Rail transit virtual marshalling train dynamics model construction, application method and system

Abstract

The application discloses a kind of track traffic virtual marshalling train dynamics model construction, application method and system, and it is related to track traffic train control technical field.The present application utilizes the operation data collected in the process of train operation, and constructs the dynamics model of virtual marshalling train in the case of considering air resistance coefficient.And, in the process of model construction, model parameter optimization and model performance evaluation and verification are carried out, the dynamics behavior of train can be accurately estimated when the following distance between trains is small, to solve the controller debugging difficulty caused by model precision, control model is difficult to evaluate, main additional cost and other problems.

Description

Technical Field

[0001] The present invention relates to the field of rail transit train control technology, and in particular to a method and system for constructing and applying a dynamics model of a virtual marshaled train for rail transit. Background Art

[0002] As an indispensable mode of transportation in modern society, rail transit boasts advantages such as high capacity, high speed, safety, and reliability. With the gradual acceleration of rail transit construction, the demand for rail transit capacity is also rapidly increasing. To meet this demand, there are generally two solutions: one is to build new railway lines based on demand, which is costly and inflexible; the other is to meet capacity demand by reducing train running intervals and increasing line utilization, which has been the direction the rail transit industry has been committed to in recent years.

[0003] In order to shorten the interval between trains, many solutions have been proposed and used, such as moving block technology. Nowadays, moving block technology has been applied to some urban rail transit systems. In a moving block system, each train can brake and stop before reaching the last known position of the previous train. However, due to the large inertia of the train and the long braking distance, there is still room for further optimization of the safe running interval between adjacent trains. Therefore, virtual marshaling technology has been proposed as a more advanced train control solution. Virtual marshaling is similar to the mode of road traffic, where the vehicle maintains a safe distance from the vehicle in front, and the rear vehicle responds to the vehicle in front in real time. Figure 2 As shown, because this scheme takes the braking distance of the preceding train into account, the running intervals between adjacent trains are much smaller than those under a moving block scheme, resulting in more flexible train scheduling and higher resource utilization. Virtual marshaling enables trains to maintain the same speed through train-to-train communication without the need for physical couplers. When multiple trains enter the mainline, they form a platoon through train-to-train communication, with each train following closely behind the previous one. When the trains arrive at a station, they automatically leave the platoon.

[0004] like Figure 3 As shown, accurate system dynamics models play a vital role in the design and performance evaluation of train control systems. If the model is inaccurate, the controller may not operate the system as expected, resulting in degraded performance. This may manifest as delayed response time, oscillations, instability, or failure to achieve the desired performance indicators. Due to the small spacing between trains in a formation, factors such as airflow between trains have a significant impact on air resistance, making it difficult for traditional basic train resistance models to accurately describe the amount of resistance a train experiences. Therefore, establishing a virtual train resistance model that accounts for changes in air resistance is crucial for the design of virtual train control systems.

[0005] The train dynamics models used in the design and research of existing virtual train controllers are mostly train control models based on Newton's laws of kinematics, as shown in the following formula (1).

[0006] (1).

[0007] Where, Indicates the mass of the train; 、 and Represent the position, speed and acceleration of the train respectively; is the traditional basic train resistance model (Davis resistance model), in which , , are all parameters of the Davis drag model and are usually related to the specific vehicle model. represents the train resistance, Indicates the location Due to the slope The resulting train running resistance.

[0008] The traditional Davis drag model is designed for single-vehicle operation scenarios and does not consider the interactions between vehicles in multi-vehicle platooning. Directly applying it to the design of virtual train controllers can lead to difficulties in selecting control parameters and evaluating control schemes. When vehicles are platooning, factors such as airflow between trains significantly impact air resistance, which is also the single most significant factor affecting train dynamics models. However, the train drag models currently used in virtual train control studies still fail to account for the effects of changes in air resistance. This can lead to a series of issues, including difficulty debugging controllers, difficulty evaluating control models, and additional costs. Summary of the Invention

[0009] In order to solve the above problems existing in the prior art, the present invention provides a method and system for constructing and applying a dynamic model of a virtual train in rail transit.

[0010] To achieve the above objectives, the present invention provides the following solutions.

