Minimum angle regression sparse identification method based on absolute angle stop criterion and application

Abstract

The present application relates to a kind of minimum angle regression sparse identification method, device and application based on absolute angle stop criterion, comprising: the sparse parameter identification model of establishing system input-output relationship;Collect input-output data, construct information matrix and output vector;The standard deviation of all model items in information matrix and output vector is clamped acute angle;Using minimum angle regression algorithm, model items in information matrix are gradually screened, form effective set and calculate residual, calculate the angle of effective set corresponding model item and residual, until the angle and standard deviation meet absolute angle stop criterion, output final sub-information matrix, to calculate sparse parameter vector estimate, obtain model to carry out system input-output control.The present application introduces absolute angle stop criterion as evaluation, without knowing the sparsity of parameter vector, without additional iteration, improve the model parameter identification efficiency, fitting degree is better, and can facilitate the design of control system, reduce enterprise production cost.

Description

Technical Field

[0001] This invention relates to the field of industrial process system identification and modeling technology, and in particular to a minimum angle regression sparse identification method, apparatus and application based on the absolute angle stopping criterion. Background Technology

[0002] The strong coupling, nonlinearity, large time delays, difficulty in accurate modeling, uncertainty, and complex multi-objective challenges inherent in industrial processes make modeling and controlling these processes extremely difficult, severely impacting control effectiveness. Therefore, in many practical industrial systems, due to their inherent complexity, identification modeling is necessary to establish nonlinear models of complex industrial systems.

[0003] There are two common modeling methods: mechanistic modeling and identification modeling. Mechanistic modeling requires a clear understanding of the dynamic processes of the system, and the physical meaning of each parameter in the model must be clear. However, it requires the introduction of certain assumptions and cannot effectively model disturbances to the system, thus it cannot fully reflect the dynamic processes of the system. The resulting system mechanistic model has a complex structure, and the parameters are difficult to identify. Identification modeling, on the other hand, involves designing identification experiments, collecting and analyzing input and output sample data, and using statistical methods to uncover the dynamic characteristics of the system. It is an effective method for modeling dynamic systems; its models are often used in the design of advanced control systems such as model predictive control and adaptive control.

[0004] Traditional system identification methods typically require selecting a class of stochastic models, choosing or estimating the order of the system, and then identifying the parameters. If the model validation results are not good, the selection of the order, parameter identification, and model validation need to be repeated. Finally, the best model is selected under the principle of model cost-saving. Such a modeling process is time-consuming and has a high identification cost.

[0005] Dual-tank systems are a typical type of liquid level control system, exhibiting typical weak nonlinearity and time delay characteristics. Many devices in industrial processes, such as boilers, chemical synthesis reactors, and petroleum refining units, can be simulated using dual-tank systems. Modeling the liquid level system directly affects the design, cost, and effectiveness of the control method; existing modeling methods require repeated order selection, parameter identification, and model verification, resulting in long modeling times and low efficiency.

[0006] In summary, when solving the identification problem of sparse systems in industrial processes, existing identification models are time-consuming and costly to build, and cannot improve the accuracy of identification results while ensuring the efficiency of parameter identification, thus making it impossible to achieve effective control of the output of industrial systems. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the identification model in the prior art cannot simultaneously guarantee identification efficiency and identification result accuracy, resulting in the inability to effectively control the output of the industrial system.

[0008] To address the aforementioned technical problems, this invention provides a minimum angle regression sparse identification method based on the absolute angle stopping criterion, comprising:

[0009] Establish a sparse parameter identification model for the system input-output relationship;

[0010] The system collects input and output data and constructs an information matrix and output vector based on the identification model.

[0011] Calculate the standard deviation of the acute angle between the output vector and all model terms in the information matrix;

[0012] The least angle regression algorithm is used to progressively filter the model items in the information matrix. In each iteration, the target model item with the highest absolute correlation with the output residual vector after the previous iteration is selected and added to the sub-information matrix. The predicted output and the output residual vector are updated. Based on the maximum absolute correlation between all model items and the updated output residual vector, the angle between the target model item and the updated output residual vector is calculated. It is then determined whether the difference between π / 2 and the angle is less than or equal to the standard deviation. If it is less than or equal to the standard deviation, the current sub-information matrix is ​​output as the final sub-information matrix.

[0013] The sparse parameter vector estimate is calculated based on the final sub-information matrix.

[0014] In one embodiment of the present invention, the step of establishing a sparse parameter identification model for the system input-output relationship, and collecting the system's input-output data, and constructing an information matrix and output vector based on the identification model, includes:

[0015] A sparse parameter identification model is constructed based on the Hammerstein nonlinear model.

[0016] Its nonlinear part is represented by the following model:

[0017] Where u(t) is the system input, t represents the discrete time, f(·) is the nonlinear function, and h j Let h1 be the parameter of the nonlinear system to be identified, and m be the order of the nonlinearity to be identified. Without loss of generality, let h1 = 1.

[0018] Its linear part is represented by the following model:

[0019] y(t) = x(t) + w(t),

[0020]

[0021]

[0022] Where y(t) is the system output; x(t) is the noiseless output of the system; G(z) is the pulse transfer function of the linear part, d is the time delay; A(z) and B(z) are the unit shift operators z -1 A polynomial with constant coefficients, and the unit shift operator z. -1 y(t) = y(t-1); N(z) is a noise shaping filter, v(t) is zero-mean white noise; w(t) is the noise output;

[0023] The sparse parameter identification model is represented in pseudo-linear regression form:

[0024]

[0025] We introduce the maximum nonlinear order length p (p≥m) and the maximum input data regression length l (l≥d+n). b This yields a sparse parameter identification model in vector form, expressed as:

[0026]

[0027] in,

[0028]

[0029]

[0030]

[0031] n a n b The input is a linear order, and P is the dimension of the parameter vector θ; 0 k Let represent a row vector containing k zero elements, and T represent the transpose of the vector or matrix; y(tj) is the output regression term, j = 1, 2, ..., n. a u(tq) is the input regression term, q = 1, 2, ..., l;

[0032] Based on the input and output data of the acquisition system, a sparse identification model is constructed in matrix form, represented as follows:

[0033] y = Φθ + V;

[0034] Wherein, the output vector Information Matrix φ i Let i = 1, 2, ..., P be the model term, where P represents the total number of parameters, N represents the amount of data, and V = [v(1), v(2), ..., v(N)] be the noise vector matrix. T .

