ESN-GWO-based train high-density tracking interval optimization method

Abstract

The invention discloses a train high-density tracking interval optimization method based on ESN-GWO, and the method combines the acting force during the operation of a train to construct an accurate high-speed railway train dynamic model, accurately describes the stress and motion change process of the high-speed train in various scenes, and provides a model basis for the high-density tracking optimization of the high-speed train. A train tracking model is built in combination with a high-speed railway train dynamic model, and reliable and stable description of a high-speed train tracking scene is achieved; and finally, constructing a multi-objective optimization function suitable for the high-speed railway on the basis, and performing optimization solution in combination with an ESN-GWO algorithm to realize train high-density tracking interval optimization.

Description

Technical Field

[0001] The present invention relates to the field of rail transit technology, and in particular to an ESN-GWO-based train high-density tracking interval optimization method. Background Art

[0003] At present, train tracking intervals mainly include the following two types of solutions:

[0004] Solution 1: Chinese invention patent with authorization number CN114298398B, "A virtual reconnected high-speed train tracking interval control method based on model prediction", is as follows: According to the actual arrival information of the train, the operation plan of the preceding train and the initial operation strategy of the section, a flexible adjustment mechanism is designed, and the tracking train is optimized offline using a static crowd search algorithm, including the departure interval and train operation strategy; then, in the section, the real-time operation status information and surrounding environment information of the preceding train are collected, and combined with the transportation demand, the operation adjustment strategy of the tracking train in the remaining section is optimized online through a flexible adjustment strategy and a dynamic crowd search algorithm to obtain the optimal operation interval under the current state. However, the defects of this solution are: (1) There is a lack of accurate and effective train dynamics model analysis. The changes in the motion state of the train during operation are all derived from the real-time force analysis of the train. Accurate and effective optimization and adjustment of the train motion state should be based on the dynamic force condition of the train, but this solution does not consider the construction of the train dynamics model. (2) The optimization model of this scheme takes the train operating efficiency and the number of operating condition switching as the target. The optimization target does not conform to the target trend of high-speed rail development, avoids the key difficulties in the development of railway train control system technology, and does not meet the engineering and actual travel needs.

[0005] Solution 2, Chinese invention patent application with publication number CN118182584A, "A method and system for determining group train tracking interval time", is as follows: obtain the group train interval tracking interval time, the group train station departure interval time and the group train station arrival interval time; determine the group train tracking interval time according to the maximum value of the group train interval tracking interval time, the group train station departure interval time and the group train station arrival interval time. However, the defects of this solution are: (1) it only considers the group train tracking interval time, including the group train departure interval time, arrival interval time and interval tracking interval time, and gives a calculation method for each part of the time. The model is relatively simple and cannot accurately fit the state of nonlinear operation changes of the train. (2) No effective optimization algorithm is provided.

[0006] In view of this, the present invention is proposed. Summary of the invention

[0007] The purpose of the present invention is to provide a train high-density tracking interval optimization method based on ESN-GWO, which can realize the high-density tracking interval optimization of trains on high-speed railways.

[0008] The objective of the present invention is achieved through the following technical solutions:

[0009] A train high-density tracking interval optimization method based on ESN-GWO, comprising:

[0010] The high-speed railway train dynamics model is constructed based on the forces acting during train operation;

[0011] In combination with the high-speed railway train dynamics model, a train tracking model is constructed;

[0012] Combining the high-speed railway train dynamics model with the train tracking model, a multi-objective optimization function suitable for high-speed railway is established;

[0013] Based on the ESN-GWO algorithm combined with the high-speed railway train dynamics model and the train tracking model, the multi-objective optimization function is optimized to obtain the optimal train tracking interval corresponding to the optimal multi-objective optimization function.