[0011] A method for constructing a dynamic model of a virtual train formation in rail transit comprises: obtaining running data of trains in a formation; the running data comprises the position of the train, the speed of the train, the acceleration of the train and the running resistance of the train.

[0012] An initial virtual train basic resistance model is constructed based on the operation data.

[0013] A gradient descent method is used to perform parameter optimization operation of the initial virtual marshaling train basic resistance model to obtain the virtual marshaling train basic resistance model.

[0014] The performance of the basic resistance model of the virtual train formation is evaluated using mean absolute error, root mean square error, and mean absolute percentage error to obtain evaluation results.

[0015] The dynamic model of the virtual marshalling train is constructed based on the basic resistance model and resistance correction coefficient estimation model of the virtual marshalling train whose evaluation results meet the set requirements.

[0016] Optionally, a gradient descent method is used to perform parameter optimization of the initial virtual marshaling train basic resistance model. In the process of obtaining the virtual marshaling train basic resistance model, the objective function used is: .

[0017] Where, Indicates the Train No. Estimated resistance of group sample data, Indicates the Train No. The train resistance of the group sample data, Indicates the number of groups of sample data, Indicates the number of trains in the formation, and min indicates the minimum value.

[0018] Optionally, the mean absolute error is expressed as: .

[0019] Where, Indicates the The mean absolute error of the train, Indicates the Train No. Estimated resistance of group sample data, Indicates the Train No. The train resistance of the group sample data, Indicates the number of groups of sample data.

[0020] Optionally, the root mean square error is expressed as: .

[0021] Where, Indicates the The root mean square error of the train, Indicates the Train No. Estimated resistance of group sample data, Indicates the Train No. The train resistance of the group sample data, Indicates the number of groups of sample data.

[0022] Alternatively, the mean absolute percentage error is expressed as: .

[0023] Where, Indicates the The mean absolute percentage error of the train, Indicates the Train No. Estimated resistance of group sample data, Indicates the Train No. The train resistance of the group sample data, Indicates the number of groups of sample data.

[0024] Optionally, the virtual train dynamics model is: .

[0025] Where, Indicates the mass of the train; Indicates the The location of the train, Indicates the The speed of the train, Indicates the The acceleration of the train, Indicates the Train at speed The train resistance at Indicates the Train in position Due to the slope The train running resistance generated by represents the acceleration due to gravity, 、 and All are Davis parameters of the train, Indicates the The drag correction factor of the train, 、 and Both indicate that unknown parameters related to the train, Indicates the number of trains in the formation.

[0026] A system for constructing a dynamic model of a virtual train set for rail transit is provided. The system is used to implement the method for constructing a dynamic model of a virtual train set for rail transit provided above. The system comprises: an operation data acquisition module, an initial model construction module, a model parameter optimization module, a model performance evaluation module and a final model construction module.

[0027] The operation data acquisition module is used to obtain the operation data of the trains in the formation; the operation data includes the position of the train, the speed of the train, the acceleration of the train and the operation resistance of the train.

[0028] The initial model building module is used to build an initial virtual train basic resistance model based on the operation data.

[0029] The model parameter optimization module is used to use the gradient descent method to perform parameter optimization operations on the initial virtual marshaling train basic resistance model to obtain the virtual marshaling train basic resistance model.

[0030] The model performance evaluation module is used to evaluate the performance of the basic resistance model of the virtual marshaled train by using mean absolute error, root mean square error and mean absolute percentage error to obtain an evaluation result.

[0031] The final model construction module is used to construct a dynamic model of a virtual marshalling train based on the basic resistance model and resistance correction coefficient estimation model of the virtual marshalling train whose evaluation results meet the set requirements.

[0032] A method for applying a dynamic model of a virtual marshaling train for rail transit is disclosed. The method adopts the dynamic model of a virtual marshaling train to control the virtual marshaling train for rail transit. The dynamic model of the virtual marshaling train is constructed using the method for constructing a dynamic model of a virtual marshaling train for rail transit provided above.

[0033] According to a specific embodiment provided by the present invention, the present invention discloses the following technical effects: The present invention utilizes operational data collected during train operation to construct a dynamic model of a virtual train formation, taking into account the air resistance coefficient. Furthermore, during the model construction process, model parameter optimization and model performance evaluation and verification are performed. This allows accurate estimation of train dynamic behavior when the following distance between trains is small, thus resolving issues such as difficulty in controller debugging, difficulty in evaluating the control model, and significant additional costs caused by model accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 This is a flow chart of the method for constructing a dynamic model of a virtual train set for rail transit provided by the present invention.