[0035] In one embodiment of the present invention, the input and output data of the acquisition system, after constructing an information matrix and an output vector based on the identification model, include:

[0036] The columns of the information matrix are standardized so that the l2 norm of each column is 1 and the mean is 0.

[0037] The output vector is centered so that its mean is 0.

[0038] In one embodiment of the present invention, the calculation of the standard deviation of the acute angle between the output vector and all model terms is expressed as:

[0039]

[0040] in, C0 represents the mean of the acute angle between the system output vector and all model terms; e0 represents the initial maximum absolute correlation; P represents the initial output residual vector; and P represents the total number of parameters.

[0041] In one embodiment of the present invention, the step of progressively filtering model items in the information matrix using the least angle regression algorithm, in each iteration selecting the target model item with the highest absolute correlation to the output residual vector after the previous iteration from all model items and incorporating it into the sub-information matrix, updating the predicted output and the output residual vector, calculating the angle between the target model item and the updated output residual vector based on the maximum absolute correlation between all model items and the updated output residual vector, and determining whether the difference between π / 2 and the angle is less than or equal to the standard deviation; if it is less than or equal to, then the current sub-information matrix is ​​output as the final sub-information matrix, including:

[0042] Predicted output after initial iteration The output residual vector after iteration is e0 = y, the sub-information matrix is ​​Φ0 = [], and the effective set is... Invalid set I0 = {1, 2, ..., P}, k = 1;

[0043] Let k = 1, and calculate the output residual vector after the (k-1)th iteration:

[0044] Calculate the correlation between all model terms and the output residual vector after the (k-1)th iteration:

[0045] Calculate the model terms corresponding to the invalid set and e k-1 Correlation: And obtain the maximum absolute correlation:

[0046]

[0047] Calculate the index of the target model term based on the maximum absolute correlation:

[0048] Based on the index λ of the target model item k Update valid set Λ k and invalid set I k The target model terms are then incorporated into the sub-information matrix Φ. k , represented as:

[0049] Λ k =Λ k-1 ∪{λ k};

[0050] I k =I k-1 \{λ k};

[0051]

[0052] Based on the maximum absolute correlation and the index λ of all target model terms j The correlation sign was calculated as follows:

[0053]

[0054] Calculate the modified sub-information matrix based on the correlation symbols. And calculate the unit angle bisector vector v k =Φ' k w k ;

[0055] in The vector of linear combination coefficients. To correct the columns and angle bisector vector v in the sub-information matrix k The inner product, To correct the Gram matrix of the sub-information matrix;

[0056] Calculate the step size:

[0057]

[0058] Among them, z k,i The inner product of the model term and the angle bisector vector;

[0059] Update the predicted output based on the unit angle bisector vector and the step size:

[0060] Calculate the k-th output residual vector Let k = k + 1, until the target model term φ is reached. k With the output residual vector e kThe difference between the included angle and π / 2 is not greater than the standard deviation, and the current sub-information matrix is ​​output as the final sub-information matrix.

[0061] In one embodiment of the present invention, the calculation of the k-th output residual vector Let k = k + 1, until the target model term φ is reached. k With the output residual vector e k The angle between the two sub-information matrices, and the difference between the angle and π / 2, is not greater than the standard deviation. The current sub-information matrix is ​​output as the final sub-information matrix, including:

[0062] Calculate the target model term φ at the k-th iteration. k With residual vector e k The included angle:

[0063]

[0064] judge Or whether k = P is true:

[0065] like If neither k = P nor k = P holds true, then let k = k + 1, and return to calculate the residual vector after the (k-1)th iteration.

[0066] like If any term in k = P holds true, then the final sub-information matrix Φ will be output. k .

[0067] In one embodiment of the present invention, the calculation of the sparse parameter vector estimate based on the final sub-information matrix is ​​expressed as:

[0068] Sparse parameter vector estimates:

[0069] The sparse parameter vector estimate is filtered using preset filtering parameters, and the parameter estimate is restored to P dimensions based on the sub-information matrix, where P represents the total number of parameters, to obtain the sparse parameter vector.

[0070] Where, Φ k Represents the final sub-information matrix. Let y represent the transpose of the final sub-information matrix, and y represent the system output.

[0071] This invention also provides a minimum angle regression sparse identification device based on the absolute angle stopping criterion, comprising:

[0072] The model building module is used to establish a sparse parameter identification model of the system's input-output relationship;

[0073] The information construction module is used to collect the system's input and output data, and construct an information matrix and output vector based on the identification model.

[0074] The standard deviation calculation module is used to calculate the standard deviation of the acute angle between the output vector and all model terms in the information matrix;

[0075] The iterative module is used to progressively filter the model items in the information matrix using the least angle regression algorithm. In each iteration, the target model item with the highest absolute correlation to the output residual vector after the previous iteration is selected from all model items and added to the sub-information matrix. The predicted output and the output residual vector are updated. Based on the maximum absolute correlation between all model items and the updated output residual vector, the angle between the target model item and the updated output residual vector is calculated, and it is determined whether the difference between π / 2 and the angle is less than or equal to the standard deviation. If it is less than or equal to the standard deviation, the current sub-information matrix is ​​output as the final sub-information matrix.

[0076] The vector estimation module is used to calculate the sparse parameter vector estimate based on the final sub-information matrix.

[0077] This invention also provides an application of the minimum angle regression sparse identification method based on the absolute angle stopping criterion as described above in the field of water tank level systems, including:

[0078] An identification experiment was designed based on the working principle of the water tank level system, and input and output data were collected to construct a water tank level dataset.

[0079] The water tank level dataset is preprocessed and divided into a training set and a test set;

[0080] The input and output data of the water tank level system are collected, and an information matrix and output vector are constructed based on the sparse parameter identification model.

[0081] The model terms of the information matrix are standardized, and the output vector is centered.

