Calculation Method for Onboard Platform and Train Operation Curve of Heavy-Duty Freight DC Electric Locomotive

Abstract

A method for calculating the train running curve of a heavy-haul freight DC electric locomotive's onboard platform is proposed, employing a step-by-step iterative optimization algorithm using dynamic programming. The method presets the number of running steps and step size, defining a set of selectable actions within each step. Starting from the current train state, each action in the action set is evaluated in each iteration step, calculating the possible next train state. An objective cost function is used to evaluate all possible train state changes, sorting them by cost value from smallest to largest, and prioritizing the action with the lowest cost value for subsequent calculations. If the cost value of all actions in the current step exceeds the limit, the method backtracks to the previous iteration step and reselects. After iterating to the maximum number of steps, all train state changes are stored, ultimately obtaining the optimal train running curve under the objective function constraint. This invention optimizes the control strategy through dynamic programming, improving prediction accuracy, optimizing action selection, accelerating convergence, reducing redundancy, and enhancing operational stability, safety, and algorithm efficiency.

Description

Technical Field

[0001] This invention relates to the field of heavy-duty freight transport, and in particular to an onboard platform for a heavy-duty freight DC electric locomotive and a method for calculating train operation curves. Background Technology

[0002] In railway transportation, especially in the field of heavy-haul freight, the operational efficiency and safety of trains have always been key areas of technological research. Traditional train control methods mostly rely on manual driving or automatic control systems based on fixed control rules, which often fail to achieve optimal coordination between operational efficiency and safety in complex operating environments. This is particularly true for heavy-haul freight trains driven by DC electric power, where the trains are large and have strong inertia. How to plan a reasonable operating curve to achieve smooth and efficient traction and braking control has become a major technical bottleneck.

[0003] Existing train operation curve planning methods include quadratic programming (QP), particle filtering (PF), and genetic algorithms (GA). Quadratic programming is suitable for linearly convex problems and can efficiently calculate smooth velocity-acceleration curves, but it has poor adaptability to nonlinear operating conditions and discrete control constraints. Particle filtering can handle state estimation for non-Gaussian and nonlinear systems and is suitable for real-time updates, but it has a high computational burden and suffers from severe degradation. Genetic algorithms possess global search capabilities and are suitable for optimizing complex control strategies, but they struggle to guarantee constraint feasibility and have slow convergence speeds. Furthermore, none of these methods effectively meet the current acceleration / deceleration constraints and operating condition transition constraints that DC electric locomotives must satisfy during operation.

[0004] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Summary of the Invention

[0005] The purpose of this invention is to provide an onboard platform for heavy-duty freight DC electric locomotives and a method for calculating train operation curves. By optimizing the control strategy through dynamic programming algorithms, the prediction accuracy is improved, the action selection is optimized, convergence is accelerated, redundancy is reduced, and the operational stability, safety, and algorithm efficiency are significantly improved.

[0006] To achieve the above objectives, the present invention provides a method for calculating the train operation curve of a heavy-haul freight DC electric locomotive, comprising: The number of steps and step length are preset during the operation, and the optional actions within each step length are predefined to form a set of actions; Starting from the current state of the train, the optimization calculation is performed using a step-by-step iterative approach with a dynamic programming algorithm. In each iteration step, each action in the action set is evaluated one by one, and the next train state that may be transitioned to after taking these actions is calculated. The objective cost function is used to evaluate all possible train state changes and sort them in ascending order of cost value. When the cost value is less than or equal to the limit value, the action with the smallest cost value is selected for subsequent calculations. If the cost of all actions in the current iteration step is greater than the limit, then return to the previous iteration step, and continue to select the next action with the smallest cost value for subsequent calculations, provided that the cost constraint is satisfied. The calculation is iterated until the preset maximum number of iterations is reached, and the train state changes at each iteration step are stored. Finally, the optimal train operation curve under the constraint of the objective cost function is obtained.

[0007] The current state, operating condition transition state, and air brake state are used as state variables in the dynamic programming algorithm. The current status includes: traction current value and braking current value; The operating condition transition states include: the train operating condition changes from traction state to braking state, or the intermediate state of the train operating condition changing from braking state to traction state. The air brake states include: air brake activation state, air brake holding state, and air brake release state.

[0008] The step size in dynamic programming includes one variable step size and multiple fixed step sizes; Set the step size of the first step to a variable step size: For time-constrained actions, a time step is used for planning; the time-constrained actions include at least: current increase / decrease, application of air brake, release of air brake, and change of operating condition. For actions without time constraints, the differential distance is used as the step size for planning; the actions without time constraints include at least: current holding, coasting holding, and air braking holding. A fixed distance step size is uniformly adopted as the subsequent step size.

[0009] The objective cost function is: (1) in, The kinetic energy per step of the train, in units ; For train quality, unit ; The following speed per step of the train, in units ; Under the premise of meeting train operation constraints, priority should be given to actions with large traction current, small braking current, late application of air brakes, and early release of air brakes.

[0010] The method for calculating train state transitions includes: within each step, using differential calculations to complete the train state transition and determine the train's speed state under the current current state or air braking state.

[0011] The calculation method for train running curves without air brakes includes: 1. Define train state variables and actions: The train state variables include: traction state Q, electric braking state Z, operating condition transition state C, and intermediate state M; The traction state Q is divided into multiple states based on the magnitude of the traction current; The electric braking state Z is divided into multiple states based on the magnitude of the braking current; The operating condition transition state C includes CQ ( ) and CZ ( Two states, CQ ( CZ indicates the current state is transitioning from braking to traction. This indicates that the current state is transitioning from traction to braking. and Indicates the elapsed time between operating conditions. ; The intermediate state M includes the traction intermediate state MQ ( ) and braking intermediate state MZ ( ), MQ ( The traction current in the current electric traction state is _____. MZ ( The braking current in the current electric braking state is _____. ; The actions include: current rise U, current / operating condition transition hold K, current fall D, operating condition transition operation C, and minimum efficiency operation S; 2. State transition and differential calculation: According to the pre-set state transition table, differential calculations are performed sequentially from top to bottom to ensure that the optimal state transition path is selected within the current step size; In the state transition table, actions that are more conducive to efficient train operation are listed at the top. By using differential calculations, all possible states within the current step length are evaluated sequentially, and the states that can successfully reach the end of the step length without exceeding the speed limit are selected. The train's velocity state within each step is obtained by dynamic differential calculation, and the train dynamic equations are as follows: (3) in, The final kinetic energy is expressed in J. The initial kinetic energy is expressed in J. The electric traction force of the train, in N; Electric braking force of the train, in N; The length of the differential interval is in meters. For ramp resistance, unit ; For curve resistance, unit ; The basic resistance for train operation, unit .

[0012] When a train will exceed its speed limit on a curve without air brakes, curve planning with air brakes will be triggered. The calculation method for train operation curves with air brakes includes: 1. Define train state variables and actions: The train state variables include: traction state Q, electric braking state Z, operating condition transition state C, intermediate state M, and air braking state A; The air brake state A includes the air brake establishment state A0 ( ), air brake holding state A1, and air brake release state A2 ( ), This indicates the time when the braking system has begun to be established. This indicates the time at which the braking has begun to ease. 实时建立时间 and t 实时缓解时间 The value ranges from 0 to the vehicle braking setup time. Between or 0 to the full vehicle braking release time between; The actions include: current increase U, current / operating condition switch hold K, current decrease D, operating condition switch operation C, minimum efficiency operation S, air brake pressure reduction increase AU, air brake pressure reduction hold AK, air brake pressure reduction decrease AD, and start applying air brake SA. 2. State transition and differential calculation: The state transition and differential calculation process with air brakes is the same as that without air brakes; The system is set to stop calculating the electric braking force once the air brakes are applied. Calculate the air braking force using an air braking model: (4) in, For the entire vehicle's air braking force, The air braking force for each locomotive or carriage, This refers to the pressure of a single train brake cylinder. The number of brake shoes per locomotive or car. and These represent the air pressure during the rise and fall of the train's brake cylinder pressure, respectively. These are fixed values ​​related to the vehicle's own characteristic parameters. To and The relevant coefficients, A coefficient related to train speed. Related to the type of brake shoe, It reflects the pressure change during brake application or release within a single brake cylinder; Let the time elapsed after the air brakes are applied to the following cars in a certain trainset be . 0 < < Or, the time elapsed after the train begins to release the air brakes is 0 < < Then the total air braking force of the train at that moment is: (5) (6) make: (7) (8) Then we have: (9) The train's velocity state within each step is obtained by dynamic differential calculation, and the train dynamic equations are as follows: (10) in, It is the final kinetic energy, measured in J. It is the initial kinetic energy, in J; It is the air braking force of the train, measured in N; It is the length of the differential interval, in meters (m). It is the slope resistance, in units of ; It is the resistance of a curved road, in units of... ; It is the basic resistance of train operation, in units of .

