Multi-objective speed curve optimization method and device considering train wheel-rail adhesion safety

Abstract

The application discloses a kind of multi-objective speed curve optimization method and device considering train wheel adhesion safety, it is related to train operation automatic control technical field, this method includes according to train operation characteristic and structure characteristic establishes the longitudinal dynamics model of train operation process;According to longitudinal dynamics model and the adhesion force constraint between train wheel and rail establishes the multi-objective optimization model of train operation curve;Multi-objective optimization model includes safety evaluation function, energy-saving evaluation function, smooth evaluation function and efficient evaluation function;Application subsection linear affine method and big M method are nonlinear part in longitudinal dynamics model is transcribed into linear part, obtain reconstruction longitudinal dynamics model;Based on reconstruction longitudinal dynamics model, solve multi-objective optimization model using MILP algorithm, obtain optimal speed displacement operation curve.The application considers multi-objective optimization, and considers the adhesion force constraint between wheel and rail, realizes train safety, smooth, energy-saving, efficient operation.

Description

Technical Field

[0001] This application relates to the field of automatic train operation control technology, and in particular to a multi-objective speed curve optimization method and device that takes into account the safety of train wheel-rail adhesion. Background Technology

[0002] Heavy-haul trains are large freight train formations. Due to their heavy loads, the fact that many lines are located in mountainous areas with complex terrain, and the difficulty of operation, optimal driving technology for heavy-haul trains has become a particularly important challenge for my country's transportation system. Currently, manual driving of heavy-haul trains in my country still relies on the driving experience of skilled drivers, and the scientific validity and accuracy of the target operating curves used for driving are insufficient. With the continuous increase in train weight and traction weight, safety issues in heavy-haul transportation, such as difficult operation, derailment, insufficient adhesion leading to starting difficulties, or control forces exceeding adhesion limits causing wheel slippage and wheel-rail wear, are becoming increasingly prominent. At the same time, due to the subjective factors involved in manual driving, driving strategies are often too conservative, resulting in excessively long braking distances when formulating braking and stopping strategies, which seriously affects operating efficiency. In addition, the computing power of existing onboard locomotives is very limited. Traditional target curve optimization often uses offline solutions followed by online table lookups, but the actual environment is often changing. For example, weather changes can lead to changes in rail surface conditions, and train speeds also change, causing the adhesion coefficient to change in real time. Therefore, offline solution methods cannot cope with the constantly changing dynamics of train operation. To solve these problems, it is necessary to have a thorough and accurate analysis of the characteristics and requirements of heavy-haul trains, and to study suitable online optimization algorithms to optimize the target operation curve of the trains and improve various evaluation indicators during their operation.

[0003] The practical application requirements of heavy-haul train operation include limited computing power of the train's control system, complex terrain, and dynamic changes in adhesion. Traditional heuristic algorithms, with their iterative optimization process, are extremely time-consuming and computationally demanding, far from meeting the practical needs of online solution or adjustment. However, a mathematical programming algorithm, utilizing a mature solver, can achieve a total operation process solution within seconds, meeting the 100-millisecond computation requirement for a single point. For problems such as changes in train load and weather-related changes in adhesion, it can quickly and efficiently solve for and update the target operating curve to conform to current operating conditions. Furthermore, this algorithm has low computational requirements, meeting the basic requirements for online application deployment on the train's control system.

[0004] Optimization of heavy-haul train operation curves mainly involves single-objective optimization and multi-objective optimization. Single-objective optimization solves a problem for a single objective within certain constraints, while multi-objective optimization requires handling multiple mutually constrained or conflicting variables simultaneously, making it more difficult to solve. For optimizing the operation of heavy-haul trains, multi-objective optimization is more in line with practical needs. For example, increasing train speed may decrease safety, making it difficult to guarantee, which is a significant contradiction in multi-objective optimization; multiple traction and braking conditions during train operation can reduce travel time but increase energy consumption, another contradiction. Using multi-objective optimization methods to optimize train operation curves allows the various performance indicators required by heavy-haul trains to reach an optimal balance within the constraints. Summary of the Invention

[0005] The purpose of this application is to provide a multi-objective speed curve optimization method and device that takes into account the safety of train wheel-rail adhesion. It considers multi-objective optimization and wheel-rail adhesion constraints, thereby achieving safe, stable, energy-saving and efficient train operation.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] Firstly, this application provides a multi-objective speed curve optimization method that considers train wheel-rail adhesion safety, including:

[0008] A longitudinal dynamic model of the train operation process is established based on the train's operating characteristics and structural characteristics;

[0009] A multi-objective optimization model for the train's running curve is established based on the longitudinal dynamics model and the wheel-rail adhesion constraint. The multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function. The safety evaluation function and the energy-saving evaluation function take into account the soft wheel-rail adhesion constraint when they are constructed.