[0014] It can be seen from the technical solution provided by the present invention that an accurate high-speed railway train dynamics model is constructed in combination with the forces acting on the train during operation, which accurately describes the force and motion changes of the high-speed train in various scenarios, and provides a model basis for the high-density tracking optimization of high-speed trains; a train tracking model is constructed in combination with the high-speed railway train dynamics model to achieve a reliable and stable description of the high-speed train tracking scenario; the above two types of models can accurately fit the state of nonlinear operation changes of the train; finally, a multi-objective optimization function suitable for high-speed railways is constructed on the above basis, and the ESN-GWO algorithm is combined for optimization and solution to achieve high-density tracking interval optimization of trains. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0016] Figure 1 A flow chart of a method for optimizing the high-density tracking interval of trains based on ESN-GWO provided in an embodiment of the present invention;

[0017] Figure 2 A schematic diagram of a high-speed railway train dynamics model is provided for an embodiment of the present invention;

[0018] Figure 3 A schematic diagram of the implementation process of the ESN-GWO algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the protection scope of the present invention.

[0020] First, the terms that may be used in this article are explained as follows:

[0021] The terms "include", "comprises", "contains", "has" or other descriptions with similar semantics should be interpreted as non-exclusive inclusion. For example, including certain technical feature elements (such as raw materials, components, ingredients, carriers, dosage forms, materials, dimensions, parts, components, mechanisms, devices, steps, procedures, methods, reaction conditions, processing conditions, parameters, algorithms, signals, data, products or products, etc.) should be interpreted as including not only certain technical feature elements explicitly listed, but also other technical feature elements known in the art that are not explicitly listed.

[0022] The term "consisting of..." means excluding any technical feature elements not explicitly listed. If this term is used in a claim, it will make the claim closed, so that it does not contain technical feature elements other than the technical feature elements explicitly listed, except for the conventional impurities related to them. If this term only appears in a clause of a claim, it only limits the elements explicitly listed in the clause, and the elements recorded in other clauses are not excluded from the overall claim.

[0023] The following is a detailed description of a train high-density tracking interval optimization method based on ESN-GWO provided by the present invention. The contents not described in detail in the embodiments of the present invention belong to the prior art known to professional and technical personnel in the field. If no specific conditions are specified in the embodiments of the present invention, they shall be carried out according to the conventional conditions in the field or the conditions recommended by the manufacturer.

[0024] like Figure 1 As shown in FIG. 1 , a train high-density tracking interval optimization method based on ESN-GWO mainly includes the following steps:

[0025] Step 1: Construct a high-speed railway train dynamics model based on the forces acting during train operation.

[0026] Step 2: construct a train tracking model in combination with the high-speed railway train dynamics model.

[0027] Step 3: Combine the high-speed railway train dynamics model and the train tracking model to establish a multi-objective optimization function suitable for high-speed railways for optimizing high-density tracking intervals of trains.

[0028] Step 4: Based on the ESN-GWO algorithm, the multi-objective optimization function is optimized in combination with the high-speed railway train dynamics model and the train tracking model to obtain the optimal train tracking interval corresponding to the optimal multi-objective optimization function.

[0029] The above scheme provided by the embodiment of the present invention constructs an accurate high-speed railway train dynamics model in combination with the forces acting on the train during operation, accurately describes the force and motion change process of the high-speed train in various scenarios, and provides a model basis for high-density tracking optimization of high-speed trains; constructs a train tracking model in combination with the high-speed railway train dynamics model to achieve a reliable and stable description of the high-speed train tracking scenario; finally, on the basis of the above, constructs a multi-objective optimization function suitable for high-speed railways, and combines the ESN-GWO algorithm for optimization and solution to achieve multi-objective optimization.

[0030] In order to more clearly demonstrate the technical solution and technical effects provided by the present invention, the method provided by the embodiment of the present invention is described in detail with reference to specific embodiments below.

[0031] 1. Construct a high-speed railway train dynamics model.

