimized to make the optimized train operation process continuous, so that mathematical optimization tools can be effectively applied to achieve energy consumption optimization: ① The operation data of the train can be obtained, and based on the operation data of the train, an operation model of the train can be constructed to transform the train operation process into a mathematical model. ② An optimization algorithm can be used to optimize the train operation model, reduce the irregularity of the train operation model, and make the optimized train operation model continuous, so that mathematical optimization tools can be effectively applied. ③ Multiple constraint conditions can be constructed for the optimized train operation model, and by combining the train operation model and multiple constraint conditions, a nonlinear optimization problem can be constructed, and the train energy consumption can be optimized by solving this nonlinear optimization problem.

[0090] Specifically:

[0091] It is possible to: collect and analyze the operation data of the train, construct a mathematical model to describe the train operation process. Then apply an optimization algorithm to optimize the model, reduce its irregularity, and make the model continuous. And set multiple constraint conditions for the optimized model, and these conditions can include key factors in actual operation such as safety standards, timetable requirements, and track capacity limitations. Finally, combine these constraint conditions to construct a nonlinear optimization problem, and optimize the train energy consumption and operation efficiency by solving this problem to ensure the minimization of energy consumption while meeting all operation requirements.

[0092] The train operation trajectory optimization method according to the embodiments of the present application constructs a calculation model and constraint conditions based on the input data related to the train, and then smooths the calculation model and constraint conditions, converting the originally discrete or non-differentiable model and constraint conditions into a continuous and differentiable form. This process solves the limitations of traditional optimization algorithms in dealing with irregularity and non-differentiability problems, enabling the optimization process to make full use of the tools and methods in mathematical analysis. Subsequently, a smooth optimization model is constructed based on the smooth calculation model and smooth constraint conditions. By constructing the smooth optimization model and using test data for solution, this method can effectively find multiple optimal solutions, thereby determining the train operation trajectory under the condition of the lowest energy consumption. This method improves the efficiency of train energy consumption optimization.

[0093] Based on the above creative findings, the technical solution of the present application is proposed.

[0094] The application scenarios of the train operation trajectory optimization method provided by the embodiments of the present invention are introduced below. Figure 1 It is a schematic diagram of the application scenario of the train operation trajectory optimization method provided by the embodiments of the present application. As Figure 1 shown, in this application scenario, it includes a mobile terminal 101 and a server 102. The mobile terminal 101 sends multiple input data to the server 102. The server 102 constructs a calculation model and constraint conditions based on the multiple input data, and smooths them. Subsequently, a smooth optimization model is constructed based on the smooth calculation model and smooth constraint conditions. The mobile terminal 101 sends test data to the server 102. The server 102 solves the smooth optimization model according to the test data to obtain multiple optimal solutions, and the multiple optimal solutions are used to represent the train operation trajectory when the train has the lowest energy consumption.

[0095] The embodiments of the present invention are introduced below in conjunction with the accompanying drawings of the specification.

[0096] Figure 2 It is a schematic flowchart of the train operation trajectory optimization method provided by the embodiments of the present application. As Figure 2 shown, in this embodiment, the execution subject of the embodiments of the present invention is the server. Then the train operation trajectory optimization method provided by this embodiment includes the following steps:

[0097] S201. Obtain multiple input data.

[0098] Specifically, various input data related to train operation can be collected through a sensor network, historical operation data records, or an external data interface, etc. These input data may include the train's speed, acceleration, position, and track conditions, etc. Obtaining these data can provide the necessary basic information for subsequent calculation model construction to accurately simulate the train operation trajectory.

[0099] S202. Construct multiple computational models and multiple constraint conditions based on multiple input data; among them, the multiple computational models and multiple constraint conditions are discrete or non-differentiable.

[0100] Specifically, data analysis tools and algorithms such as machine learning and physical modeling can be used to transform the obtained input data into mathematical models and constraint conditions. These models and constraint conditions are used to describe the physical characteristics, operation limitations, and environmental impacts of train operation, etc. Constructing these models and constraint conditions can provide an accurate and operable mathematical framework for the subsequent optimization process, so that the train operation trajectory can be effectively evaluated and improved during the optimization process.

[0101] S203. Smooth the multiple computational models and multiple constraint conditions to obtain multiple smooth computational models and multiple smooth constraint conditions; among them, the multiple smooth computational models and multiple smooth constraint conditions are continuous and differentiable.

[0102] Specifically, approximation functions, regularization methods, or other smoothing methods can be used to transform the originally discrete or non-differentiable models and constraint conditions into continuous and differentiable forms, obtaining multiple smooth computational models and multiple smooth constraint conditions. Smoothing can eliminate the discontinuities and non-differentiabilities in the models, enabling the subsequent optimization process to use gradient descent optimization algorithms for solution. This processing helps to improve the stability and efficiency of the optimization process, thereby accurately determining the train operation trajectory under the condition of the lowest energy consumption.

[0103] S204. Construct a smooth optimization model according to the multiple smooth computational models and multiple smooth constraint conditions.

[0104] Specifically, the smooth computational models can be used as the objective function, and the smooth constraint conditions can be used as the limiting conditions of the optimization problem to construct a mathematical optimization problem. This optimization problem is usually a continuous and differentiable function, suitable for using gradient optimization algorithms for solution. After constructing the smooth optimization model, the parameter configuration of train operation can be found through optimization calculations under the given constraint conditions, so as to achieve the goal of the lowest energy consumption.

[0105] S205. Solve the smooth optimization model according to the preset test data to obtain multiple target operation data; among them, the multiple target operation data are used to represent the operation trajectories of multiple trains when the energy consumption of multiple trains is the lowest.

[0106] Specifically, the test data can be input into the smooth optimization model, and optimization algorithms such as gradient descent, Newton's method, or genetic algorithms can be used to solve it. The preset test data is used to simulate the actual operating conditions and provide the initial conditions and parameters required by the optimization model. By solving the smooth optimization model, a set of optimized operating parameters, that is, multiple target operating data, can be obtained, which are used to indicate the train's operating trajectory under the condition of the lowest energy consumption.