[0010] The nonlinear part of the longitudinal dynamics model is transcribed into the linear part by applying the piecewise linear affine method and the big M method, resulting in a reconstructed longitudinal dynamics model.

[0011] Based on the reconstructed longitudinal dynamic model, the MILP algorithm is used to solve the multi-objective optimization model and obtain the optimal velocity-displacement running curve.

[0012] Secondly, this application provides a multi-objective speed curve optimization device that considers train wheel-rail adhesion safety, including:

[0013] The dynamics model building module is used to establish a longitudinal dynamics model of the train operation process based on the train's operating characteristics and structural characteristics;

[0014] The multi-objective optimization model construction module is used to establish a multi-objective optimization model for the train operation curve based on the longitudinal dynamics model and the wheel-rail adhesion constraint of the train. The multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function. The safety evaluation function and the energy-saving evaluation function take into account the soft adhesion constraint between the train's wheel and rail when they are constructed.

[0015] The dynamic model reconstruction module is used to transcribe the nonlinear part of the longitudinal dynamic model into the linear part by applying the piecewise linear affine method and the big M method, so as to obtain the reconstructed longitudinal dynamic model.

[0016] The optimal velocity-displacement running curve solution module is used to solve the multi-objective optimization model based on the reconstructed longitudinal dynamic model and the MILP algorithm to obtain the optimal velocity-displacement running curve.

[0017] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described multi-objective speed curve optimization method considering train wheel-rail adhesion safety.

[0018] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described multi-objective speed curve optimization method that considers train wheel-rail adhesion safety.

[0019] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0020] This application provides a multi-objective speed curve optimization method and apparatus that considers train wheel-rail adhesion safety. By establishing a longitudinal dynamic model and combining wheel-rail adhesion constraints with actual train track conditions, a safe, energy-saving, stable, and efficient multi-objective optimization strategy is proposed. The MILP algorithm is used to optimize the running curve in real time, enabling the various performance indicators required by the basic requirements of heavy-haul trains to reach a balanced optimal state within the constraints, thus achieving safe, stable, energy-saving, and efficient train operation. This application is applicable to the running curve optimization of 10,000-ton-class heavy-haul trains. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1This is an application environment diagram of a multi-objective speed curve optimization method considering train wheel-rail adhesion safety in one embodiment of this application;

[0023] Figure 2 A flowchart illustrating a multi-objective speed curve optimization method considering train wheel-rail adhesion safety, provided as an embodiment of this application;

[0024] Figure 3 A schematic diagram illustrating the technical concept of a multi-objective speed curve optimization method considering train wheel-rail adhesion safety, provided in an embodiment of this application;

[0025] Figure 4 A schematic diagram of longitudinal force analysis of a heavy-haul train provided in an embodiment of this application;

[0026] Figure 5 This is a schematic diagram of the optimal adhesion principle provided in an embodiment of this application;

[0027] Figure 6 A dynamic diagram of the adhesion coefficient under different rail surface conditions, including traction and braking conditions, is provided for an embodiment of this application.

[0028] Figure 7 This application provides line data for a portion of the experimental section of the Daqin Railway, as an embodiment of the present application.

[0029] Figure 8 HX linearized using PWA is provided as an embodiment of this application. D1 A schematic diagram of the fitting curve of the traction characteristic curve of a heavy-haul train and its original curve.

[0030] Figure 9 HX linearized using PWA is provided as an embodiment of this application. D1 A schematic diagram of the fitting curve of the braking characteristics of a heavy-haul train and its original curve;

[0031] Figure 10 A schematic diagram of the adhesion coefficient of a train running on a changing rail surface, provided as an embodiment of this application;

[0032] Figure 11 This is a schematic diagram comparing the target running curves of the MILP algorithm and the AGA algorithm provided in an embodiment of this application;

[0033] Figure 12 This is a schematic diagram comparing the target running curves before and after adding adhesion constraints to the MILP algorithm provided in one embodiment of this application;

[0034] Figure 13 This is a schematic diagram comparing the control force curves before and after adding adhesion constraints to the MILP algorithm provided in one embodiment of this application.