[0032] Accurate dynamic model and reliable tracking control technology of high-speed trains are crucial. Accurate mathematical modeling of the train tracking process is the premise for studying high-density train tracking technology. The operation process of the train is affected by multiple forces (traction, braking force, friction, etc.). The construction of an accurate train dynamic model should be able to accurately describe the force and motion changes of high-speed trains in various scenarios, and provide a model basis for the high-density tracking optimization of high-speed trains. Among them, the traction and braking forces are clearly known at a specific time, while the resistance encountered by the train during operation will vary due to different line conditions, operating environment, etc.

[0033] In the embodiment of the present invention, various factors in the train operation process are balanced and analyzed to construct a high-speed railway train dynamics model, such as Figure 2 As shown in the figure, the high-speed railway train dynamics model is established by combining the traction force F, braking force B and total resistance f during train operation. The acceleration a and speed v of the train are calculated as follows:

[0034]

[0035] v=a·ΔT

[0036] Where m is the weight of the train, ΔT is the duration of the acceleration a, and r is the vehicle rotation mass coefficient. It is provided by the vehicle designer or manufacturer to convert the inertial resistance moment of the rotating mass into the inertial resistance of the translational mass, so as to accurately calculate and evaluate the kinematic performance of the train.

[0037] The total resistance f is expressed as:

[0038] f=f0+f i +f r +f s

[0039] Among them, f0 is the basic resistance of the train, which is calculated in combination with the resistance parameters of the train; f i is the additional resistance of the slope on the train, f r is the additional resistance of the train passing through the curve (i.e. track curve), f s Add air resistance to the train; specifically:

[0040] (1) Basic resistance: f0 = (a' + bv + cv 2 )×G, where G is the weight of the train, G=m·g, and a', b, and c are the resistance parameters of different vehicle models.

[0041] (2) Additional resistance of ramp: f i = sinθ·kN = 1000sinθ, where kN is the unit conversion, k is kilo, N is Newton (unit), that is, the geometric length is converted into mechanical units, and θ is the slope angle. Because railway lines must meet certain conditions, the slope angle is generally very small, otherwise it will cause safety risks. When θ is small, sinθ≈tanθ. In order to further facilitate calculation, the engineering adds a resistance f to the ramp. i The approximate calculation formula is: i =sinθ·kN=1000sinθ≈1000tanθ≈θ.

[0042] (3) Additional resistance through the curve:

[0043] (4) Additional air resistance: f s =0.00013L tun ·G, the above formula is for the convenience of engineering processing, to calculate the additional air resistance when the train passes through the tunnel, L tun is the length of the tunnel; when the train is not running in the tunnel, L tun =0.

[0044] 2. Build a train tracking model.

[0045] High-speed and high-density train tracking has gradually become an important scenario in high-speed rail operations. The environment faced by high-speed trains during actual operation is complex, and the actual operating speed and traction braking acceleration of the train will be affected by many factors. Combined with the constructed train dynamics model, a reliable and stable description of the high-speed train tracking scenario can be achieved.

[0046] Analyze the train tracking scenario and assume that the dynamic tracking distance between the front train Train 1 and the rear train Train 2 is L tra , expressed as:

[0047]

[0048] Among them, L2 is the braking distance of the rear vehicle, and L1 is the braking distance of the front vehicle. Both are calculated by the high-speed railway train dynamics model. Specifically: v1 and a1, v2 and a2 are the speed and acceleration of the leading vehicle and the speed and acceleration of the trailing vehicle respectively calculated by the aforementioned high-speed railway train dynamics model. The acceleration of the leading vehicle and the trailing vehicle needs to be optimized using a multi-objective optimization function to optimize the tracking interval (dynamic tracking distance). The specific multi-objective optimization function will be introduced later. In addition, to improve the safety of the model, the acceleration a2 should consider the most unfavorable factor and use the common braking acceleration of the trailing vehicle, that is, when calculating L min hour a ser is the common braking acceleration; similarly, the acceleration a1 should take into account the most unfavorable factor and use the emergency braking acceleration of the preceding vehicle, that is, when calculating L min hour a em is the emergency braking acceleration; l a is the length of the front car, ψ2 and ψ1 are the confidence distances of the front car’s parking space of the rear car, The time period from the braking of the front vehicle to the start of deceleration of the rear vehicle is t react The reaction distance,

[0049] Requirement L tra ≥L min , L min It is the minimum tracking section length, which can be given according to different line conditions in actual engineering applications. By optimizing the multi-objective optimization function to optimize the acceleration of the following vehicle, and then optimize the braking distance of the following vehicle, the high-density tracking interval of the train can be optimized.