[0107] A train operation trajectory optimization method provided by this embodiment includes: obtaining multiple input data; constructing multiple calculation models and multiple constraint conditions according to the multiple input data; performing smooth processing on the multiple calculation models and multiple constraint conditions to obtain multiple smooth calculation models and multiple smooth constraint conditions; constructing a smooth optimization model according to the multiple smooth calculation models and multiple smooth constraint conditions; and solving the smooth optimization model according to the preset test data to obtain multiple target operating data. A train operation trajectory optimization method achieves the following technical effects: performing smooth processing on the calculation models and constraint conditions, converting the originally discrete or non-differentiable models into continuous and differentiable forms. This process solves the limitations of traditional optimization algorithms in dealing with irregularities and non-differentiable problems, enabling the optimization process to make full use of tools and methods in mathematical analysis. By constructing a smooth optimization model and using test data for solution, this method can effectively find multiple optimal solutions, thereby determining the train's operating trajectory under the condition of the lowest energy consumption, and this method improves the efficiency of train energy consumption optimization.

[0108] In a possible design, the multiple input data includes multiple train data, multiple line data, multiple timetable data, and multiple traction power supply system data, and the multiple calculation models include an energy coupling model and a safety separation operation model. S202 constructing multiple calculation models and multiple constraint conditions according to the multiple input data includes:

[0109] S2021. Construct an energy coupling model according to the multiple traction power supply system data and multiple timetable data; wherein, the energy coupling model is used to describe the energy transmission relationship between the traction power supply system that supplies energy to multiple trains and the multiple trains.

[0110] Specifically, system modeling technology can be used to combine the data of the traction power supply system, such as voltage, current, and power, with the train operation timetable, such as the train's departure time, running interval, etc., to establish a mathematical model that describes the energy transmission relationship between the power supply system and the train. The energy coupling model can simulate how the power supply system provides energy to the train, thereby considering the efficiency and limitations of energy transmission in the optimization process.

[0111] For example, Figure 3This is the equivalent circuit model diagram of the multi-train traction power supply system provided by the embodiments of the present application. As Figure 3 shown, for a typical urban rail operation line, its structure is a two-way line type, and there are multiple substations distributed along the line. Every two adjacent substations form a power supply section. In the power supply section, multiple trains may be running simultaneously in both line types, and these trains are all supplied with electric energy by the substations on both sides. According to the electrical characteristics, the substation can be equivalent to a voltage source in series with a resistor, and the train can be equivalent to a power source. The transmission loss of electric energy on the traction network is characterized by a resistor linearly related to the line distance, thus constructing Figure 3 the equivalent circuit model diagram.

[0112] Figure 3 In u , starting from the left substation, all the nodes are numbered in sequence as {0, 1, …, N + 1} in the clockwise direction, where N is the number of trains. Among them, nodes 0 and N u + 1 represent the bilateral substation nodes, and N u is the number of upward trains. U n represents the voltage of node n, I n represents the branch current between nodes n and n + 1, R n represents the equivalent resistance between nodes n and n + 1, P n represents the electric power of train n, U s and R s represent the equivalent voltage and internal resistance of the substation respectively. It can be seen from this equivalent circuit model diagram that at any moment t, the following energy coupling relationship is satisfied between the train and the traction power supply system:

[0113]

[0114] Among them, is the electric power of train n at moment t, is the voltage of node n at moment t, is the branch current between nodes n - 1 and n at moment t, is the branch current between nodes n and n + 1 at moment t. The branch current can be calculated according to Ohm's law as follows:

[0115]

[0116]

[0117] Among them, is the voltage of node n - 1 at moment t, is the voltage of node n at moment t, is the equivalent resistance between nodes n - 1 and n at moment t, Let \(R_{eq}\) be the equivalent resistance between node \(n\) and node \(n + 1\) at time \(t\). The electric power of the train is calculated as follows:

[0118]

[0119] where \(f\) n and \(v\) n represent the control force and speed of train \(n\) respectively, represents the efficiency of the train traction drive system. The power \(P\) of the substation s can be calculated through the node voltage and the resistance between nodes as follows:

[0120]

[0121] In addition, to ensure the healthy operation of the catenary during train operation, the node voltage should only fluctuate between the minimum allowable voltage \(U\) min and the maximum allowable voltage \(U\) max :

[0122]

[0123] S2022. Construct a safe separation operation model based on multiple train data, multiple timetable data, and a preset spacing; wherein, the safe separation operation model is used to describe the positional relationship between multiple trains.

[0124] Specifically, train data such as speed, acceleration, braking distance, etc., and timetable data such as departure time, arrival time, and stop time, etc., can be used, combined with the preset safe spacing requirements, to establish a mathematical model that is used to ensure the safe distance between trains during operation. The safe separation operation model can ensure that there is a sufficient safe distance between trains when optimizing the train operation trajectory, preventing collisions or other safety accidents.

[0125] For example, in a two-way urban rail line, for any consecutive train formation in any line, the distance between any adjacent trains should always be not less than a minimum safe spacing, which consists of two parts: the emergency braking distance \(L\) n of the train and a safety margin \(L\) c , Figure 4 is a schematic diagram of the minimum allowable safe spacing between adjacent trains provided by the embodiment of the present application. As shown in Figure 4 , at any time \(t\), the minimum allowable safe spacing between adjacent trains \(n\) and \(n - 1\) is expressed as follows:

[0126]

[0127] where \(L\) c is a constant, \(L\) nIt is jointly determined by the running speed and braking performance of train n and is calculated as follows:

[0128]

[0129] Among them, represents the braking deceleration that can be provided by train n with the maximum braking force at time t, represents the running speed of train n at time t. Therefore, the safety separation condition of adjacent trains can be expressed by the train state as follows:

[0130]

[0131] Among them, and represent the positions of train n and n - 1 at time t, respectively.

[0132] S2023. Construct multiple constraint conditions based on multiple train data, multiple line data, multiple timetable data, and multiple traction power supply system data; among them, the multiple constraint conditions are used to constrain the running trajectories of multiple trains and the voltage of the traction power supply system.

