Method, device and equipment for optimizing running track of heavy-load group train under continuous ramp

Abstract

The application discloses a continuous ramp heavy-load group train operation track optimization method, device and equipment, and relates to the heavy-load train operation control field.The method comprises the following steps: determining a dynamic tracking cooperative operation mode of the heavy-load group train; constructing an operation process of the heavy-load group train, and constructing a multi-particle dynamics model; based on the dynamic tracking cooperative operation mode and the multi-particle dynamics model, considering the influence of the ramp on the minimum safe tracking distance, constructing a multi-objective evaluation model of the heavy-load group train with safety, stability, energy saving and high efficiency as indexes; based on the multi-objective evaluation model, the improved chaotic evolution optimization algorithm is adopted to cooperatively optimize the tracks of the trains in the heavy-load group train, so that the heavy-load group train operation track is obtained; wherein the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm with a sine piecewise linear chaotic mapping introduced. The application can improve the safety, stability, energy saving and high efficiency of the heavy-load group train operation process.

Description

Technical Field

[0001] This application relates to the field of heavy-haul train operation control, and in particular to a method, apparatus and equipment for optimizing the running trajectory of heavy-haul group trains on a continuous slope. Background Technology

[0002] Heavy-haul railways, as a vital channel for transporting bulk commodities, are characterized by large capacity, high efficiency, and low transportation costs, attracting widespread attention and vigorous development from countries worldwide that handle a significant proportion of bulk commodities such as coal and ore. With the continuous growth in railway freight demand, increasing heavy-haul transport capacity has become an urgent priority. Currently, heavy-haul railways primarily increase capacity by lengthening train formations and increasing axle loads. However, this directly leads to dynamic problems such as a sharp increase in coupler force and intensified longitudinal impulse, significantly increasing train operation safety risks and accelerating infrastructure wear and tear. Against this backdrop, train group operation has emerged. Train groups, based on train-to-ground and train-to-train wireless communication technology, combine multiple heavy-haul trains into a coordinated operating group, effectively shortening the tracking distance between trains, increasing line density, and improving overall transport efficiency.

[0003] Heavy-haul railway lines are characterized by complex conditions, a high bridge-to-tunnel ratio, and numerous curves and long gradients. Under these conditions, the operation of heavy-haul train groups is highly susceptible to the influence of track conditions, making it difficult to simultaneously meet the multiple operational requirements of safety, smoothness, energy conservation, and transportation efficiency through manual driver control alone. Therefore, conducting multi-objective optimization research on the operating trajectory of heavy-haul train groups is of great significance, especially considering the complex track conditions of heavy-haul railways. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus, and equipment for optimizing the running trajectory of heavy-load group trains on continuous slopes, which can improve the safety, stability, energy efficiency, and high efficiency of heavy-load group train operation.

[0005] To achieve the above objectives, this application provides the following solution.

[0006] In the first aspect, this application provides a method for optimizing the running trajectory of heavily loaded train groups on continuous slopes, including the following steps.

[0007] A dynamic tracking and cooperative operation mode for heavy-load train groups is determined. The dynamic tracking and cooperative operation mode includes: for two adjacent trains in the heavy-load train group, the reference trajectory of the following train is determined based on the relative speed, relative position and minimum safe tracking distance between the following train and the preceding train; the minimum safe tracking distance varies with the gradient of the line.

[0008] The operation process of a heavy-load train group is constructed, and a multi-mass dynamic model is built.

[0009] Based on the dynamic tracking and cooperative operation mode and the multi-mass dynamics model, and considering the minimum safe tracking distance, a multi-objective evaluation model for heavy-haul train groups is constructed with safety, stability, energy saving, and high efficiency as indicators.

[0010] Based on the multi-objective evaluation model, an improved chaotic evolution optimization algorithm is used to collaboratively optimize the trajectories of each train in the heavy-load train group, thereby obtaining the running trajectory of the heavy-load train group; wherein, the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm that introduces a sinusoidal piecewise linear chaotic mapping.

[0011] Secondly, this application provides a device for optimizing the running trajectory of heavily loaded train groups on continuous slopes, including the following modules.

[0012] The operation mode determination module is used to determine the dynamic tracking and cooperative operation mode of heavy-load group trains; the dynamic tracking and cooperative operation mode includes: for two adjacent trains in the heavy-load group trains, the reference trajectory of the rear train is determined based on the relative speed, relative position and minimum safe tracking distance between the rear train and the front train; the minimum safe tracking distance varies with the gradient of the line.

[0013] The dynamics model building module is used to construct the operation process of heavy-load train groups and build a multi-mass dynamics model.

[0014] The multi-objective evaluation model construction module is used to construct a multi-objective evaluation model for heavy-haul train groups based on the dynamic tracking cooperative operation mode and the multi-mass dynamics model, taking into account the minimum safe tracking distance, with safety, stability, energy saving and efficiency as indicators.

[0015] The trajectory optimization module is used to collaboratively optimize the trajectories of each train in the heavy-load group train based on the multi-objective evaluation model and an improved chaotic evolution optimization algorithm to obtain the running trajectory of the heavy-load group train; wherein, the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm that introduces a sinusoidal piecewise linear chaotic mapping.

[0016] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the method for optimizing the running trajectory of heavy-load group trains on continuous slopes as described above.

[0017] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method, device, and equipment for optimizing the running trajectory of heavy-load group trains on continuous slopes. Based on the dynamic tracking cooperative operation mode and multi-mass dynamics model, considering the minimum safe tracking distance, a multi-objective evaluation model for heavy-load group trains is constructed with safety, stability, energy saving, and efficiency as indicators. Based on the multi-objective evaluation model, a chaotic evolution optimization algorithm that introduces a sinusoidal piecewise linear chaotic mapping is used to collaboratively optimize the running trajectory of each train in the heavy-load group train, thereby obtaining the running trajectory of the heavy-load group train. Compared with the method of relying solely on manual operation by the driver, this improves the safety, stability, energy saving, and efficiency of the heavy-load group train operation process. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, 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.

