Model predictive control method and system for seismic simulation shaking table, medium, and terminal

Abstract

A model predictive control method for a seismic simulation shaking table, comprising: S1: acquiring offline data of input signals and output signals of a seismic simulation shaking table; S2, on the basis of the acquired offline data, using sparse regression to identify a kinetic equation of the seismic simulation shaking table; and S3, on the basis of the kinetic equation, predicting output signals of the seismic simulation shaking table under different input signals, and using an optimization model to correct the input signals; moreover, on the basis of real-time data of the input signals and the output signals collected by the seismic simulation shaking table in the control process, performing parameter updating on the kinetic equation; and repeating the processes of prediction, optimization of input signals, and parameter updating until a preset target signal has been reproduced. The method has good precision and stability, and can effectively improve the control performance of the seismic simulation shaking table. The present invention further relates to a model predictive control system for a seismic simulation shaking table, a medium, and a terminal.

Description

Earthquake simulation vibration table model predictive control method, system, medium and terminal Technical Field

[0001] The present invention relates to the field of earthquake simulation vibration table control, and in particular to an earthquake simulation vibration table model prediction control method, system, medium and terminal. Background Art

[0002] As a key instrument for studying the seismic performance of civil engineering structures, earthquake simulation shake tables have been widely studied and applied over the past few decades. However, due to their complex operating mechanisms and significant dynamic feedback from the structural model, traditional control methods based on model identification often suffer from poor accuracy in reproducing high-frequency seismic motions. The nonlinearity of earthquake simulation shake tables primarily stems from the amplitude attenuation and phase lag of the second-order dynamic system of the torque motor, valve disc, and valve shaft, the nonlinear relationship between valve opening and flow rate, and oil compression and leakage within the actuator, which are difficult to accurately simulate. Furthermore, when the mass of the structural model is comparable to that of the steel platform, control-structure coupling further exacerbates the nonlinearity of the earthquake simulation shake table-structure system. Model identification of earthquake simulation shake tables is particularly important for the design of controllers such as model predictive control (MPC). Existing model identification methods primarily include gray-box and black-box methods. The gray-box method establishes the dynamic equations of the earthquake simulation shake table system through theoretical simplification and then identifies the equation parameters based on experimental data. The gray-box method offers a clear concept and often achieves good identification accuracy at low frequencies. On the other hand, due to its extensive simplification, the gray-box method cannot fully reflect the dynamic characteristics of the system across the entire performance range, especially in the high-frequency range, where its identification accuracy is generally poor. The black-box method does not focus on the operating mechanism of the earthquake simulation vibration table, but only establishes the input-output mapping relationship of the system through experimental data. Black-box methods mainly include multi-layer perceptrons and radial basis functions. Through extensive training, these methods can generally achieve higher accuracy than gray-box models. However, the black-box method requires the collection of a large amount of experimental data, which means that its application cost is generally high. On the other hand, the black-box method has poor extrapolation capabilities and lacks a clear physical meaning, which further hinders its application in actual control systems.

[0003] While the black-box method has been used to some extent, its inherent flaws hinder its widespread adoption. The widely used gray-box method, however, is limited by the complexity of its theoretical model, making it difficult to significantly improve its accuracy. In the field of earthquake simulation shaker control, there is an urgent need to develop an identification method that is conceptually clear, highly accurate, and readily applicable. By integrating this method with an MPC control framework, high-precision control of earthquake simulation shakers can be achieved.

[0004] Summary of the Invention

[0005] The present invention provides a method, system and medium for predictive control of an earthquake simulation vibration table model, wherein the method solves the problems of unclear concepts, low precision and great application difficulty in identification methods.

[0006] In a first aspect, the present invention provides a model predictive control method for an earthquake simulation shaking table, comprising:

[0007] S1: Obtain offline data of input and output signals of earthquake simulation shaking table;

[0008] S2: Based on the acquired offline data, sparse regression is used to identify the dynamic equations of the earthquake simulation shaking table;

[0009] S3: The output signal of the earthquake simulation vibration table under different input signals is predicted based on the dynamic equation, and the input signal is corrected using the optimization model. At the same time, the parameters of the dynamic equation are updated based on the real-time data of the input and output signals collected by the earthquake simulation vibration table during the control process. The process of prediction, input signal optimization, and parameter update is repeated until the preset target signal is reproduced.