[0133] Specifically, a series of mathematical constraint conditions can be established using train data, line data, timetable data, and traction power supply system data. These constraint conditions are used to limit the running trajectories of trains to ensure that they operate within a safe and reliable range, while meeting the requirements of energy consumption, timetable, and power supply system. These constraint conditions play the role of boundaries and limitations in the optimization process to ensure that the optimization results are feasible and effective in actual operation.

[0134] For example, write the longitudinal dynamics equation of the train and many running constraints such as safety, punctuality, and comfort. The dynamic process of the longitudinal movement of the train should conform to Newton's second law of motion:

[0135]

[0136] Among them, a, b, and c are the basic resistance coefficients of the train, represents the mass of train n, represents the acceleration due to gravity, represents the position of the line slope at.

[0137] The dynamic running constraints suffered by the train mainly include control force constraints, speed limit constraints, and start - point and end - point constraints as follows:

[0138]

[0139] Among them, and respectively represent the maximum tractive force and the maximum braking force that can be applied determined by the train speed, represents the line speed limit at the nth position of the train, and respectively represent the departure time and the arrival time of the train, represents the position of the end of the line, and the starting position of the line is defaulted to 0.

[0140] After obtaining the energy coupling model, the safe separation operation model and multiple constraint conditions, the train operation trajectory optimization problem can be transformed into an optimal control problem, and the optimal control problem can be expressed as:

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] This optimal control problem aims to minimize the electric energy consumed by the substation during the operation of multiple trains by co-optimizing the operation speed curves of all trains, under the satisfaction of numerous constraints such as the train dynamics equation, operation constraints, vehicle-network energy coupling relationship, and safe separation conditions between adjacent trains. Therefore, the state variable x of this optimal control problem is the positions and speeds of all trains, a total of 2N, and the control variable u is the control forces of all trains, a total of N, which are expressed as follows:

[0153]

[0154]

[0155] The technical effects of this solution in this embodiment are as follows: An energy coupling model, a safe separation operation model, and multiple constraint conditions are constructed. The energy coupling model describes the energy transfer relationship between the traction power supply system and the train, ensuring the efficient utilization of energy. The safe separation operation model ensures the safety of train operation by describing the positional relationship between trains, preventing collisions or overly close distances between trains. The introduction of multiple constraint conditions effectively constrains the running trajectory of the train and the voltage of the traction power supply system, ensuring the stability and safety of system operation.

[0156] In a possible design, the multiple smooth calculation models include a smooth energy coupling model and a smooth safe separation operation model. S203 performs smoothing on the multiple calculation models and the multiple constraint conditions to obtain multiple smooth calculation models and multiple smooth constraint conditions, including:

[0157] S2031. Obtain the equivalent power of the substation; wherein, the equivalent power of the substation is used to represent the electric power provided by the substation to the traction power supply system.

[0158] Specifically, sensors and monitoring devices can be used to measure parameters such as the output voltage and current of the substation in real time, and the equivalent power of the substation can be calculated through electrical calculation formulas. In addition, historical operation data can be combined to predict the power output of the substation under different operating conditions. Obtaining the equivalent power of the substation can provide necessary input parameters for constructing the smooth energy coupling model to accurately describe the energy transfer relationship between the substation and the traction power supply system.

[0159] S2032. Construct a smooth energy coupling model based on the equivalent power of the substation and the energy coupling model.

[0160] Specifically, smoothing techniques such as interpolation, fitting, or regularization methods can be used to transform the discrete or discontinuous energy coupling model into a continuous and differentiable form, and at the same time incorporate the equivalent power of the substation as an input parameter. The construction of the smooth energy coupling model aims to provide an accurate and computable framework to effectively simulate and optimize the energy transfer relationship between the traction power supply system and the train during the optimization process, thereby minimizing the energy consumption of train operation.

[0161] For example, there is a max function in the energy coupling model, which is non-differentiable at the origin. By introducing a pseudo-control variable representing the equivalent power of the substation, which is always non-negative and not less than the actual power of the substation, the smooth energy coupling model can be expressed as:

[0162]

[0163]

[0164] Introducing a pseudo-control variable can achieve the smoothing of the objective function. Since it relaxes the actual power constraint of the substation, it replaces the non-differentiable maximum function with a new variable that is always greater than or equal to the actual power. This relaxation method does not affect the optimality of the problem because the substation energy consumption increases monotonically with power. Therefore, the introduced pseudo-variable can make the objective function smooth and differentiable without introducing errors, facilitating subsequent optimization and solution.

[0165] S2033. Construct a smooth safe separation operation model based on multiple train data and the safe separation operation model.

[0166] Specifically, by using train data in combination with the safe separation operation model and applying smoothing techniques such as function approximation, interpolation, or regularization methods, the originally discrete or discontinuous model can be transformed into a continuous and differentiable form. The construction of the smooth safe separation operation model aims to ensure that the safe distance between trains can be accurately calculated and adjusted during the optimization process, so that when optimizing the train operation trajectory, both the safety of the trains and the energy consumption optimization effect can be improved.

[0167] For example, the maximum deceleration that a train can apply needs to be calculated through the train longitudinal dynamics equation. The safe separation constraint between adjacent trains can be re-modeled as a set of the following two constraints to achieve the smoothing of the functional relationship:

[0168]

[0169]

[0170]

[0171] Among them, and are the smooth maximum braking forces that the train can provide using the maximum braking force and maximum braking power respectively, and is the smooth slope function. Re-modeling the safe separation constraint between adjacent trains as two constraint sets can achieve the smoothing of the functional relationship. Because by expressing the maximum braking force and maximum braking power as smooth functions respectively, the discontinuity caused by the changes in speed and braking force in the original constraint can be avoided. This decomposition enables each constraint to remain continuous and differentiable under its specific conditions, thus achieving the smoothing of the constraint conditions as a whole.

[0172] S2034. Smoothly process multiple constraint conditions based on multiple train data and multiple line data to obtain multiple smooth constraint conditions.