[0019] Figure 1 This is a flowchart illustrating the method for optimizing the trajectory of heavily loaded train groups on continuous slopes, as provided in an embodiment of this application.

[0020] Figure 2 This is a schematic diagram of the dynamic tracking and cooperative operation mode of group trains provided in an embodiment of this application.

[0021] Figure 3 This is a schematic diagram illustrating the minimum safe tracking distance provided in an embodiment of this application.

[0022] Figure 4 This is a schematic diagram of the force analysis of a group of trains provided in an embodiment of this application.

[0023] Figure 5 A schematic diagram of the dynamic characteristic curve of the QKX100 type buffer provided in the embodiments of this application.

[0024] Figure 6 This is a schematic diagram of the dynamic characteristic curve of the MT-2 type buffer provided in the embodiments of this application.

[0025] Figure 7 This is a schematic diagram of the multi-objective optimization process for heavy-load train groups using the ICEO algorithm, provided in an embodiment of this application.

[0026] Figure 8 This is a schematic diagram of the line data for a certain experimental section of a railway provided in an embodiment of this application.

[0027] Figure 9A schematic diagram of the optimal operating trajectory of the pilot train provided in the embodiments of this application.

[0028] Figure 10 A schematic diagram of the maximum coupler force curve of the pilot train provided in this application embodiment.

[0029] Figure 11 This is a schematic diagram of the optimized trajectory for group train operation provided in an embodiment of this application.

[0030] Figure 12 A schematic diagram showing the tracking distance of the lead train 1 and the follower train 2 provided in the embodiments of this application.

[0031] Figure 13 This is a schematic diagram showing the tracking distance of following train 2 and following train 3 as provided in the embodiments of this application.

[0032] Figure 14 A schematic diagram of the functional modules of the continuous slope heavy-load group train operation trajectory optimization device provided in the embodiments of this application.

[0033] Figure 15 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0034] 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.

[0035] This application addresses the problem that it is difficult to adapt to the differences in track and performance of individual trains when tracking the same reference trajectory on complex lines. It constructs a dynamic tracking and collaborative operation mode for heavy-load train groups, and considers the relationship between gradient and minimum safe tracking distance. A multi-objective evaluation model for train groups is established with safety, stability, energy saving and efficiency as indicators. An improved Chaotic Evolutionary Optimization (ICEO) algorithm is designed to collaboratively optimize the trajectory settings of each train in the group, so as to achieve safe, stable, energy-saving and efficient operation of train groups.

[0036] 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.

[0037] In one exemplary embodiment, such as Figure 1As shown, a method for optimizing the running trajectory of heavily loaded train groups on continuous slopes is provided, including the following steps.

[0038] Step 101: Determine the dynamic tracking and cooperative operation mode of the heavy-load train group.

[0039] The dynamic tracking and cooperative operation mode includes: in the heavy-load group trains, the reference trajectory of the following train is determined based on the relative speed, relative position and minimum safe tracking distance between the following train and the preceding train; the minimum safe tracking distance varies with the gradient of the line.

[0040] Step 102: Construct the operation process of the heavy-load train group and build a multi-mass dynamic model.

[0041] Step 103: Based on the dynamic tracking cooperative operation mode and the multi-mass dynamics model, and considering the minimum safe tracking distance, construct a multi-objective evaluation model for heavy-haul train groups with safety, stability, energy saving, and high efficiency as indicators.

[0042] Step 104: Based on the multi-objective evaluation model, an improved chaotic evolutionary optimization algorithm is used to collaboratively optimize the trajectories of each train in the heavy-load group train to obtain the running trajectory of the heavy-load group train.

[0043] Among them, the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm that introduces a sine-piecewise linear chaotic map (SPM).

[0044] In another exemplary embodiment of this application, in step 101, taking a 3-unit 10,000-ton heavy-haul train as an example, a dynamic tracking and cooperative operation mode for heavy-haul group trains is constructed: based on the influence of actual track conditions on braking distance, the minimum safe tracking distance between the front and rear trains is dynamically set, considering multiple operational constraints and multiple operational objectives, the optimal reference trajectory of each train is optimized, and the group trains are ensured to track each other safely while cooperating in operation by tracking their respective optimal reference trajectories.

[0045] In another exemplary embodiment of this application, the formula for calculating the minimum safe tracking distance is as follows.

[0046] .

[0047] in, Minimum safe tracking distance; This refers to the travel distance of the following train caused by communication delays between adjacent trains during operation. This is the emergency braking distance of the vehicle in front. The distance required for the following vehicle to stop with maximum braking force in non-emergency braking mode (i.e., the maximum common braking distance of the following vehicle). This is the static safety protection distance; and Determined based on track gradient. The minimum safe tracking distance between adjacent trains within a group should be greater than or equal to the static safety protection distance.

[0048] When calculating train braking distance, this embodiment considers the impact of actual track conditions on braking distance, including the braking distance of freight trains. The calculation method is shown in the following formula.

[0049] .

[0050] In the formula, This refers to the distance the train traveled empty. The effective braking distance of the train. Indicates the initial braking velocity. This refers to the time the train travels empty. Indicates the final braking speed. This indicates the converted friction coefficient of the brake shoe. This indicates the converted braking rate of the train. The basic resistance is represented by the equivalent unit of distance. Indicates the gradient of the route.

[0051] The calculation method for the empty travel time of freight trains is shown in the following formula.

[0052] .

[0053] In the formula, This refers to the time the train travels empty during emergency braking. This refers to the train's normal braking idle time. Indicates the number of vehicles towed by the locomotive. This indicates the amount of pressure reduction in the train pipe.

[0054] As can be seen from the above formula, both the train's empty running distance and effective braking distance are related to the track gradient, which in turn affects the train's braking distance and further affects the minimum safe following distance.

[0055] In another exemplary embodiment of this application, in step 102, a multi-mass force analysis is performed on the operation process of the heavy-haul train group to establish the first... A multi-mass dynamics model of a heavy-haul train is provided, and the expression of the multi-mass dynamics model is as follows.