[0010] Furthermore, in S2, the dynamic equation of the earthquake simulation shaking table is:

[0011] Φ(X,U)=[1 T X T U T (X P ) T …sin(αX) T cos(ηX) T ]

[0012] in, is the time domain differential of the earthquake simulation shaking table state variable X; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force; U represents the input signal of the earthquake simulation shaking table; Φ is the symbolic function library; Λ is the coefficient matrix; P is the polynomial order; α and η are parameters that characterize the shape of the sine and cosine functions; the function type and parameters in Φ are selected according to the specific shaking table dynamics and regression results.

[0013] Furthermore, in S2, the expression of the sparse regression coefficient matrix is:

[0014] in, is the time domain differential of the earthquake simulation shaking table state variable X; Φ is the symbolic function library; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force; U represents the input signal of the earthquake simulation shaking table; Λ is the coefficient matrix; λ is the regularization term weight coefficient; is the optimal coefficient matrix obtained by sparse regression.

[0015] Furthermore, the specific process of solving the coefficients of sparse regression is as follows:

[0016] A1: Use the least squares method to solve the coefficient equation:

[0017] A2: Filter separately The subscript set whose elements are less than the coefficient threshold δ The set of subscripts greater than the coefficient threshold δ Specifically:

[0018] Among them, ξ i ,ξ j The coefficient matrices are Elements in

[0019] A3: Set the elements smaller than the coefficient threshold δ to zero:

[0020] A4: Use the ridge regression algorithm to re-solve the coefficient values ​​of the elements that are greater than the coefficient threshold δ:

[0021] in, is the coefficient set obtained by the ridge regression algorithm;

[0022] A5: Repeat A2-A4 until the number of iterations reaches the preset value, and output the optimal solution of the coefficient matrix

[0023] Furthermore, in S3, the expression for parameter update is:

[0024] in, represents the optimal coefficient set in the actual control process; is the time domain differential of the earthquake simulation shaking table state variable X; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force; U represents the input signal of the earthquake simulation shaking table; is the weight coefficient that limits the range of coefficient change; Subscript set Corresponding symbolic function library; Subscript set The corresponding coefficient set; is the coefficient set obtained by sparse regression.

[0025] Furthermore, in S3, the optimization function of the optimization model is specifically as follows:

[0026] in, is the optimal dynamic equation after parameter update; u k 、 represents the actual input signal and predicted input signal of the earthquake simulation shaking table system at the kth time step; J represents the optimization function; Represents the kth time step and k-1 time step The increment of x k 、 are the actual state, predicted state, and target state of the earthquake simulation shaking table respectively; m p 、m c are the number of prediction steps and the number of control steps respectively; μ1, μ2, and μ3 are all weight coefficients.

[0027] Furthermore, in S3, the cost function C of the optimization model is specifically:

[0028] Among them, u min 、u max are the minimum and maximum values ​​of the input signal respectively; Δu min , Δu max are the minimum and maximum values ​​of the input increment respectively; the above cost function satisfies the relationship: Δu min ≤Δu k ≤Δu max ,u min ≤u k ≤u max .

[0029] In a second aspect, the present invention provides a model predictive control system for an earthquake simulation shaking table, comprising:

[0030] Offline data acquisition module: used to obtain offline data of the input and output signals of the earthquake simulation shaking table;

[0031] Sparse regression module: used to identify the dynamic equations of the earthquake simulation shaking table based on the acquired offline data using sparse regression;

[0032] Prediction, signal optimization and parameter update module: used to predict the output signal of the earthquake simulation vibration table under different input signals based on the dynamic equation, and use the optimization model to correct the input signal; at the same time, based on the real-time data of the input and output signals collected by the earthquake simulation vibration table during the control process, the parameters of the dynamic equation are updated; the process of prediction, input signal optimization and parameter update is repeated until the preset target signal is reproduced.

