Semi-active control method, device, equipment and medium for axle vibration

Abstract

The present invention relates to a semi-active control method, device, equipment and medium for vehicle bridge vibration, and belongs to the field of railway bridges. The semi-active control method for vehicle bridge vibration includes constructing a vehicle bridge equation with added control, constructing a state equation considering vehicle axle weight and an observation equation with acceleration as an observation vector based on the vehicle bridge equation; transforming the state equation to determine the relationship between the control vector and the state vector, and determining the optimal control based on a preset initial optimal control and the relationship between the control vector and the state vector; constructing an extended state equation and an extended observation equation based on the optimal control, the state equation and the observation equation, using Kalman filtering to predict the extended state equation and the extended observation equation in real time to obtain an optimal estimate of the state vector, and adjusting the mass, damping and stiffness of the vehicle bridge system based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the vehicle bridge vibration response, thereby improving the efficiency of vibration control.

Description

Technical Field

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

[0002] Bridge structures are an important part of modern transportation. Their safety and stability are crucial to people's lives and travel. The effects of running vehicles and other loads often cause significant vibrations in bridges, affecting the safety and durability of bridge structures. Controlling the vehicle-induced vibration response of bridges has always been an important issue in the field of structural engineering.

[0003] Existing semi-active control methods can only achieve overall optimal control of the bridge over the entire time period. However, in vehicle-bridge coupled vibration, the states of the bridge and vehicle change in real time, and the vehicle parameters cannot be determined, which has significant limitations and leads to inefficient control of vibration responses. Summary of the Invention

[0004] In view of this, it is necessary to provide a semi-active control method, device, equipment and medium for vehicle bridge vibration to solve the technical problem that the semi-active control of vehicle bridge vibration response does not take into account the real-time status of the bridge and the vehicle, resulting in low control efficiency of the vibration response.

[0005] In order to solve the above problems, the present invention provides a semi-active control method for axle vibration, comprising:

[0006] Constructing a vehicle-bridge equation with added control, and constructing a state equation taking vehicle axle weight into account and an observation equation taking acceleration as an observation vector based on the vehicle-bridge equation;

[0007] Transforming the state equation to determine the relationship between the control vector and the state vector, and determining the optimal control based on the preset initial optimal control and the relationship between the control vector and the state vector;

[0008] Based on the optimal control, state equation and observation equation, an extended state equation and an extended observation equation are constructed, and a Kalman filter is used to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector;

[0009] The mass, damping and stiffness of the axle system are adjusted based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the axle vibration response.

[0010] In one possible implementation, the axle equation is calculated as follows:

[0011] ,

[0012] ,

[0013] in, is the mass matrix of the vehicle-bridge system, C is the damping matrix of the vehicle-bridge system, is the stiffness matrix of the vehicle-bridge system, is the vertical displacement of the axle system, is the vertical acceleration of the vehicle-bridge system, is the vertical velocity of the vehicle-bridge system, is the load vector, is the vehicle axle load vector, Enter the matrix for track irregularity, is the track irregularity value.

[0014] In a possible implementation, the magnitude and strength of the axle vibration are measured by the state vector of the state equation; the calculation formula of the state equation is:

[0015] ,

[0016] in, is the state equation, is the state vector, 、 、 is a time-varying matrix;

[0017] The calculation formula of the state vector is:

[0018] ,

[0019] in, for The state vector at time t, is the vertical displacement vector of the vehicle-bridge system, is the vertical velocity vector of the vehicle-bridge system, For time.

[0020] In a possible implementation, the relationship between the control vector and the state vector is calculated as follows:

[0021] ,

[0022] in, is the control vector, is a positive semidefinite matrix;

[0023] The calculation formula of the optimal control is:

[0024] ,

[0025] ,

[0026] in, For optimal control, is the initial optimal control, for Tuning the damping mass at all times, for The damping of time, for The stiffness of the moment, is a positive definite matrix, is the matrix transpose, is the time step, is the time-varying matrix of the tuned damping mass pair Find the partial derivative, is the time-varying matrix of the damping Find the partial derivative, is the time-varying matrix of stiffness Find the partial derivative, For the previous moment, is the state vector.