[0056] ; in, , and They represent the first The first heavy-haul train The speed, displacement, and mass of the vehicle; for The first derivative; for The first derivative; Indicates the locomotive's traction force or electric braking force; Indicates the first The braking force provided by the air braking system of a heavy-haul train; This indicates the additional resistance caused by curves, slopes, and tunnels along the track; Indicates the first The first heavy-haul train Section of vehicles and the first The coupling force between the vehicles; Indicates the first The first heavy-haul train Section of vehicles and the first The coupling force between the vehicles; Indicates the first The first heavy-haul train The basic resistance experienced by a vehicle includes: mechanical friction resistance, impact vibration resistance, and air resistance.

[0057] In another exemplary embodiment of this application, step 103 specifically includes the following steps.

[0058] (1) Based on the dynamic tracking cooperative operation mode and the multi-mass dynamic model, a safety evaluation model is constructed according to the coupler force during train operation and the speed of the train when passing through a curve. A stability evaluation model is constructed according to the acceleration of train operation and the control force of train operation. An energy-saving evaluation model is constructed according to the running time, operating conditions and current active current. An efficient evaluation model is constructed according to the running time and the minimum safe tracking distance.

[0059] (2) Based on the safety evaluation model, the stability evaluation model, the energy-saving evaluation model and the high-efficiency evaluation model, a multi-objective evaluation model for heavy-haul group trains is constructed by weighted summation.

[0060] In another exemplary embodiment of this application, the expression of the security evaluation model is as follows.

[0061] .

[0062] in, This is the safety evaluation value; For the train The maximum hook force that occurs during this operation; For the train The absolute value of the maximum hooking force that occurs during this operation; This represents the average value of the maximum hooking force during train operation within the population. This represents the average value of the maximum hook-up force during train operation within the population. For the train The number of times the coupler force exceeds the set coupler force value during each operation, where the set coupler force value is the rated maximum coupler force multiplied by a coefficient. The obtained value; This represents the average number of times the train force exceeds the set coupler force value during train operation within the population. For the train During this operation and The reciprocal of the difference; For the train Speed ​​when passing through curves during the next run; Speed ​​limits are set for curves; , , and The weighting coefficients of the safety evaluation model satisfy the following conditions: .

[0063] The expression for the stationary evaluation model is as follows.

[0064] .

[0065] in, The evaluation value is stable. For the train Root mean square of control force during each run; For the train Root mean square of acceleration during each run; It represents the average value of the root mean square of the train operation control force in the population; This represents the average root mean square value of the train's acceleration within the population. and To ensure the stability of the evaluation model's weight coefficients, the following conditions must be met: .

[0066] The expression for the energy-saving evaluation model is as follows.

[0067] .

[0068] in, This is the energy-saving evaluation value; For the train Energy consumption during each run; For the train Energy consumption during traction operation in the first run; For the train Energy consumption during coasting, braking and stopping during each run; This represents the average energy consumption of train operation within the population.

[0069] The high-efficiency evaluation model includes the lead train high-efficiency evaluation model and the follow train high-efficiency evaluation model.

[0070] The expression for the high-efficiency evaluation model of the pilot train is as follows.

[0071] .

[0072] The expression for the efficient evaluation model of the following train is as follows.

[0073] .

[0074] in, The high efficiency evaluation value for the leading train; To provide an efficient evaluation value for following trains; For the lead train The runtime of each run; The travel time for the lead train in each section; The total number of intervals; This represents the average travel time of the lead train within the population. This is the minimum safe tracking distance between adjacent trains in each section; This represents the actual tracking distance between adjacent trains in each section. To follow the train The sum of the differences between the actual tracking distance and the minimum safe tracking distance in each interval during the next run; It is the average of the differences between the actual tracking distance and the minimum safe tracking distance in each section of the population when following the train.

[0075] Under the condition of satisfying all constraints, considering the proportion of the importance of safety, stability, energy saving and efficiency to the operation of the train group, and selecting appropriate weighting coefficients, the expression of the multi-objective evaluation model is as follows.

[0076] .

[0077] .

[0078] in, For the multi-objective evaluation value of the leading train, To obtain the multi-objective evaluation value for following the train, the multi-objective evaluation value is used as the multi-objective fitness value; , , and The weight coefficients of the multi-objective evaluation model for the pilot train satisfy the following conditions. , , , and The weighting coefficients of the multi-objective evaluation model for following trains must satisfy... .

[0079] In another exemplary embodiment of this application, the Chaotic Evolutionary Optimization (CEO) algorithm is improved. Considering that the CEO algorithm utilizes the hyperchaotic characteristics of a two-dimensional discrete memristor map to provide diverse evolutionary directions during iteration, but its initial population is random, it is difficult to guarantee uniform coverage of the search space, which to some extent limits its global search capability. Faced with the diverse changes in heavy-haul railway lines, to further improve the global search capability, an improved CEO algorithm based on the SPM chaotic mapping is designed, generating the optimal running trajectory adapted to heavy-haul train groups based on a multi-objective evaluation model for group trains.

[0080] Step 104 of this embodiment specifically includes the following steps.

[0081] (1) Obtain train line data for heavy-load train groups. The train line data includes: line gradient data, line curve data, and line tunnel data, etc.

[0082] (2) The initial operating condition sequence population of each train is generated by using SPM chaotic mapping; each individual in the initial operating condition sequence population corresponds to an initial operating condition sequence.

[0083] The SPM chaotic mapping method in this embodiment has the following function expression.

[0084] .

[0085] .

[0086] in, This represents modulo-1 operation. and These are the control parameters for the chaotic mapping, taken here as... =0.4, =0.3. and These represent the iterations of the chaotic sequence, respectively. Step and the first The chaotic state values ​​of the step, both of which take values ​​of [0,1); Indicates will Substitute into the SPM chaotic mapping function The chaotic state values ​​calculated in the middle; The phase parameter represents an interval. Random numbers on the array.

[0087] SPM chaotic sequence The initial working condition sequence obtained by mapping to the solution space The expression is as follows.

[0088] .