[0035] Figure 14 A schematic diagram of the functional modules of a multi-objective speed curve optimization device that considers train wheel-rail adhesion safety, provided in an embodiment of this application;

[0036] Figure 15 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0037] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0038] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] The multi-objective speed curve optimization method considering train wheel-rail adhesion safety provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, the terminal communicates with the server via a network. The data storage system stores the data the server needs to process. The data storage system can be set up independently, integrated into the server, or placed in the cloud or on another server. The terminal can send the train's operating and structural characteristics to the server. After receiving these characteristics, the server establishes a longitudinal dynamics model of the train's operation based on these characteristics. Based on the longitudinal dynamics model and the wheel-rail adhesion constraints, a multi-objective optimization model of the train's running curve is established. The multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function. The safety and energy-saving evaluation functions consider the soft wheel-rail adhesion constraints during construction. The nonlinear parts of the longitudinal dynamics model are converted into linear parts using a piecewise linear affine method and the Big M method, resulting in a reconstructed longitudinal dynamics model. Based on the reconstructed longitudinal dynamics model, the MILP algorithm is used to solve the multi-objective optimization model, yielding the optimal speed-displacement running curve. The server can then feed back the obtained optimal speed-displacement running curve to the terminal.

[0040] The terminal can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. The server can be a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0041] In one exemplary embodiment, such as Figure 2 and Figure 3 As shown, a multi-objective speed curve optimization method considering train wheel-rail adhesion safety is provided. Taking a heavy-haul train as an example, this method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 The following steps, 101 to 104, are used as an example to illustrate the process of using a server in the example.

[0042] Step 101: Establish a longitudinal dynamic model of the train operation process based on the train's operating characteristics and structural characteristics.

[0043] Step 102: Establish a multi-objective optimization model for the train running curve based on the longitudinal dynamics model and the wheel-rail adhesion constraint of the train; the multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function; the safety evaluation function and the energy-saving evaluation function take into account the soft adhesion constraint between the train's wheel and rail when they are constructed.

[0044] Step 103: Apply the piecewise linear affine method and the big M method to transcribe the nonlinear part of the longitudinal dynamics model into the linear part, and obtain the reconstructed longitudinal dynamics model.

[0045] Step 104: Based on the reconstructed longitudinal dynamic model, the MILP algorithm is used to solve the multi-objective optimization model to obtain the optimal velocity-displacement running curve.

[0046] Implementing steps 101 to 104 above, heavy-haul trains, with their heavy loads, complex tracks, and volatile operating environments, exhibit significant hysteresis and nonlinear characteristics. During operation, improper driving can lead to derailment due to broken couplers, wheel-rail damage caused by traction / braking forces exceeding the maximum available adhesion limit, and energy waste due to emergency braking. Furthermore, issues such as unstable operation, inefficiency due to improper speed control, and scheduling disruptions exist. This application, by establishing a longitudinal dynamic model and combining wheel-rail adhesion constraints, proposes a multi-objective optimization strategy based on real-world track conditions, aiming for safety, energy conservation, stability, and high efficiency. Employing the MILP algorithm for real-time optimization of the operating curve, it enables the various performance indicators required for heavy-haul trains to achieve optimal balance within constraints, thus realizing safe, stable, energy-efficient, and high-efficiency train operation. This application is applicable to the optimization of operating curves for 10,000-ton-class heavy-haul trains.

[0047] In another exemplary embodiment of this application, in step 101, a continuous-time longitudinal dynamics model of the heavy-haul train is established. For example... Figure 4 As shown, Figure 4 In Let acceleration be the acceleration. By performing a force analysis on the heavy-haul train, the dynamic differential equation for the entire operation of the heavy-haul train can be written as:

[0048] (1)

[0049] In the formula, The total mass of the train; The rotational mass factor; For train speed; For time, The location of the train; The effective traction force or effective braking force of a train can be determined by the train's traction / braking characteristic curve. The basic resistance experienced by the train mainly includes friction and impact between various components of the locomotive and rolling stock, between the locomotive and rolling stock and the air, and between the wheels and the rails. It can be summarized as: mechanical resistance plus air resistance. The additional resistance experienced by the train due to track conditions, primarily caused by gradients, curves, and tunnels. As an example, M is 10,800 tons. It is 1.06.

[0050] The resistance caused by the slope refers to the component of the force exerted on the train by its own weight when the train is running on a slope, and its expression is as follows:

[0051] (2)

[0052] In the formula, This indicates the resistance caused by the ramp; It is the acceleration due to gravity; For elevation difference; This is the length of the ramp; The slope angle is denoted by .

[0053] The resistance caused by curves is related to many factors such as the curve radius, train speed, and locomotive wheelbase, making it difficult to calculate using theoretical formulas; empirical formulas are usually employed. Based on experiments, the mathematical model for the resistance caused by curves is as follows:

[0054] (3)

[0055] In the formula, This indicates the resistance caused by the curve; It is the radius of the curve.

[0056] Trains experience higher air resistance when running in tunnels, depending on the tunnel type and the smooth length of the tunnel walls. If there is a limiting ramp in the tunnel, the empirical formula for the air resistance caused by the tunnel is given by equation (4); if there is no limiting ramp, equation (5) is used.