[0082] Calculate the standard deviation of the acute angle between the output vector and all model terms of the information matrix;

[0083] The least angle regression algorithm is used to iterate the model terms of the information matrix. After each iteration, the model term with the highest absolute correlation to the output residual vector after the previous iteration is obtained and used as the target model term, which is then incorporated into the sub-information matrix.

[0084] Based on the absolute correlation between the model terms and the output residual vector, update the sub-information matrix, predict the output, and the output residual vector; obtain the target model term with the maximum absolute correlation with the updated output residual vector among all model terms in the information matrix, and calculate the angle between the target model term and the updated output residual vector; stop iterating until the difference between π / 2 and the angle is no greater than the standard deviation, and output the current sub-information matrix as the final sub-information matrix;

[0085] Based on the final sub-information matrix, obtain the estimated value of the sparse parameter vector;

[0086] The input of the water tank level system is adjusted based on the sparse parameter vector estimation value, thereby controlling the output of the water tank level system to achieve the preset performance index.

[0087] The technical solution of the present invention has the following advantages compared with the prior art:

[0088] The minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion described in this invention establishes a sparse parameter identification model based on the input and output of a nonlinear industrial system, collects the system's input and output data, and constructs an information matrix and an output vector. The standard deviation of the acute angle between the output vector and all model terms in the information matrix is ​​calculated as an evaluation criterion. The minimum angle regression algorithm is used to progressively filter the model terms in the information matrix, selecting target model terms and incorporating them into a sub-information matrix. The angle between the target model term and the output residual vector is calculated until the angle satisfies the absolute angle stopping criterion based on the standard deviation and the angle, resulting in the final sub-information matrix for calculating the sparse parameter vector estimate. This invention does not require prior knowledge of the sparsity of the parameter vectors, stops iteration when the absolute angle stopping criterion is met, and simplifies the iterative calculation process by eliminating the need for additional iterations, thus improving the efficiency of model parameter identification. Furthermore, it offers better fitting and outperforms existing methods in both identification accuracy and calculation method, improving the prediction accuracy of modeling models in industrial process systems. After obtaining the estimated value of the sparse parameter vector, the input of the nonlinear industrial system is adjusted, and the output of the nonlinear industrial system is controlled to achieve the preset performance index, so that the industrial system operates under optimal conditions, reducing enterprise production costs and obtaining economic benefits.

[0089] The minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion described in this invention, when applied to a water tank level system, eliminates the need to measure parameters such as the cross-sectional area of ​​the water tank, the area of ​​the drain hole, the length of the drain pipe, and the water flow velocity. It only requires real-time measurement of the control valve voltage and the water level height, facilitating data acquisition. Furthermore, it directly obtains the system model's parameters, order, and time delay, eliminating the need for repeated order selection, parameter identification, and model verification. The absolute angle stopping criterion for model order acquisition, compared to other order selection methods, reduces computational load and storage requirements, resulting in higher identification efficiency and lower cost. The model established using this method has a simpler structure than mechanistic models, making it more conducive to the implementation of advanced control methods such as predictive control and adaptive control. Attached Figure Description

[0090] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0091] Figure 1 This is a flowchart of the steps of the minimum angle regression sparse identification method based on the absolute angle stopping criterion provided by the present invention;

[0092] Figure 2 This is a structural block diagram of the Hammerstein model provided by the present invention;

[0093] Figure 3 This is a diagram of the experimental apparatus for the dual-tank water level system provided by the present invention;

[0094] Figure 4 This is a flowchart of the steps for sparse parameter identification in the dual-tank water level system provided by the present invention.

[0095] Figure 5 This is a schematic diagram of the input and output data of the dual-tank water level system provided by the present invention;

[0096] Figure 6 This is the output fitting curve of the model training and testing of the dual-tank liquid level system provided by the present invention;

[0097] Figure 7 This is a comparison chart of the training output errors of the LAR algorithm using different model selection criteria under different data volumes, provided by this invention.

[0098] Figure 8 This is a comparison chart of the test output errors of the LAR algorithm using different model selection criteria under different data volumes, provided by this invention;

[0099] Figure 9This is a comparison chart of parameter estimation errors and test output errors of the AS-LAR algorithm, LASSO algorithm, AIC-OMP algorithm, and AIC-FS algorithm provided by this invention under different data volumes;

[0100] Figure 10 This is a structural block diagram of the device for minimum angle regression sparse identification based on the absolute angle stopping criterion provided by the present invention. Detailed Implementation

[0101] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0102] Example 1:

[0103] Reference Figure 1 As shown, the minimum angular regression coefficient identification method based on the absolute angle stopping criterion of the present invention includes the following specific steps:

[0104] S101: Establish a sparse parameter identification model for the system input-output relationship;

[0105] S102: Collect the input and output data of the system, and construct an information matrix and output vector based on the identification model;

[0106] S103: Calculate the standard deviation of the acute angle between the output vector and all model terms in the information matrix:

[0107]

[0108] in, C0 represents the mean of the acute angle between the system output vector and all model terms; e0 represents the initial maximum absolute correlation; P represents the initial output residual vector; and P represents the total number of parameters.

[0109] S104: The least angle regression algorithm is used to progressively filter the model items in the information matrix. In each iteration, the target model item with the highest absolute correlation with the output residual vector after the previous iteration is selected from all model items and incorporated into the sub-information matrix. The predicted output and output residual vector are updated. Based on the maximum absolute correlation between all model items and the updated output residual vector, the angle between the target model item and the updated output residual vector is calculated, and it is determined whether the difference between π / 2 and the angle is less than or equal to the standard deviation. If it is less than or equal to the standard deviation, the current sub-information matrix is ​​output as the final sub-information matrix.

[0110] S105: Calculate the sparse parameter vector estimate based on the final sub-information matrix;

[0111] Sparse parameter vector estimates:

[0112] The sparse parameter vector estimate is filtered using preset filtering parameters, and the parameter estimate is restored to P dimensions based on the sub-information matrix, where P represents the total number of parameters, to obtain the sparse parameter vector.

[0113] Where, Φ k Represents the final sub-information matrix. Let y represent the transpose of the final sub-information matrix, and y represent the system output.