[0036] Figure 2 This is a schematic diagram of the existing train moving block and virtual marshaling; Figure 2 (a) is a schematic diagram of the moving block of the train. Figure 2 (b) is a schematic diagram of the virtual train formation.

[0037] Figure 3 Schematic diagram of the existing train control system.

[0038] Figure 4 A flow chart for constructing a rail transit virtual train dynamics model provided in an embodiment of the present invention.

[0039] Figure 5 Schematic diagram of data smoothing using the moving speed averaging method provided in an embodiment of the present invention.

[0040] Figure 6 A schematic diagram of data collected during fluid mechanics simulation provided by an embodiment of the present invention.

[0041] Figure 7 A schematic diagram of the fitting results of the virtual train formation dynamics model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0043] The purpose of the present invention is to provide a method and system for constructing and applying a dynamic model of a virtual train formation for rail transit taking into account air resistance, which can solve the problems existing in the prior art such as difficulty in controller debugging, difficulty in evaluating the control model, and major additional costs.

[0044] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] like Figure 1 As shown, the method for constructing a rail transit virtual train dynamics model provided by the present invention includes the following steps 100 to 104.

[0046] Step 100: Acquire the running data of the trains in the formation. The running data includes the position, speed, acceleration and running resistance of the trains.

[0047] Step 101: Construct an initial virtual train basic resistance model based on operation data.

[0048] Step 102: Using the gradient descent method to perform parameter optimization operation of the initial virtual marshaling train basic resistance model to obtain the virtual marshaling train basic resistance model.

[0049] Step 103: Use the mean absolute error, root mean square error, and mean absolute percentage error to evaluate the performance of the basic resistance model of the virtual train formation to obtain an evaluation result.

[0050] Step 104: Construct a dynamic model of a virtual train set based on the basic resistance model of the virtual train set and the resistance correction coefficient estimation model whose evaluation results meet the set requirements.

[0051] The following provides several embodiments based on the design concept and design principle of the present invention. Figure 4 The implementation process of the rail transit virtual marshaling train dynamics model method provided by the present invention is specifically described with reference to the implementation process of the present invention.

[0052] Example 1

[0053] (1) Establishment of the basic resistance model of the initial virtual train.

[0054] During the train operation, the basic resistance of the train is mainly composed of mechanical resistance and air resistance. middle, It is called mechanical resistance. It is called air resistance. Since the change of basic resistance when the train formation is running is mainly due to the change of air resistance, it is considered Add a drag coefficient correction term to To correct the air resistance error caused by the interaction between the platooning vehicles. Specifically, for a For a train formation consisting of 20 trains, the basic resistance model of the virtual train formation consists of a resistance model and a correction model. The proposed resistance model is shown in formula (2).

[0055] (2).

[0056] Where, Indicates the first train in the formation (i.e. train 1) to the The resistance of the train, Indicates the first train to the The real-time speed of the train. , , Represents the Davis parameter vector associated with each train in the formation.

[0057] In this example, the goal is to develop a model to describe the drag correction factor and vehicle formation parameters (following distance The modeling rules mainly come from the following analysis.

[0058] [1] When a train formation maintains a short following distance, the trailing train will enter the wake of the leading train, meaning the leading train becomes a wind barrier for the trailing train. The drag reduction effect on the trailing train depends mainly on the airflow covering the trailing train, and the drag reduction effect is more pronounced at this point.

[0059] [2] As the distance between vehicles increases, the influence of the vehicles in front and behind gradually decreases. The smaller the distance, the more obvious this trend becomes. This phenomenon is similar to the trend of an exponential function.

[0060] [3] For a sufficiently large formation, the aerodynamic performance of the train in the middle of the formation is significantly more stable. The front train is directly affected by the front flow, while the rear train is affected by the low pressure area at the rear of the formation.

[0061] Based on the above analysis, the resistance correction coefficient estimation model is designed as formula (3).

[0062] (3).