[0027] In a possible implementation, the calculation formulas of the extended state equation and the extended observation equation are:

[0028] ,

[0029] in, is the extended state vector, To expand the observation vector, is the expanded time-varying matrix, is the expanded output matrix, is the expanded coefficient matrix, is the process noise at the previous moment, is the noise measured at the current moment, For the current moment, For the previous moment.

[0030] In one possible implementation, the use of Kalman filtering to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector includes:

[0031] Using Kalman filtering to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector at the current moment;

[0032] updating the state equation based on the optimal estimate of the current state vector;

[0033] The optimal control at the current moment is obtained, and the optimal estimate of the state vector at the next moment is determined based on the optimal control at the current moment, the updated state equation, and the observation equation.

[0034] In one possible implementation, the calculation formula of the Kalman filter is:

[0035] ,

[0036] ,

[0037] ,

[0038] in, is the predicted value of the state vector at the current moment, is the predicted value of the state vector at the previous moment, is the time-varying matrix after expansion at the previous moment, is the time-varying matrix of the previous moment, is the track irregularity value at the previous moment, is the forecast error covariance matrix, is the prediction error covariance matrix of the previous moment, is the semi-positive definite matrix at the previous moment, is the Kalman filter gain matrix, is the positive definite matrix at the current moment, Transpose the matrix.

[0039] In another aspect, the present invention further provides a semi-active control device for axle vibration, comprising:

[0040] A bridge equation construction module is used to construct a bridge equation with added control, and based on the bridge equation, a state equation that takes vehicle axle weight into account and an observation equation that takes acceleration as an observation vector are constructed;

[0041] an optimal control determination module, configured to transform the state equation to determine a relationship between a control vector and a state vector, and determine an optimal control based on a preset initial optimal control and the relationship between the control vector and the state vector;

[0042] A state estimation module is used to construct an extended state equation and an observation equation based on the optimal control, state equation and observation equation, and use Kalman filtering to perform real-time prediction on the extended state equation and observation equation to obtain an optimal estimate of the state vector;

[0043] A semi-active control module is used to adjust the mass, damping and stiffness of the axle system based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the axle vibration response.

[0044] On the other hand, the present invention also provides an electronic device, comprising: a processor and a memory;

[0045] The memory stores a computer-readable program executable by the processor;

[0046] When the processor executes the computer-readable program, the processor implements the steps of the semi-active control method for vehicle axle vibration as described above.

[0047] 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 semi-active control method of vehicle axle vibration as described above.

[0048] The beneficial effects of the present invention are: constructing a vehicle-bridge equation with added control, adjusting the mass, damping and stiffness of the vehicle-bridge system by adding semi-active control, constructing a state equation considering the vehicle mass and an observation equation with acceleration as the observation vector, considering the influence of the applied control and the real-time state of the vehicle on the vehicle-bridge system, using the observation equation to monitor the mid-span acceleration of the vehicle and the bridge in real time, and measuring the state vector by acceleration, constructing an extended state equation and an extended observation equation based on the optimal control, the state equation and the observation equation, using Kalman filtering to predict the extended state equation and the extended observation equation in real time, obtaining the optimal estimate of the state vector, adjusting the mass, damping and stiffness of the vehicle-bridge system based on the optimal estimate of the state vector, so as to realize the instantaneous optimal semi-active control of the vehicle-bridge vibration response, considering the real-time state of the vehicle-bridge system, reducing the structural vibration of the vehicle-bridge system, realizing the optimal control of the vehicle-bridge vibration response, and improving the efficiency of vibration control. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A flow chart of an embodiment of a semi-active control method for axle vibration provided by the present invention;

[0050] Figure 2 A schematic diagram of the estimated and actual vehicle mass and acceleration results of the semi-active control method for axle vibration provided by the present invention;