[0173] Specifically, train data and line data can be utilized to smooth the constraint conditions related to these parameters. Methods such as function fitting, interpolation, or regularization techniques are adopted to transform the originally discrete or discontinuous constraint conditions into a continuous and differentiable form. The construction of smooth constraint conditions aims to ensure that during the optimization process, the constraint conditions can be accurately applied and adjusted, thereby improving the efficiency and stability of the optimization algorithm.

[0174] The technical effect of this solution in this embodiment is as follows: By smoothing the energy coupling model and the safe separation operation model, combining the equivalent power of the substation with train and line data, the originally discrete or non-differentiable models and constraint conditions are transformed into a continuous and differentiable form. This process improves the computational efficiency and solution accuracy of the optimization model, enabling the effective simulation and adjustment of the energy transfer relationship between the train and the power supply system and the safe distance between trains when optimizing the train operation trajectory. Through the smoothing process, the efficiency and accuracy of the optimization solution process are enhanced.

[0175] In a possible design, multiple train data includes a position function, multiple braking parameters, multiple speed limit values, and multiple control forces, and multiple constraint conditions include position constraint conditions, braking force constraint conditions, speed constraint conditions, and power constraint conditions. S2034 smooths the multiple constraint conditions according to the multiple train data and the multiple line data to obtain multiple smooth constraint conditions, including:

[0176] S20341. Construct a smooth position constraint condition according to the position function, multiple braking parameters, and the position constraint condition.

[0177] Specifically, smoothing techniques such as function fitting or interpolation methods can be applied to transform the position constraint condition into a continuous and differentiable form to obtain a smooth position constraint condition. The construction of the smooth position constraint condition aims to ensure that during the optimization process, the position constraint of the train can be accurately calculated and adjusted, thereby improving the safety of train operation and the efficiency of the optimization algorithm, while ensuring the precise positioning and safe operation of the train on the track.

[0178] S20342. Construct a smooth braking force constraint condition according to the position function, multiple braking parameters, and the braking force constraint condition.

[0179] Specifically, smoothing techniques can be applied to transform the braking force constraint condition into a continuous and differentiable form to obtain a smooth braking force constraint condition. The construction of the smooth braking force constraint condition aims to ensure that during the optimization process, the application of the braking force can be accurately calculated and adjusted, thereby improving the braking efficiency and safety of the train, while optimizing the train operation trajectory to minimize energy consumption.

[0180] S20343. Construct a smooth speed constraint condition based on multiple speed limit values, position functions, and speed constraint conditions.

[0181] Specifically, the original speed constraint condition can be smoothed by combining the speed limit information on the track with the motion state of the train, and the speed constraint condition can be transformed into a continuous and differentiable form. The construction of the smooth speed constraint condition aims to ensure that during the optimization process, the adjustment of the train speed can be accurately calculated, thereby improving the safety and efficiency of train operation, and ensuring that the speed of the train in different track sections meets the specified speed limit requirements.

[0182] For example, the speed limit value of an urban rail line is generally a piecewise constant function with respect to position, and it is discontinuous at the position where the speed limit changes. In view of this characteristic of constant jump, a Sigmoid function can be introduced here and modified to process the speed limit. The standard Sigmoid function can achieve a jump from 0 to 1. By modifying the Sigmoid function, a smooth change between adjacent speed limits and can be achieved. The smooth functional relationship of the two-piece constant speed limit value function h with respect to position is as follows:

[0183]

[0184] where is the position of train n, is the smooth function of the two adjacent piecewise constant speed limit value functions h with respect to position , is the center position of the Sigmoid function drawn according to the speed limits and , and is a constant coefficient.

[0185] However, this fitting method will inevitably change the feasible region of the train speed. In order to better control the fitting error, the Sigmoid function drawn according to the speed limits and is adjusted as follows:

[0186]

[0187] where represents the speed limit change position, and is a constant coefficient. Based on the above analysis, for a line containing K speed limits , based on the initial speed limit , through the accumulation of multiple modified Sigmoid functions, the piecewise constant line speed limit can be fitted to the position In a smooth function, as follows:

[0188]

[0189] Wherein, is the smooth speed limit value. By accumulating multiple variant Sigmoid functions, the piecewise constant line speed limit can be fitted into a smooth function of position. Since the Sigmoid function has a smooth transition characteristic, it can provide a continuous change at the point where the speed limit changes. This method avoids the discontinuity of the traditional piecewise constant function at the speed limit change point, making the speed limit function continuously differentiable throughout the line, thereby realizing the smooth processing of speed and facilitating the solution of the optimization problem.

[0190] S20344. Construct a smooth power constraint according to the position function, multiple control forces and power constraint conditions.

[0191] Specifically, by combining the position information of the train with the control force parameters, the original power constraint condition can be smoothed, and the power constraint condition can be transformed into a continuous and differentiable form. The construction of the smooth power constraint aims to ensure that during the optimization process, the power output of the train can be accurately calculated, thereby optimizing the operation performance of the train, and at the same time ensuring that the application of power meets the capabilities and safety standards of the power supply system, realizing the efficient and safe operation of the train.

[0192] For example, the electric power of the train is jointly determined by the train control force , speed and the efficiency of the traction drive system. The efficiency of the traction drive system changes jointly with the train control force and speed. The dynamic efficiency is an abstract parameter and cannot be directly measured. However , , can be directly collected by on-vehicle devices. Therefore, here, according to the actual operation data of the train, is directly fitted into a smooth plane about and through the following second-order polynomial:

[0193]

[0194] Wherein, is the fitted smooth plane, are the coefficients of the second-order polynomial. Next, determine each coefficient by solving the following problem :

[0195]

[0196]

[0197] Among them, is the actual train electric power data collected by the on-vehicle device. This problem can be solved by the semi-definite optimization method. Since the constraint condition is a semi-definite Hessian matrix, it can be guaranteed to be about and a smooth plane.

[0198] By fitting the train electric power to a second-order polynomial form with respect to the train control force and speed , a smooth plane is created to approximate the actual power data. Since the traction drive system efficiency is dynamically changing and difficult to measure directly, by collecting actual operation data and using second-order polynomial fitting, the change of can be smoothly represented. By using the semi-definite optimization method to determine the polynomial coefficients, the smoothness and stability of the fitting process are ensured. Thus, in the optimization problem, the change of the electric power can be processed continuously and differentiably, avoiding the influence of discontinuity on the optimization algorithm.