[0033] In a third aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when called by a processor, executes the steps of the earthquake simulation shaking table model predictive control method as described above.

[0034] In a fourth aspect, the present invention provides an electronic terminal comprising a processor and a memory, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the earthquake simulation vibration table model predictive control method as described above. Beneficial effects

[0035] The present invention proposes a model predictive control method, system, medium, and terminal for an earthquake simulation vibration table. The method obtains offline data of the earthquake simulation vibration table's input and output signals, and then uses sparse regression based on the offline data to identify the complex nonlinear dynamic model of the earthquake simulation vibration table over its entire performance range, namely, the dynamic equation of the earthquake simulation vibration table. The dynamic equation predicts the output signal of the earthquake simulation vibration table under different input signals, and an optimization model is used to correct the input signal. Simultaneously, during the control process, the model parameters of the dynamic equation are updated based on the real-time collected input and output signal data of the earthquake simulation vibration table system to track the actual dynamic characteristics of the earthquake simulation vibration table-structure system. This method combines sparse regression with model predictive control to achieve good accuracy and stability, effectively improving the control performance of the earthquake simulation vibration table. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] 1 is a flow chart of a model predictive control method for an earthquake simulation shaking table according to an embodiment of the present invention;

[0038] FIG2 is a partial result diagram of displacement prediction using a sparse regression model and a transfer function model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] To make the objectives, technical solutions, and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other implementations obtained by those of ordinary skill in the art without inventive effort are within the scope of protection of the present invention.

[0040] Example 1

[0041] As shown in FIG1 , this embodiment provides a model predictive control method for an earthquake simulation shaking table, including:

[0042] S1: Obtain offline data of input and output signals of earthquake simulation shaking table;

[0043] S2: Based on the acquired offline data, sparse regression is used to identify the dynamic equations of the earthquake simulation shaking table;

[0044] S3: The output signal of the earthquake simulation vibration table under different input signals is predicted based on the dynamic equation, and the input signal is corrected using the optimization model. At the same time, the parameters of the dynamic equation are updated based on the real-time data of the input and output signals collected by the earthquake simulation vibration table during the control process. The process of prediction, input signal optimization, and parameter update is repeated until the preset target signal is reproduced.

[0045] By acquiring offline data from the input and output signals of a seismic simulation shaking table, sparse regression is then used to identify the complex nonlinear dynamic model of the system over the entire performance range, namely the dynamic equations of the seismic simulation shaking table. The dynamic equations predict the output signals of the seismic simulation shaking table under different input signals, and an optimization model is used to correct the input signals. Simultaneously, during the control process, the model parameters of the dynamic equations are updated based on the real-time input and output signal data of the seismic simulation shaking table system. Optimization is a required step at each time step. The target signal is usually displacement or acceleration, while the input to the shaking table from the MPC is voltage or current, which requires conversion through signal optimization. This conversion not only converts the signal type but also improves the accuracy of the voltage / current signal. The parameter update at the current time step is dependent on the signal optimization at the next time step. Therefore, optimization is performed first, followed by model parameter update, to track the actual dynamic characteristics of the seismic simulation shaking table-structure system. This combination of sparse regression and model predictive control achieves excellent accuracy and stability, effectively improving the control performance of the seismic simulation shaking table.

[0046] Furthermore, in S1, the signal types used for offline data include swept sine and white noise to fully reflect the system's frequency response characteristics. The signal frequency band and amplitude cover the entire performance range of the vibration table. Seismic waves can also be used as tracking signals. The sensor's signal sampling frequency is no less than the controller's command frequency, fully capturing the system's high-frequency characteristics.