[0050] 3. Establish a multi-objective optimization function.

[0051] At present, in order to ensure the absolute safety of high-speed train operation, the train control system sacrifices a certain degree of operation and braking efficiency in the train tracking conditions to improve safety and reliability in the face of potential dangers, which complies with the general principle of "fail-safety". However, with the substantial improvement of the computing power of the safety platform, the key to creating an intelligent, comfortable and green Chinese high-speed rail lies in realizing the efficient and intelligent train control system. Therefore, this invention proposes a multi-level dynamic train high-density tracking optimization method with comfort, green, efficiency and safety as the optimization goals. Specifically: Combined with the train dynamics model and tracking model, as well as the actual operation situation, a multi-objective optimization function suitable for high-speed railways is established, expressed as:

[0052] Φ=min(Φ C ,Φ E ,Φ T )

[0053] Among them, Φ is the multi-objective optimization function; Φ C is the train running comfort evaluation function: a is the acceleration of the train, which is obtained through the high-speed railway train dynamics model. Here, the acceleration of the following train a2 is introduced, t is the time, and d is the differential symbol; Φ E Is the train energy consumption evaluation function: F is the traction force during train operation, 0~T1 is the traction force action time, T1~T2 is the braking force action time, α is the regenerative braking energy feedback coefficient, η is the traction efficiency, α and η are coefficients that can be checked in engineering units under specific applications; Φ T is the train punctuality evaluation function: are the actual arrival time and planned arrival time of the i-th train respectively, and I is the number of trains.

[0054] By optimizing the above multi-objective optimization function, the optimal following vehicle acceleration a2 is solved, so as to realize the optimization of high-density train tracking interval in combination with the train tracking model. The optimization solution of the objective optimization function will be introduced later.

[0055] 4. ESN-GWO algorithm

[0056] Based on the establishment of a train dynamics model and a train operation tracking model, an embodiment of the present invention proposes an ESN-GWO algorithm, which uses the powerful search capability of GWO to optimize the parameters of the ESN network, and combines the global search capability with the local optimization capability, thereby improving the performance of the overall algorithm. Specifically: the combination of the ESN network and the GWO algorithm gives full play to the advantages of the ESN network in processing time series data and the ability of the GWO algorithm in global optimization. Through this combination, more efficient parameter optimization, stronger generalization ability and higher robustness can be achieved, thereby improving the performance of the ESN network in processing dynamic and complex problems such as train operation scenarios, and has broad application prospects.

[0057] According to the three objective functions (Φ C ,Φ E ,Φ T ) respectively describe comfort, energy consumption and punctuality, and the decision variable L tra , the value range [L min , L max ], L max It is the maximum tracking section length, which can be given according to different line conditions in actual engineering applications.

[0058] The ESN-GWO algorithm combines the advantages of the Echo State Network (ESN) and the Grey Wolf Optimization (GWO):

[0059] ESN network: used to predict the train's operating status (such as speed, acceleration) and objective function value.

[0060] GWO algorithm: used to optimize the train tracking interval L tra , in order to minimize the objective functions of comfort, energy consumption and punctuality.