[0013] If no state can reach the end of the step within a certain step, the process will backtrack to the previous step, select the next state as the new starting point, and continue to perform state transitions and differential calculations until a feasible state transition path is found. The situations in which the step size cannot be reached include: overspeeding during the differentiation process, or the speed dropping to 0, or the corresponding level bit not being indexed under the current speed and current.

[0014] In the dynamic programming search process, if a certain node is reached... If speeding occurs, record the step index of the current node. Speed ​​magnitude and current and elements Insert a dictionary to accelerate the search when a subsequent search reaches a certain node. At that time, indexing is performed in the accelerated search dictionary; if a certain node exists in the accelerated search dictionary... It satisfies the following formula: (2) This indicates that continuing the search path along this node will definitely result in a speeding error, so a backtracking should be triggered directly.

[0015] Methods for determining the current train status include: 1. Determine the pressure of the equalization cylinder: 1.1 If the pressure of the equalizing cylinder is 50 kPa ± 3 kPa, then continue to determine the pressure of the tail duct: If the pressure in the tailpipe is > 553 kPa, and the time elapsed from the start of braking is... 0 < < Then it is determined that the train is in the air brake activation state A0( ); If the pressure in the tail duct is 550 kPa ± 3 kPa, then the train is judged to be in the normal initial braking pressure holding state A1. 1.2 If the pressure of the equalizing cylinder is 0 kPa + 3 kPa, then continue to determine the pressure of the tail duct: If the pressure in the tailpipe is < 597 kPa, and the time elapsed from the start of braking release is... 0 < < If so, the train is determined to be in the air brake release state A2. ); If the pressure in the tail duct is 600 kPa ± 3 kPa, it means the train is no longer in air braking mode; continue to assess the current status. 2. Determine the current state: 2.1 If the current is 0A ±5A, then continue to determine the time during which the current remains at 0A: If the timing starts from when the train receives the operating condition change command, the time to maintain 0 current is... If the time is less than 10 seconds, then the train is judged to be in CQ (Current Position). ) state; if If the time is ≥ 10s, the train is determined to be in state Q0. If the timing starts from when the train receives the operating condition change command, the time to maintain 0 current is... If the time is less than 10 seconds, then the train is considered to be in CZ (Current Zone). ) state; if If the time is ≥ 10s, the train is determined to be in state Z0.

[0016] 2.2 If the current is not 0A ±5A, continue to determine whether the current is in the corresponding traction or braking state: If so, the train is determined to be in traction state Q or electric braking state Z; If not, then the train is determined to be in the intermediate traction state MQ( ) or braking intermediate state MZ ( ).

[0017] Preprocess the protection curve by redrawing a new protection curve based on the original one. This new curve is then used as input to the dynamic programming algorithm to determine whether the search iteration process has exceeded its speed limit.

[0018] The preprocessing method for the protection curve without air braking includes: starting from the tail end of the original protection curve, starting from the maximum level of electric braking, and performing dynamic differentiation from back to front. 1. Initialization state: Set the initial state to the untouched state, that is, the state where the differential velocity is less than the original curve velocity; 2. Speed ​​Comparison and Status Update: Determine the final velocity between the current micro-partitions Speed ​​corresponding to the original protection curve Size relationship: like Then take The new protection curve is used as the velocity value at that point, and the current state is set to the touched state, that is, the differential velocity is greater than the original curve velocity. like Then take The velocity value at this location serves as the new protection curve; 3. State transition and interval iteration: Proceed to the next micro-partition judgment: If the current state is a touched state, then determine whether the original velocity corresponding to this differential interval is the same as the original velocity of the previous interval: If they are the same, then take that speed directly as the speed value of the new protection curve at that point; If they are not the same, set the current state to untouched and return to step 2; If the current state is untouched, continue to step 2; 4. Execute in a loop: Repeat the above steps until the preprocessing of the entire protection curve is completed.

[0019] The preprocessing method for protection curves with air brakes includes: when performing dynamic differentiation on the protection curves with air brakes, the braking force provided by the commonly used initial braking pressure of 50 kPa for the entire train is used as the basis, and dynamic differentiation is performed from back to front. The remaining processing methods are the same as those for protection curves without air brakes.

[0020] When a cycle of the dynamic programming algorithm reaches the first variable step size of the previous dynamic programming, it will trigger the calculation of a new train operation curve; when the speed limit information in a certain cycle changes abruptly, it will also trigger the calculation of a new train operation curve.

[0021] The set of actions for the least efficient operation S includes: The train gradually reduces the traction current at a rate of 30A per second until the traction current drops to 0A. The train undergoes a change of operating conditions, which is completed in 10 seconds, and then switches to braking mode. The train gradually increases the braking current at a rate of 40A per second until it reaches the maximum braking current; The train remains in braking position 0.

[0022] The present invention also provides an onboard platform for a heavy-duty freight DC electric locomotive, wherein the onboard platform executes the train operation curve calculation method for the heavy-duty freight DC electric locomotive.

[0023] The present invention has the following significant advantages: 1. Considering the characteristics of heavy-haul freight DC electric locomotives, the current state, operating condition transition state, and air brake state are used as state variables in a dynamic programming (DP) algorithm. This can effectively satisfy the constraints of current acceleration, deceleration, and operating condition transition, thereby improving the smoothness and reliability of automatic train operation.

[0024] 2. The DP step size is divided into "variable step size" and "fixed step size". By fully combining the advantages of variable step size and distance step size, it can provide better performance during the train acceleration phase while ensuring safe prediction distance coverage. This achieves optimization effect and makes up for the shortcomings of different step size methods.

[0025] 3. By adopting a refined dynamic differential method and combining dynamic factors such as traction force, gradient resistance, curve resistance and aerodynamic braking force, the accuracy of state transition is improved, which can more accurately predict changes in train speed and energy consumption and improve the real-time response capability of the system.

[0026] 4. Optimize action selection through a greedy strategy, prioritizing actions that promote efficient operation. For example, at the same speed, prioritize actions with larger traction current and smaller braking current, and delay the application of air brakes while advancing their release. This prioritization simplifies the decision-making process, avoids exhaustive search, and improves the algorithm's operating efficiency.

[0027] 5. The S-action mechanism is introduced. The S (Superdown) action is designed for minimum efficiency operation control. By flexibly combining multiple state operations (such as current reduction, coasting, and braking), it can deal with overspeed risks and complex operation constraints, significantly reducing the number of DP backtracking and improving the convergence speed and efficiency of the algorithm.

[0028] 6. A simplified calculation strategy for air braking is adopted, which involves pre-calculating the factor curves (in formula (9)) for the three stages of air braking (establishment, maintenance, and release) before driving. The use of tabular format greatly reduces the real-time computing burden and improves the system's real-time performance and computing efficiency.

[0029] 7. A protection curve preprocessing mechanism is introduced. For the two cases of with and without air braking, the protection curve is regenerated using inverse differentiation and serves as the DP input boundary. This method accelerates the convergence speed of the DP algorithm and ensures the safety and reliability of train operation.

[0030] 8. An accelerated search dictionary mechanism is adopted. During the DP search process, nodes that fail due to speeding are recorded. When a subsequent search reaches a node, if the state of that node exceeds the range recorded in the dictionary, the system will skip that node and backtrack. This optimization strategy effectively reduces redundant calculations and improves the overall efficiency of the algorithm. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the dynamic programming algorithm.

[0032] Figure 2 This is a diagram illustrating the setting of the step size variable.

[0033] Figure 3 This is a schematic diagram of the train's state variables without air braking.

[0034] Figure 4 yes Figure 3 A diagram showing the motion transition relationship in the traction state.

[0035] Figure 5yes Figure 3 Diagram showing the motion transition relationship during braking.

[0036] Figure 6 yes Figure 3 A diagram showing the motion transition relationships during the transition between different operating conditions.

[0037] Figure 7 yes Figure 3 Action transition relationship diagram of intermediate state.

[0038] Figure 8 This is a schematic diagram of state transitions from top to bottom based on the state transition table.

[0039] Figure 9 This is a schematic diagram of the state transition backtracking mechanism.

[0040] Figure 10 This is a schematic diagram of the dynamic differential process.