[0057] (4)

[0058] (5)

[0059] In the formula, This indicates the air resistance caused by the tunnel; The length of the tunnel is in meters (m). The train's speed is expressed in km / h.

[0060] In another exemplary embodiment of this application, in step 102, since the train travels on the rails, its driving force comes from the adhesion between the wheels and the rails. The train's control force (including traction and braking force) is limited by the adhesion between the wheels and rails. If the train's traction force exceeds the adhesion force, it will cause energy waste and train slippage; while if the braking force exceeds the adhesion force, it will not only reduce the actual effective braking force, but also prolong the braking distance, causing the train to slide or even damage the tread. Therefore, effectively limiting the train's control force within the adhesion force range can not only reduce energy waste, but also effectively reduce the risks of train slippage and sliding. The adhesion constraint of the train's control force (the soft constraint of the adhesion between the train's wheels and rails) can be expressed by equation (6):

[0061] (6)

[0062] In the formula, This refers to the control force output by the locomotive. Under traction conditions, its value is the traction force output by the motor; under braking conditions, its value is the braking force output by the train's brake shoes. This value may be greater than the maximum available adhesion force. Any portion exceeding this limit is considered invalid, which will not only waste energy (under traction conditions) but may also cause idling or slippage. , The maximum adhesion force that can be provided between the wheel and the rail; The maximum adhesion coefficient; This refers to the vertical force between the wheel and the rail.

[0063] Based on the current "Traction Calculation Code" and empirical formulas obtained from experiments, the adhesion coefficients corresponding to traction and braking of domestically produced electric locomotives are... The adhesion coefficient can be approximated by equations (7) and (8) respectively. The dynamic diagrams of the adhesion coefficient under different rail surface conditions are as follows: Figure 5 As shown, the optimal adhesion principle diagram is as follows: Figure 6 As shown.

[0064] (7)

[0065] (8)

[0066] The maximum adhesion coefficient under traction conditions is determined according to equation (7), and the maximum adhesion coefficient under braking conditions is determined according to equation (8). Figure 5 middle, This represents the actual adhesion coefficient value at time t; This represents the maximum dynamic friction coefficient, which is less than or equal to the maximum static friction coefficient. .

[0067] Based on the characteristics of heavy-haul train operation, this application considers the soft constraint of wheel-rail adhesion (Equation 6), the operating rules of heavy-haul trains (such as the need for electric locomotives to switch from one phase to another when passing through different traction substations, and the setting of a contact network de-energized area, i.e., the phase-separated area, between the two power supply areas to ensure circuit stability, the train loses its power source when traveling in this area and needs to maintain a coasting condition, with zero train control force), and real line data conditions, and establishes a multi-objective optimization model with safety, energy saving, stability, and efficiency as the four main optimization objectives.

[0068] According to train operation safety requirements, the train speed must meet the section speed limit safety requirements. Furthermore, the train's control force is constrained by adhesion force, and adhesion safety plays a decisive role in the safety of train operation. Based on this, a safety evaluation function is established as follows:

[0069] (9)

[0070] In the formula, As a penalty factor; For the first The remaining adhesion margin in each interval; For the first The adhesion over-limit indicator variable for each interval (takes a value of 1 when the control force exceeds the specified limit, otherwise it is 0); Location of the train Speed ​​limits at the section; For train speed; , , These are the weighting coefficients. N represents the total number of sections divided into the train's travel path.

[0071] The remaining adhesion margin represents the margin remaining after the locomotive applies traction (or braking force) at the maximum available adhesion traction (or braking force). For a specific operating condition, the expression for the remaining adhesion margin is as shown in equation (10); regardless of the operating condition, the remaining adhesion margin... Practical utilization of adhesive force Interval stickiness overlimit indicator variable The calculation formula is as shown in formula (11):

[0072] (10)

[0073] (11)

[0074] In the formula: This represents the remaining adhesion margin; These represent the maximum available adhesion force under traction and braking conditions, respectively. These are the control forces under traction and braking conditions, respectively. The maximum adhesive force that can be provided between the wheel and rail is the actual utilization of adhesive force. The maximum value or maximum adhesion coefficient of the function and wheel-rail vertical force The product; when When the value is greater than 0 or less than 0, it corresponds to normal operation or idling speed, respectively, reflecting the presence or insufficiency of available adhesion between the wheel and rail. For interval The maximum available adhesive force; For the first The control force output by the locomotive in each section is used for energy consumption calculation, while the traction force is taken. For interval In practice, the adhesive force is utilized, which is the locomotive's effective output control force. For interval The remaining adhesion margin; The minimum viscosity coefficient required to output control force under ideal conditions; For interval The maximum adhesion coefficient.