[0061] Since the ESN network cannot achieve global optimization search, the calculation results cannot be broken through locally. Therefore, each time the ESN network calculates a cycle, it will use the GWO algorithm to optimize the output of this cycle. The result after GWO optimization is then input into the ESN network for the next cycle calculation. The two complement each other to complete the optimization. In each cycle, each gray wolf position (candidate solution) output by the GWO algorithm corresponds to a set of reserve pool parameters of the ESN network. The ESN network uses the reserve pool parameters to predict the train operation status and calculate the multi-objective optimization function (referred to as the objective function value), that is, the predicted value of comfort, energy consumption and punctuality. The GWO algorithm evaluates the train's operating performance based on the multi-objective optimization function value (used to determine whether it meets the previous constraint range and whether it is a valid solution), and optimizes the train tracking interval by updating the gray wolf position (guiding the next prediction direction of the ESN network) before entering the next cycle.

[0062] The specific implementation process of the ESN-GWO algorithm is as follows: First, the ESN network is based on the gray wolf position of the GWO algorithm and combined with the objective function Φ C ,Φ E ,Φ T The definition of and the high-speed railway train dynamics model are used to predict the running status of the train (such as the speed and acceleration of the following vehicle), thereby calculating the objective function value (i.e. the predicted value of comfort, energy consumption and punctuality). Then, the objective function value calculated by the ESN network is passed to the GWO algorithm to calculate and optimize the train tracking interval in combination with the train tracking model, and output the updated gray wolf position. After the GWO algorithm is calculated, the parameter variables of the updated GWO algorithm are passed back to the ESN network for the next calculation until the termination condition set in advance is reached. After the termination condition is reached, the final objective function value is output. As mentioned above, the multi-objective optimization function contains three functions, each of which has a different focus (for example, focusing on comfort, energy consumption, and punctuality). The corresponding acceleration can be determined according to different focuses to control the operation of the following vehicle, thereby achieving tracking interval optimization.

[0063] For each iteration, the following steps are performed:

[0064] (1) Calculate the objective function value:

[0065] For each gray wolf (each candidate solution), the train running status is predicted through the ESN network, and then brought into the multi-objective optimization function to calculate the objective function value.

[0066] (2) Update archive:

[0067] In the GWO algorithm, for each gray wolf position, according to its corresponding objective function value, it is detected whether it can be added to the archive. Specifically: the Pareto dominance relationship is used to update the non-dominated solutions in the archive; if the current solution is not dominated by any solution in the archive, it is added to the archive and the dominated solution is removed.

[0068] (3) Choose the leader:

[0069] Choose Alpha Wolf, Beta Wolf, and Delta Wolf from the archive.

[0070] α wolf is the best solution in the current population, β wolf and δ wolf are the second best solution and the third best solution respectively.

[0071] (4) Update the position of the gray wolf:

[0072] Use the GWO position update formula to update the position of the gray wolf. The specific method will be introduced later.

[0073] (5) Boundary check:

[0074] Make sure the updated gray wolf position is in [Lmin , L max ] range.

[0075] (6) Repeated iteration:

[0076] Repeat steps (1) to (5) until the maximum number of iterations is reached or other termination conditions are met.

[0077] GWO is the gray wolf optimization algorithm, which is a global optimization algorithm based on swarm intelligence, simulating the social hierarchy and hunting behavior of gray wolves, and has strong global search capabilities. It can effectively explore the search space and avoid falling into the local optimal solution.

[0078] The ESN network is a recursive neural network with an efficient reservoir structure that can process complex time series data. However, the performance of the ESN network depends heavily on the selection of its parameters, and manually adjusting these parameters is time-consuming and error-prone. Through the global search capability of the GWO algorithm, the optimal parameter configuration of the ESN network can be automatically searched, reducing human intervention and improving the automation and efficiency of the model.

[0079] By optimizing the parameters of the ESN network through the GWO algorithm, a better combination of parameters can be found, thereby improving the ESN's ability to fit the training data and generalize on the test data. This helps the ESN to perform better when handling complex tasks. The global search capability of the GWO algorithm can help the ESN avoid falling into a local optimal solution, thereby improving the robustness of the model, enabling the algorithm to maintain a more stable and reliable performance, and more suitable for the high safety and high reliability requirements of the railway train control system.

