A data-driven train fault-tolerant tracking control method

Abstract

The present invention belongs to the technical field of train speed tracking control, and discloses a data-driven train fault-tolerant tracking control method. The method of the present invention combines data driving under a fault-tolerant control framework, realizes all-round and high-precision monitoring of the operating state of train actuators. Once an anomaly or potential fault is detected, the control system can immediately trigger an emergency response mechanism, effectively avoiding the occurrence of accidents and improving the train safety guarantee. In addition, the present invention adds fault-tolerant control on the basis of a data-driven model, and can still quickly adjust and track the desired speed curve in the case of a fault, realizing precise speed tracking. Furthermore, the present invention combines data-driven technology and fault-tolerant control, can optimize the system output according to the fault situation to obtain the optimal output driving force, significantly reducing the energy consumption during train operation, reducing the operation cost and alleviating the burden of the train system on the environment, and reducing the train energy consumption.

Description

Technical Field

[0001] The present invention belongs to the technical field of train speed tracking control, and relates to a data-driven train fault-tolerant tracking control method. Background Art

[0002] Currently, rail transit trains detect faults by manually detecting vibration conditions, abnormal sounds, dashboard indicators, etc., or through the automated monitoring system equipped on the train. According to devices such as axle counters, balises, and speed sensors, the monitoring system will monitor key parameters such as the speed, position, and traction force of the train, and compare them with preset safety thresholds. Once an abnormality is detected, the system will immediately issue an alarm and display the type and location of the fault. When a fault in a certain system or component is detected, the train will first attempt to automatically isolate the faulty component, and dynamically adjust the train's control strategy according to the type and scope of the fault. In the fault-tolerant control mode, the train can continue to operate in a degraded mode. Even if some functions are limited, the safety of passengers can still be guaranteed. For example, the system may limit the maximum speed of the train or adjust the acceleration / deceleration to adapt to the current fault condition. The communication between the train and the ground control center ensures the transmission of real-time information. The ground control center can dynamically adjust and optimize the train operation strategy according to the latest status information and fault conditions, ensuring the safe and efficient operation of the train.

[0003] Under the current train fault-tolerant control mode, there is a delay in the isolation response after fault detection. The system cannot quickly switch to the redundant module, depends on an accurate physical model, and is difficult to implement in a complex rail transit system. The switching and coordination of redundant modules are likely to cause system instability, require additional control logic and resources, and have a non-negligible impact on the safe operation of the train. Specifically, the existing train control methods mainly rely on problems of classical control strategies such as traditional PID control and LQR control. These methods perform well under normal train operation conditions, but when a fault occurs, such as an actuator fault or a sensor fault, it is difficult to quickly adjust the control strategy, resulting in a decrease in the safety and stability of train operation. In addition, since these methods rely on an accurate physical model to describe the dynamic behavior of the train, establishing an accurate physical model requires a large amount of prior knowledge and a complex parameter identification process. In practical applications, the operating environment of the train is complex and changeable, and it is difficult for the physical model to comprehensively and accurately reflect the actual operating state of the train, which makes the traditional control methods have great limitations in fault-tolerant performance.

[0004] With the development of data-driven technologies, data-driven models are becoming an important means in the field of control, enabling trains to more accurately predict and optimize their operating states. The data-driven model collects the operating data of the train, including information such as position, speed, and acceleration, and uses advanced algorithms to analyze and model this data. During the train operation, the data-driven model can update the train's state prediction in real-time and generate optimal control strategies based on the current operating conditions and future expected states. The train is controlled based on these strategies, which can not only improve the operating efficiency but also enhance safety.