[0075] The traditional energy-saving evaluation function, which does not consider adhesion, calculates the energy consumption for each traction condition interval by multiplying the traction force by the travel distance. The sum of all intervals represents the total energy consumption. The energy-saving evaluation function is as follows:

[0076] (12)

[0077] in, Indicates that the train is in the section. The distance traveled, i.e., the interval The length.

[0078] However, this is under ideal conditions where the train's traction is fully utilized. In reality, the portion of the traction force exceeding the maximum adhesion force is useless or even harmful. Therefore, the original energy-saving evaluation function is improved. Based on the calculation of the original energy consumption, the impact of the maximum adhesion force under the current road conditions on energy consumption is considered. The improved energy-saving evaluation function is as follows:

[0079] (13)

[0080] In the formula, As a penalty factor, For trains in the section traction force.

[0081] Stability mainly considers the acceleration and longitudinal impulse during train operation, and the stability evaluation function is established as follows:

[0082] (14)

[0083] in, (15)

[0084] (16)

[0085] In the formula, and As an example, the weighting coefficients are used. , ; The number of sections into which the train's route is divided; This represents the average acceleration of the train across all sections during its operation. For trains during operation in the section The mean of acceleration; For the first The average acceleration during train operation is obtained by summing the accelerations in each interval and then averaging them. This represents the average longitudinal impulse generated during train operation.

[0086] The efficient evaluation function considers the total travel time of the train. The efficient evaluation function is:

[0087] (17)

[0088] In the formula, For trains in the section The actual running time.

[0089] Based on the above-described multi-objective optimization model for constructing train operation curves, its expression is:

[0090]

[0091] In another exemplary embodiment of this application, in step 103, a hybrid logic dynamics (MILD) model based on the MILP algorithm is established. For the constructed longitudinal dynamics model (Equation (1)), unit kinetic energy is introduced. Rewrite them as equations (18) and (19).

[0092] (18)

[0093] (19)

[0094] Basic resistance Additional resistance Reconstructed into the following form:

[0095] (20)

[0096] (twenty one)

[0097] In the formula, , , , The drag constant is determined by the vehicle type and wind speed. Equations (20) and (21) are the basic drag values ​​in equation (1). and additional resistance It is derived by fitting the deformation by introducing unit kinetic energy.

[0098] Assume that the traction / braking force is a constant value within each interval. For each interval... The differential equation for kinetic energy (i.e., equation (18)) can be expressed as:

[0099] (twenty two)

[0100] in, , , , For interval The corresponding resistance constant.

[0101] Solving equation (22) yields:

[0102] (twenty three)

[0103] In the formula:

[0104] ; ; ; ; ; .and . and Indicates the train's arrival location and Kinetic energy at the point, and They are intervals The starting point and the ending point. It is an interval Internal control.

[0105] Regarding the time differential equation (i.e., equation (19)), the trapezoidal integration rule is adopted:

[0106] (twenty four)

[0107] In the formula, For trains in the section runtime , .

[0108] Define a function: The nonlinear equation (i.e., formula (24)) can be rewritten as a linear equation:

[0109] (25)

[0110] For functions A three-segment affine transformation can be rewritten as:

[0111] (26)

[0112] In the formula, , Piecewise affine coefficients , , , , , Please refer to Table 1 for the possible values. and Values. , , and Please refer to Table 1 for the possible values. , The value of .

[0113] Table 1 Piecewise Affine Coefficients , , , , , The value of

[0114]

[0115] For the adhesion coefficient, which is also a nonlinear equation (i.e., equations (7) and (8)), it can be rewritten as a linear equation:

[0116]

[0117] In the formula, the piecewise affine coefficients , , , , , Please refer to Table 2 for the possible values. and Values, , , and Please refer to Table 2 for the possible values. , The value of .

[0118] Table 2 Piecewise Affine Coefficients , , , , , The value of

[0119]

[0120] When solving the model, all nonlinear constraints need to be converted into linear ones with viscosity coefficients. As part of the adhesive force calculation, in equation (6), adhesive force is used as a constraint, and the adhesion coefficient... Since there is nonlinearity, it needs to be converted into a linear equation.

[0121] Time after linear processing The recurrence relation (i.e., equation (25)) can be transformed into:

[0122] (27)

[0123] In the formula, there exists , , making , Established.

[0124] The piecewise model with PWA constraints mentioned above (Equation (27)) has piecewise parameters. Logical judgments can be transformed into linear inequalities by introducing logical and auxiliary variables. Specifically, introducing logical variables... ,definition:

[0125] (28)

[0126] Substituting equation (28) into equation (26), we get:

[0127] (29)

[0128] Introduce logical variables , equivalent to:

[0129] (30)

[0130] Auxiliary variables are introduced based on the Big M method. , equivalent to:

[0131] (31)

[0132] Substituting equations (30) and (31) into equation (29), we get:

[0133] (32)

[0134] In the formula, , .

