A method and system for cross-convergence mapping causal test of large deformation plate state parameters

Abstract

The present invention provides a method and system for cross-convergent mapping causality test of large deformation plate state parameters, belonging to the technical field of nonlinear time series analysis of dynamic systems, including: constructing a vibration control equation of a large deformation plate, and iteratively solving to obtain two state parameters of the large deformation plate; adopting a constant parameter phase space reconstruction method, and obtaining two constant parameter phase space reconstruction attractors according to the two state parameters; taking the two constant parameter phase space reconstruction attractors as shadow manifolds, and solving the cross-convergent mapping correlation coefficient between the true value and the predicted value of the system state parameters through a cross-convergent mapping algorithm; constructing a causality test index based on the difference of the cross-convergent mapping correlation coefficient, and testing the causality between the state parameters of the large deformation plate according to its positive and negative signs. The present invention breaks through the problems of parameter uncertainty, low test efficiency, and weak big data processing ability caused by relying on traditional phase space reconstruction in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of nonlinear time series analysis of power systems, and particularly relates to a method and system for cross-convergent mapping causality test of state parameters of large deformation plates. Background Art

[0002] Nonlinear time series often come from real power systems, such as the nonlinear vibration system of large deformation plates. The internal evolution mechanism of the power system will lead to complex causal relationships among system variables. Through causality tests, the causal laws of the dynamic evolution of system variables can be explained, providing reliable scientific support for system dynamic behavior prediction, abnormal dynamic behavior detection, etc. The cross-convergent mapping method is one of the common causality test methods, and its core element is the shadow manifold based on the phase space reconstruction attractor, which can effectively characterize the asymmetric causal relationship among system state variables.

[0003] However, traditional phase space reconstruction methods need to perform complex optimization and selection of embedding parameters (delay time and embedding dimension). Due to the lack of a unified optimal selection standard, the reconstructed attractors under different optimized embedding parameters are non-unique, reducing the efficiency and reliability of the cross-convergent mapping causality test of the state parameters of large deformation plates. Summary of the Invention

[0004] To solve the above problems, based on the constant parameter phase space reconstruction method, the present invention proposes an improved method for cross-convergent mapping causality test of state parameters of large deformation plates with constant parameter phase space reconstruction. Compared with the existing test methods, the method of the present invention is based on the constant parameter phase space reconstruction attractor, and can quickly obtain the high-precision shadow manifold required for the cross-convergent mapping causality test, thereby improving the efficiency and accuracy of the state parameter causality test of large deformation plates.

[0005] To achieve the above object, the present invention provides the following technical solutions.

[0006] The present invention provides a method for cross-convergent mapping causality test of state parameters of large deformation plates, including the following steps:

[0007] Construct a vibration control equation of the large deformation plate, and iteratively solve to obtain two state parameters of the large deformation plate;

[0008] Adopt the constant parameter phase space reconstruction method, and obtain two constant parameter phase space reconstruction attractors according to the two state parameters;

[0009] Take the two constant parameter phase space reconstruction attractors as the shadow manifold, and solve the cross-convergent mapping correlation coefficient between the true value and the predicted value of the system state parameters through the cross-convergent mapping algorithm;

[0010] Construct a causal test index based on the difference in cross-convergence mapping correlation coefficients, and determine the ability of the cross-prediction state parameters of the attractor in the phase space of the constant parameters according to the positive and negative values of the causal test index, as well as test the causal relationship between different state parameters.

[0011] Preferably, the steps of constructing the vibration control equation of the large-deformation plate and determining two state parameters of the large-deformation plate include the following:

[0012] Construct a vibration control equation of the large-deformation plate in the form of a Duffing system, that is, the vibration control equation is a second-order constant-coefficient nonlinear differential equation containing a cubic nonlinear term, as shown in the following formula:

[0013] ;

[0014] Where is the damping coefficient, and are the coefficients of the first-order and third-order terms respectively, and are the amplitude and frequency of the harmonic load respectively; is x the second derivative with respect to time;

[0015] Rewrite the vibration control equation of the large-deformation plate into a first-order differential equation system for easy numerical solution, x and y The solved values are state parameters, and are respectively x and y the first derivatives with respect to time, and its mathematical form is:

[0016] ;

[0017] Determine the coefficients of the vibration control equation of the large-deformation plate, and use the fourth-order Runge-Kutta method to solve the first-order differential equation system to obtain the time history curves of the state parameters X ( t ) and Y ( t ).