[0063] Where, Indicates the Train (i.e. train ) and Following distance between trains, 、 、 and Respectively represent For the first and last trains in the formation, the resistance correction factor Respectively and Regarding the trains in the formation , resistance correction factor With the Column and Following distance between columns and Column and Following distance between columns related.

[0064] (2) Basic resistance model parameters of the initial virtual train Calculation.

[0065] Based on the basic resistance model of virtual train formation, A set of sample data is used to determine its unknown parameters. Among them, each set of sample data ,include , and train resistance .

[0066] Then, the estimated resistance can be calculated according to formula (2) and formula (3): . Therefore, by minimizing the objective function [i.e., formula (4)], the optimal parameters in formula (2) and formula (3) can be obtained. In this way, the virtual marshaling resistance model problem can be transformed into an unconstrained nonlinear optimization model, and the optimal solution (or local optimal solution) under a given training data sample can be generated by the stochastic gradient descent algorithm. That is, the gradient descent method is used to perform the parameter optimization operation of the initial virtual marshaling train basic resistance model to obtain the virtual marshaling train basic resistance model. Among them, the objective function used is formula (4).

[0067] (4).

[0068] Where, Indicates the Train No. Estimated resistance of group sample data, Indicates the Train No. The train resistance of the group sample data, Indicates the number of groups of sample data, Indicates the number of trains in the formation, and min indicates the minimum value.

[0069] Defining the optimizer: The optimizer's role is to find the model parameters that minimize the loss as quickly as possible. Adam is one of the most widely used optimizers. It uses first-order moment estimates (i.e., the mean of the gradient) and second-order moment estimates (i.e., the uncentered variance of the gradient) to dynamically adjust the learning rate of each parameter. It is applicable to most non-convex optimization scenarios and high-dimensional spaces. By using Adam as the optimizer, the optimal parameters of the initial virtual train basic resistance model are obtained, and then the virtual train basic resistance model is obtained.

[0070] (3) Evaluation and verification method of basic resistance model of virtual train formation.

[0071] In order to evaluate the performance of the initial virtual marshaling train basic resistance model, in this embodiment, the mean absolute error (MAE), root mean squared error (RMSE) and mean absolute percentage error (MAPE) are used to verify the effectiveness of the established model. The output of the virtual marshaling train basic resistance model is the resistance of each train in the formation. Therefore, in order to evaluate the description of the resistance of each train in the formation by the virtual marshaling train basic resistance model, the first Three performance indicators are defined for each train, namely formula (5) to formula (7).

[0072] (5).

[0073] (6).

[0074] (7).

[0075] Where, Indicates the The mean absolute error of the train, Indicates the The root mean square error of the train, Indicates the The mean absolute percentage error of the train.

[0076] (4) Establishment of the final dynamic model of the virtual train.

[0077] After verification and meeting the requirements, the basic resistance model in the traditional train dynamics model in formula (1) is replaced with the basic resistance model of the virtual marshaling train to realize the construction of the virtual marshaling train dynamics model considering air resistance. For a train, its dynamic model is shown in the following formula (8).

[0078] (8).

[0079] Based on the above description, the present invention has the following advantages over the prior art.

[0080] 1) The present invention can more accurately reflect the dynamic characteristics of trains in a formation when the train following distance is small.

[0081] 2) The impact of changes in air resistance on train dynamics is taken into account, alleviating the problems caused by model accuracy in the controller design process.

[0082] 3) The present invention can collect actual train operation resistance data for training, saving testing costs.

[0083] Example 2

[0084] In this embodiment, the construction of the virtual train dynamics model mainly includes the following steps: (1) obtaining train operation data. (2) establishing the initial virtual train basic resistance model. (3) optimizing the parameters of the initial virtual train basic resistance model. (4) evaluating and verifying the initial virtual train basic resistance model. (5) establishing the virtual train dynamics model.

[0085] Step 1. Obtain train operation data.

[0086] Step 1.1 Obtain the original train data.

[0087] Wheel-rail force sensors, traction force sensors, and aerodynamic drag sensors are installed on the train. By measuring the magnitude and direction of these forces, the total drag of the train under different speeds and conditions can be calculated. The acceleration, velocity, and position sequences of the train are collected by the accelerometers, velocity sensors, and positioning devices installed on the train. The time interval is defined as , after sorting, we get m time steps The running data sequence of the train formation is shown in Table 1.