[0080] Since high-density train tracking optimization is a multi-objective nonlinear problem, ESN-GWO can optimize multiple nonlinear objective functions simultaneously, effectively balancing the search efficiency and computational cost, and further improving the computational efficiency.

[0081] Before applying the ESN-GWO algorithm to the optimization of multi-objective optimization functions, the algorithm needs to be trained, such as Figure 3 As shown, the training steps mainly include:

[0082] 1. Data preparation: Collect time series data for training and testing, and divide them into training set and test set after preprocessing. Specifically include:

[0083] (1) Data collection: Collect time series data for training and testing.

[0084] (2) Data preprocessing: Normalize the data to ensure that the data is within a certain range (for example, [0, 1]) to improve the training effect and convergence speed of the model.

[0085] (3) Data segmentation: Divide the dataset into training set and test set.

[0086] 2. Initialization: Initialize the parameters in the ESN network and define the fitness function; initialize the GWO algorithm and initialize the gray wolf position in the parameter space of the ESN network. Each gray wolf represents a set of ESN network parameters. Specifically include:

[0087] (1) Initialize ESN.

[0088] (1.1) Set ESN parameters: including pool size, spectrum radius, input weight, pool weight, and output weight.

[0089] (1.2) Generate a reserve pool: Randomly generate a connection weight matrix for the reserve pool.

[0090] (1.3) Initialize output weights: Usually the output weights are initialized to zero or small random values.

[0091] The ESN network is introduced as follows:

[0092] set up: is the input vector of the nth step. is the state vector of the reservoir at step n. is the output vector of the nth step. The dynamic equation of the ESN network can be expressed as: in: is the input weight matrix, is the reserve pool weight matrix, is the output weight matrix, f res and f out are the activation functions of the reservoir and output, respectively, N x 、N u 、N y They represent the reserve pool matrix, algorithm input parameter matrix, and algorithm output vector matrix respectively.

[0093] (2) Define the fitness function.

[0094] (2.1) Select evaluation indicators: Select appropriate evaluation indicators according to task requirements, such as mean square error (MSE), classification accuracy, etc.

[0095] Taking the mean square error (MSE) as an example, it is expressed as:

[0096]

[0097] in, The optimization target for the preset setting.

[0098] (2.2) Define fitness function: The evaluation index is used as the fitness function to evaluate the performance of the ESN network under given parameters.

[0099] (3) Initialize GWO.

[0100] (3.1) Set GWO parameters: including population size, maximum number of iterations, search space range, etc.

[0101] (3.2) Initialize the gray wolf position: Randomly initialize the gray wolf position in the search space of ESN network parameters, and each position represents a set of ESN parameters.

[0102] 3. Iterative optimization process.

[0103] (1) Fitness evaluation: For each gray wolf individual, that is, each set of reserve pool parameters, the ESN network is used for forward propagation and the fitness value is calculated according to the fitness function.

[0104] (2) Update the positions of wolf α, wolf β, and wolf δ according to their fitness values.

[0105] (3) Update the positions of all gray wolves except α wolf, β wolf and δ wolf according to the update formula of GWO.

[0106] (4) Check the termination condition: Determine whether the termination condition is met (for example, whether the maximum number of iterations is reached or the fitness value meets the preset condition). If so, stop the iterative optimization; if not, return to the initialization step.

[0107] GWO is introduced as follows:

[0108] GWO simulates the social hierarchy of gray wolves, including: α wolf (Alpha): the optimal solution; β wolf (Beta): the second-best solution; δ wolf (Delta): the third-best solution; ω wolf (Omega): other solutions.