[0041] Figure 11 This is a schematic diagram of the increased train state variables when air braking is involved.

[0042] Figure 12 yes Figure 11 Action transfer relationship diagram.

[0043] Figure 13 It is the braking characteristic curve of a single brake cylinder.

[0044] Figure 14 It is the air braking characteristic curve of all brake cylinders taking into account the air propagation time.

[0045] Figure 15 It consists of the air brake activation, air brake holding, and air brake release phases. curve.

[0046] Figure 16 It is the differential calculation process of the air braking process.

[0047] Figure 17 This is a flowchart of a method for calculating the train operation curve of a heavy-duty freight DC electric locomotive provided in an embodiment of the present invention.

[0048] Figure 18 yes Figure 17 The timing logic diagram.

[0049] Figure 19 This is a flowchart for determining the current train status.

[0050] Figure 20 This is a schematic diagram of a curve preprocessing method without air braking.

[0051] Figure 21This is a schematic diagram of a curve preprocessing method involving air braking.

[0052] Figure 22 This is a schematic diagram of a time-constrained action with variable step size.

[0053] Figure 23 This is a diagram illustrating the situation where the index cannot reach the level position during the DP iteration process.

[0054] Figure 24 This is a diagram illustrating the rules for selecting the S action.

[0055] Figure 25 This is a schematic diagram of the simulation results of curve planning control. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following description. It should be noted that the drawings are in a very simplified form and use non-precise proportions, used only to facilitate and clearly illustrate the embodiments of the present invention. Please refer to the drawings to make the objectives, features, and advantages of the present invention more apparent and understandable. It should be understood that the structures, proportions, sizes, etc., depicted in the accompanying drawings are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the implementation conditions of the present invention. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to the size, without affecting the effects and objectives achieved by the present invention, should still fall within the scope of the technical content disclosed in the present invention.

[0057] This invention provides a method for calculating the train operation curve of a heavy-haul freight DC electric locomotive. This calculation method operates on an onboard platform, such as... Figure 1As shown, within the framework of dynamic programming (DP) algorithm, starting from the current train state, optimization calculations are performed using a step-by-step iterative approach. First, the number of steps and step size in the process are determined (considering actual computing power limitations and a safe planning distance; generally, the planning distance is at least 2 kilometers. Then, based on actual computing power, the DP steps, DP step size, and differential step size are set. The step size of each step can be flexibly adjusted according to actual needs; for example, a single curve planning can be divided into 10 steps, with each step size being 100m or 200m, depending on the requirements). Simultaneously, optional actions within each step size are predefined to form an action set. Next, in each iteration step, each action in the action set is evaluated one by one, and the next train state that might be transitioned to after taking these actions is calculated. To ensure optimization effectiveness, an objective cost function is used to evaluate all possible train state changes and sort them according to their cost value from smallest to largest. Within the limit of the cost value, actions with lower costs are prioritized for subsequent iterations. If the cost of all actions in the current iteration exceeds the limit, the process reverts to the previous iteration and, while still satisfying the cost constraint, selects the next action with the lowest cost for subsequent calculations. This recursive iterative process continues until the preset maximum number of iterations is reached. By storing the train state changes at each iteration step, the optimal train running curve under the objective cost function constraint can ultimately be obtained.

[0058] The selection criteria for DP state variables are as follows: In studying the actual driving operation of the Suning SS4B locomotive, it was found that the crew mainly controls the train speed by adjusting changes in traction or braking current and the timing of applying and releasing air brakes. Furthermore, the rate of change of current over time is another important constraint. Specifically, the crew achieves smooth control of current changes by slowly adjusting the speed control handwheel, thereby reducing current surges and protecting train operation safety. In actual operation, the selectable values ​​for traction or braking current are relatively limited; therefore, using the values ​​of traction and braking current as train state variables at each step of the DP algorithm has high applicability.

[0059] In addition to using traction and braking current values ​​as state variables, it is also necessary to set the operating condition transition state, that is, the intermediate state of the train operating condition from traction state to braking state or from braking state to traction state, in order to ensure the smooth operation of the train.

[0060] In dynamic programming (DP) with air brakes, in addition to considering the train's current state and operating condition transition state, it is also necessary to determine the three key states of air brakes based on the current air brake decompression amount of the train: air brake establishment, maintenance, and release.

[0061] Specifically, it is divided into: 1. Air Brake Establishment: When deceleration or stopping is required, the train establishes air braking force by supplying compressed air to the brake pipes and depressurizing it. This state is usually accompanied by a gradual increase in the brake depressurization.

[0062] 2. Air Brake Holding State: After reaching the target decompression level, the system will maintain the current decompression state to maintain stable braking force. This state typically corresponds to the train decelerating at a constant speed or maintaining a constant deceleration process.

[0063] 3. Air Brake Release State: When it is necessary to restore train speed or cancel the brakes, the system will gradually release compressed air, reducing the pressure reduction until the brakes are canceled. This state usually accompanies the end of train deceleration or the process of accelerating back to normal.

[0064] The selection criteria for the DP step size variable are as follows: In the train curve planning problem, the step size variable of the dynamic programming (DP) algorithm can be either the time step or the space step. Each of these two options has its own advantages and they complement each other in practical applications.

[0065] The advantages of choosing time as the step size are mainly reflected in the following two aspects: 1. It more directly satisfies time-related constraints. For example, constraints on the rate of current change and time requirements for operating condition transitions are directly related to time. Therefore, using a time step can more intuitively satisfy these constraints.

[0066] 2. Greater flexibility in action selection. For example, after selecting a step to perform a current change action for a specific duration, the next step can immediately select a new action without waiting for the train to travel a certain distance. This allows the train to fully utilize its performance during acceleration, improving operational efficiency.

[0067] However, the disadvantage of time step is that when the train is running at low speed, the distance traveled per unit time is short, which may result in the planning range not being able to cover the safe predicted distance, thus creating a planning gap in some cases.

[0068] In contrast, choosing distance as the step size has the following advantages: it is more suitable for the driving needs of heavy-haul freight trains. Heavy-haul trains need to predict track conditions and speed limits over long distances. With limited computing power, using a distance step size can ensure that the planning range covers the safe predicted distance (usually the maximum electric braking distance), thereby ensuring the safe operation of the train.

[0069] However, the disadvantage of the distance step size is that during the train acceleration phase, the train's power performance may not be fully utilized, resulting in a relatively slow acceleration process.

[0070] Comparing the two step size selection methods, distance step size is more suitable for driving heavy-haul freight trains because coverage of safe prediction distances is a fundamental requirement for planning. However, using only a fixed distance step size may fail to fully utilize train performance in certain situations. To address this issue, this invention proposes an improved spatiotemporal combined DP step size setting scheme: like Figure 2 As shown, the step size of the first step is set to a variable step size: 1. For time-constrained actions (current increase / decrease, air brake activation and deactivation, operating condition transition), time steps are used for planning; 2. For actions without time constraints (current holding, coasting holding, air braking holding), the differential distance is used as the step size for planning.

[0071] For subsequent step sizes, a fixed distance step size is uniformly adopted. This fixed distance setting takes into account factors such as train performance and the time required to complete the action, ensuring that the corresponding action planning can be completed within the fixed distance. In this way, the sum of the fixed distance step sizes can cover the safe predicted distance, ensuring the basic requirements of the planning. Since the curve planning is re-executed after each step size, the actual tracked speed curve is mainly based on the planning result of the first step with variable step size, thereby maximizing train performance while ensuring safety.

[0072] This spatiotemporal combined step size setting method makes full use of the advantages of both time step size and distance step size, ensuring coverage of safe predicted distance and achieving better performance during train acceleration, thus achieving an optimized effect that combines the strengths of both.

[0073] Methods for calculating train state transitions include: In the dynamic programming (DP) algorithm, based on the selection of traction and braking currents as state variables, the corresponding state transition actions can be defined as operations that change or maintain the traction / braking current, and operations that apply or release the air brake. Within each DP step, differential calculations are used to complete the train state transition and determine the train's speed state under the current current state (or air brake state).

[0074] The advantages of using differential calculations are mainly reflected in the following two aspects: 1. The traction force, braking force, and running resistance of a train change with its speed. Simultaneously, the gradient resistance experienced by the train at different positions also changes accordingly. By employing differential calculations within each step, the changes in these forces within that step can be considered more precisely, resulting in more accurate speed state updates within that step. This precision directly affects the initial state of the next DP step, thereby improving the overall computational accuracy of the DP algorithm. 2. Differential calculations can effectively control the rate of change of current, thereby satisfying the constraints of current variation. This characteristic is of great significance for simulating the actual operation of train crew members and is also a key factor in ensuring the safety of train operation.