[0018] Preferably, the values of the coefficients of the vibration control equation of the large-deformation plate are , , , , ;

[0019] Use the fourth-order Runge-Kutta method to numerically solve the first-order differential equation system, and its initial condition is , the time step h = 0.0125 s, and the total calculation duration is 750 s, the data lengthN = 60000;

[0020] Among them, based on the numerical solution of the fourth-order Runge-Kutta method x and y The iteration formula is:

[0021] ;

[0022] Among them, , , , , , , and are intermediate variables, is time, and the calculation formula is:

[0023] .

[0024] Preferably, the constant parameter phase space reconstruction method is adopted, and two constant parameter phase space reconstruction attractors are obtained according to two state parameters, including the following steps:

[0025] Select the constant parameters for phase space reconstruction. Among them, the time delay and the embedding dimension ;

[0026] According to the state parameter X Construct the reconstructed attractor , as shown in the following formula:

[0027] ;

[0028] Among them, represents the i th phase point coordinate, M represents the number of phase points;

[0029] Calculate the autocorrelation matrix of the reconstructed attractor :

[0030] ;

[0031] Perform eigenvalue decomposition on the autocorrelation matrix:

[0032] ;

[0033] Among them, is the eigenvalue matrix, represents the eigenvector;

[0034] Project the reconstructed attractor along the direction of the main eigenvector to obtain the constant parameter phase space reconstruction attractor :

[0035] ;

[0036] Normalize the reconstructed attractor to the interval , and obtain the final normalized constant-parameter reconstructed attractor M x ;

[0037] Solve for the state parameter Y according to the above steps to obtain the normalized constant-parameter phase-space reconstructed attractor M y .

[0038] Preferably, using the two constant-parameter phase-space reconstructed attractors as the shadow manifolds, solve for the cross-convergence mapping correlation coefficient between the true values and predicted values of the system state parameters through the cross-convergence mapping algorithm, including the following steps:

[0039] Solve for the normalized constant-parameter phase-space reconstructed attractor M y The Euler distances between each phase point, sort them from smallest to largest, and denote the M y th phase point in i as , and the first points with the smallest distance to m +1 = 3 points are , where represents the time corresponding to the phase point , and calculate the distance between the phase point and as follows:

[0040] ;

[0041] Among them, the operator represents the Euler distance between the vectors , ;

[0042] Calculate the weight coefficient of the phase point :

[0043] ;

[0044] Among them, , is the normalization coefficient;

[0045] Extract the state parameter M y obtained from the reconstructed attractor X at time Predicted value:

[0046] ;

[0047] Further solve for the state parameters X Cross-convergence mapping correlation coefficient between the true value and the predicted value:

[0048] ;

[0049] Among them, the operator represents the standard Pearson correlation coefficient between variables A , B ;

[0050] Reconstruct the attractor M x Repeat the above steps to obtain the state parameters Y Cross-convergence mapping correlation coefficient between the true value and the predicted value:

[0051] .

[0052] Preferably, the calculation formula of the causal test index is as follows:

[0053] ;

[0054] Among them, is the causal test index.

[0055] Preferably, determining the ability of the constant parameter phase space reconstruction attractor to cross-predict the state parameters according to the positive and negative values of the causal test index, and testing the causal relationship between different state parameters includes the following steps:

[0056] If the causal test index , it indicates that the state parameter M x can be accurately predicted by the reconstructed attractor Y , that is, the state parameter Y drives the state parameter X ;

[0057] If the causal test index , it indicates that the state parameter M y can be accurately predicted by the reconstructed attractor X , that is, the state parameter X drives the state parameter Y ;

[0058] If the causal test index , it indicates that the state parameter M y predicts the state parameterX The ability, as compared with the reconstructed attractor M y To predict the state parameters X Is consistent, that is, the state parameters X And the state parameters Y Have no significant causal relationship.