[0135] Substituting equation (32) into the time recursion equation (i.e., equation (27)) and then integrating it with equation (23) yields the following MILD model, which is the reconstructed longitudinal dynamics model:

[0136] (33)

[0137] in:

[0138] ;

[0139] ;

[0140] ;

[0141] ;

[0142] ;

[0143]

[0144] ;

[0145]

[0146] .

[0147] The MILD model constructed above can be solved using solvers such as CPLEX and GUROBI. The resulting velocity-displacement running curve is the optimal velocity-displacement running curve of the train after optimization based on the MILP algorithm as required by this application. Driving according to this curve can ensure the safety, energy saving, stability and efficiency of train operation. At the same time, the rapid solution of this application can also meet the requirements of online adjustment and solution to cope with emergencies.

[0148] In this application, a longitudinal dynamic model of the operation process of a 10,000-ton heavy-haul train is established based on the operating characteristics and structural features of the heavy-haul train. The nonlinear part is converted into linearity through piecewise linear affine transformation (PWA), and the longitudinal dynamic model is reconstructed into a mixed integer logic dynamic (MILD) model for online solution. The optimal segment point (referring to the value of E in Tables 1 and 2 above) is determined by simulated annealing algorithm. Considering the adhesion constraints of different rail surface states and the reconstructed constraints of line conditions (such as gradient parameters, curve parameters, tunnel parameters, line speed limits, and phase transitions), a multi-objective optimization model is established with safety, stability, energy saving, and efficiency as indicators. Based on the reconstructed MILD model, the MILP algorithm is used to solve the multi-objective optimization model, thereby optimizing the speed-displacement operation curve of the 10,000-ton heavy-haul train, improving the safety, stability, energy saving, and efficiency of the operation process of the 10,000-ton heavy-haul train, and significantly improving the solution efficiency. This provides a solution for problems such as online application and real-time updates.

[0149] To verify the effectiveness of the method in this application, this application is implemented based on a certain HX of the Datong-Qinhuangdao Railway. D The train speed-displacement operation curve based on the experience of skilled heavy-haul train drivers was optimized and simulated using real line data from the Hudong No. 2 Yard to Yangyuan section of the Daqin Railway. Simulation parameters were as follows: two HX trains were used. D The train consisted of 1 locomotive and 104 C80 freight cars. Specifically, the target operating curve and parameters optimized using the MILP algorithm were compared with those optimized using the Adaptive Genetic Algorithm (AGA).

[0150] The actual slope and curve data of the section from Hudong No. 2 to Yangyuan are as follows: Figure 7 Starting from the Hudong Second Yard (25km mark), the entire route is approximately 59.16km long. Except for the section from 34.8 to 38.6km, the track surface is dry and clean. A sudden wet track surface is set up in the section from 34.8 to 40.6km to simulate the change in the adhesion coefficient of the train due to water accumulation in the tunnel or rain ahead.

[0151] Figure 8 HX after PWA linearization D1 The fitted curve of the traction characteristic curve of a heavy-haul train and its original curve. Figure 9 HX after PWA linearization D1 The fitting curve of the braking characteristics of heavy-haul trains and its original curve. Figure 10 This is a diagram showing the adhesion coefficient of the track surface during operation. Figure 11 This is a comparison chart of the target running curves of the MILP algorithm and the AGA algorithm. Figure 12 A comparison of the target running curves before and after MILP algorithm optimization. Figure 13 A comparison of control force curves before and after MILP algorithm optimization.

[0152] from Figure 8 , Figure 9 As can be seen, within the speed limit range, the fitted curve after PWA linearization is highly similar to the original curve, thus restoring the HX curve. D1 The trend of traction and braking characteristics of heavy-haul trains, with the fitted curve having a small error compared to the original curve, can be used as an effective linearization method. Figure 10 This is a diagram showing the adhesion coefficient of the train on the changing track surface during operation. From... Figure 10 As can be seen, the adhesion coefficient is dynamically changing, and the traction adhesion coefficient and the braking adhesion coefficient are different. The adhesion coefficient of a dry rail surface is much greater than that of a wet rail surface. Under dry rail surface conditions, the traction adhesion coefficient is usually much greater than the braking adhesion coefficient; while under wet rail surface conditions, the traction adhesion coefficient may actually be less than the braking adhesion coefficient.

[0153] from Figure 13 As can be seen, the control force considering wheel-rail adhesion constraints is reasonably limited to the range of maximum usable adhesion force, and it is not exceeded in either traction or braking conditions. Without considering wheel-rail adhesion, the control force is only exceeded in the starting section under dry conditions and in the wet section under wet conditions.