[0051] Figure 3 A schematic diagram of the bridge mid-span acceleration control effect of applying passive control to the semi-active control method for vehicle bridge vibration provided by the present invention;

[0052] Figure 4 A schematic diagram of the bridge mid-span acceleration control effect of applying semi-active control of the vehicle bridge vibration semi-active control method provided by the present invention;

[0053] Figure 5 A schematic structural diagram of an embodiment of a semi-active control device for vehicle axle vibration provided by the present invention;

[0054] Figure 6 This is a schematic structural diagram of an embodiment of an electronic device provided by the present invention. DETAILED DESCRIPTION

[0055] The preferred embodiments of the present invention will be 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, and are not used to limit the scope of the present invention.

[0056] The present invention discloses a semi-active control method, device, equipment, and medium for axle vibration control, 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.

[0057] A specific embodiment of the present invention discloses a semi-active control method for vehicle bridge vibration, which can be executed by a computer, specifically by one or more processors of the computer. Figure 1 This is a flow chart of the semi-active control method for axle vibration provided by an embodiment of the present invention. Figure 1 , the semi-active control methods for axle vibration include:

[0058] S101, constructing a vehicle-bridge equation with added control, and constructing a state equation taking into account the vehicle axle weight and an observation equation taking acceleration as the observation vector based on the vehicle-bridge equation;

[0059] S102, transforming the state equation to determine the relationship between the control vector and the state vector, and determining the optimal control based on the preset initial optimal control and the relationship between the control vector and the state vector;

[0060] S103, constructing an extended state equation and an extended observation equation based on optimal control, the state equation, and the observation equation, and using Kalman filtering to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector;

[0061] S104 , adjusting the mass, damping, and stiffness of the vehicle-bridge system based on the optimal estimation of the state vector to achieve instantaneous optimal semi-active control of the vehicle-bridge vibration response.

[0062] Among them, semi-active control is to change the stiffness or damping parameters of the structure through a small amount of energy to reduce structural vibration. Through semi-active control, the mass, damping and stiffness of the axle system are adjusted in real time. That is, when the axle responds to vibration, the mass, damping and stiffness of the tuned damper (TMD) are adjusted to adjust the mass, damping and stiffness of the axle system. A state equation that considers the vehicle axle weight is constructed, and 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, and the state vector is represented by acceleration. The extended state equation and extended observation equation are predicted in real time through Kalman filtering to obtain the optimal estimate of the state vector.

[0063] Compared with the prior art, the semi-active control method for axle vibration provided in this embodiment constructs an axle equation with added control. The mass, damping, and stiffness of the axle system are adjusted by adding semi-active control. A state equation that considers the vehicle axle weight and an observation equation with acceleration as the observation vector are constructed based on the axle equation. The effects of the applied control and the real-time state of the vehicle on the axle system are considered. The observation equation is used to monitor the mid-span acceleration of the vehicle and bridge in real time. The state equation is transformed to determine the relationship between the control vector and the state vector. The optimal control is determined based on a preset initial optimal control and the relationship between the control vector and the state vector. An extended state equation and an extended observation equation are constructed based on the optimal control, the state equation, and the observation equation. A Kalman filter is used to predict the extended state equation and the extended observation equation in real time to obtain an optimal estimate of the state vector. The vehicle mass is identified through the state vector of the state equation. The mass, damping, and stiffness of the axle system are adjusted based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the axle vibration response. The mass, damping, and stiffness of the tuned damper are adjusted to achieve instantaneous optimal semi-active control, achieving optimal control of the axle vibration response and improving the efficiency of vibration control.