[0075] In dynamic programming (DP) algorithms, the cost function is used to evaluate the quality of state transitions, and its design directly affects the final optimization result of the algorithm. In the train operation curve planning problem, the cost function usually needs to comprehensively consider multiple objectives, including core indicators such as efficiency, energy saving, and stability. However, this invention mainly focuses on the efficiency objective, that is, prioritizing ensuring that the train operates at maximum efficiency.

[0076] To achieve this goal, the following cost function is defined: (1) in, The kinetic energy per step of the train, in units ; For train quality, unit ; The following speed per step of the train, in units .

[0077] As shown in formula (1), For the sake of operational efficiency, this formula is the objective cost function for performing optimization.

[0078] Within the framework of dynamic programming (DP) algorithms, the objective cost function adopts a single-objective cost function form. This allows for the direct prioritization of actions that maximize efficiency in each DP iteration, without needing to traverse the entire feasible solution space by calculating and comparing the costs of all possible actions. This optimization strategy significantly improves the computational efficiency of the algorithm. However, it also raises a crucial question: how to determine which actions are more conducive to maximizing efficiency without calculating specific costs? Through in-depth research on the operating characteristics of the SS4B electric locomotive, the following conclusions were drawn: under the same train speed, actions such as larger traction current, smaller braking current, later application of air brakes, and earlier release of air brakes all contribute to improving train operating efficiency. Based on this, a clear priority ranking rule for actions can be established: under the premise of satisfying train operating constraints, actions with larger traction current, smaller braking current, later application of air brakes, and earlier release of air brakes are prioritized.

[0079] This "greedy strategy" based on locomotive operating characteristics can quickly determine the most efficient action at each step, thus searching along the optimal path. The core advantage of this method lies in its ability to significantly reduce computational complexity by utilizing known locomotive operating characteristics and simplified decision rules, while still efficiently approximating the optimal solution. The application of this strategy fully demonstrates the efficiency of "greedy algorithms" in specific problem scenarios within dynamic programming problems.

[0080] For planning train running curves without air brakes, firstly, when a certain cycle of dynamic programming (DP) (i.e., the software cycle, which is a fixed cycle) happens to reach the first variable step size of the previous dynamic programming (DP), the system will trigger a new curve planning; secondly, when the speed limit information changes abruptly within a certain cycle (for example, the speed limit curve ahead changes), the system will also start a new planning process.

[0081] The calculation method for train running curves without air brakes is as follows: 1. Define train state variables and actions: like Figure 3 As shown, the train state variables are divided into traction state (Q), electric braking state (Z), operating condition transition state (C), and intermediate state (M). The traction state (Q) is further divided into 7 states, numbered Q0 to Q6 based on the magnitude of the traction current (standard value ±8A). The electric braking state (Z) is divided into 5 states, numbered Z0 to Z4 based on the magnitude of the braking current (standard value ±10A). The operating condition transition state (C) includes CQ (…). ) and CZ ( Two states, CQ ( CZ indicates the current state is transitioning from braking to traction. This indicates that the current state is transitioning from traction to braking. and Indicates the elapsed time for the changeover between operating conditions ( The intermediate state (M) refers to a state that is not in any of the above states, and it is divided into two categories: traction intermediate states (MQ). ) and braking intermediate state MZ ( ), MQ ( The traction current in the current electric traction state is _____. MZ ( The braking current in the current electric braking state is _____. .

[0082] After the corresponding action is taken, a transition will occur between the various train state variables. The state transition table, which forms the transition relationship between each state and the action, is as follows: Figures 4-7 As shown in the diagram, the meanings of the actions corresponding to each letter are as follows: U represents current increase (up); K represents current / condition transition hold (keep); D represents current decrease (down); C represents condition transition operation (change); and S represents minimum efficiency operation (super down). Besides easily understood actions like U (current increase), K (current hold), D (current decrease), and C (condition transition), the S action has a more complex meaning and function. Specifically, the S action corresponds to the operation with the lowest efficiency within the current DP step, and its specific manifestation varies depending on the initial current state of the current DP step. S actions may include reducing traction current, transitioning to braking condition, and increasing braking current. These operations can occur individually or in combination according to actual needs, depending on the specific DP step. The significance of setting S actions is to fully explore and utilize the locomotive's deceleration capability. By taking appropriate operational measures at specific times, these measures can effectively reduce the probability of overspeed risk and also help reduce the number of backtracking operations during the DP algorithm's execution. This optimization not only improves the efficiency of the algorithm but also ensures the safety and stability of the train during operation, thereby achieving optimization of operation control.

[0083] 2. State transition and differential calculation: like Figure 8 As shown, during dynamic programming (DP), the system performs differential calculations sequentially from top to bottom according to a pre-defined DP state transition table to ensure the selection of the optimal state transition path within the current DP step. In the state transition table, actions that are more conducive to efficient train operation are listed at the top, for example, increasing traction current by 300A > increasing by 150A > maintaining traction current > decreasing traction current. Specifically, the system evaluates all possible states within the current DP step in sequence, that is, it uses differential calculations to select the state that can successfully reach the end of the step without exceeding the speed limit. This state selection mechanism ensures the safety and efficiency of the train during operation.

[0084] like Figure 9 As shown, if within a certain DP step, none of the states can reach the step's end (overspeed, speed dropping to 0, or the corresponding bit cannot be indexed at the current speed and current), the system will initiate a backtracking mechanism. Specifically, the system will backtrack to the previous DP step, select the next state as the new starting point, and continue state transitions and differential calculations. This process will continue until a feasible state transition path is found. This state transition and backtracking mechanism ensures that the train remains safe and stable even in complex operating environments.

[0085] Accelerated search dictionary mechanism: During the DP search process, if a certain node is reached... If an overspeeding event occurs, record the DP step index of the current node. Speed ​​magnitude and current (If it is traction current, count it as a positive value; if it is braking current, count it as a negative value), and then... Insert a dictionary to accelerate the search when a subsequent search reaches a certain node. At that time, indexing is performed in the accelerated search dictionary; if a certain node exists in the dictionary... It satisfies the following formula: (2) This indicates that continuing the DP search along this node will inevitably result in a speeding problem, therefore backtracking should be triggered directly. This optimization strategy effectively reduces redundant computation and improves the overall efficiency of the algorithm.

[0086] Differential calculation process: The train velocity state within each DP step is obtained by dynamic differential calculation. The train dynamic equations are as follows: (3) The meanings of each variable are as follows: The final kinetic energy is expressed in J. The initial kinetic energy is expressed in J. The electric traction force of the train, in N; Electric braking force of the train, in N; The length of the differential interval is in meters. For ramp resistance, unit ; For curve resistance, unit ; The basic resistance for train operation, unit .

[0087] like Figure 10 The diagram illustrates the dynamic differential process of reducing the traction current from 600A to 300A within a dynamic programming (DP) step. The specific process is as follows: 1. Initial state setting: Within this DP range, the initial state of the traction current is 600A, while the final state is selected as 300A.

[0088] 2. Differential Interval Calculation: Within the first differential interval of the DP step size, the system performs calculations through the following steps: 2.1 Level Index: Based on the current level index and speed The corresponding level was indexed from the "Traction Current-Speed-Level Relationship Table" obtained from the locomotive manufacturer. .

[0089] 2.2 Traction force calculation: Based on the obtained level... and speed The corresponding traction force was indexed from the "Traction Force-Speed-Level and Relationship Table" obtained from the locomotive manufacturer. .

[0090] 2.3 Dynamics Calculation: Utilizing this traction force Current speed The corresponding basic train resistance and the track resistance between micro-sections are substituted into formula (3) for calculation, based on E=0.5mv 2 The final velocity between the micro-partitions is obtained. .

[0091] 2.4 Running Time Calculation: Based on the current speed and final velocity Combining differential distance Calculate the running time between the micro-partitions. : 3. Traction current update: based on operating time Based on the "Table of Traction Current Decrease over Time" (this table is set according to the operating specifications based on the constraints of traction current change over time; for traction current, the rise rate must not exceed 30A per second, and the fall rate must not exceed 60A per second; for braking current, the rise rate must not exceed 40A per second, and the fall rate must not exceed 80A per second), the system calculates the initial current value for the next DP step. (That is, first calculate the start time of the next step, and then use the time to look up the current value in the table).