[0199] The technical effect of this solution in this embodiment is: by generating smooth position constraint conditions, smooth braking force constraint conditions, smooth speed constraint conditions and smooth power constraint conditions, the continuity and differentiability of the constraint conditions are improved. This process ensures that in the optimization solution process, various physical and operation constraints can be accurately incorporated into the calculation model, reducing the computational complexity and improving the convergence speed and accuracy of the solution.

[0200] In a possible design, S20341 constructs smooth position constraint conditions according to the position function, multiple braking parameters and position constraint conditions, including:

[0201] S203411: Perform function fitting according to the position function to obtain a slope height function; among them, the slope height function is used to represent the change of the slope height of the running lines of multiple trains with position.

[0202] Specifically, the position function can be used to describe the position change of the train on the track, and by collecting the elevation data along the track and applying function fitting techniques such as polynomial fitting and spline interpolation, a continuous slope height function can be generated. The slope height function is used to represent the change of the elevation of the train running line with position, thus providing a basis for further calculating the smooth slope function. The construction of the slope height function aims to accurately describe the terrain features of the track so as to consider the influence of the terrain on the train energy consumption and power demand when optimizing the train running trajectory.

[0203] Among them, the elevation of the train operation line refers to the vertical height of a certain point on the line relative to a reference plane. This reference plane usually refers to the sea level or other known reference planes. The elevation change will cause the line to go uphill or downhill, which has a direct impact on the traction demand and braking requirements of the train. Therefore, it needs to be considered in detail in railway design and operation.

[0204] S203412. Calculate the smooth slope function according to the slope height function; among them, the smooth slope function is used to represent the change of the slope of the operation lines of multiple trains with position.

[0205] Specifically, the slope height function represents the change of the elevation of the track with position. By calculating the first derivative of this function, the slope of the track, that is, the smooth slope function, can be obtained. This smooth slope function is used to describe the change of the track slope with position and provides a continuous and differentiable representation. The construction of the smooth slope function aims to provide accurate terrain information for the optimization of the train operation trajectory, so that the power output and energy consumption strategy of the train can be better adjusted when considering the terrain impact.

[0206] For example, the ramps of urban rail lines can generally be divided into multiple sections, each section corresponding to a constant slope. The slope values of the lines in different sections are different. Therefore, at the point where the ramp changes, the slope function is non-differentiable.

[0207] The line ramp is usually irregular in shape. Here, the discrete Fourier transform is introduced, and the slope height is fitted into a smooth function about the position through the accumulation of trigonometric functions. The specific form is as follows:

[0208]

[0209] Among them, is the fitted smooth slope height function, , , and are the constants solved by the discrete Fourier transform. L is the number of trigonometric function terms used for fitting, usually set artificially. The higher the number of terms, the better the fitting effect. Then, the obtained smooth slope height function is differentiated with respect to the position to obtain the smooth function relationship between the tangent value of the ramp and the position:

[0210]

[0211] Based on this, the smooth function relationship of the slope function with respect to the position is realized:

[0212]

[0213] By introducing the discrete Fourier transform, the originally piecewise-constant and non-differentiable slope function at the section junctions is transformed into a smooth function. By accumulating trigonometric functions, the slope height is fitted into a smooth function of the position , and then the derivative of this function is taken to obtain the smooth functional relationship between the tangent value of the ramp and the position. This method eliminates the discontinuity at the slope change points, making it possible to be represented continuously and differentiably.

[0214] S203413. Construct a smooth position constraint condition according to the smooth slope function, multiple braking parameters, and position constraint conditions.

[0215] Specifically, using the track slope change information provided by the smooth slope function and combining multiple braking parameters, such as braking distance and deceleration, etc., the position constraint conditions are adjusted and smoothed. Through mathematical modeling and optimization techniques, these factors are integrated into a continuous and differentiable smooth position constraint condition. This smooth position constraint condition is used to ensure that the train can safely adapt to the terrain changes of the track during operation and maintain stability during braking.

[0216] The technical effect of this solution in this embodiment is: By accurately modeling and smoothing the terrain information of the train operation line, a continuous and differentiable smooth position constraint condition is generated, ensuring that during the train operation trajectory optimization process, the influence of the terrain on the train's power and braking performance can be fully considered, thereby achieving the improvement of the train operation safety and energy consumption efficiency, and ensuring the smooth and efficient operation of the train under complex terrain conditions.

[0217] In a possible design, the multiple braking parameters include the maximum traction force and the maximum braking force corresponding to the constant force area in the train control force boundary, and the maximum traction power and the maximum braking power corresponding to the constant power area. S20342 constructs a smooth braking force constraint condition according to the position function, multiple braking parameters, and braking force constraint conditions, including:

[0218] S203421. Calculate the speed function according to the position function; where the position function and the speed function are respectively used to represent the positions and speeds of multiple trains changing with time;

[0219] Specifically, the position function describes the variation of the train's position over time. By taking the first derivative of this function, the velocity function can be obtained, which represents the variation of the train's velocity over time. The calculation of the velocity function provides the necessary motion information for further dynamic analysis. Especially when constructing the smooth braking force constraint conditions, the velocity function is used to evaluate the dynamic requirements and braking capabilities of the train at different speeds, thus ensuring that the train can efficiently adjust its speed and power output within the safety and power limits during operation.

[0220] S203422. Construct a first smooth braking force constraint condition according to the maximum traction force, maximum braking force, and braking force constraint conditions; wherein, the first smooth braking force constraint condition is used to limit the forces that multiple trains can exert.

[0221] Specifically, it is first necessary to clarify the maximum traction force and maximum braking force of the train under different operating trajectories, and then, in combination with the braking force constraint conditions, use smoothing techniques to transform these discrete or piecewise constraint conditions into a continuous and differentiable form. The first smooth braking force constraint condition is used to ensure that the forces exerted by the train during operation are always within the safety and physical limits.