[0109] The update formula of GWO is:

[0110] D α =|C1·X α -X j ∣

[0111] D β =|C2·X β -X j ∣

[0112] D δ =|C3·X δ -X j ∣

[0113] X1=X α -A1·D α

[0114] X2=X β -A2·Dβ

[0115] X3=X δ -A3·D δ

[0116]

[0117] Among them, X j , X j ' is the position before and after the jth gray wolf is updated; A1, A2, A3, C1, C2, C3 are coefficient vectors used to simulate the search behavior of gray wolves; X α , X β , X δ are the positions of wolf α, wolf β and wolf δ respectively, D α , D β , D δ , X1, X2, and X3 are the intermediate parameters calculated when updating the position of the j-th gray wolf.

[0118] The update formula of the coefficient vector is (subscript omitted): is a linearly decreasing coefficient, is a random vector.

[0119] 4. Train the ESN network: Use the best parameters (i.e. α wolf) obtained through the iterative optimization process to set up the ESN network, and use the training data to train the ESN network. Specifically include:

[0120] (1) Use optimized parameters: Use the best parameters found during the GWO optimization process to set up the ESN network.

[0121] (2) Training the ESN network: Use the training data to train the ESN network and adjust the output weights. This can usually be done through linear regression or other optimization methods.

[0122] The training of ESN network is mainly done by calculating the output weight W out The training process usually includes the following steps:

[0123] (1) State collection: Run the ESN network and collect the reserve pool state X and the corresponding target output Y; (2) Linear regression: Use linear regression or other optimization methods to calculate the output weight W out :W out =YX T (XX T +λI) -1 , where λ is the regularization parameter and I is the identity matrix.

[0124] 5. Testing and evaluation: Use the test set to test the trained ESN network and evaluate the performance of the trained ESN network based on the fitness function.

[0125] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by means of software plus necessary general hardware platforms. Based on such understanding, the technical solutions of the above embodiments can be embodied in the form of software products, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.), including several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0126] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A train high-density tracking interval optimization method based on ESN-GWO, characterized in that: include: The high-speed railway train dynamics model is constructed based on the forces acting during train operation; In combination with the high-speed railway train dynamics model, a train tracking model is constructed; Combining the high-speed railway train dynamics model with the train tracking model, a multi-objective optimization function suitable for high-speed railway is established; Based on the ESN-GWO algorithm combined with the high-speed railway train dynamics model and the train tracking model, the multi-objective optimization function is optimized to obtain the optimal train tracking interval corresponding to the optimal multi-objective optimization function.

2. The method for optimizing the high-density train tracking interval based on ESN-GWO according to claim 1, characterized in that: The high-speed railway train dynamics model constructed by combining the forces during train operation includes: The high-speed railway train dynamics model is established by combining the traction force F, braking force B and total resistance f during train operation. The acceleration a and speed v of the train are calculated as follows: v=a·ΔT Where m is the weight of the train, ΔT is the duration of the acceleration a, and r is the vehicle rotation mass coefficient.

3. The method for optimizing the high-density train tracking interval based on ESN-GWO according to claim 2 is characterized in that: The total resistance f is expressed as: f=f0+f i +f r +f s Among them, f0 is the basic resistance of the train, which is calculated in combination with the resistance parameters of the train; f i is the additional resistance of the slope on the train, f r is the additional resistance of the train passing through the curve, f s Add air resistance to the train.

4. The method for optimizing train high-density tracking interval based on ESN-GWO according to claim 1, characterized in that: The step of constructing a train tracking model in combination with the high-speed railway train dynamics model includes: Analyze the train tracking scenario and assume that the dynamic tracking distance between the front train Train 1 and the rear train Train 2 is L tra , expressed as: Among them, L2 is the braking distance of the rear vehicle, and L1 is the braking distance of the front vehicle. Both are calculated by the high-speed railway train dynamics model and optimized by the multi-objective optimization function; a is the length of the front car, ψ2 and ψ1 are the confidence distances of the front car’s parking space of the rear car, It is the reaction distance of the rear vehicle from the time the front vehicle brakes to the time it starts to decelerate.