[0089] In the formula, and These are the upper and lower bounds of the population solution space, respectively. Based on population size... Repeat the SPM chaotic mapping operation to generate Each initial working condition sequence individual constitutes the initial working condition sequence population.

[0090] (3) The multi-objective fitness value of each individual in the initial working condition sequence population is calculated using the multi-objective evaluation model.

[0091] (4) Select two different individuals from the current population and perform two-dimensional memristor hyperchaotic mapping respectively. Perform mutation and crossover operations on each mapped individual to generate experimental individuals. Construct the corresponding current experimental population based on the experimental individuals of each individual. In the first iteration, the current population is the initial working condition sequence population.

[0092] (5) For the current experimental population corresponding to either of the two selected individuals, calculate the multi-objective fitness value of each experimental individual in the current experimental population, and determine the current optimal experimental individual based on the current multi-objective fitness value.

[0093] (6) For the current best experimental individual corresponding to either of the two selected individuals, the elite selection strategy is adopted to compare the current best experimental individual with the multi-objective fitness value of the corresponding selected individual, and the individual with the smaller multi-objective fitness value is selected to update the selected individual.

[0094] (7) Determine whether each individual in the current population has been selected once, and obtain the first judgment result.

[0095] If the first judgment result is negative, return to step (4) to reselect two individuals, and execute steps (4)-(6) again to determine whether each individual in the current population has been selected once. If the first judgment result is positive, determine whether the maximum number of iterations has been reached to obtain the second judgment result.

[0096] If the second judgment result is negative, the updated population is used as the current population, and the process returns to step (4). If the second judgment result is positive, the updated population is used as the optimal population, and the multi-objective fitness value of each individual in the optimal population is calculated to determine the optimal individual. The working condition sequence corresponding to the optimal individual is determined as the global optimal working condition sequence. The global optimal working condition sequence is decoded to obtain the speed-displacement curve of the train in the heavy-load group. The speed-displacement curve represents the train's running trajectory.

[0097] The method for optimizing the trajectory of heavy-load group trains on continuous slopes in this embodiment realizes the multi-objective optimization process of the trajectory of heavy-load group trains using the ICEO algorithm. It considers the relationship between the slope and the minimum safe tracking distance, establishes a multi-objective evaluation model of safety, stability, energy saving and efficiency, and performs collaborative optimization of the trajectories of each group train through the ICEO algorithm, thereby achieving safe, stable, energy-saving and efficient operation of heavy-load group trains.

[0098] The following section uses three 10,000-ton heavy-haul trains as an example to further explain the optimization method for the running trajectory of heavy-haul train groups on continuous slopes.

[0099] This embodiment addresses the problem of difficulty in adapting to the differences in track conditions and performance among individual trains when tracking a single reference trajectory on complex lines. It constructs a dynamic tracking and collaborative operation mode for group trains. To ensure that the group trains operate according to this mode, a dynamic model needs to be established for each train. To accurately simulate the operating state and stress conditions of the group trains, each car of each heavy-haul train is simplified as a point mass, establishing a multi-point mass dynamic model. Based on the established group train tracking operation mode and multi-point mass dynamic model, considering the relationship between gradient and minimum safe tracking distance, a multi-objective evaluation model for the group trains is established with safety, stability, energy saving, and high efficiency as indicators. The ICEO algorithm is used to collaboratively optimize the trajectories of each train in the group.

[0100] The multi-objective optimization process of the heavy-load group train operation trajectory based on the ICEO algorithm in this embodiment is as follows.

[0101] (1) Constructing a dynamic tracking and collaborative operation mode for group trains. This embodiment takes three 10,000-ton heavy-haul trains as an example to construct a dynamic tracking and collaborative operation mode for group trains. Figure 2The diagram illustrates a dynamic tracking and collaborative operation mode for group trains. Based on the order of their tracking positions, trains are divided into lead train 1, following train 2, and following train 3. First, the optimal reference trajectory for lead train 1 is optimized with the goals of safety, stability, energy conservation, and efficiency. For following train 2, it does not directly track the tail of lead train 1 at the same speed. Instead, its reference trajectory is optimized based on the relative speed and position of following train 2 and following train 1, as well as the influence of track gradient on the minimum safe tracking distance. This trajectory is then used for following train 2's tracking operation. Following train 3, with following train 2 as its lead train, employs the same optimization strategy.

[0102] (2) Minimum safe following distance setting between trains. During train group operation, the distance between trains is no longer based solely on the static state of the preceding train, but also considers the relative speed and position of the trains. The minimum safe following distance between trains is as follows: Figure 3 As shown: If the preceding train encounters an emergency and applies emergency braking, its status information is transmitted to the following train via train-to-train communication. To ensure train safety, the following train will activate its maximum service braking, bringing both trains to a stop. Once the trains have come to a complete stop, a static safety distance will still be maintained between the following and preceding trains.

[0103] Therefore, in the worst-case scenario, a minimum safe tracking distance can be set between the vehicles in front and behind. The specific expression will not be elaborated here.

[0104] (3) Calculate the train braking distance. The specific expression will not be repeated here.

[0105] (4) Departure process of group trains. In order to significantly shorten the departure interval, the departure process of group trains is set as follows: After the lead train 1 departs from the main line, the follow train 2 waits for departure on the siding, while the follow train 3 enters the main line to wait for the departure opportunity. When the lead train 1 travels to a position that is 1 static safety protection distance away from the follow train 2, the follow train 2 departs. Similarly, when the follow train 2 travels to a position that is 1 static safety protection distance away from the follow train 3, the follow train 3 departs.

[0106] The formula for calculating the actual tracking distance between adjacent trains during operation is as follows.

[0107] .

[0108] In the formula, This indicates the actual tracking distance between following train 2 and lead train 1. The actual tracking distance between following train 3 and following train 2. , and These are the distances traveled by the lead train 1, the following train 2, and the following train 3 during their operation. Indicates the length of the train.

[0109] It should be noted that the tracking distance here refers to the distance between the front of the following vehicle and the rear of the preceding vehicle. The position of the rear of the preceding vehicle is determined by its overall vehicle position and the integrity of the train.