[0222] S203423. Construct a second smooth braking force constraint condition according to the maximum traction power, maximum braking power, velocity function, and braking force constraint conditions; wherein, the second smooth braking force constraint condition is used to limit the maximum power of multiple trains.

[0223] Specifically, it is first necessary to determine the maximum traction power and maximum braking power of the train at different speeds, and then, in combination with the velocity function and braking force constraint conditions, apply smoothing techniques to transform these discrete or piecewise power limit conditions into a continuous and differentiable form. The second smooth braking force constraint condition is used to ensure that the power output of the train during operation is always within the safety and physical limits, thereby ensuring the balance of the dynamic and braking performance of the train at different speeds.

[0224] S203424. Generate a smooth braking force constraint condition according to the first smooth braking force constraint condition and the second smooth braking force constraint condition.

[0225] Specifically, first integrate the first smooth braking force constraint condition and the second smooth braking force constraint condition to ensure that they are mathematically compatible and continuously differentiable. Through optimization algorithms or numerical methods, the intersection or combination of these two constraint conditions is transformed into a unified smooth braking force constraint condition. This smooth braking force constraint condition is used to provide a comprehensive limiting framework during the train operation, ensuring that the train operates under the dual limitations of force and power, optimizing the energy consumption efficiency, while maintaining safety and stability.

[0226] For example, the maximum control force that a train can use is determined by the train speed. Whether in the traction or braking mode, the maximum control force that the train can use is divided into two parts: a constant force region and a constant power region. The control force boundaries in both the traction and braking modes are non-differentiable at the intersection of the constant force region and the constant power region. The range of the control force is the intersection of the constant force constraint and the constant power constraint on the entire speed axis. Therefore, the boundary constraint equation of the control force can be re-modeled as follows:

[0227]

[0228] Wherein, and respectively represent the maximum traction force and braking force corresponding to the constant force region in the train control force boundary, and respectively represent the maximum traction power and braking power corresponding to the constant power region.

[0229] By re-modeling the train control force boundary as the intersection of the constant force and constant power constraints within the entire speed range, this method unifies the piecewise definitions in different speed intervals into an overall mathematical expression. When the speed changes, the calculation of the control force no longer exhibits discontinuity or non-differentiability. This unified expression eliminates the abrupt changes between different intervals, making the control force boundary continuous and differentiable mathematically, thus achieving smooth processing. This method does not require approximation, maintaining the integrity and accuracy of the original constraints while ensuring the continuity and differentiability of the control force boundary during the optimization process.

[0230] The smooth optimization model can be expressed as:

[0231]

[0232]

[0233]

[0234]

[0235]

[0236]

[0237]

[0238]

[0239]

[0240]

[0241]

[0242]

[0243]

[0244]

[0245]

[0246] The state variable x of this non - linear optimization problem remains the positions and speeds of all trains, a total of 2N, but the control variable u includes, in addition to the control forces of all trains, the voltages of each node in the equivalent circuit model, as well as the introduced pseudo - control variables, a total of 2N + 3, which are represented as follows:

[0247]

[0248]

[0249] The technical effect of this solution in this embodiment is as follows: By constructing a comprehensive smooth braking force constraint condition, precise control of the power and braking performance during the train operation is achieved. By combining the maximum traction force, maximum braking force, maximum traction power, maximum braking power, and speed dynamic characteristics, continuous and differentiable constraint conditions are formed to ensure that the train can operate efficiently within the safe and physical limit range under different speeds and operating trajectories. This method improves the safety and stability of operation, ensuring that the train can smoothly adjust the power output and braking force under complex operating conditions.

[0250] Figure 5 This is a schematic structural diagram of the train operation trajectory optimization device provided by the embodiment of the present application. As Figure 5 shown, this train operation trajectory optimization device includes:

[0251] An acquisition module 501, configured to acquire a plurality of input data.

[0252] A first construction module 502, configured to construct a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data; wherein, the plurality of calculation models and the plurality of constraint conditions are discrete or non - differentiable.

[0253] A smoothing processing module 503, configured to perform smoothing processing on the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smooth calculation models and a plurality of smooth constraint conditions; wherein, the plurality of smooth calculation models and the plurality of smooth constraint conditions are continuous and differentiable.

[0254] A second construction module 504, configured to construct a smooth optimization model according to the plurality of smooth calculation models and the plurality of smooth constraint conditions.

[0255] The model solving module 505 is configured to solve the smooth optimization model according to preset test data to obtain multiple target operation data; wherein, the multiple target operation data is used to represent the operation trajectories of multiple trains when the energy consumption of multiple trains is the lowest.

[0256] In a possible design, the multiple input data includes multiple train data, multiple line data, multiple timetable data, and multiple traction power supply system data, and the multiple calculation models include an energy coupling model and a safe separation operation model. The first construction module 502 includes:

[0257] The energy coupling model construction unit is configured to construct an energy coupling model according to the multiple traction power supply system data and the multiple timetable data; wherein, the energy coupling model is used to describe the energy transmission relationship between the traction power supply system supplying energy to multiple trains and the multiple trains.

[0258] The safe separation operation model construction unit is configured to construct a safe separation operation model according to the multiple train data, the multiple timetable data, and a preset spacing; wherein, the safe separation operation model is used to describe the positional relationship between multiple trains.

[0259] The constraint condition construction unit is configured to construct multiple constraint conditions according to the multiple train data, the multiple line data, the multiple timetable data, and the multiple traction power supply system data; wherein, the multiple constraint conditions are used to constrain the operation trajectories of multiple trains and the voltage of the traction power supply system.

[0260] In a possible design, the multiple smooth calculation models include a smooth energy coupling model and a smooth safe separation operation model. The smooth processing module 503 includes:

[0261] The equivalent power acquisition unit is configured to acquire the substation equivalent power; wherein, the substation equivalent power is used to represent the electric power provided by the substation to the traction power supply system.

[0262] The smooth energy coupling model construction unit is configured to construct a smooth energy coupling model according to the substation equivalent power and the energy coupling model.

[0263] The smooth safe separation operation model construction unit is configured to construct a smooth safe separation operation model according to the multiple train data and the safe separation operation model.