[0005] Compared with traditional train control methods, the data-driven model can better adapt to complex operating environments. By mining and utilizing big data, it realizes the cooperative control between trains, thereby improving the overall operating efficiency of the rail transit system. The current data-driven model predictive control scheme for train optimal operation, although it can use data-driven methods to construct a linear approximation model of train dynamics, still has deficiencies in fault detection and handling. Traditional data-driven train control models mainly rely on fixed training data sets. When a fault occurs, since the model fails to be updated in real-time, it is difficult for the control strategy to quickly adapt to the new operating state. In addition, when formulating the control strategy, this method fails to fully consider the changes in the real-time operating environment and the impacts of different fault types, making it difficult to quickly respond to sudden faults that occur during train operation. Summary of the Invention

[0006] Aiming at the above problems existing in the existing data-driven control schemes, the present invention proposes a data-driven train fault-tolerant tracking control method, enabling the speed tracking controller to adapt to and compensate for faults in real-time, so that when a sudden fault occurs during train operation, the control model can be timely changed to adjust the strategy, thereby ensuring the train operation efficiency and safety.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A data-driven train fault-tolerant tracking control method includes the following steps:

[0009] Step 1. Obtain the initial historical operation data of the train, and use a data-driven method combined with a deep neural network to train and extract operators from the initial historical operation data of the train, and construct a linear dynamic system model in a high-dimensional space;

[0010] Among them, through the lifting function obtained by the DNN neural network, the train's non-linear control model is mapped into a linear system in a high-dimensional space, and the (A, B, C) matrices of the state space are iteratively solved using the dynamic mode decomposition method to construct an initial train data-driven linear state space model; A is the state transition matrix, B is the control input matrix, and C is the state projection matrix;

[0011] Step 2. Based on the train data-driven linear state space model obtained in Step 1, update the train data-driven linear state space model according to the possible actuator faults and additional faults that may occur in the train, obtain a train data-driven linear state space model with fault tolerance, and integrate this model into the MPC framework to replace the fault detection unit of the train;

[0012] Step 3. After the ATO system has been running for a period of time, use the train operation data obtained during this period to initialize the fault-tolerant control matrix through the dynamic mode decomposition method and , and establish a sliding window for train operation state data of a fixed size. According to a set of system snapshots taken within a given time window, recursively update the fault-tolerant control matrix in real time;

[0013] Step 4. For each train control cycle, obtain the state information required for training through the train sensors, and recursively update the fault-tolerant control matrix at this moment through the state information and the fault-tolerant control matrix at the previous moment , and use it to update the train data-driven linear state space model for model predictive control;

[0014] Adopt model predictive control. According to the motion target and constraint conditions of the train, obtain a sequence of control laws by minimizing the cost function of the MPC, and use the first element of the sequence of control laws as the traction force / braking force to drive the train;

[0015] Measure new state variables after the train responds, and enter the calculation of the next cycle for continuous rolling optimization.

[0016] In addition, the present invention also proposes a computer device, which includes a memory and one or more processors. An executable code is stored in the memory, and when the processor executes the executable code, it is used to implement the data-driven train fault-tolerant tracking control method described above.

[0017] In addition, the present invention also proposes a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, it is used to implement the data-driven train fault-tolerant tracking control method described above.

[0018] The present invention has the following advantages:

[0019] As described above, the present invention relates to a data-driven train fault-tolerant tracking control method. This method combines data-driven technology within a fault-tolerant control framework, enabling comprehensive and high-precision monitoring of the operating status of train actuators. Once an anomaly or potential fault is detected, the control system can immediately trigger an emergency response mechanism, thereby effectively avoiding accidents, providing a higher level of safety protection for passengers and staff, and enhancing train safety. Additionally, compared with traditional data-driven control methods that cannot determine system faults when a train fails and do not adjust the control model that can use the fault, resulting in the inability to accurately track the speed curve due to the output driving force / braking force, the method of the present invention adds fault-tolerant control on the basis of a data-driven model, enabling rapid adjustment to track the desired speed curve even in fault scenarios, providing a comfortable riding environment for passengers, and achieving precise speed tracking. Furthermore, to address the problem that the control system fails to recognize train actuator faults, leading to excessive output driving force and a decrease in energy utilization, the method of the present invention combines data-driven technology and fault-tolerant control, can optimize the system output according to the fault situation to obtain the optimal output driving force, significantly reducing the energy consumption during train operation, reducing operating costs, and alleviating the burden on the environment by the train system, and reducing train energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flowchart framework for constructing a train linear model using a data-driven method in an embodiment of the present invention.