[0114] Specifically, in steps S101 and S102, refer to Figure 2 As shown, a sparse parameter identification model is constructed based on the Hammerstein nonlinear model:

[0115] Its nonlinear part is represented by the following model:

[0116] Where u(t) is the system input, t represents the discrete time, f(·) is the nonlinear function, and h j Let h1 be the parameter of the nonlinear system to be identified, and m be the order of the nonlinearity to be identified. Without loss of generality, let h1 = 1.

[0117] Its linear part is represented by the following model:

[0118] y(t) = x(t) + w(t),

[0119]

[0120]

[0121] Where y(t) is the system output; x(t) is the noiseless output of the system; G(z) is the pulse transfer function of the linear part, d is the time delay; A(z) and B(z) are the unit shift operators z -1 A polynomial with constant coefficients, and the unit shift operator z. -1 y(t) = y(t-1); N(z) is a noise shaping filter, v(t) is zero-mean white noise; w(t) is the noise output;

[0122] The sparse parameter identification model is represented in pseudo-linear regression form:

[0123]

[0124] We introduce the maximum nonlinear order length p (p≥m) and the maximum input data regression length l (l≥d+n). b This yields a sparse parameter identification model in vector form, expressed as:

[0125]

[0126] in,

[0127]

[0128]

[0129]

[0130] n a n b The input is a linear order, and P is the dimension of the parameter vector θ; 0 k Let represent a row vector containing k zero elements, and T represent the transpose of the vector or matrix; y(tj) is the output regression term, j = 1, 2, ..., n. a u(tq) is the input regression term, q = 1, 2, ..., l;

[0131] Based on the input and output data of the acquisition system, a sparse identification model is constructed in matrix form, represented as follows:

[0132] y = Φθ + V;

[0133] Wherein, the output vector Information Matrix φ i Let i = 1, 2, ..., P be the model term, where P represents the total number of parameters, N represents the amount of data, and V = [v(1), v(2), ..., v(N)] be the noise vector matrix. T .

[0134] Specifically, after step S102, the method further includes: standardizing each column of the information matrix so that the l2 norm of each column is 1 and the mean is 0; and centering the output vector so that the mean is 0.

[0135] Specifically, step S104 includes:

[0136] definition This is the predicted output of the algorithm after the k-th iteration. Let Λ be the output residual vector after the k-th iteration, and Λ be the effective set. k The set of indices for the selected model items during the iteration process, and the invalid set I. k The set of indices for the unselected model items; define the model item φ. i The correlation with the residual vector after the k-th iteration is The index of the target model term selected in the k-th iteration is λ. k , The sub-information matrix is ​​the target model term selected in the k-th iteration.

[0137] Predicted output after initial iteration The output residual vector after iteration is e0 = y, the sub-information matrix is ​​Φ0 = [], and the effective set is... Invalid set I0 = {1, 2, ..., P}, k = 1;

[0138] Let k = 1, and calculate the output residual vector after the (k-1)th iteration:

[0139] Calculate the correlation between all model terms and the output residual vector after the (k-1)th iteration:

[0140] Calculate the model terms corresponding to the invalid set and e k-1 Correlation: And obtain the maximum absolute correlation:

[0141]

[0142] Calculate the index of the target model term based on the maximum absolute correlation:

[0143] Based on the index λ of the target model item k Update valid set Λ k and invalid set I k The target model terms are then incorporated into the sub-information matrix Φ. k , represented as:

[0144] Λ k =Λ k-1 ∪{λ k};

[0145] I k =I k-1 \{λ k};

[0146]

[0147] Based on the maximum absolute correlation and the index λ of all target model terms j The correlation sign was calculated as follows:

[0148]

[0149] Calculate the modified sub-information matrix based on the correlation symbols. And calculate the unit angle bisector vector v k =Φ' k w k ;

[0150] in The vector of linear combination coefficients. To correct the columns and angle bisector vector v in the sub-information matrix k The inner product, To correct the Gram matrix of the sub-information matrix;

[0151] Calculate the step size:

[0152]

[0153] Among them, z k,i The inner product of the model term and the angle bisector vector;

[0154] Update the predicted output based on the unit angle bisector vector and the step size:

[0155] Calculate the k-th output residual vector Let k = k + 1, until the target model term φ is reached. k With the output residual vector e k The difference between the included angle and π / 2 is not greater than the standard deviation, and the current sub-information matrix is ​​output as the final sub-information matrix.

[0156] Specifically, the target model term φ is calculated at the k-th iteration. k With residual vector e k The included angle:

[0157]

[0158] judge Or whether k = P is true:

[0159] like If neither k = P nor k = P holds true, then let k = k + 1, and return to calculate the residual vector after the (k-1)th iteration.

[0160] like If any term in k = P holds true, then the final sub-information matrix Φ will be output. k .

[0161] The minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion described in this invention establishes a sparse parameter identification model based on the input and output of a nonlinear industrial system, collects the system's input and output data, and constructs an information matrix and an output vector. The standard deviation of the acute angle between the output vector and all model terms in the information matrix is ​​calculated as an evaluation criterion. The minimum angle regression algorithm is used to progressively filter the model terms in the information matrix, selecting target model terms and incorporating them into a sub-information matrix. The angle between the target model term and the output residual vector is calculated until the angle satisfies the absolute angle stopping criterion based on the standard deviation and the angle, resulting in the final sub-information matrix for calculating the sparse parameter vector estimate. This invention does not require prior knowledge of the sparsity of the parameter vector and stops iteration when the absolute angle stopping criterion is met, eliminating the need for additional iterations and reducing computational load. Furthermore, the iterative calculation process using the absolute angle stopping criterion simplifies the iterative calculation process, resulting in better fitting. It outperforms existing methods in both identification accuracy and calculation method, improving the prediction accuracy of modeling models in industrial process systems. After obtaining the estimated value of the sparse parameter vector, the input of the nonlinear industrial system is adjusted, and then the output of the nonlinear industrial system is controlled to achieve the preset performance index, so that the industrial system is kept in the optimal working condition, reducing the enterprise's production cost and obtaining economic benefits.