[0059] The present invention also provides a causal test system for cross-convergent mapping of large deformation plate state parameters, including:

[0060] A processor;

[0061] A memory, on which a computer program that can run on the processor is stored;

[0062] Wherein, when the computer program is executed by the processor, the steps of the above-mentioned causal test method for cross-convergent mapping of large deformation plate state parameters are realized.

[0063] The present invention also provides a computer-readable storage medium, on which a data processing program is stored, and when the data processing program is executed by a processor, the steps of the causal test method for cross-convergent mapping of large deformation plate state parameters are realized.

[0064] Advantages of the present invention:

[0065] The present invention proposes a causal test method and system for cross-convergent mapping of large deformation plate state parameters. The method obtains a reconstructed attractor with high topological similarity to the large deformation plate nonlinear vibration system through the constant parameter phase space reconstruction method, uses it as a shadow manifold to improve the traditional cross-convergent mapping algorithm, calculates the cross-convergent mapping correlation coefficients based on the shadow manifolds of different state variables, and then constructs a causal test index to quantitatively characterize the causal relationship between the large deformation plate state parameters, providing reliable scientific support for the prediction of large deformation plate dynamic behavior, detection of abnormal dynamic behavior, etc. Compared with existing methods, this method breaks through the problems of high dependence on phase space embedding parameters and low causal test efficiency under large data samples in the existing cross-convergent mapping, and effectively improves the accuracy and efficiency of causal testing. Description of the Drawings

[0066] Figure 1 Is the flowchart of the method of the embodiment of the present invention;

[0067] Figure 2 Is the large deformation plate state parameter of the embodiment of the present invention X And Y Time history curve graph;

[0068] Figure 3 Is the graph of the change trend of the convergence of the cross-convergent mapping correlation coefficient with the data length in the embodiment of the present invention;

[0069] Figure 4 is the state parameter of the embodiment of the present invention X cross-convergence mapping correlation image between the true value and the predicted value;

[0070] Figure 5 is the state parameter of the embodiment of the present invention Y cross-convergence mapping correlation image between the true value and the predicted value;

[0071] Figure 6 is the state parameter of the embodiment of the present invention X and Y phase space reconstruction attractor shadow manifold diagram of the constant parameter and its cross-convergence mapping diagram; wherein, Figure 6 in (a) of M x to M y cross-convergence mapping; Figure 6 in (b) of M y to M x cross-convergence mapping. Detailed implementation manners

[0072] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0073] Embodiment 1

[0074] Traditional phase space reconstruction methods need to perform complex optimization selection on the embedding parameters (delay time and embedding dimension). Due to the lack of a unified optimization criterion, the reconstructed attractors under different optimized embedding parameters are non-unique, reducing the efficiency and reliability of the cross-convergence mapping causal test of state parameters. It is found that the constant parameter phase space reconstruction method can map the reconstructed attractor to the main direction of the phase trajectory through singular value decomposition under fixed embedding parameters, and can obtain high-precision reconstructed attractors for low-dimensional dynamic systems such as the large deformation plate nonlinear vibration system, overcoming the deficiency of the traditional phase space reconstruction method that depends on the optimization of embedding parameters. Therefore, based on the constant parameter phase space reconstruction method, the present invention proposes an improved cross-convergence mapping causal test method for the state parameters of large deformation plates using constant parameter phase space reconstruction. Compared with the existing cross-convergence mapping causal test methods, the method of the present invention is based on the constant parameter phase space reconstruction attractor and can quickly obtain the high-precision shadow manifold required for the cross-convergence mapping causal test, thereby improving the efficiency and accuracy of the causal test of the state parameters of large deformation plates. Specifically, as Figure 1 shown Figure 1Flowchart of the causal test method for cross-convergence mapping of large-deformation plate state parameters, specifically including the following steps:

[0075] S1: Construct the vibration control equation of the large-deformation plate and iteratively solve to obtain two state parameters of the large-deformation plate.