[0021] Figure 2 It is a schematic diagram of a sliding window of train operation data in an embodiment of the present invention.

[0022] Figure 3 It is an overall flowchart of a data-driven train fault-tolerant tracking control method in an embodiment of the present invention.

[0023] Figure 4 It is a schematic diagram for comparing train speed tracking under normal conditions in an embodiment of the present invention.

[0024] Figure 5 It is a schematic diagram for comparing train speed errors under normal conditions of the actuator in an embodiment of the present invention.

[0025] Figure 6 It is a schematic diagram for comparing train displacement tracking under normal conditions of the actuator in an embodiment of the present invention.

[0026] Figure 7 It is a schematic diagram for comparing train speed tracking under actuator fault conditions in an embodiment of the present invention.

[0027] Figure 8 It is a schematic diagram for comparing train speed tracking errors under actuator fault conditions in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0029] Embodiment 1

[0030] In view of the above technical problems existing in the existing data-driven control scheme, the present invention describes a data-driven train fault-tolerant tracking control method. The method of the present invention constructs a data-driven model using the historical operation data of the system to capture the nonlinear behavior and fault characteristics of the system. By online estimation of the data-driven model to solve the fault impact, the method of the present invention allows adjustment of the Model Predictive Control (MPC) control law to offset the fault impact. By adding an online update process, the data-driven model can characterize the dynamic characteristics of the fault system. Therefore, the MPC controller can adapt to and compensate for faults in real time. Integrating the fault-tolerant train data-driven linear state space model into the MPC controller without a separate fault detection unit highlights the ability of the controller to mitigate faults and maintain the desired system behavior.

[0031] As Figure 1 and Figure 3 shown, the data-driven train fault-tolerant tracking control method in this embodiment includes the following steps:

[0032] Step 1. Obtain the initial historical operation data of the train, and use the data-driven method combined with a deep neural network to train and extract operators from the initial historical operation data of the train, and construct a linear dynamic system model in a high-dimensional space.

[0033] Through the lifting function obtained by the DNN neural network, map the train nonlinear control model into a linear system in a high-dimensional space, and use the Extended Dynamic Mode Decomposition (EDMD) method to iteratively solve the (A, B, C) matrices of the state space to construct the initial train data-driven linear state space model.

[0034] As Figure 1 shown, first obtain the historical operation data information of the ATO system during train operation, including actual state information and control information, and use the historical operation data information to form a training set.

[0035] The actual state self-information includes speed, position, etc., and the control information includes driving force / braking force and the corresponding command percentage, etc.

[0036] Among them, the input of the neural network training is a combination of state information and control information, and the output is the state information at the next moment. Preprocess, normalize, and denoise the training set data so as to fully reflect the nonlinear dynamics information of the train.

[0037] Construct a DNN neural network to learn the characteristics of the observation function performance system. Set the training time, batch size, and learning rate parameters, and determine whether to save the network parameters after reaching the maximum training time or when the training error is less than the set value.

[0038] After obtaining the observation function, define a finite observable vector as:

[0039] (1)

[0040] where represents the extended state, represents the first element of the input sequence, represents the train state; The state observation function can be expressed as follows:

[0041] (2)

[0042] where is the boosting function trained by the DNN neural network, used to capture the train operation characteristics, is the size of the boosted dimension.

[0043] Adopt the extended dynamic mode decomposition method to calculate a finite-dimensional operator, and the approximate form of the operator is The dynamic mode decomposition method solves the least squares problem by minimizing the following cost function to obtain the approximate closed estimation form of the operator:

[0044] (3)

[0045] where represents the Koopman operator, represents the operator dimension, represents the dimensional space of the operator, represents the dataset size, represents the train state at time i, represents the train state at the next time of i, represents the observation function of represents the observation function of represents the system output traction / braking force at time i.

[0046] In the optimization iteration process of the above formula, the state transition matrix A and the control input matrix B of the train data-driven linear state space model are obtained. The state projection C of this model is optimized by minimizing the squared difference between the predicted value and the actual output value, and the expression form is as follows:

[0047] (4)

[0048] Describe the data set obtained from the train historical operation data as:

[0049] (5)

[0050] (6)

[0051] (7)

[0052] where represents the train status information sequence, represents the status at a certain moment, which is composed of speed and position, represents the train status information sequence at the next moment after the action of U, represents the train output traction / braking force sequence, represents the output traction / braking force at a certain moment.