[0264] The constraint condition smooth processing unit is configured to perform smooth processing on the multiple constraint conditions according to the multiple train data and the multiple line data to obtain multiple smooth constraint conditions.

[0265] In a possible design, the multiple train data includes a position function, multiple braking parameters, multiple speed limit values, and multiple control forces, and the multiple constraint conditions include a position constraint condition, a braking force constraint condition, a speed constraint condition, and a power constraint condition. The constraint condition smoothing processing unit includes:

[0266] A smooth position constraint condition construction device, configured to construct a smooth position constraint condition according to the position function, the multiple braking parameters, and the position constraint condition.

[0267] A smooth braking force constraint condition construction device, configured to construct a smooth braking force constraint condition according to the position function, the multiple braking parameters, and the braking force constraint condition.

[0268] A smooth speed constraint condition construction device, configured to construct a smooth speed constraint condition according to the multiple speed limit values, the position function, and the speed constraint condition.

[0269] A smooth power constraint condition construction device, configured to construct a smooth power constraint condition according to the position function, the multiple control forces, and the power constraint condition.

[0270] In a possible design, the smooth position constraint condition construction device includes:

[0271] A slope height function fitting component, configured to perform function fitting according to the position function to obtain a slope height function; wherein, the slope height function is used to represent the change of the slope height of the running lines of the multiple trains with the position.

[0272] A smooth slope function calculation component, configured to calculate a smooth slope function according to the slope height function; wherein, the smooth slope function is used to represent the change of the slope of the running lines of the multiple trains with the position.

[0273] A smooth position constraint condition construction component, configured to construct a smooth position constraint condition according to the smooth slope function, the multiple braking parameters, and the position constraint condition.

[0274] In a possible design, the multiple braking parameters include the maximum traction force and the maximum braking force corresponding to the constant force area in the train control force boundary, and the maximum traction power and the maximum braking power corresponding to the constant power area. The smooth braking force constraint condition construction device includes:

[0275] A speed function calculation component, configured to calculate a speed function according to the position function; wherein, the position function and the speed function are respectively used to represent the change of the positions and speeds of the multiple trains with time.

[0276] A first smooth braking force constraint condition construction component, configured to construct a first smooth braking force constraint condition according to the maximum traction force, the maximum braking force, and the braking force constraint condition; wherein, the first smooth braking force constraint condition is used to limit the forces that the multiple trains can apply.

[0277] The second smooth braking force constraint condition construction component is used to construct the second smooth braking force constraint condition according to the maximum traction power, the maximum braking power, the speed function, and the braking force constraint condition; wherein, the second smooth braking force constraint condition is used to limit the maximum power of multiple trains.

[0278] The smooth braking force constraint condition generation component is used to generate the smooth braking force constraint condition according to the first smooth braking force constraint condition and the second smooth braking force constraint condition.

[0279] The train operation trajectory optimization device provided in this embodiment can execute Figure 2 the technical solutions of the method embodiment shown, and its implementation principle and technical effects are Figure 2 similar to those of the method embodiment shown, and will not be elaborated here one by one.

[0280] Figure 6 This is a schematic hardware structure diagram of the electronic device provided in the embodiment of the present application. As Figure 6 shown, the electronic device includes: at least one processor 610 and a memory 620. The electronic device also includes a communication component 630. Among them, the processor 610, the memory 620, and the communication component 630 are connected through a bus 640.

[0281] In the specific implementation process, at least one processor 610 executes the computer execution instructions stored in the memory 620, so that at least one processor 610 is used to implement the train operation trajectory optimization method of the above embodiment.

[0282] The specific implementation process of the processor 610 can be referred to the above method embodiment, and its implementation principle and technical effects are similar, and will not be elaborated here in this embodiment.

[0283] In the above embodiment, it should be understood that the processor 610 may be a central processing unit (Central Processing Unit, CPU), or other general-purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the invention can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

[0284] The memory 620 may include a high-speed RAM memory, and may also include a non-volatile storage NVM, such as at least one disk memory.

[0285] The bus 640 can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, etc. The bus 640 can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, the bus 640 in the drawings of this application is not limited to only one bus or one type of bus.

[0286] The functions implemented for the electronic device and the main control device are introduced for the solution provided by the embodiments of the present invention. It can be understood that in order for the electronic device or the main control device to implement the above functions, it includes the corresponding hardware structures and / or software modules for executing each function. Combining the units and algorithm steps of each example described in the embodiments disclosed in the embodiments of the present invention, the embodiments of the present invention can be implemented in the form of hardware or a combination of hardware and computer software. Whether a certain function is executed in the way of hardware or computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art 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 the technical solution of the embodiments of the present invention.

[0287] The embodiments of this application also provide a computer-readable storage medium. Computer-executable instructions are stored in the computer-readable storage medium. When the computer-executable instructions are executed by a processor, they are used to implement the train operation trajectory optimization method of the above embodiments. Among them, in the specific implementation of the above train operation trajectory optimization method, each module can be implemented as a processor.

[0288] The above-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, a magnetic disk or an optical disc. The readable storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0289] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from the readable storage medium and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can be located in an Application Specific Integrated Circuits (ASIC). Of course, the processor and the readable storage medium can also exist as discrete components in an electronic device or a master device.

[0290] An embodiment of the present application also provides a computer program product, including a computer program which, when executed by a processor, is used to implement the train operation trajectory optimization method in the above embodiment.

[0291] The computer program is stored in a readable storage medium. At least one processor can read the computer program from the readable storage medium, and at least one processor executes the computer program to execute the solution provided in any of the above embodiments.

[0292] Those of ordinary skill in the art can understand that all or part of the steps to implement the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps including the above method embodiments; and the foregoing storage medium includes various media such as ROM, RAM, magnetic disks, or optical discs that can store program codes.