[0162] Example 2;

[0163] Based on the above embodiments, in this embodiment, the minimum angle regression sparse identification method based on the absolute angle stopping criterion provided by the present invention is used to identify sparsity such as... Figure 3 The sparse parameter identification of the dual-tank water level system shown in this invention is performed to verify the accuracy of the sparse parameter identification method provided by this invention. (Refer to...) Figure 4 As shown, the specific steps include:

[0164] S201: Design an identification experiment for a water tank level system, collect the input voltage of the control valve and the water tank level data, and construct a data set for the level system.

[0165] S202: Perform zero-mean preprocessing on the dataset of the water tank level system and divide the dataset into training and testing sets;

[0166] S203: Select a model class, preset the regression length and nonlinearity of the input data, and establish a sparse parameter regression stacking model for the water tank level system.

[0167] S204: Standardize and center the sparse stacking model;

[0168] S205: Iterative initialization, output estimate, residual, sub-information matrix, initial value of effective set;

[0169] S206: Calculate the standard deviation of the acute angle between the output vector and all model terms of the information matrix;

[0170] S207: Use the least angle regression algorithm to iteratively filter the model items in the information matrix;

[0171] S208: Calculate the angle between the target model term and the updated residual vector; stop iterating until the difference between π / 2 and the angle is not greater than the standard deviation, and use the current sub-information matrix as the final sub-information matrix;

[0172] S209: Based on the least squares method and the final sub-information matrix, obtain the low-dimensional parameter vector estimate;

[0173] S210: Based on the effective set, reconstruct high-dimensional sparse parameter vector estimation, read the estimated values ​​of the system's time delay and the model's order according to the sparse structure, and thus obtain the dynamic mathematical model of the water tank level system.

[0174] Specifically, after obtaining the dynamic mathematical model of the water tank level system, the dynamic mathematical model of the water tank level system is validated using test set data. If the model identification result does not meet the preset standard, the model class is changed and the model is reconstructed; if the model identification result meets the preset standard, the dynamic model of the level system is obtained.

[0175] Specifically, in this embodiment, a dual-tank water level system is used as the experimental setup. This system includes two tanks, A and B, and three regulating valves. The input is the voltage value of regulating valve f1, which controls the water inflow into the upper tank. Water from the storage tank enters tank A through this regulating valve, then flows into tank B through a small hole at the bottom of tank A and regulating valve f2. Water from tank B flows into the storage tank through regulating valve f3. The experiment ensures that the water in the tanks does not overflow. The voltage value of the input signal is controlled by a computer, generating a random number with an amplitude uniformly distributed within the range of [0, 2.5V]. Each random number is converted to an A / D converter using a zero-order hold circuit. One clock cycle consists of 30 sampling points. The output is the water level value of tank B, measured using a capacitive sensor. The sampling time is 5 seconds, resulting in 2500 sets of sampled data. Figure 5 As shown. Based on the obtained dataset, the DC component of the input and output data was removed, and the first 2000 sets of data were used for identification training, while the last 500 sets of data were used for model testing.

[0176] Based on the weak nonlinearity and time-delay characteristics of the water tank level system, the Hammerstein nonlinear model is selected for modeling. The mathematical model expression is as follows:

[0177]

[0178] y(t) = x(t) + w(t),

[0179]

[0180]

[0181] Where u(t) is the system input control voltage, t represents the discrete time, f(·) is the nonlinear function, and h j Let be the parameters of the nonlinear system to be identified, m be the order of the nonlinearity to be identified, y(t) be the system liquid level output, x(t) be the noiseless output of the system, G(z) be the pulse transfer function of the linear part, d be the time delay, and A(z) and B(z) be the unit shift operators z. -1 constant coefficient polynomial (z -1 y(t) = y(t-1); N(z) is a noise shaping filter, v(t) is zero-mean white noise, and w(t) is the noise output.

[0182] The water tank level system model is rewritten in pseudo-linear regression form:

[0183]

[0184] Optionally, a maximum nonlinear order length p (p≥m) and a maximum input data regression length l (l≥d+n) are introduced. b This yields a sparse parameter identification model in vector form, expressed as:

[0185]

[0186] in,

[0187]

[0188]

[0189]

[0190] Based on the collected input and output data, construct an information matrix and an output vector;

[0191] Output vector:

[0192] Information matrix:

[0193] Among them, φ in the information matrix Φ i The model terms are i = 1, 2, ..., P; P represents the total number of parameters; N represents the amount of data; and T represents the matrix transpose.

[0194] The columns of the information matrix are standardized so that their l2 norm is 1 and their mean is 0; the output vector is centered so that its mean is 0.

[0195] Initialization settings e0 = y, Φ0 = [], I0 = {1,2,…,P}, k = 1;

[0196] Calculate the standard deviation of the acute angle between the output vector and all model terms of the information matrix;

[0197]

[0198] Where P represents the total number of parameters; C0 represents the initial maximum absolute correlation; e0 represents the initial output residual vector; It is the mean of the acute angle between the system output vector and all model terms.

[0199] The least angle regression algorithm is used to select model terms, specifically including: definition This is the predicted output of the algorithm in the k-th iteration. Let Λ be the output residual vector after the k-th iteration, and Λ be the effective set. k The set of indices for the selected model items during the iteration process, and the invalid set I. k The set of indices for the unselected model items; define the model item φ. i The correlation with the residual vector after the k-th iteration is The index of the target model term selected in the k-th iteration is λ. k , The sub-information matrix is ​​the target model term selected in the k-th iteration.

[0200] Calculate the output residual vector after the (k-1)th iteration:

[0201] Calculate the correlation between all model terms and the output residual vector after the (k-1)th iteration:

[0202] Determine the maximum absolute correlation between all model terms and the output residual vector after the (k-1)th iteration:

[0203]

[0204] Calculate the index of the target model term based on the maximum absolute correlation:

[0205] Based on the index λ of the target model item k Update valid set Λ k and invalid set Ik And incorporate the target model terms into the sub-information matrix:

[0206] Λ k =Λ k-1 ∪{λ k};

[0207] I k =I k-1 \{λ k};

[0208]

[0209] Based on the maximum absolute correlation and the index λ of all target model terms j The correlation sign was calculated as follows:

[0210] Calculate the modified sub-information matrix based on the correlation symbols. And calculate the unit angle bisector vector v k =Φ' k w k ;

[0211] in The vector of linear combination coefficients. To correct the columns and angle bisector vector v in the sub-information matrix k The inner product, To correct the Gram matrix of the sub-information matrix;

[0212] Calculate the step size:

[0213]

[0214] Where z k,i The inner product of the model term and the angle bisector vector;

[0215] Update the predicted output based on the unit angle bisector vector and the step size:

[0216] Calculate the k-th output residual vector Calculate the correlation between all model terms and the output residual vector after the k-th iteration. Determine the maximum absolute correlation between all model terms and the output residual vector after the k-th iteration:

[0217] S8: Calculate the angle between the target model term and the updated residual vector.

