Axle vibration response active control method, device, equipment and medium

Abstract

The invention relates to an axle vibration response active control method, device, equipment and medium, and belongs to the field of railroad bridges, the axle vibration response active control method comprises the following steps: constructing an axle time-varying state equation considering control force and vehicle axle load, and constructing an observation equation taking acceleration as an observation vector; constructing an extended state vector based on the observation equation, constructing a state space model based on the extended state vector, the state equation and the observation equation, and predicting the state space model by adopting Kalman filtering to obtain an axle load predicted value, a predicted value of the extended state vector and an optimal estimated value; the target function considering the state vector and the control force is constructed through the optimal controller, the optimal control force is determined based on the predicted value of the extended state vector, the predicted value of the axle load and the target function, real-time monitoring and optimal control of the axle system are achieved, and the vibration control efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of railway bridges, and in particular to a method, device, equipment and medium for actively controlling vibration response of a vehicle bridge. Background Art

[0002] The load from moving vehicles will cause significant vibration in the bridge structure, which will not only endanger the stability and safety of the running vehicles, but also affect the working condition of the bridge. Therefore, the invention of the corresponding vibration control algorithm has important engineering significance.

[0003] Existing vibration control algorithms mainly use passive control devices and passive control algorithms, which leads to low vibration control efficiency and is difficult to meet actual engineering needs. Summary of the invention

[0004] In view of this, it is necessary to provide a method, device, equipment and medium for actively controlling the vibration response of a vehicle bridge, so as to solve the technical problem of low vibration control efficiency in vehicle bridge engineering.

[0005] In order to solve the above problems, the present invention provides a method for actively controlling axle vibration response, comprising: Construct the time-varying state equation of the axle taking into account the control force and the vehicle axle weight, and construct the observation equation with acceleration as the observation vector; An extended state vector is constructed based on the observation equation, a state space model is constructed based on the extended state vector, the state equation and the observation equation, and a Kalman filter is used to predict the state space model to obtain an axle weight prediction value, a prediction value of the extended state vector and an optimal estimate value; An objective function that considers the state vector and the control force is constructed through an optimal controller, and the optimal control force is determined based on the predicted value of the extended state vector, the predicted value of the axle weight, and the objective function.

[0006] In a possible implementation, the magnitude and strength of the bridge vibration is measured by a state vector; the calculation formula of the bridge time-varying state equation is: , in, is the time-varying axle state vector, is the input vector of track irregularity, is the axle mass coefficient matrix, is the damping coefficient matrix, is the coefficient matrix of the stiffness matrix, is the axis weight vector, is the input matrix of the control force, is the time-varying external control force, For time.

[0007] In a possible implementation, the calculation formula of the observation equation is: , in, is the observation vector, , , is the output matrix of the observation vector, is the noise vector, For the current moment, For the next moment, For control.

[0008] In a possible implementation, the calculation formula of the extended state vector is: , , in, is the extended state vector, is the state vector at the current moment, is the axis weight vector at the current moment, is the random walk noise of the axis weight vector, is the axis weight vector at the next moment, For the current moment, For the next moment.

[0009] In a possible implementation, the calculation formula of the state space model is: , in, is the extended state vector, is the observation vector, is the noise vector of the extended state vector, , , is the coefficient matrix, is the noise vector, is the output matrix of the observation vector, For the current moment, For the next moment.

[0010] In a possible implementation, the calculation formula of the Kalman filter is: , , , in, is the Kalman filter gain matrix, To predict the state vector at the next moment, is the optimal estimate of the state vector at the current moment, is the optimal estimate of the state vector at the next moment, To predict the covariance matrix for the next moment, To predict the optimal estimate of the covariance at the next moment, To predict the optimal estimate of the covariance at the current moment, is the identity matrix, , , is the coefficient matrix, is the matrix transpose, is the weight matrix of the state vector, is the weight matrix of the control force.