[0293] So far, the technical solutions of the present application have been described in conjunction with the preferred embodiments shown in the drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present application is obviously not limited to these specific embodiments. The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for optimizing the running track of a train, characterized in that, Including: Obtain a plurality of input data; Construct a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data; wherein, the plurality of calculation models and the plurality of constraint conditions are discrete or non-differentiable; Smooth the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smooth calculation models and a plurality of smooth constraint conditions; wherein, the plurality of smooth calculation models and the plurality of smooth constraint conditions are continuous and differentiable; Construct a smooth optimization model according to the plurality of smooth calculation models and the plurality of smooth constraint conditions; Solve the smooth optimization model according to preset test data to obtain a plurality of target operation data; wherein, the plurality of target operation data is used to represent the operation trajectories of the plurality of trains when the energy consumption of the plurality of trains is the lowest.

2. The train operation trajectory optimization method according to claim 1, characterized in that The plurality of input data includes a plurality of train data, a plurality of line data, a plurality of timetable data, and a plurality of traction power supply system data. The plurality of calculation models includes an energy coupling model and a safe separation operation model. Constructing a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data includes: Construct the energy coupling model according to the plurality of traction power supply system data and the plurality of timetable data; wherein, the energy coupling model is used to describe the energy transmission relationship between the traction power supply system that supplies energy to the plurality of trains and the plurality of trains; Construct the safe separation operation model according to the plurality of train data, the plurality of timetable data, and a preset spacing; wherein, the safe separation operation model is used to describe the positional relationship between the plurality of trains; Construct the plurality of constraint conditions according to the plurality of train data, the plurality of line data, the plurality of timetable data, and the plurality of traction power supply system data; wherein, the plurality of constraint conditions are used to constrain the operation trajectories of the plurality of trains and the voltage of the traction power supply system.

3. The train operation trajectory optimization method according to claim 2, characterized in that The plurality of smooth calculation models includes a smooth energy coupling model and a smooth safe separation operation model. Smoothing the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smooth calculation models and a plurality of smooth constraint conditions includes: Obtain the equivalent power of the substation; wherein, the equivalent power of the substation is used to represent the electric power provided by the substation to the traction power supply system; Construct the smooth energy coupling model according to the equivalent power of the substation and the energy coupling model; Construct the smooth safe separation operation model according to the plurality of train data and the safe separation operation model; Smooth the plurality of constraint conditions according to the plurality of train data and the plurality of line data to obtain the plurality of smooth constraint conditions.

4. The train operation trajectory optimization method according to claim 3, wherein The plurality of train data includes a position function, a plurality of braking parameters, a plurality of speed limit values, and a plurality of control forces. The plurality of constraint conditions includes a position constraint condition, a braking force constraint condition, a speed constraint condition, and a power constraint condition. Smoothing the plurality of constraint conditions according to the plurality of train data and the plurality of line data to obtain the plurality of smooth constraint conditions includes: Construct a smooth position constraint condition according to the position function, the multiple braking parameters and the position constraint condition; Construct a smooth braking force constraint condition according to the position function, the multiple braking parameters and the braking force constraint condition; Construct a smooth speed constraint condition according to the multiple speed limit values, the position function and the speed constraint condition; Construct a smooth power constraint condition according to the position function, the multiple control forces and the power constraint condition.

5. The train operation trajectory optimization method according to claim 4, wherein The constructing of the smooth position constraint condition according to the position function, the multiple braking parameters and the position constraint condition includes: Perform function fitting on the position function to obtain a slope height function; wherein, the slope height function is used to represent the change of the slope height of the running lines of the multiple trains with position; Calculate a smooth slope function according to the slope height function; wherein, the smooth slope function is used to represent the change of the slope of the running lines of the multiple trains with position; Construct the smooth position constraint condition according to the smooth slope function, the multiple braking parameters and the position constraint condition.

6. The train operation trajectory optimization method according to claim 4, characterized in that The multiple braking parameters include the maximum traction force and the maximum braking force corresponding to the constant force area in the train control force boundary, and the maximum traction power and the maximum braking power corresponding to the constant power area. The constructing of the smooth braking force constraint condition according to the position function, the multiple braking parameters and the braking force constraint condition includes: Calculate a speed function according to the position function; wherein, the position function and the speed function are respectively used to represent the change of the positions and speeds of the multiple trains with time; Construct a first smooth braking force constraint condition according to the maximum traction force, the maximum braking force and the braking force constraint condition; wherein, the first smooth braking force constraint condition is used to limit the forces that the multiple trains can apply; Construct a second smooth braking force constraint condition according to the maximum traction power, the maximum braking power, the speed function and the braking force constraint condition; wherein, the second smooth braking force constraint condition is used to limit the maximum power of the multiple trains; Generate the smooth braking force constraint condition according to the first smooth braking force constraint condition and the second smooth braking force constraint condition.

7. An apparatus for optimizing the running track of a train, characterized in that, Includes: An acquisition module, configured to acquire a plurality of input data; A first construction module, configured to construct a plurality of calculation models and a plurality of constraint conditions according to the plurality of input data; wherein, the plurality of calculation models and the plurality of constraint conditions are discrete or non-differentiable; A smooth processing module, configured to perform smooth processing on the plurality of calculation models and the plurality of constraint conditions to obtain a plurality of smooth calculation models and a plurality of smooth constraint conditions; wherein, the plurality of smooth calculation models and the plurality of smooth constraint conditions are continuous and differentiable; A second construction module, configured to construct a smooth optimization model according to the plurality of smooth calculation models and the plurality of smooth constraint conditions. A model solving module, configured to solve the smooth optimization model according to preset test data to obtain a plurality of target operation data; wherein the plurality of target operation data is used to represent the operation trajectories of the plurality of trains when the energy consumption of the plurality of trains is the lowest.

8. An electronic device, characterized in that, It includes: a processor, and a memory communicatively connected to the processor; the memory stores computer execution instructions; when the processor executes the computer execution instructions stored in the memory, it is configured to implement the train operation trajectory optimization method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Computer execution instructions are stored in the computer-readable storage medium, and when the computer execution instructions are executed by a processor, they are configured to implement the train operation trajectory optimization method according to any one of claims 1 to 6.

10. A computer program product, including a computer program, which when executed by a processor, is configured to implement the train operation trajectory optimization method according to any one of claims 1 to 6.

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