[0218] Calculate the target model term φ selected in the k-th iteration. k With residual vector e k The included angle:

[0219] Calculate the angle between the target model term and the output residual vector; when the difference between π / 2 and the angle is not greater than the standard deviation, stop the iteration and output the current sub-information matrix as the final sub-information matrix;

[0220] Calculate the target model term φ selected in the k-th iteration. k With residual vector e k The included angle:

[0221]

[0222] judge Or whether k = P holds true;

[0223] like If neither k = P nor k = P holds true, then let k = k + 1, and return to calculate the residual vector after the (k-1)th iteration.

[0224] like If any term in k = P holds true, output the sub-information matrix Φ. k .

[0225] Based on the sub-information matrix, obtain the estimated value of the sparse parameter vector;

[0226] Based on the output sub-information matrix Φ k Calculate the parameter estimates using the output vector:

[0227] Based on preset filtering parameters, the estimated values ​​of the sparse parameter vector are filtered, and then based on the effective set Λ k The parameter estimates are then reduced to P dimensions, where P represents the total number of parameters, to obtain a sparse parameter vector. The sparse parameter vector obtained in this embodiment is

[0228] Based on the sparse parameter vector estimates, the system's time delay and model order estimates are read, including:

[0229] Based on the structure of the sparse parameters, the readout delay is estimated to be d = 1; the nonlinear order is p = 1.

[0230] That is, the system model is obtained as

[0231]

[0232] Based on the training and test set data, the model's output is compared with the test set output to identify the fitted curves of the training and test outputs, as shown below. Figure 6 As shown.

[0233] The training error of the calculation model is The model test error is κ tr =2.77%. That is, both the training error and the prediction error are less than 5%, so the model accuracy is high and the model identification is effective.

[0234] The minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion described in this invention, when applied to a water tank level system, eliminates the need to measure parameters such as the cross-sectional area of ​​the water tank, the area of ​​the drain hole, the length of the drain pipe, and the water flow velocity. It only requires real-time measurement of the control valve voltage and the water level height, facilitating data acquisition. Furthermore, it directly obtains the system model parameters, order, and time delay, eliminating the need for repeated order selection, parameter identification, and model verification. The absolute angle stopping criterion for model order acquisition, compared to other order selection methods, reduces computational load and storage requirements, resulting in higher identification efficiency and lower cost. The model established using the method provided by this invention has a simpler structure than mechanistic models, making it more conducive to the implementation of advanced control methods such as predictive and adaptive control. This embodiment further illustrates that the minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion provided by this invention achieves the beneficial effect of improving the prediction accuracy of modeling models in industrial process systems, thereby enabling effective control of industrial system operations.

[0235] Based on the above embodiments, in this embodiment, simulation conditions and parameters are set, and simulation results of different algorithms are obtained for comparison, specifically including:

[0236] Let the system model be:

[0237]

[0238] A(z) = 1 - 1.600z -1 +0.800z -2 ,

[0239] B(z) = 0.850z -1 +0.650z -2 +1.250z -3 ,

[0240]

[0241] The input channel has a time delay of d = 9, the data regression length is taken as l = 20, the maximum nonlinear order is p = 10, and the true sparse parameter vector is represented as:

[0242]

[0243] Where P = n a +lp = 202, the sparsity of the parameter vector is K = n a +n b m = 11.

[0244] During the simulation, the input vector u(t) is a zero-mean, unit-variance, uncorrelated, measurable random signal, and v(t) is a signal with variance σ. 2 The zero-mean white noise is filtered with a threshold of ζ = 0.05.

[0245] Specifically, based on the above embodiments, in this embodiment, the noise variance σ is taken. 2 =0.1 2 The LAR algorithms based on the AASC, GSC, AIC, BIC, and Cp criteria were used for coefficient identification and model testing, respectively; mean squared error was used. This represents the sum of model training error and test error; refer to Figure 7 and Figure 8 The figures shown are schematic diagrams of model training error and model testing error under different data volumes N.

[0246] Reference Figure 7 and Figure 8 It can be seen that AIC-LAR, BIC-LAR, and Cp-LAR have no data when the data volume N=200, indicating that an effective estimation structure for sparse parameter vectors cannot be obtained at this time; while AS-LAR and G-LAR can obtain effective estimations with this data volume; and using the AS-LAR algorithm provided by this invention, the test and training output errors are the smallest among all LAR algorithms using other criteria, indicating that the model obtained by using the AS-LAR algorithm provided by this invention is closest to the real model and has the best recognition effect.

[0247] Specifically, based on the above embodiments, in this embodiment, the noise variance σ 2 =0.2 2 When the data volume N is 100, 200, 300, 400 and 500 respectively, under the same conditions, the minimum angle regression sparse identification algorithm based on the absolute angle stopping criterion provided in this invention, the LASSO algorithm, and the OMP and FS algorithms using AIC, BIC or Cp are each randomly run 10 times. The number of times each algorithm effectively identifies the sparse structure of the parameter vector is observed. The results are shown in Table 1:

[0248] Table 1: Sparse structure identification results of different algorithms under different data volumes

[0249]

[0250] As shown in Table 1, when the data volume N is less than the length P of the sparse vector, only LASSO and the AS-LAR algorithm provided by this invention can effectively identify the structure of the sparse vector; and the AS-LAR algorithm provided by this invention performs better than LASSO after adjusting the hyperparameters. When the data volume N is greater than the length P of the sparse vector, the minimum angle regression sparse identification AS-LAR algorithm based on the absolute angle stopping criterion provided by this invention, as well as the existing AIC-FS, AIC-OMP, and LASSO algorithms, can gradually identify the structure of the sparse vector with a higher probability.