[0053] Obtained by using the above least - squares problem formula:

[0054] (8)

[0055] where 、 represent the data after dimensionality increase of in the data set by using the observation function 、 represents and constitute the pseudo - inverse of the matrix, represents the pseudo - inverse of, and the pseudo - inverse is the inverse matrix of a non - square matrix.

[0056] After obtaining each matrix of the train data - driven linear state - space model, by defining construct the train data - driven linear state - space model as follows:

[0057] (9)

[0058] where A is the state - transition matrix, B is the control - input matrix, C is the state - projection matrix, is the state variable of the system after dimensionality increase, , where N is the dimension of, is the estimated value of the original non - linear system state x(k).

[0059] ​, , is a linear time-invariant matrix.

[0060] is the system input, representing the traction or braking force received during the train operation, . Where m represents the dimension of the control input, n is the dimension of the train state, and k is the discrete time step.

[0061] This train data-driven linear state space model can be used to design an MPC controller to obtain a stable control effect.

[0062] Step 2. Based on the train data-driven linear state space model obtained from the train historical operation data, update the train data-driven linear state space model according to the possible actuator faults and additional faults that may occur in the train, obtain a fault-tolerant train data-driven linear state space model, and integrate this model into the MPC framework to replace the fault detection unit of the train.

[0063] To add a fault-tolerant control effect to the control system, first obtain the information of the train actuators, consider the occurrence of actuator faults, and model the system input to obtain the following fault input model:

[0064] (10)

[0065] Where represents the equivalent input when the actuator fails, and the matrix is used to represent the actuator state, and its definition is:

[0066] (11)

[0067] The matrix is a diagonal matrix, representing the additional fault of the corresponding actuator.

[0068] Each diagonal element value in the matrix is between 0 and 1, representing the degree of failure of the corresponding actuator, where 0 represents complete failure and 1 represents normal operation of the actuator.

[0069] Substitute the fault input model in formula (10) into the train data-driven linear state space model in Step 1 to obtain a fault-tolerant train data-driven linear state space model, and the formula is expressed as follows:

[0070] (12)

[0071] (13)

[0072] Where, denotes the state variable of the system at the (k + 1)-th moment after dimension elevation denotes the state variable of the system at the k-th moment after dimension elevation denotes the fault-tolerant control matrix; thus far, a fault-tolerant train data-driven control model of the data-driven MPC control framework is obtained, and the matrix is continuously updated according to the fault condition of the train to cope with sudden faults

[0073] Step 3. After the ATO system has been running for a period of time, use the train operation data obtained during this period to initialize the fault-tolerant control matrix through the dynamic mode decomposition method and , and establish a sliding window for train operation state data with a fixed size, as shown in Figure 2 , and recursively update the fault-tolerant control matrix in real time according to a set of system snapshots taken within a given time window

[0074] Construct an observable sequence with a length of a + 1 from the operation data of the train system running for a period of time, and arrange the observable sequence into the following matrix :

[0075] (14)

[0076] (15)

[0077] where and respectively denote the state operation data matrix and the input sequence data matrix, which are used to calculate the fault-tolerant control matrix ; , , denotes the weight of the data in the calculation

[0078] Use the EDMD method of dynamic mode decomposition. This EDMD method uses the lifting function trained by a neural network to map the low-dimensional state space to a high-dimensional space, where the system can be better dynamically described

[0079] The EDMD method first, at each time step k, through the following formula

[0080] (16)

[0081] Solve the least squares problem through the above formula to obtain the matrix The calculation formula is as follows

[0082] (17)

[0083] Initialize the fault-tolerant control matrix with the above formula After that, establish a data sliding window for the update of the matrix.

[0084] When accessing the new data generated during the train operation, update the matrix according to a set of system snapshots taken within a given time window. Most of the data in the window remains unchanged, only the first and the last elements of the window are changed, and the remaining data elements are only shifted one unit to the left.