[0110] (5) Establish a multi-mass dynamic model for heavy-haul train groups. In this embodiment, each car of each heavy-haul train is simplified as a mass point. Taking into account traction / braking force, basic resistance, additional resistance, and coupler force, a multi-mass force analysis is performed on the train group as follows: Figure 4 As shown, then the first The dynamic differential equations for the operation of a heavy-haul train are as follows.

[0111] .

[0112] According to Davis's equation The expression is as follows.

[0113] .

[0114] In the formula, , and This is an empirical coefficient related to the train type.

[0115] The coupler buffer system employs the QKX100 / 13A coupler buffer system and the MT-2 / 16 coupler buffer system, connecting the locomotive and freight car, and the freight car and freight car, respectively. The dynamic characteristic curve of the QKX100 buffer is shown below. Figure 5 As shown, Figure 5 The solid line represents the impedance force of the QKX100 buffer when it is under load, and the dashed line represents the impedance force of the QKX100 buffer when it is under unload. The mathematical model of its coupler force is as follows.

[0116] .

[0117] In the formula, For the coupler force; For buffer switching speed; and These represent the impedance forces of the buffer when it is in the loaded and unloaded states, respectively. and The relative speed and relative displacement of the two train carriages are given.

[0118] The dynamic characteristic curve of the MT-2 buffer is as follows: Figure 6 As shown, Figure 6The solid line represents the impedance force of the MT-2 buffer when it is under load, and the dashed line represents the impedance force of the MT-2 buffer when it is under unload. The mathematical model of its coupler force is as follows.

[0119] When satisfied When using this judgment condition, Perform calculations; if the conditions are not met, then use... Perform the calculation.

[0120] In the formula, , These represent the relative displacement and relative velocity of the two particles at the current moment, respectively. , These are the relative displacements and relative velocities of the two particles at the previous moment, respectively. This refers to the structural stiffness of the buffer.

[0121] (6) Establish a multi-objective evaluation model for the operation trajectory of heavy-load group trains. In this embodiment, considering the relationship between gradient and minimum safe following distance, a multi-objective evaluation model is established with safety, stability, energy saving, and efficiency as the four main optimization objectives. Among them, the efficiency index of the lead train focuses on shortening its travel time to the end of the line as much as possible, while the efficiency index of the following train focuses on controlling its actual following distance from the preceding train, so that it is as close as possible to the dynamically changing minimum safe following distance.

[0122] ① Safety evaluation model.

[0123] The safety requirements for trains stipulate that the coupler force during train operation should be less than the value recommended by the China Academy of Railway Sciences: the maximum coupler force during normal train operation should be controlled within 1000kN to achieve the goal of safe train operation. Simultaneously, considering the impact of curves on train operation safety, the train speed when passing through curves should be as low as possible below the curve speed limit to ensure safe operation. The established safety evaluation model is as follows.

[0124] .

[0125] .

[0126] .

[0127] .

[0128] In the formula, For safety evaluation values, Indicates the train number The constantly operating coupler force This refers to the maximum rated coupler force during train operation. This is a proportionality coefficient, ranging from 0.75 to 1, for train number... During this operation, a total of At the moment, if the first time and The ratio is greater than Then the first time The value is 1 if it is true, otherwise it is 0. For the train The number of times the coupler force exceeds the set coupler force value during each operation. For the train The maximum hook force encountered during this operation For the train The absolute value of the maximum hooking force that occurs during this operation. This represents the average value of the maximum hook-up force during train operation within the population. This represents the average value of the maximum hook-up force during train operation within the population. This represents the average number of times the coupler force exceeds a set coupler force value during train operation within the population. For the train During this operation and The reciprocal of the difference For the train Speed ​​when passing through curves during this run Speed ​​limits are in place for curves. During train operation within the population and The average of the reciprocals of the differences Population size.

[0129] ②Stability evaluation model.

[0130] The stability evaluation model primarily evaluates train operation based on acceleration and control force. It requires minimal changes in acceleration and control force during train operation to achieve stable train operation. The established stability evaluation model is as follows.

[0131] .

[0132] .

[0133] In the formula, To ensure stable evaluation values, For the train The root mean square of the control force during this operation. For the train The root mean square of acceleration during this run This represents the root mean square value of the train operation control force in the population. This represents the average root-mean-square acceleration of trains within the population. Population size.

[0134] ③ Energy-saving evaluation model.

[0135] The energy-saving evaluation model requires trains to operate with minimal or no energy consumption. This model is mainly determined by operating time, operating conditions, and current active current. The established energy-saving evaluation model is as follows.

[0136] .

[0137] .

[0138] .

[0139] .

[0140] In the formula, This is the energy-saving evaluation value. Energy consumption during train traction operation. This refers to the energy consumption during train coasting, braking, and station stops. For the pantograph voltage of the locomotive; For train traction operation time, For train coasting, air braking, and station stopping time, Active current for locomotive traction power, It is related to the speed under the current traction conditions. This refers to the active current used for locomotive coasting, braking, and stopping. These are fixed parameters. Population size.

[0141] ④ High-efficiency evaluation model.

[0142] 1) High-efficiency evaluation model for leading trains.

[0143] The efficient evaluation model for the lead train requires that the travel time of the lead train to the end of the line be as short as possible. To more accurately optimize the overall travel time, the entire line is finely divided into... The model for evaluating the efficiency of the pilot train is as follows, considering several sub-intervals with similar routes.

[0144] .

[0145] .

[0146] In the formula, The high efficiency evaluation value for the leading train. For the lead train The runtime of each run. The travel time for the lead train in each section. The total number of intervals, This represents the average travel time of the lead train within the population. Population size.

[0147] 2) Train-following high-efficiency evaluation model.

[0148] Train braking distance varies with track gradient, therefore the minimum safe following distance also changes dynamically. To improve operational efficiency, the high efficiency index for following trains requires that the actual following distance to the preceding train should be as close as possible to the dynamically changing minimum safe following distance. Using the aforementioned sub-section division, the high efficiency evaluation model for following trains is established as follows.