[0064] In some embodiments, in step S101, an axle equation with added control is constructed, and the mass, damping, and stiffness of the axle system are adjusted in real time through TMD. The axle equation is constructed based on the mass, damping, and stiffness of the axle system. The calculation formula of the axle equation is:

[0065] ,

[0066] in, is the mass matrix of the vehicle-bridge system, C is the damping matrix of the vehicle-bridge system, is the stiffness matrix of the vehicle-bridge system, is the vertical displacement of the axle system, is the vertical acceleration of the vehicle-bridge system, is the vertical velocity of the vehicle-bridge system, is the load vector, which is the superposition of the mass load vector and the track irregularity load vector. The load vector calculation formula is:

[0067] ,

[0068] in, is the vehicle axle load vector, Enter the matrix for track irregularity, is the track irregularity value;

[0069] Based on the vehicle-bridge equation, the state equation considering the vehicle axle weight and the observation equation with acceleration as the observation vector are constructed. That is, the state equation is established by the vehicle-bridge equation. The calculation formula of the state equation is:

[0070] ,

[0071] in, is the state equation, is the state vector, 、 、 is a time-varying matrix, is the vehicle mass load vector, and defines the state vector , the calculation formula of its state vector is:

[0072] ,

[0073] in, for The state vector at time t, is the vertical displacement vector of the vehicle-bridge system, is the vertical velocity vector of the vehicle-bridge system, is time, and the calculation formula of its time-varying matrix is:

[0074] ,

[0075] ,

[0076] ,

[0077] in, is the mass of the axle system, is the stiffness matrix, is the identity matrix, is the damping matrix, The track irregularity input matrix is ​​used, and the vehicle axle load vector is calculated as follows:

[0078] ,

[0079] in, is the vehicle body mass, is the wheel mass, is the acceleration due to gravity, Mode function, is the matrix transpose;

[0080] The calculation formula of track irregularity input matrix is:

[0081] ,

[0082] in, is the stiffness coefficient of the wheel spring.

[0083] In some embodiments, in step S102, the state equation is transformed to determine the relationship between the control vector and the state vector, and the optimal control is determined based on the preset initial optimal control and the relationship between the control vector and the state vector, and the initial optimal control is set. , the calculation formula of the initial optimal control is:

[0084] ,

[0085] in, is the tuned damping mass at the initial moment, is the damping at the initial moment, is the stiffness at the initial moment. Within a time interval, optimal control can be achieved. The optimal control formula is:

[0086] ,

[0087] in, for Tuning the damping mass at all times, for The damping of time, for The stiffness of the moment, at the time step Above, the state vector can be expressed as:

[0088] ,

[0089] in, is the state vector, For The exponential function with base , is the time step, is a time-varying matrix;

[0090] According to the minimum principle, the state equation is transformed into an unconstrained minimization problem, and the calculation formula of the Hamiltonian function is:

[0091] ,

[0092] in, is the Hamiltonian function, is the control vector, is a positive semidefinite matrix, is a positive definite matrix, and are coefficient matrices to be adjusted;

[0093] By using the Hamiltonian function to find the partial derivatives of the state vector, control, and control vector, we can get the necessary conditions for function minimization, which is calculated as follows:

[0094] ,

[0095] ,

[0096] ,

[0097] ,

[0098] in, is the partial derivative, is the multiplier vector, which is also the control vector, is the time-varying matrix of the tuned damping mass pair Find the partial derivative, is the time-varying matrix of the damping Find the partial derivative, is the time-varying matrix of stiffness Find partial derivatives;

[0099] The relationship between the control vector and the state vector is determined by the above calculation formula. The calculation formula for the relationship between the control vector and the state vector is:

[0100] ,

[0101] in, is the control vector, is a positive semidefinite matrix, is the state vector;

[0102] The optimal control is determined based on the preset initial optimal control and the relationship between the control vector and the state vector, that is, the optimal control at the current moment is obtained. The calculation formula for the optimal control is:

[0103] ,

[0104] in, is the optimal control at the current moment, is the initial optimal control.