[0047] Furthermore, in S2, the dynamic equation of the earthquake simulation shaking table is:

[0048] Φ(X,U)=[1 T X T U T (X P ) T …sin(αX) T cos(ηX) T ]

[0049] in, is the time domain differential of the earthquake simulation shaking table state variable X; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force, U represents the input signal of the earthquake simulation shaking table, Φ is the symbolic function library, Λ is the coefficient matrix, and P is the polynomial order. α and η are parameters that characterize the shape of the sine and cosine functions. The values ​​of these parameters are continuously adjusted during the model identification process until the model accuracy is optimized. The function type and parameters in Φ are selected based on the specific earthquake simulation shaking table dynamics and regression results.

[0050] Among them, sparse regression aims to establish a more accurate flow continuity equation. Therefore, the state variable X includes variables that can characterize the piston movement flow, piston oil leakage flow, actuator chamber oil compression flow and servo valve nonlinearity, that is, Y. F represents the displacement, velocity and actuator feedback force of the earthquake simulation shaking table, respectively.

[0051] Furthermore, in S2, the expression of the sparse regression coefficient matrix is:

[0052] Among them, λ is the weight coefficient of the regularization term; is the optimal coefficient matrix obtained by sparse regression.

[0053] Furthermore, the specific process of solving the coefficients of sparse regression is as follows:

[0054] A1: Use the least squares method to solve the coefficient equation:

[0055] A2: Filter separately The subscript set whose elements are less than the coefficient threshold δ The set of subscripts greater than the coefficient threshold δ

[0056] Among them, ξ i ,ξ j The coefficient matrices are elements.

[0057] A3: Set the elements smaller than the coefficient threshold δ to zero:

[0058] A4: Use the ridge regression algorithm to re-solve the coefficient values ​​of the elements that are greater than the coefficient threshold δ:

[0059] in, is the coefficient set obtained by the ridge regression algorithm;

[0060] A5: Repeat A2-A4 until the number of iterations reaches the preset value, and output the optimal solution of the coefficients

[0061] By forcibly setting small coefficients to zero and adding coefficient norms, the sparsity of the coefficient matrix is ​​enhanced, ensuring both accuracy and simplicity in the identification results. Specifically, the coefficient threshold δ and weight coefficient λ are both related to the data dimension and the system's dynamic characteristics. The accuracy and simplicity of the extracted dynamic equations must be observed and adjusted accordingly during the calculation process. The final δ and λ values ​​ensure that the identified earthquake simulation shaking table dynamic equations are more accurate than those of general linear transfer functions. Furthermore, considering the requirements of real-time computing, the total time consumed for single-step prediction and optimization is no longer than the control time step.

[0062] Furthermore, in S3, the expression for parameter update is:

[0063] in, represents the optimal coefficient set in the actual control process; Dynamic equations for shaking tables used for earthquake simulations; is the weight coefficient that limits the range of coefficient change; Subscript set Corresponding symbolic function library; Subscript set The corresponding coefficient set; is the set of coefficients obtained by sparse regression. Offline identification obtains the dynamic equations of the earthquake simulation vibration table over the entire performance range. However, in the actual control process, the dynamic characteristics of the specimen may vary, and the earthquake simulation vibration table usually operates in a small amplitude and low frequency band. Therefore, the model parameters are updated according to the real-time measured system input and output data, and all dynamic function terms obtained by offline identification are retained. Only the coefficients of the function terms are updated to further improve the accuracy of the model and reduce the difference between offline data and the actual control process. In addition, the role of the regularization term is to limit the variation range of each coefficient to prevent the algorithm from falling into a local optimum.

[0064] Furthermore, in S3, the optimization function of the optimization model is specifically as follows:

[0065] in, is the optimal dynamic equation after parameter update; u k 、 represents the actual input signal and predicted input signal of the earthquake simulation shaking table system at the kth time step; J represents the optimization function; Represents the kth time step and k-1 time step The increment of x k 、 are the actual state, predicted state, and target state of the earthquake simulation shaking table respectively; m p 、m c where μ1, μ2, and μ3 are the prediction and control time steps, respectively; μ1, μ2, and μ3 are weight coefficients. The essence of the signal optimization module is to obtain the optimal control signal by solving a constrained optimization function. By selecting a control signal that is as small as possible and with as much continuity between adjacent signals as possible, the system avoids severe oscillations.