[0011] In a possible implementation, the objective function is calculated as follows: , in, is the objective function at the current moment, is the weight matrix of the state vector, is the weight matrix of the control force, is the matrix transpose, is the set multiplier vector, is the state vector at the next moment; The calculation formula of the optimal control force is: , in, For optimal control, is the input matrix of the control force, is the axle mass coefficient matrix, is the damping coefficient matrix, is the vehicle axle weight vector at the current moment.

[0012] On the other hand, the present invention also provides a vehicle bridge vibration response active control device, comprising: The axle equation construction module is used to construct the axle time-varying state equation taking into account the control force and vehicle axle weight, and to construct the observation equation with acceleration as the observation vector; A prediction module, used to construct an extended state vector based on the observation equation, construct a state space model based on the extended state vector, the state equation and the observation equation, and use Kalman filtering to predict the state space model to obtain an axle weight prediction value, a predicted value of the extended state vector and an optimal estimate value; The optimal control force determination module is used to construct an objective function that takes into account the state vector and the control force through an optimal controller, and determine the optimal control force based on the predicted value of the extended state vector, the predicted value of the axle weight and the objective function.

[0013] In another aspect, the present invention further provides an electronic device, comprising: a processor and a memory; The memory stores a computer-readable program executable by the processor; When the processor executes the computer-readable program, the steps in the above-mentioned active control method for vehicle axle vibration response are implemented.

[0014] On the other hand, the present invention also provides a computer-readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the steps in the active control method of vehicle bridge vibration response as described above.

[0015] The beneficial effects of the present invention are as follows: constructing a time-varying state equation of a vehicle bridge that takes into account the control force and the vehicle axle weight, taking into account the influence of the applied control force and the vehicle axle weight on the vehicle bridge, measuring the size and strength of the vibration through the state vector of the state equation, constructing an observation equation with acceleration as the observation vector, using the observation equation to monitor the vehicle axle weight and the mid-span acceleration of the bridge in real time, and measuring the state vector through acceleration, using Kalman filtering to predict the state space model, obtaining the axle weight prediction value, the extended state vector prediction value and the optimal estimate value, determining the optimal control force of the vehicle bridge based on the extended state vector prediction value, the axle weight prediction value and the objective function, realizing real-time monitoring and optimal control of the vehicle bridge system, and improving the efficiency of vibration control. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flow chart of an embodiment of the active control method for axle vibration response provided by the present invention; Figure 2 A schematic diagram of axle weight and bridge acceleration prediction for the vehicle-bridge vibration response active control method provided by the present invention; Figure 3 A schematic diagram of the acceleration control effect of the active control method for axle vibration response provided by the present invention; Figure 4 A schematic structural diagram of an embodiment of a vehicle bridge vibration response active control device provided by the present invention; Figure 5 A schematic structural diagram of an embodiment of an electronic device provided by the present invention. DETAILED DESCRIPTION

[0017] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0018] The present invention discloses a method, device, equipment and medium for active control of vehicle bridge vibration response, which can be used in a computer. The method, equipment or computer-readable storage medium involved in the present invention can be integrated with the above-mentioned equipment or can be relatively independent. A specific embodiment of the present invention discloses a method for actively controlling axle vibration response, which can be executed by a computer, specifically by one or more processors of the computer. Figure 1 is a flow chart of the active control method for axle vibration response provided by an embodiment of the present invention, please refer to Figure 1 , the active control method of axle vibration response includes: S101, constructing a time-varying state equation of the axle taking into account the control force and the vehicle axle weight, and constructing an observation equation with acceleration as the observation vector; S102, constructing an extended state vector based on the observation equation, constructing a state space model based on the extended state vector, the state equation and the observation equation, using Kalman filtering to predict the state space model, and obtaining an axle weight prediction value, a prediction value of the extended state vector and an optimal estimate value; S103. Construct an objective function that takes into account the state vector and the control force through an optimal controller, and determine the optimal control force based on the predicted value of the extended state vector, the predicted value of the axle weight, and the objective function.

[0019] Among them, a time-varying state equation of the axle considering the control force and the vehicle axle weight is constructed, the size and strength of the vibration are measured by the state vector of the state equation, an observation equation with acceleration as the observation vector is constructed, the state vector is characterized by acceleration, and the relationship between the state vector and the axle weight is determined by the constructed extended state vector. The state space model is predicted by Kalman filtering to obtain the predicted value of the axle weight and the predicted value of the state vector, and the optimal control force is determined by the objective function.