[0105] In some embodiments, in step S103, an extended state equation and an extended observation equation are constructed based on the optimal control, the state equation, and the observation equation. Discrete state equations and observation equations are established based on the optimal control, the state equation, and the observation equation. The calculation formulas of the discrete state equations and observation equations are:

[0106] ,

[0107] ,

[0108] ,

[0109] in, for The state vector at time t, for The observation vector at time t, 、 、 Both The time-varying matrix of the moment, is the track irregularity value at the previous moment, for The output matrix of the observation vector at each moment, C is the damping matrix of the bridge system, For the current moment, For the previous moment, is the coefficient matrix, for The load vector at time t, is the displacement output matrix, is the acceleration output matrix, Velocity output matrix, is the process noise at the previous moment, Measure the noise for the current moment;

[0110] When identifying vehicle mass, the vehicle mass is treated as an unknown quantity, and the extended state equation and extended observation equation are constructed based on the discrete state equation and observation equation. The calculation formulas of the extended state equation and extended observation equation are as follows:

[0111] ,

[0112] ,

[0113] ,

[0114] ,

[0115] ,

[0116] in, is the extended state vector, To expand the observation vector, is the expanded time-varying matrix, is the expanded output matrix, is the expanded coefficient matrix, is the process noise at the previous moment, for The acceleration due to gravity at that moment, is the identity matrix, is the vibration mode function, Enter the matrix for track irregularity, is the noise measured at the current moment, For the current moment, For the previous moment;

[0117] The Kalman filter is used to predict the extended state equation and the extended observation equation in real time, and the state vector at the next moment is estimated by the observation vector of the observation equation. First, the extended state equation and the extended observation equation are predicted by the Kalman filter to obtain the optimal estimate of the state vector at the current moment, and the state vector is predicted. The calculation formula is:

[0118] ,

[0119] in, is the predicted value of the state vector at the current moment, is the predicted value of the state vector at the previous moment, is the time-varying matrix after expansion at the previous moment, is the time-varying matrix of the previous moment, is the track irregularity value at the previous moment;

[0120] The prediction error covariance matrix is ​​calculated as:

[0121] ,

[0122] in, is the forecast error covariance matrix, is the prediction error covariance matrix of the previous moment, is the semi-positive definite matrix at the previous moment, is the matrix transpose;

[0123] Calculate the Kalman filter gain matrix, which is calculated as:

[0124] ,

[0125] in, is the Kalman filter gain matrix, is the positive definite matrix at the current moment;

[0126] Calculate the state estimation equation to obtain the optimal estimate of the state vector at the current moment, and obtain the predicted value of the vehicle axle weight based on the state vector. Secondly, update the state equation based on the optimal estimate of the state vector at the current moment, update the state vector and the error covariance matrix, and the calculation formula is:

[0127] ,

[0128] in, is the state vector at the current moment, is the predicted value of the state vector at the current moment, is the error covariance matrix at the current moment, is the identity matrix;

[0129] Finally, the optimal estimate of the state vector at the next moment is determined based on the optimal control at the current moment, the updated state equation, and the observation equation. That is, the extended state equation and the extended observation equation are updated through the updated state equation and the observation equation as well as the optimal control at the current moment, and the updated extended state equation and the extended observation equation are predicted through Kalman filtering to obtain the optimal estimate of the state vector at the next moment. The above process is repeated until the vehicle leaves the bridge, and the optimal control of the vehicle-bridge system and the optimal estimate of the state vector are obtained in real time, thereby realizing real-time monitoring and optimal control of the vehicle-bridge vibration response.

[0130] In some embodiments, in step S104, the mass, damping, and stiffness of the axle system are adjusted based on the optimal estimation of the state vector. By adjusting the mass, damping, and stiffness of the axle system, the vibration of the axle system is reduced to achieve instantaneous optimal semi-active control of the axle vibration response.