[0085] Definition:

[0086] (18)

[0087] (19)

[0088] The input matrix is expressed as:

[0089] (20)

[0090] Update which can recursively update and When new data in the observable sequence is accessed, the at the next moment of the matrix can be recursively calculated with the new data.

[0091] Step 4. For each train control cycle, obtain the state information required for training through the train sensors, and recursively update the fault-tolerant control matrix at this moment through the state information and the fault-tolerant control matrix at the previous moment, and use it to update the train data-driven linear state space model for model predictive control.

[0092] Adopt model predictive control. According to the motion target and constraint conditions of the train, obtain the control law sequence by minimizing the cost function of MPC, and use the first element of the sequence as the traction force / braking force to drive the train. After the train responds, measure the new state variables and enter the calculation of the next cycle for continuous rolling optimization.

[0093] After the calculation formula is simplified, it is updated with the new train operation data in the window through the following formula:

[0094] (21)

[0095] where a represents the window size, b represents the state subscript, and u represents the input subscript.

[0096] (22)​

[0097] wherein represents the identity matrix.

[0098] (23)

[0099] (24)

[0100] (25)

[0101] (26)

[0102] The matrix is updated using the following formula:

[0103] (27)

[0104] Introducing the fault-tolerant control matrix increases the fault tolerance of the controller to any unnecessary deviation. This fault-tolerant control matrix consists of two parts, namely and , represents the actual input matrix, represents the additive term for estimating the actuator state, which can be regarded as a known disturbance and is input into the MPC controller.

[0105] Therefore, this enhances the robustness of the controller to undesired deviations, including additional faults and modeling errors.

[0106] After obtaining the fault-tolerant matrix a train data-driven linear state space model with fault tolerance is obtained as the model for MPC control. Subsequently, according to the train operation control objective, the objective function and constraint conditions of the MPC optimization problem are defined.

[0107] (28)

[0108] (29)

[0109] where J is the objective function, N represents the prediction horizon size of the MPC, , and are used to penalize the tracking error and the control input change, represents the reference trajectory, represents the MPC prediction trajectory, represents the train traction / braking force change constraint; represents the actual operation trajectory Represents the dimensionality elevation of the actual operating trajectory, , , and respectively represent the control input and its variation of the minimum and maximum boundaries.

[0110] By minimizing the objective function J, an optimal control law sequence for a period of time is obtained , denotes the th input quantity, and the first input quantity in the sequence is selected as the driving force input of the train.

[0111] After the train control system responds, the state information is obtained again to enter the calculation of the next cycle.

[0112] In addition, in order to enable those skilled in the art to more clearly understand the technical solution of the present invention, the following will design simulation cases to further illustrate the technical solution of the present invention, mainly including the following two parts:

[0113] 1. Verify the performance of the established high-dimensional train model, compare and analyze the speed tracking effect with the general linearized train model when the actuator is working normally, and evaluate indicators such as the accuracy rate and error of the model.

[0114] 2. Verify the performance of the data-driven fault-tolerant predictive controller, compare and analyze it with the ordinary data-driven MPC controller when 50% of the actuators fail, and evaluate the speed and stability of the active fault tolerance of the controller.

[0115] In terms of the training and comparison of the data-driven model, the root mean square error is used to evaluate the performance of the proposed model.

[0116] (30)

[0117] In the formula, RMSE represents the root mean square error, and are respectively the simulated state and the measured state of the train speed, is the sampling time, and k is the number of measurement points. In order to obtain the operating data, the sampling time is = 0.01 s, and a discrete-time train model is used to represent the real train dynamics, where the train mass m = 194.295 t, and the model is simplified to =-(2.031 + 0.0622 * + 0.001807* ) / 194.295 + u / 194295, and then simulate 500 trajectories within 1000 sampling periods.

[0118] To obtain more comprehensive data, the control input is randomly generated uniformly within the interval [−1,2], and the obtained control input is multiplied by 50 for application to the train. The initial state of each trajectory is randomly generated and uniformly distributed on the square [0,70]. This data collection process generates and stores 500000 data points. Construct matrices X and X of size 2×2×51 + and matrix U of size 1×2×51. During the simulation process, the general linear MPC method is used for comparison. For the general linear MPC method, the prediction model is constructed as a local linearization model of the dynamics at the origin, and the linearization model is updated every 100 steps.