[0020] Compared with the prior art, the active control method for axle vibration response provided in this embodiment constructs a time-varying state equation of the axle that takes into account the control force and the vehicle axle weight, takes into account the influence of the applied control force and the vehicle axle weight on the axle, measures the size and strength of the vibration through the state vector of the state equation, constructs an observation equation with acceleration as the observation vector, uses the observation equation to monitor the axle weight of the vehicle and the mid-span acceleration of the bridge in real time, and measures the state vector through acceleration; constructs an extended state vector based on the observation equation, constructs a state space model based on the extended state vector, the state equation and the observation equation, uses Kalman filtering to predict the state space model, and obtains the axle weight prediction value, the extended state vector prediction value and the optimal estimated value; constructs an objective function that takes into account the state vector and the control force, determines the optimal control force of the axle based on the predicted value of the extended state vector, the axle weight prediction value and the objective function, and can well estimate the vehicle axle weight by observing the acceleration response of the bridge, while achieving instantaneous optimal control of the structure, thus achieving real-time monitoring and optimal control of the axle system and improving the efficiency of vibration control.

[0021] In some embodiments, in step S101, a time-varying state equation of the axle is constructed taking into account the control force and the vehicle axle weight, and the calculation formula of the time-varying state equation of the axle is: , in, is the time-varying axle state vector, is the input vector of track irregularity, is the axle mass coefficient matrix, is the damping coefficient matrix, is the coefficient matrix of the stiffness matrix, is the axis weight vector, is the input matrix of the control force, is the time-varying external control force, For time; Ignore the track irregularity value, that is , considering the noise in the process, the state equation is: , in, for The state vector at time, is the state vector at the current moment, For control, is the axle mass coefficient matrix, is the damping coefficient matrix, is the input matrix of the control force, is the vehicle axle weight vector at the current moment, is the state noise vector, For the current moment, is the next moment, and the covariance of its state noise is ; In order to facilitate the identification of the state of the vehicle bridge, a vertical accelerometer is set at the mid-span position of the bridge to record the acceleration value at the mid-span position of the bridge, and an observation equation with acceleration as the observation vector is constructed. The calculation formula of the observation equation is: , in, is the observation vector, , , is the output matrix of the observation vector, For the current moment, For the next moment, For control, is the noise vector corresponding to the observation equation, and the noise covariance is , whose observation vector Represents the time-varying observation vector of the vehicle-bridge system.

[0022] In some embodiments, in step S102, in order to predict the axle weight of the vehicle, an extended state vector is constructed based on the observation equation, and the extended state vector is composed of the state vector in the observation equation and the axle weight vector. The calculation formula of the extended state vector is: , in, is the extended state vector, for The state vector at time, for The axis weight vector at the moment; determine the relationship between the axis weight vector and time. The calculation formula for the relationship between the axis weight vector and time is: , in, is the axis weight vector at the next moment, is the random walk noise of the axis weight vector, and its covariance is ; After obtaining the extended state vector, a state space model is constructed based on the extended state vector, state equation and observation equation. The calculation formula of the state space model is: , in, is the extended state vector, is the observation vector, is the noise vector of the extended state vector, is the output matrix of the observation vector, is the noise vector of the extended state vector, , , Is the coefficient matrix, calculate the coefficient matrix in the state equation and observation equation, the calculation formula of the coefficient matrix is: , , , , in, is the identity matrix, By the state noise vector and random walk noise of the axis weight vector The noise vector of the expanded state vector is obtained by merging The noise covariance of .