[0131] In some embodiments, taking a single-span simply supported bridge as an example, the span of the single-span simply supported bridge is L=25m, and the cross-sectional inertia moment of the bridge is , the mass of the bridge is the mass per unit length of the bridge kg, elastic modulus Pa, the modal mass and modal vibration shape of the bridge are calculated as follows:

[0132] ,

[0133] in, is the modal mass, is the mode shape, is the order of the vibration mode, i.e. order vibration mode, is the bridge length, is the distance between any position on the bridge and the bridgehead;

[0134] Considering the third-order bridge mode Without considering the bridge damping, the initial moment is when the first wheel of the first vehicle just enters the bridge, and the end moment is when the first wheel of the second vehicle leaves the bridge. The vehicles are two single-axle vehicles with a distance of 5m. The vehicles move at a constant speed. From the left end to the right end, the time step of the numerical calculation is 0.001s ( ); The vertical acceleration of the bridge and the vertical acceleration of a single-axle vehicle is the observation vector, 1% Gaussian white noise is added to the observation value, the tuned damper is located in the middle of the bridge span, and its initial mass is kg, and the damping coefficient is Nm / s, the stiffness coefficient is N / s;

[0135] See the diagram for the estimated and actual vehicle mass and acceleration. Figure 2 ,like Figure 2 As shown, Figure 2 The estimated results of the vehicle mass and the comparison between the actual and estimated vertical accelerations at the mid-span of the bridge are shown in Figure 2. Figure 2 (a) shows the predicted and actual vehicle mass results. The solid line represents the actual value of the vehicle mass, and the dotted line represents the estimated value. In the initial stage, the estimated value is quite different from the actual value. This is due to the difference between the initial value and the actual value. As the vehicle moves on the bridge, the estimated value quickly converges to the actual value within 0.1s and tends to be stable. Figure 2 (b) The optimal estimation of the mid-span vertical acceleration at each moment using the Kalman filter and the actual semi-active control mid-span vertical acceleration are shown. The solid line represents the actual bridge mid-span vertical acceleration, and the dashed line represents the estimated optimal bridge mid-span vertical acceleration. The actual and estimated values ​​are basically consistent, with only a small difference.

[0136] For the effect of passive control on mid-span acceleration control of bridges, see Figure 3 ,like Figure 3 As shown in the figure, the solid line represents the mid-span acceleration response without control, and the dashed line represents the mid-span acceleration response with fixed control. For the mid-span acceleration control effect of the bridge with semi-active control, please refer to Figure 4 The dotted lines represent the mid-span acceleration response of the time-varying semi-active control, and the solid lines represent the mid-span acceleration response without control. In the initial stage, the control effect is not obvious. After 0.3s, the control effect gradually becomes obvious and tends to be stable. The control efficiency reaches 35.1% at the first peak where the control effect is obvious, indicating that the semi-active control can effectively control the vehicle-induced vibration of the bridge.

[0137] Taking vehicle-bridge interaction into account, the mass, damping, and stiffness of the vehicle-bridge system are adjusted in real time through semi-active control. The observation vector, i.e., the vertical acceleration response of the vehicle-bridge system, is used as the required observation vector. Measurement noise is added to achieve optimal control of the vehicle-bridge system.

[0138] In order to better implement the semi-active control method of the vehicle bridge vibration in the embodiment of the present invention, based on the semi-active control method of the vehicle bridge vibration, correspondingly, Figure 5 As shown, an embodiment of the present invention further provides a semi-active control device for vehicle axle vibration, and the semi-active control device 500 for vehicle axle vibration includes:

[0139] A bridge equation construction module 501 is used to construct a bridge equation with added control, and based on the bridge equation, construct a state equation that takes vehicle axle weight into account and an observation equation that takes acceleration as an observation vector;

[0140] An optimal control determination module 502 is configured to transform the state equation to determine the relationship between the control vector and the state vector, and determine the optimal control based on the preset initial optimal control and the relationship between the control vector and the state vector;

[0141] A state estimation module 503 is used to construct an extended state equation and an observation equation based on optimal control, the state equation, and the observation equation, and to perform real-time prediction on the extended state equation and the observation equation using a Kalman filter to obtain an optimal estimate of the state vector;

[0142] The semi-active control module 504 is configured to adjust the mass, damping, and stiffness of the axle system based on the optimal estimation of the state vector to achieve instantaneous optimal semi-active control of the axle vibration response.