[0066] Furthermore, in S3, the cost function C of the optimization model is specifically:

[0067] Among them, u min 、u max are the minimum and maximum values ​​of the input signal respectively; Δu min , Δu max are the minimum and maximum values ​​of the input increment respectively; the above cost function satisfies the relationship: Δu min ≤Δu k ≤Δu max ,u min ≤u k ≤u maxDue to hardware limitations, the actual control signal has a maximum and minimum value. In addition, the servo valve has an electrical signal resolution, which means that the difference between adjacent signals must be greater than this resolution. In order to avoid violent oscillations, a cost function is constructed to limit this difference.

[0068] Example 2

[0069] This embodiment provides a model predictive control system for an earthquake simulation shaking table, including:

[0070] Offline data acquisition module: used to obtain offline data of the input and output signals of the earthquake simulation shaking table;

[0071] Sparse regression module: used to identify the dynamic equations of the earthquake simulation shaking table based on the acquired offline data using sparse regression;

[0072] Prediction, signal optimization and parameter update module: used to predict the output signal of the earthquake simulation vibration table under different input signals based on the dynamic equation, and use the optimization model to correct the input signal; at the same time, based on the real-time data of the input and output signals collected by the earthquake simulation vibration table during the control process, the parameters of the dynamic equation are updated; the process of prediction, input signal optimization and parameter update is repeated until the preset target signal is reproduced.

[0073] Example 3

[0074] The present invention provides a computer-readable storage medium storing a computer program, wherein the computer program is used by a processor to execute the steps of the earthquake simulation shaking table model predictive control method described above.

[0075] Example 4

[0076] This embodiment provides an electronic terminal including a processor and a memory, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the earthquake simulation shaking table model predictive control method described above.

[0077] Those skilled in the art will appreciate that in the embodiments of the present invention, the processor referred to may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor, or the processor may be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provides instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0078] The readable storage medium is a computer-readable storage medium, which may be an internal storage unit of the controller described in any of the aforementioned embodiments, such as a hard disk or memory of the controller. The readable storage medium may also be an external storage device of the controller, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the controller. Furthermore, the readable storage medium may also include both an internal storage unit of the controller and an external storage device. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium may also be used to temporarily store data that has been output or is to be output.

[0079] Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned readable storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0080] The technical solution provided by the present invention is further described below with reference to a specific example.

[0081] In this embodiment, the control effect of Model Predictive Control (MPC) mainly depends on the accuracy of model identification, so here we only focus on the working condition design method of offline data acquisition and compare the model accuracy of sparse regression and transfer function. The method provided by this paper effectively combines sparse regression and model predictive control (MPC), so it is named SR-MPC.

[0082] The uniaxial servo-hydraulic seismic simulation shaker is composed primarily of a servo valve, actuator, steel platform, slide rails, and a hydraulic servo system. The servo valve is a Moog 760-15gpm, suitable for displacement, velocity, and pressure control. The actuator has a maximum output of 72kN and a maximum travel of ±250mm. The steel platform measures 1.2m x 1.5m and has evenly spaced bolt holes on its upper surface for specimen attachment. The slide rails guide the horizontal movement of the steel platform and have a travel of ±120mm. The hydraulic servo system provides a stable 28MPa oil pressure.

[0083] First, the offline identification module for the earthquake simulation shaking table was executed. In this example, three signal types were selected: swept sine, white noise, and seismic waves. Six inertial masses were designed to simulate different load levels. A frequency bandwidth of 0.1 to 10 Hz was selected based on the actual displacement time history of seismic waves. Four amplitude levels were set for each signal based on the performance specifications of the earthquake simulation shaking table and the actual test conditions. The final data acquisition conditions are shown in Table 1.

[0084] Table 1 Offline data collection conditions

[0085] Among them, d max It is worth noting that although d max It is mainly calculated based on the performance specifications of the earthquake simulation vibration table, but it is often difficult to achieve this theoretical value in actual implementation. For example, when the load, signal frequency and signal amplitude of the earthquake simulation vibration table are all large, excessive specimen feedback force will cause the reaction frame to oscillate violently, seriously affecting the safety of the test. Therefore, during this test, d max Determined based on the vibration table performance specifications and actual implementation.