[0092] 4. Differential Interval Iteration: Repeat the above differential interval calculation process, gradually reducing the traction current until, after several differential intervals, the traction current drops to the target value of 300A. Afterward, the system will maintain a traction current of 300A and continue calculating the next differential interval until the DP step size interval ends. The differential interval is a distance interval, usually a fixed distance, typically set to 10m considering computational limitations.

[0093] 5. State Validity Judgment: Throughout the entire dynamic differentiation process, the system continuously monitors the train's operating status. If overspeed occurs in any differentiation interval or the corresponding level cannot be indexed in the "Traction Current-Speed-Level Relationship Table," the state is determined to be untransferable, and another state is selected for calculation.

[0094] Note: In a certain differential interval, if the final current value of that interval exceeds the target current value, the final current value is adjusted to the target current value, thus ensuring that the initial current state of the next DP step is in a pre-defined non-intermediate state. For example, suppose the initial current in a certain differential interval is 295A, and the target current of the corresponding DP step is 300A. After passing through this differential interval, the current increases to 310A at an increasing rate. At this point, the final current value is set to 300A, and subsequent differential intervals will continue to differentiate with a current value of 300A (if further differentiation is required).

[0095] When curve planning without air braking cannot generate a curve that meets the requirements (relying on electric braking would result in speeding), curve planning with air braking will be triggered.

[0096] The calculation method for the train operation curve with air brakes is as follows: 1. Define train state variables and actions: DP state including air brakes Figure 3 In addition to the states shown, it also includes Figure 11 The air brake state (A) shown specifically includes the air brake setup state A0 (t 实时建立时间 ), air brake holding state A1 and air brake release state A2 (t 实时缓解时间 ),in, t represents the time at which braking has begun to be established. 实时缓解时间 This represents the time it takes for the brakes to begin releasing (corrected for the pressure in the tailpipe when assessing the train's real-time status), and its value ranges from 0 to the time it takes for the entire train's brakes to be applied. Between or 0 to the full vehicle braking release time between.

[0097] In addition to the transition logic included in the DP without air brakes, the newly added transition logic between air brake states is as follows: Figure 12 As shown, the right figure represents the newly added state transition path in the previous initial state (added to the end of the corresponding state transition table). The meanings of each action are as follows: AU is air brake decompression increase (air up); AK is air brake decompression maintenance (air keep); AD is air brake decompression decrease (air down); SA is start air brake application (startair).

[0098] 2. State transition and differential calculation: The DP iteration logic with air brakes is the same as the DP iteration logic without air brakes described above, and will not be repeated here.

[0099] Within the DP step size including air braking, the differential calculation process is identical in method to that without air braking. The only difference is that the calculation of the air braking force requires a specific air braking model. In addition, the following special handling methods are employed in the actual calculation process: Although the train can transition from any braking level to air braking state according to the state transition table (meaning that electric braking force still exists when air braking is applied), in order to simplify the calculation of DP and to conform to the driving strategy of "air braking as the main force and electric braking as the auxiliary force" adopted by the crew in actual driving operations, the following treatment is adopted in the differential calculation process: once air braking is applied, electric braking force is no longer calculated.

[0100] The following is the formula for calculating air braking force: (4) in, For the entire vehicle's air braking force, The air braking force for each locomotive or carriage, This refers to the pressure of a single train brake cylinder. The number of brake shoes per locomotive or car. and These represent the air pressure during the rise and fall of the train's brake cylinder pressure, respectively. These are fixed values ​​related to the vehicle's own characteristic parameters. To and The relevant coefficients, A coefficient related to train speed. Related to the type of brake shoe (different for locomotives and carriages), such as Figure 13 As shown, It reflects the pressure change during brake application or release within a single brake cylinder (the change begins after a fixed delay from the application of the brake command).

[0101] Figure 14 Air braking characteristic curves for all brake cylinders considering air propagation time Let the time elapsed after the air brakes are applied to the following train sets be . (0 < < (or the time elapsed after the train begins to release the air brakes) (0 < < If the total air braking force of the train at that moment is: (5) (6) make: (7) (8) Then we have: (9) in, As for train speed Related, It needs to be combined with the current train formation. Figure 14 The air braking characteristics of all brake cylinders, considering air propagation time, are calculated as shown. To save differential calculation time at different air braking stages, calculations are performed in advance based on the train formation before operation. The curve. In the three stages of air brake activation, air brake hold, and air brake release, The curve shape is roughly as follows Figure 15 As shown.

[0102] According to different stages of air braking The curve can be used to quickly calculate the braking force of the whole vehicle in the dynamic differential process according to formula (9), thus effectively simplifying the differential calculation process.

[0103] During the dynamic differentiation process, if any of the following situations occur: there is an overspeed phenomenon within the differentiation interval, the corresponding level cannot be found according to the "Traction Current-Speed-Level Relationship Table", or the train speed is lower than the specified minimum release speed (plus a threshold) during the air brake establishment process (A0), then the state should be determined as untransferable and other states need to be selected for calculation.

[0104] Specifically, when the train speed is lower than the specified minimum release speed, the current state of the train cannot be transitioned to the braking establishment state (A0); during the dynamic differentiation process, if the train is in the braking holding state (A1) in a certain differentiation interval and the speed is lower than the minimum release speed, then braking release (A2) is performed in that differentiation interval.

[0105] Figure 16 The diagram illustrates the differential calculation process for air braking. The specific process is as follows: 1. Initial state setting: Within this DP interval, the initial state is Z0, and the final state is chosen to be A0. ) / A1.

[0106] 2. Differential Interval Calculation: Within the first differential interval of the DP step size, the system performs calculations through the following steps: 2.1 Calculation of air braking force: According to formula (9), substitute the current train speed and current air brake setup time The current aerodynamic braking force of the train is calculated. .

[0107] 2.2 Dynamics Calculation: Utilizing this air braking force Current speed The corresponding basic train resistance and the track resistance between the micro-sections are substituted into formula (10) for calculation to obtain the final speed between the micro-sections. .

[0108] (10) The meanings of each variable are as follows: It is the final kinetic energy, measured in J. It is the initial kinetic energy, in J; It is the air braking force of the train, measured in N; It is the length of the differential interval, in meters (m). It is the slope resistance, in units of ; It is the resistance of a curved road, in units of... ; It is the basic resistance of train operation, in units of ; 2.3 Running Time Calculation: Based on the current speed and final velocity Combining differential distance Calculate the running time between the micro-partitions. : 3. Air brake set-off time Update: Cumulative runtime ,renew Set the current train status to A0 ( ).

[0109] 4. Differential Interval Iteration: Repeat the above differential interval calculation process until the DP step size interval ends. During the iteration process, when... If the current train status is A1, then A1 is set; otherwise, A0 is set. ).

[0110] In one embodiment of the present invention, such as Figure 17 and Figure 18 As shown, a method for calculating the train operation curve of a heavy-haul freight DC electric locomotive is provided, comprising the following steps: Step S1: Determine if the current state is air braking. If yes, proceed to step S2; otherwise, proceed to step S3. Step S2: When the train is currently in a non-air brake state, perform the following operations: First cycle: Curve planning without air brakes: If a curve that passes through normally is planned, then the planning is successful.

[0111] If parking issues arise during the planning process, the project will be withdrawn from the plan, and parking will proceed directly.

[0112] If the planning fails (all paths exceed the speed limit), the current control for the current cycle continues (if the previous cycle was in a condition transition state, then the condition transition will continue). In the second cycle, the curve planning with air brakes is re-executed based on the real-time status of the train.

[0113] Second cycle: Curve planning with air braking: If a curve that passes through normally is planned, the planning is successful, and the curve planning module outputs relevant control commands and activates the curve tracking module.

[0114] If parking occurs during the planning process, the current plan will be abandoned and the parking module will be activated directly.

[0115] If the planning fails (all routes exceed the speed limit), the parking module will be activated directly.

[0116] Step S3: The train is currently in air braking mode, and will directly enter the curve planning stage with air braking.

[0117] In addition to the initial curve programming, curve programming based on dynamic programming (DP) will be updated in the following two cases: (1) The first cycle after completing the variable step size of the previous curve planning (if it is two planning, that is, the first cycle is a planning without air braking and fails, and the second cycle is a planning with air braking, then it is the first two cycles). (2) The first cycle after a signal mutation occurs (or the first two cycles if it is a two-stage planning).

[0118] The above description ensures dynamic optimization and system stability in the curve planning process, providing a solid control foundation for safe train operation.

[0119] In step S1, the method for determining the current train status includes: Each time DP (Dynamic Programming) is executed, the real-time state of the train is used as the starting state for the planning. Based on the train's current real-time information (such as the pressure of the equalization cylinder, the pressure of the tail duct, the current status, etc.), the DP state of the train is determined.