[0143] like Figure 6 As shown, based on the semi-active control method of vehicle bridge vibration, the present invention also provides an electronic device 600, which can be a computing device such as a mobile terminal, desktop computer, notebook, PDA, server, etc. The electronic device 600 includes a processor 601, a memory 602, and a display 603. Figure 6 Only some of the components of the electronic device 600 are shown, but it should be understood that implementation of all of the shown components is not required, and more or fewer components may be implemented instead.

[0144] In some embodiments, the memory 602 may be an internal storage unit of the electronic device 600, such as a hard drive or memory of the electronic device 600. In other embodiments, the memory 602 may also be an external storage device of the electronic device 600, such as a plug-in hard drive, a Smart Media Card (SMC), a Secure Digital (SD) card, a flash memory card, etc. Furthermore, the memory 602 may include both an internal storage unit of the electronic device 600 and an external storage device. The memory 602 is used to store application software installed in the electronic device 600 and various data, such as program code installed in the electronic device 600. The memory 602 may also be used to temporarily store data that has been output or is about to be output. In one embodiment, the memory 602 stores a semi-active control program for vehicle axle vibration, which can be executed by the processor 601, thereby implementing the semi-active control method for vehicle axle vibration according to various embodiments of the present invention.

[0145] In some embodiments, the processor 601 may be a central processing unit (CPU), a microprocessor, or other data processing chip, configured to execute program codes or process data stored in the memory 602 , such as a semi-active control method for axle vibration.

[0146] In some embodiments, display 603 can be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 603 is used to display identification information for the semi-active control program for axle vibration and to display a visual user interface. Components 601-603 of electronic device 600 communicate with each other via a system bus.

[0147] In some embodiments, when the processor 601 executes the semi-active control program for axle vibration in the memory 602, the various steps of the semi-active control method for axle vibration described in the above embodiments are implemented. Since the semi-active control method for axle vibration has been described in detail above, it will not be repeated here.

[0148] 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 semi-active control method of vehicle axle vibration provided by the above-mentioned method embodiments can be implemented.

[0149] In summary, the semi-active control method, device, equipment and medium for bridge vibration provided by the present invention construct a bridge equation with added control, and construct a state equation considering the vehicle axle weight and an observation equation with acceleration as the observation vector based on the bridge equation; the state equation is transformed to determine the relationship between the control vector and the state vector, and the optimal control is determined based on the preset initial optimal control and the relationship between the control vector and the state vector; based on the optimal control, the state equation and the observation equation, an extended state equation and an extended observation equation are constructed, and a Kalman filter is used to perform real-time prediction on the extended state equation and the extended observation equation to obtain the optimal estimate of the state vector, and the mass, damping and stiffness of the bridge system are adjusted based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the bridge vibration response, thereby achieving optimal control of the bridge vibration response and improving the efficiency of vibration control.

[0150] Those skilled in the art will appreciate that all or part of the process steps of the above-described embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, such as a magnetic disk, an optical disk, a read-only memory, or a random access memory.

[0151] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A semi-active control method for vehicle bridge vibration, characterized in that: include: Constructing a vehicle-bridge equation with added control, and constructing a state equation taking vehicle axle weight into account and an observation equation taking acceleration as an observation vector based on the vehicle-bridge equation; Transforming the state equation to determine the relationship between the control vector and the state vector, and determining the optimal control based on the preset initial optimal control and the relationship between the control vector and the state vector; Based on the optimal control, state equation and observation equation, an extended state equation and an extended observation equation are constructed, and a Kalman filter is used to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector; The mass, damping and stiffness of the axle system are adjusted based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the axle vibration response.