[0086] Of the 200 signals collected, 30 were selected as data for model identification, and the remaining signals were used for model accuracy assessment. To maintain consistency with the traditional flow continuity equation, the symbol system for the performance parameters of each component of the earthquake simulation shaking table was introduced and rewritten as follows:

[0087] u=k p k t [y d (t)-y m (t)]

[0088] Among them, y d 、y m represent the target displacement and measured displacement of the earthquake simulation shaking table respectively; k p =0.32×10 -3 is the proportional gain; k t =0.43×10 -3 is the total flow gain of the servo valve; u represents the voltage input to the earthquake simulation vibration table; m t represents the mass of the earthquake simulation shaking table-specimen; F represents the actuator feedback force; A p =3.225×10 -3 is the effective cross-sectional area of ​​the piston; V t =1.116×10 -3 is the total volume of the actuator chamber; β e =1.306×10 9 is the bulk modulus of the oil; k le =7.76×10 -8 is the piston oil leakage coefficient; is the nonlinear part of the servo valve and actuator, and its expression is as follows:

[0089] In order to compare the accuracy of sparse regression model identification, another white noise signal is selected and the MATLAB system identification toolbox is used to identify the system's fourth-order transfer function model as follows:

[0090] Among them, a3 = -3.88, a2 = 5.67, a1 = -3.69, b3 = 0, b2 = 7.86 × 10 -4 , b1=0,b0=9.84×10 -4 .

[0091] Two indicators are selected to quantify the accuracy of the model: normalized root mean square error J1 and normalized peak error J2, and their expressions are as follows:

[0092] Where y d 、y m They represent the target displacement and measured displacement of the earthquake simulation shaking table respectively, and N represents the total number of signal sampling points.

[0093] The accuracy of the sparse regression model and the transfer function model were tested for the remaining 170 offline acquired signals. Figure 2 shows some of the results of earthquake simulation shaking table displacement prediction using a representative white noise signal. Table 2 shows some of the results of earthquake simulation shaking table displacement prediction using a selected time period of the white noise signal.

[0094] Table 2 Partial results of displacement prediction of earthquake simulation shaking table

[0095] The calculation results show that on the test set, the transfer function model's normalized root mean square error (J1) and normalized peak error (J2) averaged 24.5% and 32.1%, respectively, while the sparse regression model's normalized root mean square error (J1) and normalized peak error (J2) averaged 10.5% and 18.2%, respectively. These relative errors are reduced by 57.1% and 43.3%, respectively. This demonstrates that the sparse regression model achieves significant accuracy improvements over the transfer function model.

[0096] Combining the good accuracy of sparse regression models with the MPC rolling optimization framework, SR-MPC can achieve high-performance control of earthquake simulation shaking tables.

[0097] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A model predictive control method for earthquake simulation shaking table, characterized in that: include: S1: Obtain offline data of input and output signals of earthquake simulation shaking table; S2: Based on the acquired offline data, sparse regression is used to identify the dynamic equations of the earthquake simulation shaking table; S3: Predict the output signal of the earthquake simulation vibration table under different input signals according to the dynamic equation, and use the optimization model to correct the input signal; at the same time, update the parameters of the dynamic equation according to the real-time data of the input signal and output signal collected by the earthquake simulation vibration table during the control process; repeat the process of prediction, input signal optimization, and parameter update until the preset target signal is reproduced.

2. The earthquake simulation shaking table model predictive control method according to claim 1, characterized in that: In S2, the dynamic equation of the earthquake simulation shaking table is: Φ(X,U)=[1 T X T U T (X P ) T … sin(αX) T cos(ηX) T ] in, is the time domain differential of the earthquake simulation shaking table state variable X; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force; U represents the input signal of the earthquake simulation shaking table; Φ is the symbolic function library; Λ is the coefficient matrix; P is the polynomial order; α and η are parameters that characterize the shape of the sine and cosine functions; the function type and parameters in Φ are selected according to the specific earthquake simulation shaking table dynamics and regression results.