[0119] In the simulation test, constraints are imposed on the control variable range and the corresponding increment, and the prediction horizon and control horizon are = 20 and = 10 respectively. The weights of the model predictive control are , .

[0120] where the fault-tolerant controller window size = 200, and the weight factor = 0.5.

[0121] The effectiveness and superiority of the controller are evaluated in terms of displacement and velocity tracking and velocity tracking error.

[0122] The speed tracking and error results and displacement tracking of the fault-tolerant data-driven (abbreviation: KMPC) controller and the general linear MPC (abbreviation: LMPC) controller, such as speed tracking Figure 4 , error Figure 5 and displacement tracking Figure 6 are shown as corresponding. It can be seen from the figure that the modeling accuracy of the global linearization modeling strategy of the data-driven model for high-speed trains is relatively high and is superior to the local linearization modeling method of the state space. During the entire observation period, the data-driven fault-tolerant model is highly consistent with the actual data. As shown in Table 1 below, it shows the comparison schematic of the tracking RMSE in the case of normal actuators.

[0123] Table 1 Comparison of Tracking RMSE in the Case of Normal Actuators

[0124]

[0125] As can be seen from Table 1, the RMSE of displacement and velocity of the KMPC model are 0.0098 and 0.0036 respectively, and the prediction accuracy of displacement and velocity is improved by 59.5% and 70% respectively compared with the linear state space model LMPC.

[0126] In terms of comparing the effects of data-driven fault-tolerant controllers, this part evaluates the control effect of the data-driven fault-tolerant predictive controller under actuator fault conditions. On the basis of the above experiments, the effectiveness loss of 50% of the actuator is simulated when the actuator has a step size of 200 steps, and an additional fault of ( -100) is added.

[0127] Compared with ordinary data-driven controllers, that is, controllers without building a fault-tolerant model, under the same fault scenario, the speed tracking effects of the data-driven fault-tolerant predictive controller (abbreviated as fault-tolerant KMPC) and the ordinary data-driven controller (abbreviated as ordinary KMPC) are as Figure 7 shown, and the speed tracking errors are as Figure 8 shown. It can be seen from the figure that at the moment when the fault is simulated, the fault-tolerant control model can relatively more quickly reduce the error caused by the fault through model update, and because the fault information is detected through data, it is also more accurate than the ordinary data-driven model in subsequent speed tracking. Table 2 shows the comparison of RMSE for actuator fault condition tracking.

[0128] Table 2 Comparison of RMSE for actuator fault condition tracking

[0129]

[0130] As can be seen from Table 2, the RMSE of displacement and velocity of the fault-tolerant KMPC model are 0.0063 and 0.0064 respectively, which are increased by 67.9% and 73.8% compared with ordinary KMPC. Therefore, under actuator fault conditions, the data-driven train fault-tolerant tracking control method described in the present invention shows excellent accuracy and stability.

[0131] Embodiment 2

[0132] This Embodiment 2 describes a computer device, which includes a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it is used to implement the steps of the data-driven train fault-tolerant tracking control method as in Embodiment 1 above.

[0133] In this embodiment, the computer device is any device or apparatus with data processing capabilities, which will not be elaborated here.

[0134] Embodiment 3

[0135] Embodiment 3 of the present invention describes a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the data-driven train fault-tolerant tracking control method in Embodiment 1 above.

[0136] The computer-readable storage medium may be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device.

[0137] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to listing the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any person skilled in the art under the teaching of this specification fall within the substantial scope of this specification and should be protected by the present invention.