[0023] The Kalman filter is used to predict the state space model to obtain the axle weight prediction value, the prediction value of the extended state vector and the optimal estimate value. The calculation formula of the Kalman filter is: , in, To predict the state vector at the next moment, is the optimal estimate of the state vector at the next moment, is the optimal estimate of the state vector at the current moment, is the observation vector, , , is the coefficient matrix, For control; The calculation formula of the Kalman filter gain matrix is: , in, is the Kalman filter gain matrix, is the identity matrix, is the matrix transpose, To predict the covariance matrix for the next moment, is the weight matrix of control force; The calculation formula for the covariance matrix prediction value and the optimal estimate value at the next moment is: , in, To predict the covariance matrix for the next moment, To predict the optimal estimate of the covariance at the next moment, To predict the optimal estimate of the covariance at the current moment, is the identity matrix, is the weight matrix of the state vector; The state vector in the state space model is identified and predicted by Kalman filtering to obtain the state vector value and the optimal estimate value at the current moment. The state vector at the next moment is predicted by the optimal estimate at the current moment. and the optimal estimate of the state vector , and obtain the predicted value and optimal estimate of the covariance matrix at the next moment, so as to obtain the predicted value of the axle weight at the current moment. After obtaining the predicted value of the extended state vector, the values ​​of the state vector and the axle weight vector are extracted, and the optimal estimate of the state vector is used for the control link.

[0024] In some embodiments, in step S103, an objective function considering the state vector and the control force is constructed by the optimal controller, and an instantaneous optimal control solution under the discrete state equation is given by the optimal control of the optimal controller (LQR). The objective function at the current moment is constructed according to the state equation and the optimal controller, and the calculation formula of the objective function is: , in, is the objective function at the current moment, is the state vector, is the state vector at the next moment, For control, is the matrix transpose, is the weight matrix of the state vector, is the weight matrix of the control force, and its weight is set according to the actual state. The objective function under optimal control is minimized, that is, the objective function takes the minimum value. According to the Lagrange multiplier method, the Hamiltonian function H is given, and its calculation formula is: , in, is the set multiplier vector; The variational method is used to find the minimum value of the objective function. According to the minimum principle, the partial derivative of the Hamiltonian function H with respect to the state vector, multiplier vector and control force is 0, and its calculation formula is: , in, is the partial derivative, so, , Through the above calculation formula, the updated control force, that is, the optimal control force, can be obtained, and its calculation formula is: , Control can also be expressed as: , After obtaining the optimal control force, the state vector and control force are updated at the next time step, and the control force at the next moment is given according to the state at the previous moment. Updating the control force over time can reduce the system state.

[0025] In some embodiments, taking a single-span simply supported bridge as an example, the span of the single-span simply supported bridge is L=32m, and the unit length mass of the bridge is kg / m, elastic modulus The vehicle adopts a single-axle vehicle standard model. The modal analysis based on the standard railway bridge finite element model can give modal parameters such as natural frequency and vibration mode; the noise level is selected as 5%, and the noise covariance matrix is , In order to identify the state of the vehicle-bridge system, the acceleration value at the mid-span position of the bridge is recorded by an accelerometer. The vertical acceleration responses at 1 / 4, 1 / 2, and 3 / 4 of the bridge are the required observation vectors. By giving two sets of control parameter Q and R values, corresponding to two different control forces, compared with the uncontrolled situation, the first group provides a smaller control force: Its control force is: , ; The second group provides greater control, and its control force is: , ; The identification steps are: Step 1: Set the state vector and covariance The initial value of the noise vector and , select the time step ; Step 2: Establish the time-varying state equation of the bridge and construct the observation equation; Step 3: Establish a state space model and calculate the coefficient matrix; Step 4: Use Kalman filtering to predict the axle weight of the vehicle at the current moment; Step 5: Use the objective function to give the optimal control force at the current moment; Step 6: When entering the next span, update the state vector and control; Step 7: Update the time step, change k to k+1, repeat steps 4 to 6, and finally obtain the prediction and control effect of the entire time period; For a schematic diagram of axle load and bridge acceleration prediction, please refer to Figure 2 ,like Figure 2 As shown, Figure 2 (a) is the axle load prediction result, Figure 2 (b) is the prediction result of the mid-span acceleration of the bridge. The control effect of the mid-span acceleration of the bridge corresponding to different control parameters can be found in Figure 3 , the fluctuation of the acceleration control effect is larger when it is not controlled, that is, the vibration control effect is poor. When a smaller control force is applied, the fluctuation of the acceleration control effect is stronger than that when no control force is applied. When a larger control force is applied, the acceleration control effect is the best. Figure 2 and Figure 3 It can be seen that when the observation vector is used for feedback, the axle weight of the vehicle and the mid-span acceleration of the bridge can be well predicted, and a stable and effective control effect can be achieved.