[0149] .

[0150] .

[0151] In the formula, To follow the train's efficient evaluation value, This represents the minimum safe tracking distance between adjacent trains in each section. This represents the actual tracking distance between adjacent trains in each section. The total number of intervals, Population size. To follow the train During the second run, the sum of the differences between the actual tracking distance and the minimum safe tracking distance in each interval, It is the average of the differences between the actual tracking distance and the minimum safe tracking distance in each section of the population when following the train.

[0152] (7) Design of a multi-objective optimization method for the trajectory of heavy-load train groups based on the ICEO algorithm. This embodiment implements multi-objective optimization of the trajectory of heavy-load train groups based on the ICEO algorithm, and its principle diagram is shown below. Figure 7 As shown.

[0153] Step 1: Input train route data.

[0154] Step 2: Generate trains using SPM chaotic mapping. The initial operating condition sequence population.

[0155] Step 3 Calculate the train The safety, stability, energy efficiency, and high multi-objective fitness of each individual in the initial population.

[0156] Step 4: Select two different individuals from the current population and perform two-dimensional memristor hyperchaotic mapping on them respectively. Then, perform mutation and crossover operations to generate experimental individuals and form two experimental populations.

[0157] Step 5: Calculate the safety, stability, energy efficiency, and high-efficiency multi-objective fitness of each individual in the two experimental populations, and obtain the two optimal experimental individuals respectively.

[0158] Step 6: Employ an elite selection strategy, compare the fitness of the two optimal experimental individuals with that of the two currently selected individuals, select the individual with the lower fitness, and thus update the two currently selected individuals.

[0159] Step 7: Determine if each individual in the current population has been selected once, and proceed to the next iteration; otherwise, go back to Step 4 and continue the selection process.

[0160] Step 8: Determine if the maximum number of iterations has been reached, and output the train. If the global optimal operating condition sequence is not found, proceed to Step 4 and continue the cyclical update.

[0161] Step 9: Determine if all trains in the group have been optimized, then end the loop; otherwise, proceed to Step 2 to continue optimization.

[0162] Decoding the global optimal operating condition sequence of each train in the group yields the corresponding speed-displacement curves, which are the optimal operating trajectories of each train in the group after optimization based on the ICEO algorithm. Driving along these trajectories can ensure the safety, stability, energy efficiency, and high efficiency of the group train operation.

[0163] The following simulation, based on the target train operation curve obtained from the experience of an excellent driver of an HXD1 heavy-haul train on a certain railway, uses real line data from a certain section of the railway as experimental data for optimization. The simulation parameters are: three 10,000-ton heavy-haul trains are used as the experimental objects, with each train pulled by two HXD1 locomotives carrying 104 C80 freight cars. Specifically, the optimal operating trajectory of the lead train, conforming to the line control principles, is first obtained through ICEO algorithm optimization. To further verify the optimization effect of the ICEO algorithm, its results are compared and analyzed with those of a genetic algorithm (GA). Next, based on the established group train multi-objective evaluation model, the following trains are sequentially optimized using the ICEO algorithm, departing according to the aforementioned departure process. The departure interval between train 2 and train 1 is 238.8 seconds, and the departure interval between train 3 and train 2 is 229.3 seconds.

[0164] Data on gradients, curves, and tunnels of a certain section of the actual railway line, as follows: Figure 8 As shown.

[0165] Figure 9 The optimal operating trajectory of the lead train is shown. Figure 10 The maximum coupler force curve of the lead train is shown. Figure 11 The optimized trajectory for group train operation is shown. Figure 12 and Figure 13 The tracking distance between adjacent trains is shown.

[0166] from Figure 9 As can be seen, compared with the GA algorithm, the ICEO algorithm obtains a smoother trajectory change, which helps to improve the stability of train operation. From Figure 10 As can be seen, the maximum hooking force and maximum hooking force of the ICEO algorithm are less than the corresponding values ​​of the GA algorithm at most vehicle positions, indicating that the ICEO algorithm can optimize and obtain a running trajectory that significantly reduces the coupler force, which can reduce the wear on the coupler buffer device.

[0167] from Figure 11 , Figure 12 , Figure 13 As can be seen, the minimum safe tracking distance between adjacent trains during group train operation dynamically changes with the gradient. In sections with drastic gradient changes, this distance fluctuates frequently and significantly, but the actual tracking distance is always greater than the minimum safe tracking distance. Furthermore, while meeting safety constraints, the redundant tracking distance between adjacent trains is significantly reduced, thus improving operational efficiency.

[0168] To further verify the optimization effect of the ICEO algorithm, some data from the simulation results were extracted for comparative analysis. Table 1 shows a comparison of the optimization results of the lead train using the ICEO algorithm and the GA algorithm, and Table 2 shows the optimization results of the group train reference trajectory.

[0169] As shown in Table 1, compared with the GA algorithm, the ICEO algorithm optimizes the maximum hooking force, maximum hooking force, root mean square acceleration, and train running energy consumption to the minimum, and also minimizes the train running time, achieving better global optimization results for each model. Table 2 shows that when trains are running in a group, the actual tracking distance between adjacent trains is significantly reduced, and the operating efficiency is improved.

[0170] Table 1 Comparison of Optimization Results of Leading Train

[0171] Table 2 Optimization results of reference trajectory for group trains

[0172] Multiple simulation results show that optimizing the trajectory of heavy-haul train groups using the ICEO algorithm can effectively improve the safety, stability, energy efficiency, and high efficiency of the train operation process.

[0173] Based on the same inventive concept, this application also provides a device for optimizing the trajectory of heavy-load train groups on continuous slopes, used to implement the aforementioned method for optimizing the trajectory of heavy-load train groups on continuous slopes. 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 device for optimizing the trajectory of heavy-load train groups on continuous slopes provided below can be found in the limitations of the method for optimizing the trajectory of heavy-load train groups on continuous slopes described above, and will not be repeated here.