[0251] Reference Figure 9 As shown, for data volume N≥300, the noise variance σ 2 =0.2 2 At the same time, the parameter estimation error and test output error in the identification of AS-LAR, LASSO, AIC-OMP, and AIC-FS are considered; the relative error of parameter estimation is defined. Depend on Figure 9 It can be seen that the identification results of AS-LAR, AIC-OMP, and AIC-FS algorithms are almost the same, and all are better than LASSO.

[0252] When the data volume N = 500, the noise variance σ 2 =0.2 2 The runtime of AS-LAR, LASSO, AIC-OMP, and AIC-FS is shown in Table 2.

[0253] Table 2: Comparison of running times for each algorithm

[0254] algorithm AS-LAR LASSO AIC-FS AIC-OMP t / s 0.093 0.176 0.284 0.302

[0255] As shown in Table 2, the AS-LAR algorithm has the shortest running time, followed by LASSO, while the AIC-FS and AIC-OMP algorithms have the longest running time. This indicates that the minimum angle regression sparse identification algorithm based on the absolute angle stopping criterion provided in this invention has high identification efficiency.

[0256] As can be seen from Tables 1 and 2, the AS-LAR algorithm provided in this embodiment of the invention has the best overall performance in terms of recognition accuracy and calculation speed.

[0257] Based on the above embodiments, this invention provides a minimum angle regression sparse identification device based on the absolute stopping criterion, referring to... Figure 10 As shown, it specifically includes:

[0258] Model building module 100 is used to establish a sparse parameter identification model of the system input-output relationship;

[0259] The information construction module 200 is used to collect the input and output data of the system and construct an information matrix and an output vector based on the identification model.

[0260] The standard deviation calculation module 300 is used to calculate the standard deviation of the acute angle between the output vector and all model terms in the information matrix;

[0261] The iteration module 400 is used to progressively filter the model items in the information matrix using the least angle regression algorithm. In each iteration, the target model item with the highest absolute correlation with the output residual vector after the previous iteration is selected from all model items and incorporated into the sub-information matrix. The predicted output and the output residual vector are updated. Based on the maximum absolute correlation between all model items and the updated output residual vector, the angle between the target model item and the updated output residual vector is calculated, and it is determined whether the difference between π / 2 and the angle is less than or equal to the standard deviation. If it is less than or equal to the standard deviation, the current sub-information matrix is ​​output as the final sub-information matrix.

[0262] The vector estimation module 500 is used to calculate the sparse parameter vector estimate based on the final sub-information matrix.

[0263] The minimum angle regression sparse identification device based on the absolute stopping criterion in this embodiment is used to implement the aforementioned minimum angle regression sparse identification method based on the absolute stopping criterion. Therefore, the specific implementation of the minimum angle regression sparse identification device based on the absolute stopping criterion can be found in the embodiment section of the minimum angle regression sparse identification method based on the absolute stopping criterion above. For example, the model building module 100, the information building module 200, the standard deviation calculation module 300, the iteration module 400, and the vector estimation value acquisition module 500 are respectively used to implement steps S101, S102, S103, S104, and S105 in the aforementioned minimum angle regression sparse identification method based on the absolute stopping criterion. Therefore, its specific implementation can be referred to the description of the corresponding embodiments, and will not be repeated here.

[0264] The minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion described in this invention establishes a sparse parameter identification model based on the input and output of a nonlinear industrial system. It collects the system's input and output data to construct an information matrix and an output vector. The standard deviation of the acute angle between the output vector and all model terms in the information matrix is ​​calculated as an evaluation criterion. The minimum angle regression algorithm is used to progressively filter the model terms in the information matrix, selecting target model terms and incorporating them into a sub-information matrix. The angle between the target model term and the output residual vector is calculated until the angle satisfies the absolute angle stopping criterion based on the standard deviation and the angle, resulting in the final sub-information matrix. This method is then used to calculate the sparse parameter vector estimate. This invention does not require prior knowledge of the sparsity of the parameter vector and stops iteration when the absolute angle stopping criterion is met, eliminating the need for additional iterations. This simplifies the iterative calculation process and improves the efficiency of model parameter identification. Furthermore, it offers better fitting and outperforms existing methods in both identification accuracy and calculation method, improving the prediction accuracy of the model in industrial process systems. After obtaining the sparse parameter vector estimate, the input of the nonlinear industrial system is adjusted, thereby controlling the output of the nonlinear industrial system to achieve preset performance indicators, reducing enterprise production costs, and obtaining economic benefits.

[0265] The minimum angle regression sparse parameter identification method based on the absolute angle stopping criterion described in this invention, when applied to a water tank level system, eliminates the need for repeated order selection, parameter identification, and model verification, resulting in high model identification efficiency. The absolute angle stopping criterion is used to obtain the model order, which, compared to other order selection methods, requires less computation and storage, leading to higher identification efficiency and lower cost. The simple model structure is also more conducive to the implementation of advanced control methods such as predictive control and adaptive control. Furthermore, the water tank level system of this invention can simulate many devices in industrial processes, such as boilers, chemical synthesis reactors, and petroleum purification units, demonstrating wide applicability and strong scalability.