[0076] Specifically:

[0077] S1.1: Construct the vibration control equation of the large-deformation plate in the form of a Duffing system, that is, the vibration control equation is a second-order constant-coefficient nonlinear differential equation containing a cubic nonlinear term, as shown in the following formula:

[0078] ;

[0079] Among them, is the damping coefficient, and are the coefficients of the first-order and third-order terms respectively, and are the amplitude and frequency of the harmonic load respectively; is x the second derivative with respect to time.

[0080] S1.2: Rewrite the vibration control equation of the large-deformation plate into a first-order differential equation system for easy numerical solution, x and y The solution values are state parameters, denoted as X and Y , and its mathematical form is:

[0081] ;

[0082] Determine the coefficients of the vibration control equation of the large-deformation plate, and use the fourth-order Runge-Kutta method to solve the first-order differential equation system to obtain the time history curves of the state parameters X ( t ) and Y ( t ).

[0083] S1.3: Take the values of the coefficients of the vibration control equation of the large-deformation plate as , , , , .

[0084] S1.4: Numerically solve the first-order differential equation system using the fourth-order Runge-Kutta method, with its initial condition being , the time step h = 0.0125 s, the total calculation duration is 750 s, and the data length N = 60000;

[0085] Among them, based on the numerical solution of the fourth-order Runge-Kutta method x and y The iteration formula is:

[0086] ;

[0087] Among them, , , , , , , and are intermediate variables, is time, and the calculation formula is:

[0088] ;

[0089] S2: Adopt the method of reconstructing the phase space with constant parameters, and obtain two reconstructed attractors of the phase space with constant parameters according to two state variables.

[0090] Specifically:

[0091] S2.1: Select the constant parameters for reconstructing the phase space. Among them, the delay time and the embedding dimension .

[0092] S2.2: Construct the reconstructed attractor X according to the state variable , as shown in the following formula:

[0093] ;

[0094] Among them, represents the i th phase point coordinate, M represents the number of phase points.

[0095] S2.3: Calculate the autocorrelation matrix of the reconstructed attractor :

[0096] ;

[0097] S2.4: Perform eigenvalue decomposition on the autocorrelation matrix:

[0098] ;

[0099] Among them, is the eigenvalue matrix, represents the eigenvector.

[0100] S2.5: Project the reconstructed attractor along the direction of the main eigenvector to obtain the reconstructed attractor of the phase space with constant parameters :

[0101] ;

[0102] S2.6: Normalize the reconstructed attractor to the interval to obtain the final normalized constant-parameter reconstructed attractor M x .

[0103] S2.7: Solve for the state parameter Y according to S2.1 - S2.5 to obtain the normalized constant-parameter phase space reconstructed attractor M y .

[0104] S3: Use the two constant-parameter phase space reconstructed attractors as shadow manifolds and solve for the cross-convergence mapping correlation coefficients of the true and predicted values of the state parameters X and Y through the cross-convergence mapping algorithm.

[0105] Specifically:

[0106] S3.1: Solve for the Euler distances between the phase points of the normalized constant-parameter phase space reconstructed attractor M y , sort them from smallest to largest, and denote the M y th phase point as i , and the first m + 1 = 3 points with the smallest distance to as , where represents the time corresponding to the phase point . Calculate the distance between the phase point and as follows:

[0107] ;

[0108] where the operator represents the Euler distance between the vectors , .

[0109] S3.2: Calculate the weight coefficient of the phase point :

[0110] ;

[0111] where , is the normalization coefficient.

[0112] ​S3.3: Extract the state parameters obtained from the reconstructed attractor M y X At time Predicted value:

[0113] ;

[0114] S3.4: Further solve the cross-convergence mapping correlation coefficient between the true value and the predicted value of the state parameters X Cross-convergence mapping correlation coefficient between the true value and the predicted value:

[0115] ;

[0116] Where the operator Represents the standard Pearson correlation coefficient between variables A , B .