[0174] In one exemplary embodiment, a trajectory optimization device for heavy-load group trains on continuous slopes is provided. Addressing the trajectory optimization problem of group trains in actual heavy-load railway operations, an improved Chaotic Evolutionary Optimization (ICEO) algorithm is designed, and a trajectory optimization strategy for group trains is proposed. Considering the complexity of heavy-load railways, a dynamic tracking and cooperative operation mode and a multi-mass longitudinal dynamic model for group trains are constructed. The ICEO algorithm is used to collaboratively optimize the trajectories of each group train, improving the safety, stability, energy efficiency, and overall efficiency of heavy-load group train operations. Figure 14 As shown, the trajectory optimization device for heavy-load train groups on continuous slopes includes the following modules.

[0175] The operation mode determination module is used to determine the dynamic tracking and cooperative operation mode of heavy-load group trains; the dynamic tracking and cooperative operation mode includes: for two adjacent trains in the heavy-load group trains, the reference trajectory of the rear train is determined based on the relative speed, relative position and minimum safe tracking distance between the rear train and the front train; the minimum safe tracking distance varies with the gradient of the line.

[0176] The dynamics model building module is used to construct the operation process of heavy-load train groups and build a multi-mass dynamics model.

[0177] The multi-objective evaluation model construction module is used to construct a multi-objective evaluation model for heavy-haul train groups based on the dynamic tracking cooperative operation mode and the multi-mass dynamics model, taking into account the minimum safe tracking distance, with safety, stability, energy saving and efficiency as indicators.

[0178] The trajectory optimization module is used to collaboratively optimize the trajectories of each train in the heavy-load group train based on the multi-objective evaluation model and an improved chaotic evolution optimization algorithm to obtain the running trajectory of the heavy-load group train; wherein, the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm that introduces a sinusoidal piecewise linear chaotic mapping.

[0179] 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 15As shown, this 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 in the non-volatile storage media. The database stores the operating trajectories of heavy-load train groups. 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 executed by the processor, the computer program implements a method for optimizing the operating trajectories of heavy-load train groups on continuous gradients.

[0180] Those skilled in the art will understand that Figure 15 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer equipment to which the present application is applied. Specific computer equipment may include, for example, [the following is a list of possible additional structures]. Figure 15 The embodiments show more or fewer components, combinations of certain components, or different component arrangements. In one exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, which the processor executes to implement the steps in the above-described method embodiments.

[0181] 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.

[0182] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0183] 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.

[0184] Those skilled in the art will understand that all or part of the processes in the methods of 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 of the above methods. 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).

[0185] 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, etc., and are not limited to these.

[0186] 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.

[0187] 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 method for optimizing the trajectory of a heavy-load group train on a continuous ramp, characterized in that, include: Determine the dynamic tracking and coordinated operation mode of heavy-load train groups; The dynamic tracking and cooperative operation mode includes: in the heavy-load group trains, the reference trajectory of the following train is determined based on the relative speed, relative position and minimum safe tracking distance between the following train and the preceding train; the minimum safe tracking distance varies with the gradient of the line; The operation process of heavy-haul train groups is constructed, and a multi-mass dynamics model is built; Based on the dynamic tracking cooperative operation mode and the multi-mass dynamics model, and considering the minimum safe tracking distance, a multi-objective evaluation model for heavy-haul group trains is constructed with safety, stability, energy saving, and high efficiency as indicators. Based on the multi-objective evaluation model, an improved chaotic evolution optimization algorithm is used to collaboratively optimize the trajectories of each train in the heavy-load train group, thereby obtaining the running trajectory of the heavy-load train group; wherein, the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm that introduces a sinusoidal piecewise linear chaotic mapping.

2. The method for optimizing the trajectory of heavily loaded train groups on continuous slopes according to claim 1, characterized in that, Based on the dynamic tracking and cooperative operation mode and the multi-mass dynamics model, and considering the minimum safe tracking distance, a multi-objective evaluation model for heavy-haul train groups is constructed with safety, stability, energy saving, and high efficiency as indicators. Specifically, this includes: Based on the dynamic tracking cooperative operation mode and the multi-mass dynamics model, a safety evaluation model is constructed according to the coupler force during train operation and the speed of the train when passing through a curve; a stability evaluation model is constructed according to the acceleration of train operation and the control force of train operation; an energy-saving evaluation model is constructed according to the running time, operating conditions and current active current; and an efficiency evaluation model is constructed according to the running time and the minimum safe tracking distance. Based on the safety evaluation model, the stability evaluation model, the energy-saving evaluation model, and the high-efficiency evaluation model, a multi-objective evaluation model for heavy-haul train groups is constructed using a weighted summation method.

3. The method for optimizing the trajectory of heavily loaded train groups on continuous slopes according to claim 1, characterized in that, Based on the aforementioned multi-objective evaluation model, an improved chaotic evolutionary optimization algorithm is used to collaboratively optimize the trajectories of individual trains in a heavy-haul train group, resulting in the train group's trajectory, specifically including: Obtain train route data for heavy-load train groups; A sinusoidal piecewise linear chaotic mapping is used to generate an initial operating condition sequence population for each train; each individual in the initial operating condition sequence population corresponds to one initial operating condition sequence. The multi-objective fitness value of each individual in the initial working condition sequence population is calculated using the multi-objective evaluation model. Two different individuals are selected from the current population and subjected to two-dimensional memristor hyperchaotic mapping. Mutation and crossover operations are performed on each mapped individual to generate experimental individuals. The current experimental population is constructed based on the experimental individuals of each individual. In the first iteration, the current population is the initial working condition sequence population. For the current experimental population corresponding to either of the two selected individuals, calculate the multi-objective fitness value of each experimental individual in the current experimental population, and determine the current optimal experimental individual based on the current multi-objective fitness value; For the current best experimental individual corresponding to either of the two selected individuals, an elite selection strategy is adopted to compare the current best experimental individual with the multi-objective fitness value of the corresponding selected individual, and the individual with the smaller multi-objective fitness value is selected to update the selected individual; Determine whether each individual in the current population has been selected once to obtain the first determination result; If the first judgment result is negative, then return to the step of selecting two different individuals from the current population and performing two-dimensional memristor hyperchaotic mapping respectively; If the first judgment result is yes, then determine whether the maximum number of iterations has been reached to obtain the second judgment result; If the second judgment result is negative, then the updated population is taken as the current population, and the step of selecting two different individuals from the current population and performing two-dimensional memristor hyperchaotic mapping is returned. If the second judgment result is yes, then the updated population is taken as the optimal population, and the multi-objective fitness value of each individual in the optimal population is calculated to determine the optimal individual. The working condition sequence corresponding to the optimal individual is determined as the global optimal working condition sequence. The global optimal working condition sequence is decoded to obtain the speed-displacement curve of the train in the heavy load group; the speed-displacement curve represents the train running trajectory.