5. The method for optimizing the high-density train tracking interval based on ESN-GWO according to claim 1, characterized in that: The multi-objective optimization function is expressed as: Φ=min(Φ C ,F E ,F T ) Among them, Φ is the multi-objective optimization function; Φ C is the train running comfort evaluation function: a is the acceleration of the train, which is obtained through the high-speed railway train dynamics model. The acceleration of the following train is used to calculate the train running comfort evaluation function. t is the time, and d is the differential symbol; Φ E Is the train energy consumption evaluation function: F is the traction force during train operation, 0~T1 is the traction force action time, T1~T2 is the braking force action time, α is the regenerative braking energy feedback coefficient, η is the traction efficiency; Φ T is the train punctuality evaluation function: are the actual arrival time and planned arrival time of the i-th train respectively, and I is the number of trains.

6. The method for optimizing train high-density tracking interval based on ESN-GWO according to claim 1, characterized in that: The optimizing of the multi-objective optimization function comprises: optimizing the acceleration of the following vehicle by optimizing the multi-objective optimization function, optimizing the braking distance of the following vehicle by optimizing the acceleration of the following vehicle, and optimizing the train tracking interval in combination with the train tracking model.

7. The method for optimizing train high-density tracking interval based on ESN-GWO according to claim 1, characterized in that: The optimization of the multi-objective optimization function based on the ESN-GWO algorithm combined with the high-speed railway train dynamics model and the train tracking model includes: The ESN-GWO algorithm includes: ESN network and GWO algorithm; in each cycle, each gray wolf position output by the GWO algorithm, that is, the candidate solution, corresponds to a set of reserve pool parameters of the ESN network. The ESN network uses the reserve pool parameters to predict the train running status and calculate the multi-objective optimization function, where the train running status includes the acceleration of the following vehicle; the GWO algorithm optimizes the train tracking interval by updating the gray wolf position according to the value of the multi-objective optimization function, and then enters the next cycle.

8. The method for optimizing train high-density tracking interval based on ESN-GWO according to claim 1, characterized in that: Before applying the ESN-GWO algorithm to the optimization of multi-objective optimization functions, training is performed through the following steps Data preparation: collect time series data for training and testing, and divide them into training set and test set after preprocessing; Initialization: Initialize the parameters in the ESN network and define the fitness function; initialize GWO, initialize the gray wolf position in the ESN parameter space, and each gray wolf represents a set of reserve pool parameters; among them, GWO is the gray wolf optimization algorithm and ESN is a recursive neural network; The iterative optimization process includes: for each individual gray wolf, using the ESN network to perform forward propagation and calculate the fitness value according to the fitness function, updating the positions of the α wolf, β wolf and δ wolf according to the fitness value, and updating the positions of all gray wolves except the α wolf, β wolf and δ wolf according to the GWO update formula; judging whether the stop condition is met, if so, stopping the iterative optimization, if not, returning to the initialization step; wherein the α wolf, β wolf and δ wolf are the optimal solution, the second optimal solution and the third optimal solution respectively; Training the ESN network: Use the best parameters obtained through the iterative optimization process to set up the ESN network and use it to train the ESN network; Testing and evaluation: Use the test set to test the trained ESN network and evaluate the performance of the trained ESN network based on the fitness function.

9. The method for optimizing the high-density train tracking interval based on ESN-GWO according to claim 8, characterized in that: The updating formula of GWO is used to update the positions of all gray wolves: D α =∣C1·X α -X j ∣ D β =∣C2·X β -X j ∣ D δ =∣C3·X δ -X j ∣ X1=X α -A1·D α X2=X β -A2·D β X3=X δ -A3·D δ Among them, X j , X j ' is the position of the jth wolf before and after updating; A1, A2, A3, C1, C2, C3 are coefficient vectors; X α , X β , X δ are the positions of wolf α, wolf β and wolf δ respectively, D α , D β , D δ , X1, X2, and X3 are the intermediate parameters calculated when updating the position of the j-th gray wolf.

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