2. The semi-active control method for axle vibration according to claim 1, characterized in that: The calculation formula of the axle equation is: ， ， in, is the mass matrix of the vehicle-bridge system, C is the damping matrix of the vehicle-bridge system, is the stiffness matrix of the vehicle-bridge system, is the vertical displacement of the axle system, is the vertical acceleration of the vehicle-bridge system, is the vertical velocity of the vehicle-bridge system, is the load vector, is the vehicle axle load vector, Enter the matrix for track irregularity, is the track irregularity value.

3. The semi-active control method for axle vibration according to claim 2, characterized in that: The magnitude and strength of the axle vibration are measured by the state vector of the state equation; the calculation formula of the state equation is: ， in, is the state equation, is the state vector, 、 、 is a time-varying matrix; The calculation formula of the state vector is: ， in, for The state vector at time t, is the vertical displacement vector of the vehicle-bridge system, is the vertical velocity vector of the vehicle-bridge system, For time.

4. The semi-active control method for vehicle bridge vibration according to claim 3, characterized in that: The calculation formula of the relationship between the control vector and the state vector is: ， in, is the control vector, is a positive semidefinite matrix; The calculation formula of the optimal control is: ， ， in, For optimal control, is the initial optimal control, for Tuning the damping mass at all times, for The damping of time, for The stiffness of the moment, is a positive definite matrix, is the matrix transpose, is the time step, is the time-varying matrix of the tuned damping mass pair Find the partial derivative, is the time-varying matrix of the damping Find the partial derivative, is the time-varying matrix of stiffness Find the partial derivative, For the previous moment.

5. The semi-active control method for vehicle bridge vibration according to claim 4, characterized in that: The calculation formulas of the extended state equation and the extended observation equation are: ， in, is the extended state vector, To expand the observation vector, is the expanded time-varying matrix, is the expanded output matrix, is the expanded coefficient matrix, is the process noise at the previous moment, is the noise measured at the current moment, For the current moment, For the previous moment.

6. The semi-active control method for vehicle bridge vibration according to claim 5, characterized in that: The method of using Kalman filtering to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector includes: Using Kalman filtering to perform real-time prediction on the extended state equation and the extended observation equation to obtain an optimal estimate of the state vector at the current moment; updating the state equation based on the optimal estimate of the current state vector; The optimal control at the current moment is obtained, and the optimal estimate of the state vector at the next moment is determined based on the optimal control at the current moment, the updated state equation, and the observation equation.

7. The semi-active control method for vehicle bridge vibration according to claim 6, characterized in that: The calculation formula of the Kalman filter is: ， ， ， in, is the predicted value of the state vector at the current moment, is the predicted value of the state vector at the previous moment, is the time-varying matrix after expansion at the previous moment, is the time-varying matrix of the previous moment, is the track irregularity value at the previous moment, is the forecast error covariance matrix, is the prediction error covariance matrix of the previous moment, is the semi-positive definite matrix at the previous moment, is the Kalman filter gain matrix, is the positive definite matrix at the current moment, Transpose the matrix.

8. A semi-active control device for axle vibration, characterized in that: include: A vehicle-bridge equation construction module is used to construct a vehicle-bridge equation with added control, and based on the vehicle-bridge equation, a state equation that takes vehicle axle weight into account and an observation equation that takes acceleration as an observation vector are constructed; an optimal control determination module, configured to transform the state equation to determine a relationship between a control vector and a state vector, and determine an optimal control based on a preset initial optimal control and the relationship between the control vector and the state vector; A state estimation module is used to construct an extended state equation and an observation equation based on the optimal control, state equation and observation equation, and use Kalman filtering to perform real-time prediction on the extended state equation and observation equation to obtain an optimal estimate of the state vector; A semi-active control module is used to adjust the mass, damping and stiffness of the axle system based on the optimal estimate of the state vector to achieve instantaneous optimal semi-active control of the axle vibration response.

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 processor implements the steps of the semi-active control method for vehicle axle vibration according to any one of claims 1 to 7.

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 of the semi-active control method for vehicle axle vibration according to any one of claims 1 to 7.

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