Claims

1. A data-driven train fault-tolerant tracking control method, characterized in that It includes the following steps: Step 1. Obtain the initial historical operation data of the train, and use a data-driven method combined with a deep neural network to train and extract operators from the initial historical operation data of the train, and construct a linear dynamic system model in a high-dimensional space; Among them, through the lifting function obtained by the DNN neural network, the non-linear control model of the train is mapped into a linear system in a high-dimensional space, and the (A, B, C) matrices of the state space are iteratively solved using the dynamic mode decomposition method to construct an initial train data-driven linear state space model; A is the state transition matrix, B is the control input matrix, and C is the state projection matrix; Step 2. Based on the train data-driven linear state space model obtained in Step 1, update the train data-driven linear state space model according to the possible actuator faults and additional faults that may occur in the train, obtain a train data-driven linear state space model with fault tolerance, and integrate this model into the MPC framework to replace the fault detection unit of the train; Step 3. After the ATO system has been running for a period of time, use the train operation data obtained during this period to initialize the fault-tolerant control matrix through the dynamic mode decomposition method and , and establish a sliding window for train operation status data with a fixed size. According to a set of system snapshots taken within a given time window, recursively update the fault-tolerant control matrix in real time; Step 4. For each train control period, obtain the state information required for training through train sensors, and recursively update the fault-tolerant control matrix at this moment through the state information and the fault-tolerant control matrix at the previous moment and use it to update the train data-driven linear state space model for model predictive control; ​ Adopt model predictive control. According to the motion target and constraint conditions of the train, obtain a control law sequence by minimizing the cost function of the MPC, and use the first element of the control law sequence as the traction force / braking force to drive the train; Measure new state variables after the train responds, and enter the calculation of the next cycle for continuous rolling optimization.

2. The data-driven train fault-tolerant tracking control method according to claim 1, characterized in that The specific content of Step 1 is as follows: First, obtain the historical operation data information of the ATO system during train operation, including the actual state information, i.e., speed, position, and control information, i.e., driving force / braking force and the corresponding instruction percentage, and use the historical operation data information to form a training set; The input of the neural network training is a combination of state information and control information, and the output is the state information at the next moment; preprocess, normalize, and denoise the training set data so as to fully reflect the non-linear dynamics information of the train; Construct a DNN neural network to learn the observation function to represent the system characteristics, set the training time, batch size, and learning rate parameters, and determine whether to save the network parameters after reaching the maximum training time or the training error is less than the set value; After obtaining the observation function, define a finite observable vector as follows: (1) Among them, represents the extended state, represents the first element of the input sequence, represents the train state; is the state observation function, which is expressed as follows: (2) Among them is the boosting function trained by the DNN neural network, is the size of the boosted dimension; Compute a finite-dimensional operator using the extended dynamic mode decomposition method, and the approximate form of the operator is , and the dynamic mode decomposition solves the least-squares problem by minimizing the following cost function to obtain an approximate closed estimate form of the operator: (3) Among them represents the Koopman operator represents the operator dimension represents the dimensional space of the operator represents the dataset size represents the train state at time i represents the train state at the next moment of i represents the observation function of represents the observation function of represents the system output traction / braking force at time i; In the optimization iteration process of the above formula (3), the state transition matrix A and the control input matrix B of the train data-driven linear state space model are obtained; the state projection C of this train data-driven linear state space model is optimized by minimizing the mean square error between the predicted value and the actual output value, and the expression form is as follows: (4) Describe the data set obtained from the train historical operation data as: (5) (6) (7) Among them, represents the train status information sequence, represents the status at a certain moment, and the status information at each moment is composed of speed and position; represents the train status information sequence at the next moment after the action of U; Represents the train output traction / braking force sequence, Represents the output traction / braking force at a certain moment; Obtain using the least squares problem formulas in the above formulas (3) and (4): (8) where 、 represent the data after dimensionality increase of the dataset using the observation function ; 、 ; denotes and constitute the pseudo-inverse of the matrix, denotes 's pseudo-inverse, and the pseudo-inverse is the inverse matrix of a non-square matrix; After obtaining the matrices A, B, and C of the train data-driven linear state space model, by defining , the train data-driven linear state space model is constructed as follows: (9) where \(A\) is the state transition matrix, \(B\) is the control input matrix, and \(C\) is the state projection matrix; is the state variable of the system after dimensionality increase, , \(N\) is the dimension of the estimated value of the state of the original nonlinear system ; , , is a linear time-invariant matrix; is the system input, representing the traction or braking force received during the train operation, where m represents the dimension of the control input, n is the dimension of the train state, and k is the discrete time step; This train data-driven linear state space model can be used to design an MPC controller to obtain a stable control effect.