4. The method for optimizing the trajectory of heavily loaded train groups on continuous slopes according to claim 2, characterized in that, The expression for the safety evaluation model is: ； in, This is the safety evaluation value; For the train The maximum hook force that occurs during this operation; For the train The absolute value of the maximum hooking force that occurs during this operation; This represents the average value of the maximum hooking force during train operation within the population. This represents the average value of the maximum hook-up force during train operation within the population. For the train The number of times the coupler force exceeds the set coupler force value during each operation; This represents the average number of times the coupler force exceeds a set coupler force value during train operation within the population. For the train During this operation and The reciprocal of the difference; For the train Speed ​​when passing through curves during the next run; Speed ​​limits are set for curves; , , and The weighting coefficients of the safety evaluation model satisfy the following conditions: ; The expression for the stationary evaluation model is: ； in, The evaluation value is stable. For the train Root mean square of control force during each run; For the train Root mean square of acceleration during each run; It represents the average value of the root mean square of the train operation control force in the population; This represents the average root mean square value of the train's acceleration within the population. and To ensure the stability of the evaluation model's weight coefficients, the following conditions must be met: ; The expression for the energy-saving evaluation model is: ； in, This is the energy-saving evaluation value; For the train Energy consumption during each run; For the train Energy consumption during traction operation in the first run; For the train Energy consumption during coasting, braking and stopping during each run; This represents the average energy consumption of train operation within the population. The high-efficiency evaluation model includes the leading train high-efficiency evaluation model and the following train high-efficiency evaluation model; The expression for the high-efficiency evaluation model of the pilot train is: ； The expression for the efficient evaluation model of the following train is: ； in, The high efficiency evaluation value for the leading train; To provide an efficient evaluation value for following trains; For the lead train The runtime of each run; The travel time for the lead train in each section; The total number of intervals; This represents the average travel time of the lead train within the population. This is the minimum safe tracking distance between adjacent trains in each section; This represents the actual tracking distance between adjacent trains in each section. To follow the train The sum of the differences between the actual tracking distance and the minimum safe tracking distance in each interval during the next run; It is the average of the differences between the actual tracking distance and the minimum safe tracking distance in each section of the population when following the train.

5. The method for optimizing the trajectory of heavy-load train groups on continuous slopes according to claim 4, characterized in that, The expression for the multi-objective evaluation model is: ； ； in, For the multi-objective evaluation value of the leading train, To obtain the multi-objective evaluation value for following the train, the multi-objective evaluation value is used as the multi-objective fitness value; , , and The weight coefficients of the multi-objective evaluation model for the pilot train satisfy the following conditions. , , , and The weighting coefficients of the multi-objective evaluation model for following trains must satisfy... .

6. The method for optimizing the trajectory of heavily loaded train groups on continuous slopes according to claim 1, characterized in that, The expression for the multi-mass dynamics model is: ； in, , and They represent the first The first heavy-haul train The speed, displacement, and mass of the vehicle; for The first derivative; for The first derivative; Indicates the locomotive's traction force or electric braking force; Indicates the first The braking force provided by the air braking system of a heavy-haul train; This indicates the additional resistance caused by curves, slopes, and tunnels along the track; Indicates the first The first heavy-haul train Section of vehicles and the first Coupler force between vehicles; Indicates the first The first heavy-haul train Section of vehicles and the first The coupling force between the vehicles; Indicates the first The first heavy-haul train The basic resistance experienced by a vehicle includes: mechanical friction resistance, impact vibration resistance, and air resistance.

7. The method for optimizing the trajectory of heavily loaded train groups on continuous slopes according to claim 1, characterized in that, The formula for calculating the minimum safe tracking distance is: ； in, Minimum safe tracking distance; This refers to the travel distance of the following train caused by communication delays between adjacent trains during operation. This is the emergency braking distance of the vehicle in front. The distance required for the following vehicle to stop with maximum braking force in non-emergency braking mode; This is the static safety protection distance; and Determined based on the gradient of the line.

8. A device for optimizing the trajectory of heavily loaded train groups on continuous slopes, characterized in that, include: The operation mode determination module is used to determine the dynamic tracking and cooperative operation mode of heavy-load train groups; The dynamic tracking and cooperative operation mode includes: in the heavy-load group trains, the reference trajectory of the following train is determined based on the relative speed, relative position and minimum safe tracking distance between the following train and the preceding train; the minimum safe tracking distance varies with the gradient of the line; The dynamics model building module is used to construct the operation process of heavy-haul train groups and build a multi-mass dynamics model; The multi-objective evaluation model construction module is used to construct a multi-objective evaluation model for heavy-haul train groups based on the dynamic tracking cooperative operation mode and the multi-mass dynamics model, taking into account the minimum safe tracking distance, with safety, stability, energy saving and efficiency as indicators. The trajectory optimization module is used to collaboratively optimize the trajectories of each train in the heavy-load group train based on the multi-objective evaluation model and an improved chaotic evolution optimization algorithm to obtain the running trajectory of the heavy-load group train; wherein, the improved chaotic evolution optimization algorithm is a chaotic evolution optimization algorithm that introduces a sinusoidal piecewise linear chaotic mapping.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the method for optimizing the trajectory of a heavy-load group train on a continuous slope as described in any one of claims 1-7.

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