[0154] To further verify the optimization effect of the MILP algorithm, partial data from the simulation results of the two algorithms were extracted for comparison. Six operational data items from the simulation results with added wheel-rail adhesion constraints under two different rail surface conditions were extracted for comparison. Table 3 shows the main optimization operational data of different algorithms, and Table 4 shows the multi-objective optimization operational data under different rail surface conditions.

[0155] As shown in Table 3, the MILP algorithm outperforms the AGA algorithm in both running time and energy consumption, with a significantly shorter solution time. Table 4 shows that the optimized curves considering wheel-rail adhesion constraints, whether on dry or abruptly wetted surfaces, exhibit significantly reduced energy consumption and better stability while maintaining similar running times. Furthermore, the target curves considering wheel-rail adhesion safety have significantly more remaining adhesion margin than those without, and the number of intervals where the control force exceeds the maximum available adhesion force is zero. Simultaneously, the complete target curve solution time using the MILP algorithm is within 20 seconds, meeting the requirements for online solution applications.

[0156] Table 3. Main Optimization Data of Different Algorithms

[0157]

[0158] Table 4. Multi-objective optimization operation data under different orbital planes

[0159]

[0160] Multiple simulation results show that when using the MILP algorithm to optimize the target running curve of heavy-load trains considering wheel-rail adhesion safety, the solution speed is fast, and it has greater advantages in the overall optimization effect of safety, stability, energy saving and efficiency during operation.

[0161] This application also provides an application scenario in which the above-mentioned multi-objective speed curve optimization method considering train wheel-rail adhesion safety is applied. Specifically, the multi-objective speed curve optimization method considering train wheel-rail adhesion safety provided in this embodiment can be applied to the scenario of optimizing the running curve of heavy-haul trains. This scenario includes an information acquisition stage, an information processing stage, and a command control stage; the information acquisition stage is used to collect the running characteristics and structural characteristics of heavy-haul trains; the information processing stage is used to perform multi-objective speed curve optimization considering train wheel-rail adhesion safety based on the collected running characteristics and structural characteristics of heavy-haul trains; the command control stage is used to issue control commands to the train based on the optimization results. The multi-objective speed curve optimization method considering train wheel-rail adhesion safety provided in this embodiment belongs to the information processing stage.

[0162] Based on the same inventive concept, this application also provides a multi-objective speed curve optimization device that considers train wheel-rail adhesion safety for implementing the multi-objective speed curve optimization method that considers train wheel-rail adhesion safety as described above. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the multi-objective speed curve optimization device considering train wheel-rail adhesion safety provided below can be found in the limitations of the multi-objective speed curve optimization method considering train wheel-rail adhesion safety described above, and will not be repeated here.

[0163] In one exemplary embodiment, such as Figure 14 As shown, a multi-objective speed curve optimization device considering train wheel-rail adhesion safety is provided, comprising:

[0164] The dynamic model building module M1 is used to establish a longitudinal dynamic model of the train operation process based on the train's operating characteristics and structural characteristics.

[0165] The multi-objective optimization model construction module M2 is used to establish a multi-objective optimization model for the train operation curve based on the longitudinal dynamics model and the wheel-rail adhesion constraint of the train. The multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function. The safety evaluation function and the energy-saving evaluation function take into account the soft adhesion constraint between the wheel and rail of the train when they are constructed.

[0166] The dynamic model reconstruction module M3 is used to transcribe the nonlinear part of the longitudinal dynamic model into the linear part by applying the piecewise linear affine method and the big M method, thus obtaining the reconstructed longitudinal dynamic model.

[0167] The optimal velocity-displacement running curve solution module M4 is used to solve the multi-objective optimization model based on the reconstructed longitudinal dynamic model and the MILP algorithm to obtain the optimal velocity-displacement running curve.

[0168] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 15 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores multi-objective speed curve optimization data considering train wheel-rail adhesion safety. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a multi-objective speed curve optimization method considering train wheel-rail adhesion safety.