[0026] The vehicle-bridge interaction is taken into consideration and three observation vectors are used, namely the vertical acceleration responses at 1 / 4, 1 / 2 and 3 / 4 of the bridge as the required observation vectors. Measurement noise is added to achieve real-time monitoring and optimal control of the vehicle-bridge system, which has the advantages of timely feedback, accuracy and high efficiency.

[0027] In order to better implement the active control method for axle vibration response in the embodiment of the present invention, based on the active control method for axle vibration response, correspondingly, Figure 4 As shown, the embodiment of the present invention further provides a vehicle bridge vibration response active control device, and the vehicle bridge vibration response active control device 400 includes: A vehicle-bridge equation construction module 401 is used to construct a vehicle-bridge time-varying state equation taking into account control force and axle load, and to construct an observation equation taking acceleration as an observation vector; Prediction module 402, used to construct an extended state vector based on the observation equation, construct a state space model based on the extended state vector, the state equation and the observation equation, use Kalman filtering to predict the state space model, and obtain the axle weight prediction value, the extended state vector prediction value and the optimal estimate value; The optimal control force determination module 403 is used to construct an objective function that takes into account the state vector and the control force through an optimal controller, and determine the optimal control force based on the predicted value of the extended state vector, the predicted value of the axle weight and the objective function.

[0028] like Figure 5 As shown, based on the active control method of axle vibration response, the present invention also provides an electronic device 500, which can be a computing device such as a mobile terminal, a desktop computer, a notebook, a palm computer, and a server. The electronic device 500 includes a processor 501, a memory 502, and a display 503. Figure 5 Only some components of the electronic device 500 are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0029] In some embodiments, the memory 502 may be an internal storage unit of the electronic device 500, such as a hard disk or memory of the electronic device 500. In other embodiments, the memory 502 may also be an external storage device of the electronic device 500, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device 500. Further, the memory 502 may also include both an internal storage unit of the electronic device 500 and an external storage device. The memory 502 is used to store application software and various data installed in the electronic device 500, such as program codes installed in the electronic device 500. The memory 502 may also be used to temporarily store data that has been output or is to be output. In one embodiment, the memory 502 stores an active control program for axle vibration response, which can be executed by the processor 501, thereby realizing the active control method for axle vibration response of each embodiment of the present invention.

[0030] In some embodiments, the processor 501 may be a central processing unit (CPU), a microprocessor or other data processing chip, which is used to run program codes or process data stored in the memory 502, such as the active control method of axle vibration response.

[0031] In some embodiments, the display 503 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 503 is used to display identification information of the axle vibration response active control program and to display a visual user interface. The components 501-503 of the electronic device 500 communicate with each other via a system bus.

[0032] In some embodiments, when the processor 501 executes the axle vibration response active control program in the memory 502, various steps in the axle vibration response active control method described in the above embodiments are implemented. Since the axle vibration response active control method has been described in detail above, it will not be repeated here.

[0033] Accordingly, an embodiment of the present application also provides a computer-readable storage medium, which is used to store computer-readable programs or instructions. When the program or instructions are executed by a processor, the steps or functions of the active control method of vehicle axle vibration response provided by the above-mentioned method embodiments can be implemented.

[0034] In summary, the active control method, device, equipment and medium for the vibration response of the vehicle bridge provided by the present invention construct a time-varying state equation of the vehicle bridge taking into account the control force and the axle weight of the vehicle, and construct an observation equation with acceleration as the observation vector; construct an extended state vector based on the observation equation, construct a state space model based on the extended state vector, the state equation and the observation equation, and use Kalman filtering to predict the state space model to obtain the axle weight prediction value, the extended state vector prediction value and the optimal estimate value; construct an objective function taking into account the state vector and the control force through the optimal controller, and determine the optimal control force based on the prediction value of the extended state vector, the axle weight prediction value and the objective function, thereby realizing real-time monitoring and optimal control of the vehicle bridge system and improving the efficiency of vibration control.