[0120] like Figure 19 As shown, the specific procedure for determining the current train status is as follows: 1. Determine the pressure of the equalization cylinder: (1) If the pressure of the equalizing cylinder is 50 kPa (±3 kPa), then continue to determine the pressure of the tail duct: If the pressure in the tailpipe is > 553 kPa, and the time elapsed from the start of braking is... (0 < < (and will be corrected according to the pressure of the tail duct), then the train is judged to be in the air brake establishment state A0 ( ).

[0121] If the pressure in the tail duct is 550 kPa (±3 kPa), then the train is judged to be in the normal initial braking pressure maintenance state (A1).

[0122] (2) If the pressure of the equalizing cylinder is 0 kPa (+3 kPa), then continue to determine the pressure of the tail duct: If the pressure in the tailpipe is < 597 kPa, and the time elapsed from the start of braking release is... (0 < < (and will be corrected according to the air pressure in the tail duct), then the train is judged to be in the air brake release state A2 ( ).

[0123] If the pressure in the tailpipe is 600 kPa (±3 kPa), it indicates that the train is no longer in air braking mode, and the current status should be further assessed.

[0124] 2. Determine the current state: (1) If the current is 0A (±5A), then continue to determine the time during which the current remains at 0: If the timing starts from when the train receives the operating condition change command (from braking condition to traction condition), the time maintained at 0 current is... If the time is less than 10 seconds, then the train is judged to be in CQ (Current Position). ) state; if If the time is ≥ 10s, the train is determined to be in state Q0.

[0125] If the timing starts from when the train receives the operating condition change command (from traction operating condition to braking operating condition), the time to maintain 0 current is... If the time is less than 10 seconds, then the train is considered to be in CZ (Current Zone). ) state; if If the time is ≥ 10s, the train is determined to be in state Z0.

[0126] (2) If the current is not 0A (±5A), then continue to determine whether the current is in the corresponding DP traction or braking state: If so, the train is determined to be in state Q1-Q6 or Z1-Z4.

[0127] If not, then the train is determined to be in an intermediate traction state (MQ). ()) or braking intermediate state (MZ( )).

[0128] State transition constraints: (1) CQ( The state can only transition to the Q0 state; (2) CZ( The state can only transition to state Z0; Note: The working condition transition time is uniformly set to 10 seconds.

[0129] Preprocessing of the protection curve refers to redrawing a new protection curve based on the original one, which serves as input to dynamic programming (DP) to determine whether overspeeding has occurred during the search iteration process. Corresponding preprocessing methods are designed for different DP methods. The following are detailed descriptions of the DP curve preprocessing methods without and with air brakes: 1. Preprocessing method for DP curves without air brakes: like Figure 20 As shown, the preprocessing method starts from the tail end of the original protection curve and performs dynamic differentiation from back to front at the electric braking level 0 (maximum level) (differentiation interval length is 1m). During the differentiation process, the changes in line resistance, basic resistance and train electric braking force need to be comprehensively considered. The dynamic equation is shown in formula (3). The specific steps are as follows: (1) Initialization state: Set the initial state to the untouched state (i.e., the differential velocity is less than the original curve velocity).

[0130] (2) Speed ​​comparison and state update: Determine the final velocity between the current micro-partitions Speed ​​corresponding to the original protection curve Size relationship: like Then take The new protection curve is set to the velocity value at that point, and the current state is set to the touched state (i.e., the differential velocity is greater than the original curve velocity).

[0131] like Then take The velocity value at this location serves as the new protection curve.

[0132] (3) State transition and interval iteration: Proceed to the next micro-partition judgment: If the current state is a touched state, then determine whether the original velocity corresponding to this differential interval is the same as the original velocity of the previous interval: If they are the same, then take that speed directly as the speed value of the new protection curve at that location.

[0133] If they are different, set the current state to untouched state and return to step (2).

[0134] If the current state is untouched, then continue with step (2).

[0135] (4) Execute in a loop: Repeat the above steps until the preprocessing of the entire protection curve is completed.

[0136] 2. Preprocessing method for DP curves including air brakes: like Figure 21 As shown, the preprocessing method for DP curves with air brakes is basically the same as that without air brakes, with the main difference being the processing method for dynamic differentiation. Specifically, when performing dynamic differentiation on DP curves with air brakes, the braking force provided by the commonly used initial braking pressure of 50 kPa (which varies with speed) is used as the basis, and dynamic differentiation is performed from back to front, with a differentiation interval length of 1 meter.

[0137] In this invention, the step size of the first step DP is set to a variable step size. The core significance of this design is that the train always tracks the speed curve within the first variable step size during actual operation, thereby making full use of the train's acceleration and deceleration performance.

[0138] The dynamic differential cutoff strategy with variable step size varies depending on the action, as detailed below: 1. Time-constrained actions (current boosting / reducing, air brake activation and deactivation, operating condition switching): Planning is performed using time steps. Taking current increment as an example, if the current real-time traction current of the train is 150A, then in the first interval of DP, the traction current of 450A (Q3) is preferentially selected as the transitionable state. The dynamic differentiation process is the process of the traction current increasing from 150A to 450A at a rate of 30A per second, until a certain differentiation interval reaches the traction current of 450A (if overspeed or inability to index the level occurs during this process, Q2 is selected for transition). At this point, the dynamic differentiation process of the first variable interval ends, and the iteration of the second DP interval begins. Figure 22 As shown.

[0139] (1) Why is it called time step? Because the exact length of the first variable step cannot be determined without performing dynamic differentiation, the time required for the first variable step is known. For example, in the above example, the time for the first variable step is (450-150) / 30 = 10 seconds. For the establishment and release process of air braking, the time step of dynamic differentiation is determined according to the current train formation, specifically the time required for the train to go from the start of braking to full establishment, and the time required from the start of braking to full release.

[0140] (2) Why don’t these actions use a 10m differential interval step size as the first step DP step size? In fact, using a 10m step size is feasible. In this case, the strategy would become a 10m step size for the first step and 250m for the remaining steps. However, the reason for using a time step strategy is that it is easier to calculate when the train state is in a non-intermediate state at the start of DP planning.

[0141] Note: In the first variable-step phase of dynamic programming (DP), the current variation is strictly limited, not exceeding 150A. For example, for state Q2, its transition target states are limited to Q1, Q2, and Q3; for state Z2, its transition target states are limited to Z1, Z2, and Z3. Specifically, when the system is in an intermediate-level state (e.g., MQ, with a specific current value of 250A), its transition target can only be two adjacent non-intermediate-level states; specifically, MQ (250A) can only transition to Q1 (150A) or Q2 (300A). In the fixed-step phase, state transitions are strictly performed according to the transition table, without the aforementioned current variation limitation.

[0142] The purpose of this rule design is twofold: First, for variable step sizes, the actions of increasing or decreasing the current can be broken down into smaller actions. For example, increasing the traction current by 300A can be broken down into two consecutive actions of increasing the traction current by 150A each. Therefore, it is unnecessary to repeatedly set up two different actions (whereas within a fixed step size, these two actions represent different current-increasing capabilities), simplifying the action space. Second, by limiting the number of transition paths at the root node, the branching factor in the state space can be effectively reduced, thereby reducing computational complexity. In particular, reducing the number of transition paths near the root node has a significant effect on improving overall computational efficiency. This design optimizes the computational efficiency of the algorithm while ensuring system stability and controllability, and at the same time improves the flexibility and manageability of state transitions.

[0143] Note: For rising and falling currents, the first variable step length is the cumulative distance of dynamic differential when the target current is reached; for establishing and releasing air brakes, the first variable step length is the cumulative distance of dynamic differential when the air brake is established or released. If this distance is greater than the fixed step length, the variable step length is the fixed step length; for operating condition transitions, the first variable step length is the cumulative distance of dynamic differential when the operating condition transition is completed.

[0144] 2. Actions without time constraints (current holding, coasting holding (i.e., zero current holding under the same operating conditions), air brake holding): The differential distance is used as the step size for planning. That is, the length of the variable interval in the first step is equal to the length of the differential interval.

[0145] Through the above strategies, the present invention can more flexibly adapt to different operating conditions during train operation and optimize the efficiency and accuracy of DP planning.

[0146] Cases where the index cannot reach the level during DP iteration: When performing dynamic differentiation of a certain DP interval, the next state may be selected or backtracking may be triggered due to the following two situations: (1) Overspeed occurs during the differentiation process; (2) Unable to index the corresponding level.