[0088]

[0089] Step 1.2: Use the average velocity method to remove noise from the original data.

[0090] In the operating data obtained, the positioning data of the high-speed train is recorded by two types of sensors, namely acceleration sensors and ground transponders. Due to the complex external environment and long cross-sectional distance of the high-speed train, it is easily affected by wheel slip and skidding, resulting in inaccurate positioning data of the acceleration sensor. In the rail transit operation system, the transponder is a positioning device installed between two tracks, which stores fixed line data. When the train passes the transponder, it corrects the accumulated error of the acceleration sensor by providing the absolute position. In the data directly collected, the position of the train may even appear to be reduced. Therefore, the original data cannot be directly used to train the basic resistance model of the virtual marshaled train.

[0091] Here, the average velocity method is used to smooth the field data set and define the The distance between For the convenience of analysis, Figure 5 As shown, any train in the formation is taken out for analysis, and the train is defined as The data collected during the operation are shown in Table 2.

[0092]

[0093] The average speed in adjacent time intervals is calculated based on the speed, which is formula (9).

[0094] (9).

[0095] The distance traveled in adjacent time intervals and the total distance traveled are estimated based on the average speed in adjacent time intervals, which are formulas (10) and (11).

[0096] (10).

[0097] (11).

[0098] Based on the estimated total distance traveled and the actual transponder spacing The distance correction value and the corrected distance are calculated as formula (12) and formula (13).

[0099] (12).

[0100] (13).

[0101] According to the corrected distance Update train position .

[0102] Step 1.3: Organize the data.

[0103] Arrange the filtered train operation data into the form required for model input. Calculate the Train and The distance between trains , which is formula (14).

[0104] (14).

[0105] After sorting The train formation The training data in each time step is shown in Table 3.

[0106]

[0107] Step 2. Establish the basic resistance model of the initial virtual train.

[0108] Before establishing the basic resistance model of the initial virtual train formation, the number of trains in the formation must be determined first. Once the number is determined, the dynamic model of the virtual marshaling train can be established according to formula (2) and formula (3).

[0109] Step 3. Optimize the parameters of the initial virtual marshaling train basic resistance model to obtain the basic resistance model of the virtual marshaling train.

[0110] Step 3.1 Parameter initialization.

[0111] Parameter initialization can accelerate the convergence of the parameters of the initial virtual train basic resistance model. In this embodiment, since the initial virtual train basic resistance model is improved by introducing correction terms based on the traditional train basic resistance model, the resistance model [Formula (2)] directly uses the train's Davis parameters as the initial values ​​of the model parameters. For the correction model [Formula (3)], the model parameters can be initialized using the zero initialization method (i.e., setting all parameters to 0).

[0112] Step 3.2 Parameter iterative update

[0113] Based on the basic resistance model of virtual train formation, the unknown parameters in the model can be determined according to the sorted data, where each set of data includes , and train resistance .

[0114] Afterwards, the estimated resistance can be calculated based on the basic resistance model of the initial virtual train set established in step 2. Therefore, by minimizing the objective function [i.e., formula (15)], the optimal parameters in formulas (2) and (3) can be obtained: The stochastic gradient descent algorithm can generate the optimal solution (or local optimal solution) for a given training data sample.

[0115] (15).

[0116] According to formula (16), the parameters are realized through iterative loop Updates.

[0117] (16).

[0118] Step 3.3 Set up the optimizer.

[0119] The role of an optimizer is to find the neural network parameters that minimize the loss as quickly as possible. Adam is one of the most widely used optimizers. It uses first-order moment estimates (i.e., the mean of the gradient) and second-order moment estimates (i.e., the uncentered variance of the gradient) to dynamically adjust the learning rate of each parameter. It is suitable for most non-convex optimization and high-dimensional spaces.

[0120] Step 4. Model evaluation and validation.

[0121] Step 4.1 Define the model evaluation method.

[0122] The model evaluation index is defined according to formula (5)-formula (7).

[0123] Step 4.2 Model evaluation.