[0169] Those skilled in the art will understand that Figure 15 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0170] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0171] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0172] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0173] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0174] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0175] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A multi-objective velocity curve optimization method considering train wheel-rail adhesion safety, characterized in that, include: A longitudinal dynamic model of the train operation process is established based on the train's operating characteristics and structural characteristics; A multi-objective optimization model for the train's running curve is established based on the longitudinal dynamics model and the wheel-rail adhesion constraint. The multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function. The safety evaluation function and the energy-saving evaluation function take into account the soft wheel-rail adhesion constraint when they are constructed. The nonlinear part of the longitudinal dynamics model is transcribed into the linear part by applying the piecewise linear affine method and the big M method, resulting in a reconstructed longitudinal dynamics model. Based on the reconstructed longitudinal dynamics model, the MILP algorithm is used to solve the multi-objective optimization model and obtain the optimal velocity-displacement running curve. The soft constraint of the wheel-rail adhesion of the train is as follows: in, In the formula, This refers to the control force output by the locomotive. Under traction conditions, its value is the traction force output by the motor; under braking conditions, its value is the braking force output by the train's brake shoes. The maximum adhesion force that can be provided between the train wheels and rails; The maximum adhesion coefficient; The vertical force is the force between the wheel and the rail. The expression for the multi-objective optimization model of the train operation curve is as follows: in, In the formula, , , , These are the safety evaluation function, energy-saving evaluation function, stability evaluation function, and efficiency evaluation function, respectively; N is the total number of intervals divided into train travel paths; For the first The remaining adhesion margin in each interval; For the first The stickiness overlimit indicator variable for each interval; Location of the train Speed ​​limits at the section; For train speed; , , These are the weighting coefficients; For trains in the section traction force; For trains in the section The walking distance; For the first Control force output by the locomotive in each section; For interval The maximum available adhesive force; and As a penalty factor; and These are weighting coefficients; This represents the average acceleration of the train across all sections during its operation. This represents the average longitudinal impulse generated during train operation. For trains in the section The actual running time.

2. The multi-objective speed curve optimization method considering train wheel-rail adhesion safety according to claim 1, characterized in that, The expression for the longitudinal dynamics model is: In the formula, The total mass of the train; The rotational mass factor; For train speed; For time, The location of the train; The effective traction force or effective braking force of the train; The basic resistance experienced by the train; This adds resistance to the train due to the track conditions.

3. The multi-objective speed curve optimization method considering train wheel-rail adhesion safety according to claim 1, characterized in that, The expression for reconstructing the longitudinal dynamics model is: in, ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; In the formula, Indicates that the train is in the section. The runtime; For trains in the section Control; The total mass of the train; , , , For interval The corresponding resistance constant; The rotational mass factor; Representing an interval The corresponding kinetic energy; Indicates that the train is in the section. The walking distance; , , , , , Representing an interval The corresponding piecewise affine coefficients; , , , , , Representing an interval The corresponding piecewise affine coefficients; , and For defined logical variables, .

4. A multi-objective speed curve optimization device considering train wheel-rail adhesion safety, characterized in that, include: The dynamics model building module is used to establish a longitudinal dynamics model of the train operation process based on the train's operating characteristics and structural characteristics; The multi-objective optimization model construction module is used to establish a multi-objective optimization model for the train operation curve based on the longitudinal dynamics model and the wheel-rail adhesion constraint of the train. The multi-objective optimization model includes a safety evaluation function, an energy-saving evaluation function, a stability evaluation function, and an efficiency evaluation function. The safety evaluation function and the energy-saving evaluation function take into account the soft adhesion constraint between the train's wheel and rail when they are constructed. The soft constraint of the wheel-rail adhesion of the train is as follows: in, In the formula, This refers to the control force output by the locomotive. Under traction conditions, its value is the traction force output by the motor; under braking conditions, its value is the braking force output by the train's brake shoes. The maximum adhesion force that can be provided between the train wheels and rails; The maximum adhesion coefficient; The vertical force is the force between the wheel and the rail. The expression for the multi-objective optimization model of the train operation curve is as follows: in, In the formula, , , , These are the safety evaluation function, energy-saving evaluation function, stability evaluation function, and efficiency evaluation function, respectively; N is the total number of intervals divided into train travel paths; For the first The remaining adhesion margin in each interval; For the first The stickiness overlimit indicator variable for each interval; Location of the train Speed ​​limits at the section; For train speed; , , These are the weighting coefficients; For trains in the section traction force; For trains in the section The walking distance; For the first Control force output by the locomotive in each section; For interval The maximum available adhesive force; and As a penalty factor; and These are weighting coefficients; This represents the average acceleration of the train across all sections during its operation. This represents the average longitudinal impulse generated during train operation. For trains in the section The actual running time; The dynamic model reconstruction module is used to transcribe the nonlinear part of the longitudinal dynamic model into the linear part by applying the piecewise linear affine method and the big M method, so as to obtain the reconstructed longitudinal dynamic model. The optimal velocity-displacement running curve solution module is used to solve the multi-objective optimization model based on the reconstructed longitudinal dynamic model and the MILP algorithm to obtain the optimal velocity-displacement running curve.

5. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the multi-objective speed curve optimization method considering train wheel-rail adhesion safety as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the multi-objective speed curve optimization method considering train wheel-rail adhesion safety as described in any one of claims 1-3.

Images