[0266] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0267] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0268] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0269] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0270] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A minimum angle regression sparse identification method based on an absolute angle stop criterion, characterized in that, The method comprises the following steps: Based on the working principle of the water tank liquid level system, an identification experiment is designed, input and output data are collected, and a water tank liquid level data set is constructed; The water tank liquid level data set is preprocessed and divided into a training set and a test set; Collect the input and output data of the water tank liquid level system, and based on the sparse parameter identification model, construct the information matrix and the output vector, including: Based on the weak nonlinearity and time delay characteristics of the water tank liquid level system, a Hammerstein nonlinear model is selected for modeling, and the mathematical model expression is: ， ， ， ， wherein, is the system input control voltage, denotes discrete time, is a nonlinear function, is the nonlinear system parameter to be identified, is the nonlinear order to be identified, is the system liquid level output; is the system noiseless output; is the pulse transfer function of the linear part, is the time delay, and is the unit delay operator is a constant coefficient polynomial ; is a noise shaping filter, is a zero mean white noise, is the noise output; Rewrite the water tank liquid level system model into a pseudo-linear regression form: ， introducing the maximum non-linear order length , and the maximum input data regression length , resulting in a sparse parameter identification model in vector form, denoted as: ； Wherein, ， ， ； Based on the collected input and output data, the information matrix and the output vector are constructed; Output vector: ; Information matrix: ; wherein the information matrix is the model terms, ; denotes the total number of parameters; denotes the amount of data; T denotes the matrix transpose; The model terms of the information matrix are standardized, and the output vector is centralized; Calculate the standard deviation of the acute angle between the output vector and all model terms of the information matrix; Use the minimum angle regression algorithm to iterate the model terms in the information matrix, and obtain the model term with the maximum absolute correlation with the output residual error vector after each iteration as the target model term, and incorporate it into the sub-information matrix; According to the absolute correlation between the model term and the output residual error vector, update the sub-information matrix, the predicted output and the output residual error vector; obtain the target model term with the maximum absolute correlation with the updated output residual error vector among all model terms of the information matrix, calculate the included angle between the target model term and the updated output residual error vector; until the difference between π / 2 and the included angle is not greater than the standard deviation, stop iteration, and output the current sub-information matrix as the final sub-information matrix; Based on the final sub-information matrix, the sparse parameter vector estimate value is obtained; According to the sparse parameter vector estimate value, the input of the water tank liquid level system is adjusted, so that the liquid level of the water tank liquid level system reaches the preset performance index.

2. The absolute angle stop criterion based minimum angle regression sparse identification method according to claim 1, characterized in that, After collecting the input and output data of the system and constructing the information matrix and the output vector based on the sparse parameter identification model, including: The columns of the information matrix are normalized so that each column has a norm of 1 and a mean of 0. The columns of the information matrix are normalized so that each column has a norm of 1 and a mean of 0. The output vector is centralized to have a mean value of 0.

3. The absolute angle stop criterion based minimum angle regression sparse identification method according to claim 1, characterized in that, The calculation of the standard deviation of the acute angle between the output vector and all model terms is represented as: ， where is the mean of the acute angle between the system output vector and all model terms; denotes the initial maximum absolute correlation; denotes the initial output residual vector; denotes the total number of parameters.

4. The method of claim 1, wherein the method is based on an absolute angle stop criterion. The minimum angle regression algorithm is used to gradually screen the model terms in the information matrix, and the target model term with the maximum absolute correlation with the output residual error vector after each iteration is incorporated into the sub-information matrix, and the predicted output and the output residual error vector are updated. According to the maximum absolute correlation between all model terms and the updated output residual error vector, the included angle between the target model term and the updated output residual error vector is calculated, and it is judged whether the difference between π / 2 and the included angle is less than or equal to the standard deviation. If it is less than or equal to, the current sub-information matrix is output as the final sub-information matrix, including: initialized prediction output , output residual vector after iteration , sub-information matrix , active set , inactive set , ; Let , compute the first iteration output residual vector: ; Compute all model terms and the first correlation of the output residual vector after the second iteration: ; Computing the correlation of the null set of model terms and , and taking the maximum absolute correlation:​ ； calculating an index of a target model term based on the maximum absolute correlation: ; According to the index of the target model term Update the active set and the inactive set and incorporate the target model term into the sub-information matrix is represented as: ； ； ； According to the maximum absolute correlation and the index of all target model terms The correlation sign is calculated: ； computing a modified sub-information matrix according to the correlation symbol and computing a unit angle bisector vector ; in The vector of linear combination coefficients. To correct the columns and angle bisector vectors in the sub-information matrix The inner product, To correct the Gram matrix of the sub-information matrix; Calculate the step size: ； wherein is the inner product of the model term and the angle bisector vector; Updating the prediction output according to the unit angle bisector vector and the step length: ; calculating the first output residual vector , let , until the difference between the angle of the target model term and the output residual vector and π / 2 is not greater than the standard deviation, outputting the current sub-information matrix as the final sub-information matrix.

5. The method of claim 4, wherein the absolute angle stop criterion based minimum angle regression sparse identification method is characterized by, The computing the first output residual vector , let , until the target model term and the output residual vector The angle with π / 2, the difference value is not greater than the standard deviation, the current sub-information matrix is output as the final sub-information matrix, comprising: The computation of the angle between the target model term at the first iteration and the residual vector at the first iteration is performed as follows: ； determining or is true: If or are not true, then let and return the residual vector after the th iteration. If or any of the above, output the final sub-information matrix .

6. The absolute angle stop criterion based minimum angle regression sparse identification method according to claim 1, characterized in that, Based on the final sub-information matrix, the sparse parameter vector estimate value is obtained, represented as: Sparse parameter vector estimate: ; filtering the sparse parameter vector estimate with a predetermined filter parameter, restoring the parameter estimate to dimensions, denoting the total number of parameters, obtaining a sparse parameter vector; wherein, represents the final sub-information matrix, represents the final sub-information matrix transpose matrix, represents the system output.

7. A device based on the absolute angle stop criterion based minimum angle regression sparse identification method according to any one of claims 1 to 6, characterized in that, Including: A model construction module is configured to establish a sparse parameter identification model of the input and output relationship of the system; An information construction module is configured to collect the input and output data of the system, and construct an information matrix and an output vector based on the sparse parameter identification model; a standard deviation calculation module configured to calculate a standard deviation of an angle between the output vector and each model term in the information matrix; an iteration module configured to perform step-by-step filtering of the model terms in the information matrix by using a minimum angle regression algorithm, in each iteration, select a target model term with the maximum absolute correlation with the output residual vector after the last iteration from all the model terms and incorporate the target model term into a sub-information matrix, update the predicted output and the output residual vector, calculate an angle between the target model term and the updated output residual vector according to the maximum absolute correlation between all the model terms and the updated output residual vector, and determine whether a difference between π / 2 and the angle is less than or equal to the standard deviation, and if so, output the current sub-information matrix as a final sub-information matrix; a vector estimate acquisition module configured to calculate a sparse parameter vector estimate based on the final sub-information matrix.

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