[0117] S3.5: Repeat S3.1 - S3.4 for the reconstructed attractor M x to obtain the cross-convergence mapping correlation coefficient between the true value and the predicted value of the state parameters Y Cross-convergence mapping correlation coefficient between the true value and the predicted value:

[0118] ;

[0119] S4: Construct a causal test index based on the difference in the cross-convergence mapping correlation coefficient, and determine the ability of the cross-prediction of the state parameters of the constant parameter phase space reconstruction attractor according to the positive and negative values of the causal test index, and test the causal relationship between different state parameters

[0120] Causal test index , and the specific calculation formula is:

[0121] ;

[0122] Test the causal relationship between state parameters and X according to the positive and negative signs of the causal test index Y , specifically:

[0123] (1) If , it indicates that the state parameter M x can accurately predict the state parameter Y , that is, the state parameter Y drives the state parameter X , briefly recorded as Y → X ;

[0124] (2) If , it indicates that the state parameter obtained from the reconstructed attractor​M y Can accurately predict the state parameter X , that is, the state parameter X Drives the state parameter Y , briefly recorded as X → Y ;

[0125] (3) If , it indicates that the ability to predict the state parameter M y from the reconstructed attractor X is the same as the ability to predict the state parameter M y from the reconstructed attractor X , that is, there is no significant causal relationship between the state parameter X and the state parameter Y .

[0126] In this embodiment, to verify the effectiveness of a causal test method for cross-convergent mapping of state parameters of a large-deformation plate with improved constant-parameter phase space reconstruction in the present invention, a numerical simulation experiment is carried out, and two state parameters X and Y of the large-deformation plate nonlinear vibration system are extracted for analysis.

[0127] The overall process of the method of the present invention is referred to Figure 1 . In this embodiment, the coefficients of each term of the large-deformation plate nonlinear vibration control equation are: , , , , ; The initial condition is , the time step h = 0.0125 s, the total calculation duration is 750 s, and the data length N = 60000.

[0128] The iterative numerical solution is carried out by the classical fourth-order Runge-Kutta algorithm to obtain the time history curves of the large-deformation plate state parameters X and Y , as shown in Figure 2 . The reconstructed attractors X and Y based on the true state parameters M x and M y are obtained by applying the constant-parameter phase space reconstruction method, and they are used as the shadow manifolds in the cross-convergent mapping algorithm to calculate the cross-convergent mapping correlation coefficients X and Y of the state parameters C YX and CXY , and their convergence curves with respect to the data length are respectively as shown by the solid line and the dashed line in Figure 3 .

[0129] It can be seen from Figure 3 that when the data length is greater than 2000, the correlation coefficient C YX i.e., converges, while the correlation coefficient C XY gradually converges after the data length is greater than 10000. Therefore, the data length of 60000 in this embodiment meets the requirements of the convergence of the correlation coefficient. In addition, the cross-convergence mapping correlation images of the true values and predicted values of the state parameters X and Y are respectively as shown in Figure 4 and Figure 5 .

[0130] It can be seen from Figure 4 that the predicted value of the state parameter X is not exactly the same as its true value, indicating that the state variable X is not the entire cause for driving the formation of M y ; while it can be seen from Figure 5 that the predicted value of the state parameter Y corresponds to the true value, indicating that the state variable Y is the entire cause for driving the formation of M x . Specifically, Figure 6 is the shadow manifold diagram of the phase space reconstruction of the attractor based on the state parameters X and Y constant parameters and its cross-convergence mapping diagram. The connection line from the black square to the white pentagram in the figure represents a mapping of the shadow manifold, and the narrower the mapping range, the stronger the causal relationship between the two. It can be seen from Figure 6 (b) that the cross-convergence mapping range from M y to M x is narrower, indicating that the state parameter Y drives the state parameter X .