3. The earthquake simulation shaking table model predictive control method according to claim 1, characterized in that: In S2, the expression of the coefficient matrix of sparse regression solution is: in, is the time domain differential of the state variable X of the earthquake simulation shaking table; Φ is the symbolic function library; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force; U represents the input signal of the earthquake simulation shaking table; Λ is the coefficient matrix; λ is the regularization term weight coefficient; is the optimal coefficient matrix obtained by sparse regression.

4. The earthquake simulation shaking table model predictive control method according to claim 3, characterized in that: The specific process of solving the coefficient matrix of sparse regression is: A1: Use the least squares method to solve the coefficient equation: A2: Filter separately The subscript set whose elements are less than the coefficient threshold δ The set of subscripts greater than the coefficient threshold δ Among them, ξ i , j The coefficient matrices are Elements in A3: Set the elements smaller than the coefficient threshold δ to zero: A4: Use the ridge regression algorithm to re-solve the coefficient values ​​of the elements that are greater than the coefficient threshold δ: in, is the coefficient set obtained by the ridge regression algorithm. A5: Repeat A2-A4 until the number of iterations reaches the preset value, and output the optimal solution of the coefficient matrix 5. The earthquake simulation shaking table model predictive control method according to claim 1, characterized in that: In S3, the expression for parameter update is: in, represents the optimal coefficient set in the actual control process; is the time domain differential of the earthquake simulation shaking table state variable X; X is the state variable, Y is the displacement of the earthquake simulation shaking table, is the velocity of the earthquake simulation shaking table, F is the actuator feedback force; U represents the input signal of the earthquake simulation shaking table; is the weight coefficient that limits the range of coefficient change; Subscript set The corresponding symbolic function library; Subscript set The corresponding coefficient set; is the coefficient set obtained by sparse regression.

6. The earthquake simulation shaking table model predictive control method according to claim 1, characterized in that: In S3, the optimization function of the optimization model is as follows: in, is the optimal dynamic equation after parameter update; u k , represents the actual input signal and predicted input signal of the earthquake simulation shaking table system at the kth time step; J represents the optimization function; Represents the kth time step and k-1th time step The increment of x k , are the actual state, predicted state, and target state of the earthquake simulation shaking table respectively; m p 、m c are the prediction time steps and the control time steps respectively; μ1, μ2 and μ3 are weight coefficients.

7. The earthquake simulation shaking table model predictive control method according to claim 1, characterized in that: In S3, the cost function C of the optimization model is specifically: Among them, u min 、u max are the minimum and maximum values ​​of the input signal respectively; Δu min , Δu max are the minimum and maximum values ​​of the input increment respectively; the above cost function satisfies the relationship: Δu min ≤Δu k ≤Δu max ,u min ≤u k ≤u max .

8. A model predictive control system for earthquake simulation shaking table, characterized in that: include: Offline data acquisition module: used to obtain offline data of input and output signals of earthquake simulation shaking table; Sparse regression module: used to identify the dynamic equations of the earthquake simulation shaking table based on the acquired offline data by using sparse regression; Prediction, signal optimization and parameter update module: used to predict the output signal of the earthquake simulation vibration table under different input signals according to the dynamic equation, and use the optimization model to correct the input signal; at the same time, according to the real-time data of the input signal and output signal collected by the earthquake simulation vibration table during the control process, the parameters of the dynamic equation are updated; the process of prediction, input signal optimization and parameter update is repeated until the preset target signal is reproduced.

9. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is called by the processor, it executes: the steps of the earthquake simulation shaking table model predictive control method according to any one of claims 1 to 7.

10. An electronic terminal, characterized in that: It comprises a processor and a memory, wherein the memory stores a computer program, and the processor calls the computer program to execute: the steps of the earthquake simulation shaking table model predictive control method according to any one of claims 1 to 7.

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