[0124] In order to verify the method proposed above in the present invention, the computational fluid dynamics simulation (CFD) method was used to simulate the operating conditions of the train formation during operation, and the train operation data was obtained. Specifically, the operation of two train formations was simulated. At the initial moment, both cars in the formation maintained a stable speed of 70m / s, and the distance between the two trains remained unchanged. The rear car then accelerated from 70m / s to 75m / s at an acceleration of 1m / s2. After running for a period of time, it decelerated to 70m / s at a deceleration of 1m / s2. At this point, the train formation stabilized again with the following distance unchanged. During the whole process, the distance between the two cars decreased from 220m to 20m. The operating conditions of the formation cars and the collected resistance data are shown in Figure 2. Figure 6 shown.

[0125] The basic resistance model of the virtual train is trained and verified using the data obtained from the simulation. In order to compare with the traditional Davis model, the performance of the Davis model is evaluated using the previously defined model evaluation indicators. The results are shown in Table 4.

[0126]

[0127] It can be seen that compared with the traditional train basic resistance model, the virtual train basic resistance model can more accurately describe the basic resistance of trains in the formation because it takes into account the changes in air resistance. Especially for the last car in the formation, the average error is reduced to 29% of the original compared with the traditional train model. The fitting results of the virtual train basic resistance model are shown in the figure below. Figure 7 shown.

[0128] By comparing the model indicators, we can see whether the requirements are met. If not, we need to return to step 3 to readjust the parameters and train the model.

[0129] Step 5. Establish a virtual train dynamics model.

[0130] After completing the above steps, it is necessary to combine Newton's laws of kinematics to construct a virtual train dynamics model that takes into account air resistance. Specifically, the basic resistance in the traditional train dynamics model in formula (1) is replaced with the basic resistance model of the virtual train dynamics model to realize the virtual train dynamics model that takes into account air resistance. For a train, its dynamic model is: .

[0131] In the formula, in the formula, Indicates the mass of the train; Indicates the The location of the train, Indicates the The speed of the train, Indicates the The acceleration of the train, Indicates the Train at speed The train resistance at Indicates the Train in position Due to the slope The train running resistance generated by represents the acceleration due to gravity, 、 and All are Davis parameters of the train, Indicates the The drag correction factor of the train, 、 and Both indicate that unknown parameters related to the train, Indicates the number of trains in the formation.

[0132] Furthermore, the present invention provides a system for constructing a dynamic model of a virtual train for rail transit, which is used to implement the aforementioned method for constructing a dynamic model of a virtual train for rail transit. The system includes an operating data acquisition module, an initial model construction module, a model parameter optimization module, a model performance evaluation module, and a final model construction module.

[0133] The operation data acquisition module is used to obtain the operation data of the trains in the formation. The operation data includes the train position, train speed, train acceleration and train running resistance.

[0134] The initial model building module is used to build an initial virtual train basic resistance model based on operation data.

[0135] The model parameter optimization module is used to perform parameter optimization operation of the initial virtual marshaling train basic resistance model by using the gradient descent method to obtain the virtual marshaling train basic resistance model.

[0136] The model performance evaluation module is used to evaluate the performance of the basic resistance model of the virtual marshaling train using mean absolute error, root mean square error and mean absolute percentage error to obtain evaluation results.

[0137] The final model construction module is used to construct a dynamic model of a virtual marshalling train based on the basic resistance model and resistance correction coefficient estimation model of the virtual marshalling train whose evaluation results meet the set requirements.

[0138] Furthermore, the present invention also provides a method for applying a dynamic model of a virtual train in rail transit, wherein the method uses the dynamic model of a virtual train to control a virtual train in rail transit. The dynamic model of the virtual train is constructed using the method for constructing a dynamic model of a virtual train in rail transit provided above.

[0139] Furthermore, when the aforementioned application construction method is implemented as a computer program through software functional units and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory, a random access memory, a magnetic disk, or an optical disk.