3. The data-driven train fault-tolerant tracking control method according to claim 2, characterized in that The specific content of Step 2 is as follows: First, obtain the information of the train actuator, consider that the actuator fails, and model the system input to obtain a fault input model, as shown in formula (10): (10) Among them represents the equivalent input when the actuator fails, and the matrix is used to represent the actuator state, and its definition is as follows: (11) Matrix is a diagonal matrix, indicating an additional fault of the corresponding actuator; Matrix Each diagonal element value , between 0 and 1, represents the degree of corresponding actuator failure, where 0 represents complete failure and 1 represents normal operation of the actuator; Substitute the fault input model in formula (10) into the train data-driven linear state space model in step 1 to obtain a train data-driven linear state space model with fault tolerance, and the formula is expressed as follows: (12) (13) Among them and represent the state variables of the system at the (k + 1)-th and k-th moments after dimensionality elevation, represents the fault-tolerant control matrix.

4. The data-driven train fault-tolerant tracking control method according to claim 3, wherein The specific step 3 is as follows: Run the train system for a certain period of time, and construct an observable sequence of length a + 1 , and arrange the observable sequences into the following matrix: (14) (15) Among them, and respectively represent the state operation data matrix and the input sequence data matrix; , , represent the weights of the data when calculating; Use the dynamic mode decomposition (EDMD) method. This EDMD method uses the lifting function trained by a neural network to map the low-dimensional state space to a high-dimensional space, and can better describe the system dynamically in the high-dimensional space; The EDMD method first, at each time step k, through the following formula: (16) The least squares problem is solved by the above formula to obtain the initialized fault tolerance control matrix The calculation formula is as follows: (17) Initialize the fault-tolerant control matrix with the above formula After that, establish a data sliding window for the update of the matrix; When accessing new data generated during train operation, update the matrix according to a set of system snapshots taken within a given time window, only changing the first and last elements of the window, and shifting the remaining data elements of the window by only one unit to the left; Define: (18) (19) The input matrix is expressed as: (20) Update that can be updated recursively and new data in the observable sequence is accessed, and the next moment of the matrix can be calculated recursively with the new data.

5. The data-driven train fault-tolerant tracking control method according to claim 4, wherein The specific step 4 is as follows: After the calculation formula is simplified, the new train operation data of the window is updated through the following formula: (21) where a represents the window size, b represents the state subscript, and u represents the input subscript; (22) wherein represents an identity matrix; (23) (24) (25) (26) Matrix Update using the following formula: (27) Fault-tolerant control matrix It consists of two parts, namely and , denotes the actual input matrix, denotes the additive term for estimating the actuator state, which is regarded as a known disturbance and is input into the MPC controller; After obtaining the fault-tolerant matrix a train data-driven linear state space model with fault tolerance is obtained as the model for MPC control. Subsequently, according to the train operation control objectives, the objective function and constraint conditions of the MPC optimization problem are defined, as shown in Equation (28) and Equation (29) respectively; (28) (29) Among them, J is the objective function, and N represents the prediction horizon size of MPC. , and are used to penalize the tracking error and the control input variation. represents the reference trajectory. represents the MPC prediction trajectory. represents the traction / braking force variation constraint of the train. represents the actual operation trajectory. represents the dimensionality elevation of the actual operation trajectory. , , and represent the control input and its variation of the minimum and maximum boundaries, respectively. By minimizing the objective function J, an optimal control law sequence for a period of time is obtained. , denotes the th input quantity, and the first input quantity in the control law sequence is selected as the driving force input of the train. After the train control system responds, obtain the state information again and enter the calculation of the next cycle.

6. A computer device, comprising a memory and one or more processors, wherein executable code is stored in the memory, characterized in that, When the processor executes the executable code, it is used to implement the data-driven train fault-tolerant tracking control method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it is used to implement the data-driven train fault-tolerant tracking control method according to any one of claims 1 to 5.

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