[0035] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0036] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for actively controlling axle vibration response, characterized in that: include: Construct the time-varying state equation of the axle taking into account the control force and the vehicle axle weight, and construct the observation equation with acceleration as the observation vector; An extended state vector is constructed based on the observation equation, a state space model is constructed based on the extended state vector, the state equation and the observation equation, and a Kalman filter is used to predict the state space model to obtain an axle weight prediction value, a prediction value of the extended state vector and an optimal estimate value; An objective function that considers the state vector and the control force is constructed through an optimal controller, and the optimal control force is determined based on the predicted value of the extended state vector, the predicted value of the axle weight, and the objective function.

2. The active control method for axle vibration response according to claim 1, characterized in that: The magnitude and strength of the bridge vibration are measured by the state vector; the calculation formula of the bridge time-varying state equation is: ， in, is the time-varying axle state vector, is the input vector of track irregularity, is the axle mass coefficient matrix, is the damping coefficient matrix, is the coefficient matrix of the stiffness matrix, is the axis weight vector, is the input matrix of the control force, is the time-varying external control force, For time.

3. The active control method for axle vibration response according to claim 2, characterized in that: The calculation formula of the observation equation is: ， in, is the observation vector, , , is the output matrix of the observation vector, is the noise vector, For the current moment, For the next moment, For control.

4. The active control method for axle vibration response according to claim 3, characterized in that: The calculation formula of the extended state vector is: ， ， in, is the extended state vector, is the state vector at the current moment, is the axis weight vector at the current moment, is the random walk noise of the axis weight vector, is the axis weight vector at the next moment, For the current moment, For the next moment.

5. The active control method for axle vibration response according to claim 4, characterized in that: The calculation formula of the state space model is: ， in, is the extended state vector, is the observation vector, is the noise vector of the extended state vector, , , is the coefficient matrix, is the noise vector, is the output matrix of the observation vector, For the current moment, For the next moment.

6. The active control method for axle vibration response according to claim 5, characterized in that: The calculation formula of the Kalman filter is: ， ， ， in, is the Kalman filter gain matrix, To predict the state vector at the next moment, is the optimal estimate of the state vector at the current moment, is the optimal estimate of the state vector at the next moment, To predict the covariance matrix for the next moment, To predict the optimal estimate of the covariance at the next moment, To predict the optimal estimate of the covariance at the current moment, is the identity matrix, , , is the coefficient matrix, is the matrix transpose, is the weight matrix of the state vector, is the weight matrix of the control force.

7. The active control method for axle vibration response according to claim 6, characterized in that: The calculation formula of the objective function is: ， in, is the objective function at the current moment, is the weight matrix of the state vector, is the weight matrix of the control force, is the matrix transpose, is the set multiplier vector, is the state vector at the next moment; The calculation formula of the optimal control force is: ， in, For optimal control, is the input matrix of the control force, is the axle mass coefficient matrix, is the damping coefficient matrix, is the vehicle axle weight vector at the current moment.

8. An active control device for axle vibration response, characterized in that: include: The axle equation construction module is used to construct the axle time-varying state equation taking into account the control force and vehicle axle weight, and to construct the observation equation with acceleration as the observation vector; A prediction module, used to construct an extended state vector based on the observation equation, construct a state space model based on the extended state vector, the state equation and the observation equation, and use Kalman filtering to predict the state space model to obtain an axle weight prediction value, a predicted value of the extended state vector and an optimal estimate value; The optimal control force determination module is used to construct an objective function that takes into account the state vector and the control force through an optimal controller, and determine the optimal control force based on the predicted value of the extended state vector, the predicted value of the axle weight and the objective function.

9. An electronic device, characterized in that: including memory and processor; The memory stores a computer-readable program executable by the processor; When the processor executes the computer-readable program, the steps of the axle vibration response active control method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the steps in the vehicle bridge vibration response active control method according to any one of claims 1 to 7.

Images