[0140] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0141] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for constructing a dynamic model of a virtual train for rail transit, characterized in that: include: Acquiring running data of trains in the formation; the running data includes the position of the train, the speed of the train, the acceleration of the train and the running resistance of the train; An initial virtual train basic resistance model is constructed based on the operation data. The virtual train basic resistance model is as follows: Where, f r1 …f rN represents the resistance from the first train (i.e., train 1) to the Nth train in the formation, v1…v N represents the real-time speed of the first train to the Nth train in the formation, let α=[α1,…,α N ] Τ , β=[β1,…,β N ] Τ ,γ=[γ1,…,γ N ] Τ represents the Davis parameter vector associated with each train in the formation, α+βv is the mechanical resistance, γv 2 is the air resistance; The gradient descent method is used to perform parameter optimization of the initial virtual marshaling train basic resistance model to obtain the virtual marshaling train basic resistance model; the objective function used is: Where, represents the estimated resistance of the kth group of sample data of the i-th train, represents the train resistance of the kth group of sample data of the i-th train, K represents the number of groups of sample data, N represents the number of trains in the formation, and min represents the minimum value; The performance of the basic resistance model of the virtual marshaling train is evaluated by using mean absolute error, root mean square error and mean absolute percentage error to obtain an evaluation result; A dynamic model of a virtual marshaling train is constructed based on the basic resistance model and resistance correction coefficient estimation model of the virtual marshaling train whose evaluation results meet the set requirements; the resistance correction coefficient estimation model is used to describe the relationship between the resistance correction coefficient and the vehicle formation parameters; the resistance correction coefficient estimation model is designed in the form of formula: where x i is the following distance between the i-th train and the (i + 1)-th train; a i , b i , c i and d i are unknown parameters related to the i-th train respectively; for the trains within the formation, 1 < i < N; the resistance correction coefficient η i is related to the following distance x i-1 between the i-th train and the (i - 1)-th train and the following distance x i between the i-th train and the (i + 1)-th train; The dynamic model of the virtual train set is: Where M represents the mass of the train; si represents the position of the i-th train, v i represents the speed of the i-th train, κ i represents the acceleration of the i-th train, f ri (v i ) indicates that the i-th train is moving at speed v i The train resistance at time t, f gi (s i ) indicates that the i-th train is at position si due to the slope ξ(s i ) and the train running resistance generated, g represents the acceleration of gravity, α i , β i and γ i are the Davis parameters of the i-th train, η i represents the resistance correction coefficient of the i-th train, and N represents the number of trains in the formation.

2. The method for constructing a dynamic model of a virtual train for rail transit according to claim 1, characterized in that: The mean absolute error is expressed as: Where, MAE i represents the mean absolute error of the i-th train, represents the estimated resistance of the kth group of sample data of the i-th train, represents the train resistance of the kth group of sample data of the i-th train, and K represents the number of groups of sample data.

3. The method for constructing a dynamic model of a virtual train for rail transit according to claim 1, characterized in that: The root mean square error is expressed as: Where, RMSE i represents the root mean square error of the i-th train, represents the estimated resistance of the kth group of sample data of the i-th train, represents the train resistance of the kth group of sample data of the i-th train, and K represents the number of groups of sample data.

4. The method for constructing a dynamic model of a virtual train for rail transit according to claim 1, wherein: The mean absolute percentage error is expressed as: Where, MAPE i represents the mean absolute percentage error of the i-th train represents the estimated resistance of the kth group of sample data of the i-th train, represents the train resistance of the kth group of sample data of the i-th train, and K represents the number of groups of sample data.

5. A rail transit virtual train dynamics model construction system, characterized by: The system is used to implement the method for constructing a rail transit virtual marshaling train dynamics model according to any one of claims 1 to 4; the system includes: An operation data acquisition module is used to acquire the operation data of the trains in the formation; the operation data includes the position of the train, the speed of the train, the acceleration of the train and the running resistance of the train; An initial model building module, configured to build an initial virtual marshaling train basic resistance model based on the operation data; A model parameter optimization module is used to perform a parameter optimization operation of the initial virtual marshaling train basic resistance model using a gradient descent method to obtain the virtual marshaling train basic resistance model; A model performance evaluation module is used to evaluate the performance of the basic resistance model of the virtual marshaled train using mean absolute error, root mean square error and mean absolute percentage error to obtain an evaluation result; The final model construction module is used to construct a dynamic model of a virtual marshalling train based on the basic resistance model and resistance correction coefficient estimation model of the virtual marshalling train whose evaluation results meet the set requirements.

6. A method for applying a dynamic model of a virtual train in rail transit, characterized in that: The application method adopts a virtual marshaling train dynamics model to control a rail transit virtual marshaling train; the virtual marshaling train dynamics model is constructed using the rail transit virtual marshaling train dynamics model construction method according to any one of claims 1-4.

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