[0147] by Figure 23 Taking the braking current-speed-level relationship table as an example, the maximum braking current varies at different train speeds. Therefore, during the dynamic differentiation process, there may be situations where the train cannot reach the target current state at a certain speed, meaning the corresponding braking level cannot be indexed in the relationship table.

[0148] Explanation of S-action: S-action refers to the operation corresponding to minimum efficiency operation (excluding air braking) within the current fixed DP step size (Note: S-action is not used for the first variable step size). Its specific manifestation depends on the initial current state of the current DP step size. Specifically: If the train is currently in a traction current state of 900A (i.e., maximum traction current), a complete set of S-actions includes the following steps: 1. The train gradually reduces the traction current at a rate of 30A per second until the traction current drops to 0A; 2. The train undergoes a change of operating conditions, which is completed in 10 seconds, transitioning to braking mode. 3. The train gradually increases the braking current at a rate of 40A per second until it reaches the maximum braking current (i.e., braking level 0). 4. The train maintains the braking position at level 0.

[0149] An S-action is equivalent to extracting a segment from the complete set of S-actions described above. The starting point of the extraction is the train state before taking the S-action, and the ending point is the state at the end of the fixed step size. Between the starting and ending points, the train speed information within the current DP step size is calculated using dynamic differentiation. The train state at the ending point is the initial state for the next DP step size, such as... Figure 24 As shown.

[0150] The significance of setting up the S-action lies in fully exploring and utilizing the locomotive's deceleration capability. By taking appropriate operational measures at specific times, these measures can effectively reduce the probability of overspeeding and also help reduce the number of backtracking operations required by the DP algorithm. This optimization not only improves the algorithm's operational efficiency but also ensures the safety and stability of the train during operation, thereby achieving optimized operation control.

[0151] Simulation results of curve planning control: such as Figure 25 The figure shows a simulation experiment conducted on the Huangwan Railway section. The upper part of the figure shows the train operation curve controlled by the on-site crew, and the lower part shows the train operation curve under the intelligent optimization control of curve planning proposed in this invention. The train performs curve planning once for each DP section, and the length of each curve planning is 3 kilometers. Train control commands are output based on the latest planned curve in each cycle.

[0152] Simulation experiments demonstrate that the train operation curve (simulated curve shown in the figure) obtained through the intelligent optimization control of curve planning proposed in this invention has significant advantages over the actual train operation curve controlled by passengers (passenger-controlled curve shown in the figure). Specifically, the train operation controlled by this invention not only ensures the smoothness of the operation process but also effectively improves operating efficiency. The control system of this invention performs excellently in multiple performance indicators, including heavy-haul train operation specifications, traction motor current acceleration and deceleration constraints, and operating condition transitions. Especially during train operation, when facing complex conditions such as acceleration zones, deceleration zones, and long uphill and downhill slopes, the system can accurately control the train's operating state through intelligent optimization and dynamic adjustment, ensuring operational safety and stability. These experimental results fully verify the superiority of the curve optimization control system proposed in this invention in practical applications, providing important reference for improving the operation control level of heavy-haul trains.

[0153] The present invention has the following significant advantages: 1. Considering the characteristics of heavy-haul freight DC electric locomotives, the current state, operating condition transition state, and air brake state are used as state variables in a dynamic programming (DP) algorithm. This can effectively satisfy the constraints of current acceleration, deceleration, and operating condition transition, thereby improving the smoothness and reliability of automatic train operation.

[0154] 2. The DP step size is divided into "variable step size" and "fixed step size". By fully combining the advantages of variable step size and distance step size, it can provide better performance during the train acceleration phase while ensuring safe prediction distance coverage. This achieves optimization effect and makes up for the shortcomings of different step size methods.

[0155] 3. By adopting a refined dynamic differential method and combining dynamic factors such as traction force, gradient resistance, curve resistance and aerodynamic braking force, the accuracy of state transition is improved, which can more accurately predict changes in train speed and energy consumption and improve the real-time response capability of the system.

[0156] 4. Optimize action selection through a greedy strategy, prioritizing actions that promote efficient operation. For example, at the same speed, prioritize actions with larger traction current and smaller braking current, and delay the application of air brakes while advancing their release. This prioritization simplifies the decision-making process, avoids exhaustive search, and improves the algorithm's operating efficiency.

[0157] 5. The S-action mechanism is introduced. The S (Superdown) action is designed for minimum efficiency operation control. By flexibly combining multiple state operations (such as current reduction, coasting, and braking), it can deal with overspeed risks and complex operation constraints, significantly reducing the number of DP backtracking and improving the convergence speed and efficiency of the algorithm.

[0158] 6. A simplified calculation strategy for air braking is adopted, which involves pre-calculating the factor curves (in formula (9)) for the three stages of air braking (establishment, maintenance, and release) before driving. The use of tabular format greatly reduces the real-time computing burden and improves the system's real-time performance and computing efficiency.

[0159] 7. A protection curve preprocessing mechanism is introduced. For the two cases of with and without air braking, the protection curve is regenerated using inverse differentiation and serves as the DP input boundary. This method accelerates the convergence speed of the DP algorithm and ensures the safety and reliability of train operation.

[0160] 8. An accelerated search dictionary mechanism is adopted. During the DP search process, nodes that fail due to speeding are recorded. When a subsequent search reaches a node, if the state of that node exceeds the range recorded in the dictionary, the system will skip that node and backtrack. This optimization strategy effectively reduces redundant calculations and improves the overall efficiency of the algorithm.

[0161] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0162] In the description of this invention, it should be understood that the terms "center," "height," "thickness," "upper," "lower," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0163] In the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0164] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0165] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for calculating a train operation curve of a heavy freight DC electric locomotive, characterized in that, Include: The number of steps and step length are preset during the operation, and the optional actions within each step length are predefined to form a set of actions; Starting from the current state of the train, the optimization calculation is performed using a step-by-step iterative approach with a dynamic programming algorithm. In each iteration step, each action in the action set is evaluated one by one, and the next train state that may be transitioned to after taking these actions is calculated; the method for calculating the train state transition includes: within each step, using a differential calculation method to complete the train state transition and determine the train speed state under the current current state or air braking state. The objective cost function is used to evaluate all possible train state changes and sort them in ascending order of cost value. When the cost value is less than or equal to the limit value, the action with the smallest cost value is selected for subsequent calculation. If the cost of all actions in the current iteration step is greater than the limit, then return to the previous iteration step, and continue to select the next action with the smallest cost value for subsequent calculations, provided that the cost constraint is satisfied. The calculation is iterated until the preset maximum number of iterations is reached, and the train state changes in each iteration step are stored. Finally, the optimal train running curve under the constraint of the objective cost function is obtained. Among them, the current state, the operating condition transition state, and the air brake state are used as the state variables of the dynamic programming algorithm; The current status includes: traction current value and braking current value; The operating condition transition states include: the train operating condition changes from traction state to braking state, or the intermediate state of the train operating condition changing from braking state to traction state. The air braking states include: air braking establishment state, air braking holding state, and air braking release state; The step size in dynamic programming includes one variable step size and multiple fixed step sizes; Set the step size of the first step to a variable step size: For time-constrained actions, a time step is used for planning; the time-constrained actions include at least: current increase / decrease, application of air brake, release of air brake, and change of operating condition. For actions without time constraints, the differential distance is used as the step size for planning; the actions without time constraints include at least: current holding, coasting holding, and air braking holding. A fixed distance step size is uniformly adopted as the subsequent step size.

2. The method of claim 1, wherein the train operation curve of the heavy freight DC electric locomotive is calculated by the steps of: The objective cost function is: （1） wherein, is the kinetic energy of the train per step, unit ; is the mass of the train, unit ; is the following speed of the train per step, unit ; Under the premise of meeting the train operation constraints, select actions with large traction current, small braking current, late application of air brake, and early release of air brake.

3. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 2, characterized in that, The calculation method for train running curves without air brakes includes:

1. Define train state variables and actions: Train state variables include: traction state Q, electric braking state Z, operating condition transition state C, and intermediate state M; The traction state Q is divided into multiple states based on the magnitude of the traction current; The electric braking state Z is divided into multiple states based on the magnitude of the braking current; The operating condition transition state C includes CQ ( 制动转牵引 ) and CZ ( 牵引转制动 Two states, CQ ( 制动转牵引 CZ indicates the current state is transitioning from braking to traction. 牵引转制动 This indicates that the current state is transitioning from traction to braking. 制动转牵引 and 牵引转制动 Indicates the elapsed time between operating conditions. ; The intermediate state M includes the traction intermediate state MQ ( ) and braking intermediate state MZ ( ), MQ ( The traction current in the current electric traction state is _____. MZ ( The current indicates the braking current in the current electric braking state. ; The actions include: current rise U, current / operating condition transition hold K, current fall D, operating condition transition operation C, and minimum efficiency operation S; 2. State transition and differential calculation: According to the pre-set state transition table, differential calculations are performed sequentially from top to bottom to ensure that the optimal state transition path is selected within the current step size; In the state transition table, actions that are more conducive to efficient train operation are listed at the top. By using differential calculations, all possible states within the current step length are evaluated sequentially, and the states that can successfully reach the end of the step length without exceeding the speed limit are selected. The train's velocity state within each step is obtained by dynamic differential calculation, and the train dynamic equations are as follows: （3） in, The final kinetic energy is expressed in J. The initial kinetic energy is expressed in J. The electric traction force of the train, in N; Electric braking force of the train, in N; The length of the differential interval is in meters. For ramp resistance, unit ; For curve resistance, unit ; The basic resistance for train operation, unit .

4. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 3, characterized in that, When a train will exceed its speed limit on a curve without air brakes, curve planning with air brakes will be triggered. The calculation method for train operation curves with air brakes includes:

1. Define train state variables and actions: The train state variables include: traction state Q, electric braking state Z, operating condition transition state C, intermediate state M, and air braking state A; The air brake state A includes the air brake establishment state A0(t) 实时建立时间 ), air brake holding state A1, and air brake release state A2 (t 实时缓解时间 ), 实时建立时间 t represents the time at which braking has begun to be established. 实时缓解时间 This indicates the time at which the braking has begun to ease. 实时建立时间 and t 实时缓解时间 The value ranges from 0 to the vehicle braking setup time. Between or 0 to the full vehicle braking release time between; The actions include: current increase U, current / operating condition switch hold K, current decrease D, operating condition switch operation C, minimum efficiency operation S, air brake pressure reduction increase AU, air brake pressure reduction hold AK, air brake pressure reduction decrease AD, and start applying air brake SA.

2. State transition and differential calculation: The state transition and differential calculation process with air brakes is the same as that without air brakes; The system is set to stop calculating the electric braking force once the air brakes are applied. Calculate the air braking force using an air braking model: （4） in, For the entire vehicle's air braking force, The air braking force for each locomotive or carriage, This refers to the pressure of a single train brake cylinder. The number of brake shoes per locomotive or car. and These represent the air pressure during the rise and fall of the train's brake cylinder pressure, respectively. These are fixed values ​​related to the vehicle's own characteristic parameters. To and The relevant coefficients, A coefficient related to train speed. Related to the type of brake shoe, It reflects the pressure change during brake application or release within a single brake cylinder; Let the time elapsed after the air brakes are applied to the following cars in a certain trainset be . , 0 < < Or, the time elapsed after the train begins to release the air brakes is , 0 < < Then the total air braking force of the train at that moment is: （5） （6） make: （7） （8） Then we have: （9） The train's velocity state within each step is obtained by dynamic differential calculation, and the train dynamic equations are as follows: （10） in, It is the final kinetic energy, measured in J. It is the initial kinetic energy, in J; It is the air braking force of the train, measured in N; It is the length of the differential interval, in meters (m). It is the slope resistance, in units of ; It is the resistance of a curved road, in units of... ; It is the basic resistance of train operation, in units of .

5. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 4, characterized in that, If no state can reach the end of the step within a certain step, the process will backtrack to the previous step, select the next state as the new starting point, and continue to perform state transitions and differential calculations until a feasible state transition path is found. The situations in which the step size cannot be reached include: overspeeding during the differentiation process, or the speed dropping to 0, or the corresponding level bit not being indexed under the current speed and current.

6. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 5, characterized in that, In the dynamic programming search process, if a certain node is reached... If speeding occurs, record the step index of the current node. Speed ​​magnitude and current and elements Insert a dictionary to accelerate the search when a subsequent search reaches a certain node. At that time, indexing is performed in the accelerated search dictionary; if a certain node exists in the accelerated search dictionary... It satisfies the following formula: （2） This indicates that continuing the search path along this node will definitely result in a speeding error, so a backtracking should be triggered directly.

7. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 4, characterized in that, Methods for determining the current train status include:

1. Determine the pressure of the equalization cylinder: 1.1 If the pressure of the equalizing cylinder is 50 kPa ± 3 kPa, then continue to determine the pressure of the tail duct: If the pressure in the tailpipe is > 553 kPa, and the time elapsed from the start of braking is [missing information] , 0 < < Then it is determined that the train is in the air brake activation state A0( ); If the pressure in the tail duct is 550 kPa ± 3 kPa, then the train is judged to be in the normal initial braking pressure holding state A1. 1.2 If the pressure of the equalizing cylinder is 0 kPa + 3 kPa, then continue to determine the pressure of the tail duct: If the pressure in the tailpipe is < 597 kPa, and the time elapsed from the start of braking release is... , 0 < < If so, the train is determined to be in the air brake release state A2. ); If the pressure in the tail duct is 600 kPa ± 3 kPa, it means the train is no longer in air braking mode; continue to assess the current status.

2. Determine the current state: 2.1 If the current is 0A ±5A, then continue to determine the duration of maintaining 0 current: If the timing starts from when the train receives the operating condition change command, the time to maintain 0 current is... If the time is less than 10 seconds, then the train is judged to be in CQ (Current Position). ) state; if If the time is ≥ 10s, the train is determined to be in state Q0. If the timing starts from when the train receives the operating condition change command, the time to maintain 0 current is... If less than 10 seconds, the train is considered to be in CZ (Current Zone). ) state; if If the time is ≥ 10s, the train is determined to be in state Z0. 2.2 If the current is not 0A ±5A, continue to determine whether the current is in the corresponding traction or braking state: If so, the train is determined to be in traction state Q or electric braking state Z; If not, then the train is determined to be in the intermediate traction state MQ( ) or braking intermediate state MZ ( ).

8. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 4, characterized in that, Preprocess the protection curve by redrawing a new protection curve based on the original one. This new curve is then used as input to the dynamic programming algorithm to determine whether the search iteration process has exceeded its speed limit.

9. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 8, characterized in that, The preprocessing method for the protection curve without air braking includes: starting from the tail end of the original protection curve, starting from the maximum level of electric braking, and performing dynamic differentiation from back to front.

1. Initialization state: Set the initial state to the untouched state, that is, the state where the differential velocity is less than the original curve velocity; 2. Speed ​​Comparison and Status Update: Determine the final velocity between the current micro-partitions Speed ​​corresponding to the original protection curve Size relationship: like Then take The new protection curve is used as the velocity value at that point, and the current state is set to the touched state, that is, the differential velocity is greater than the original curve velocity. like Then take The velocity value at this location serves as the new protection curve; 3. State transition and interval iteration: Proceed to the next micro-partition judgment: If the current state is a touched state, then determine whether the original velocity corresponding to this differential interval is the same as the original velocity of the previous interval: If they are the same, then take that speed directly as the speed value of the new protection curve at that point; If they are not the same, set the current state to untouched and return to step 2; If the current state is untouched, continue to step 2; 4. Execute in a loop: Repeat the above steps until the preprocessing of the entire protection curve is completed.

10. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 9, characterized in that, The preprocessing method for protection curves with air brakes includes: when performing dynamic differentiation on the protection curves with air brakes, the braking force provided by the commonly used initial braking pressure of 50 kPa for the entire train is used as the basis, and dynamic differentiation is performed from back to front. The remaining processing methods are the same as those for protection curves without air brakes.

11. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 4, characterized in that, When a cycle of the dynamic programming algorithm reaches the first variable step size of the previous dynamic programming, it will trigger the calculation of a new train operation curve; when the speed limit information in a certain cycle changes abruptly, it will also trigger the calculation of a new train operation curve.

12. The method for calculating the train operation curve of a heavy-haul freight DC electric locomotive as described in claim 4, characterized in that, The set of actions for the least efficient operation S includes: The train gradually reduces the traction current at a rate of 30A per second until the traction current drops to 0A. The train undergoes a change of operating conditions, which is completed in 10 seconds, and then switches to braking mode. The train gradually increases the braking current at a rate of 40A per second until it reaches the maximum braking current; The train remains in braking position 0.

13. An onboard platform for a heavy-duty freight DC electric locomotive, characterized in that, The on-board platform performs the train operation curve calculation method for heavy-duty freight DC electric locomotives as described in any one of claims 1-12.

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