[0131] Table 1 Quantitative comparison results of the causal test efficiency and accuracy of the state variables of the large deformation plate

[0132]

[0133] Table 1 shows the quantitative comparison results of the efficiency and accuracy of the causal test of the state variables of the large-deformation plate between the method of the present invention and the original method. In terms of computational efficiency, the cross-convergence mapping method improved based on the constant-parameter phase-space reconstruction method has an efficiency improvement of more than 14%, up to 55% at most; in terms of the cross-convergence mapping correlation coefficient, there are , mutually verifying the analysis results of the state parameters Y driving the state parameters X ; in particular, the C YX = 1.0 obtained by the improved cross-convergence mapping method is more consistent with the result in the vibration control equation of the large-deformation plate, verifying the accuracy and reliability of the cross-convergence mapping method improved based on the constant-parameter phase-space reconstruction method in the causal test of the state parameters of the large-deformation plate. Therefore, a causal test method for cross-convergence mapping of the state parameters of a large-deformation plate improved by a constant-parameter phase-space reconstruction breaks through the problems of high dependence on the phase-space embedding parameters and low causal test efficiency under large data samples existing in the cross-convergence mapping in the prior art, and provides an accurate and efficient causal test method for cross-convergence mapping of the state parameters of a large-deformation plate.

[0134] The above is the causal test method for cross-convergence mapping of the state parameters of a large-deformation plate provided by an embodiment of this embodiment. Based on the same idea, this embodiment also provides a corresponding causal test system for cross-convergence mapping of the state parameters of a large-deformation plate. For the specific limitations of the causal test system for cross-convergence mapping of the state parameters of a large-deformation plate, reference can be made to the limitations of the causal test method for cross-convergence mapping of the state parameters of a large-deformation plate in the above text, which will not be elaborated here. Each module in the above causal test system for cross-convergence mapping of the state parameters of a large-deformation plate can be implemented in whole or in part by software, hardware, and their combinations. The above modules can be embedded in the processor of the computer device in hardware form or be independent of it, or can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above respective modules.

[0135] This embodiment also provides a computer-readable storage medium, which stores a computer program that can be used to execute the above Figure 1 provided causal test method for cross-convergence mapping of the state parameters of a large-deformation plate.

[0136] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above various methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0137] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A causal verification method for cross-convergence mapping of state parameters of large deformation plates, characterized in that: The following steps are involved: The vibration control equation of the large deformation plate is constructed and the two state parameters of the large deformation plate are obtained by iterative solution. Using the constant parameter phase space reconstruction method, two constant parameter phase space reconstruction attractors are obtained according to two state parameters; The two constant parameter phase space reconstructed attractors are used as shadow manifolds, and the cross-convergence mapping correlation coefficient between the real value and the predicted value of the system state parameters is solved by the cross-convergence mapping algorithm. Construct a causal test index based on the difference of the correlation coefficient of the cross-convergence mapping, determine the ability of the constant parameter phase space reconstruction attractor to cross-predict state parameters according to the positive and negative values ​​of the causal test index, and test the causal relationship between different state parameters; The construction of the vibration control equation of the large deformation plate and the determination of two state parameters of the large deformation plate include the following steps: The vibration control equation of the large deformation plate in the form of a Duffing system is constructed, that is, the vibration control equation is a second-order constant coefficient nonlinear differential equation with cubic nonlinear terms, as shown in the following formula: Among them, γ is the damping coefficient, α and β are the first and third term coefficients respectively, δ and ω are the amplitude and frequency of the simple harmonic load respectively; The vibration control equation of the large deformation plate is rewritten as a set of first-order differential equations that are easy to solve numerically. The solution values ​​of x and y are state parameters. and are the first-order derivatives of x and y with respect to time, respectively, and their mathematical form is: The coefficients of the vibration control equations of the large deformation plate are determined, and the first-order differential equations are solved by the fourth-order Runge-Kutta method to obtain the time history curves of the state parameters X(t) and Y(t); The coefficients of the vibration control equation of the large deformation plate are γ=0.01, α=1.0, β=0.9, δ=30.0, ω=1.0; The fourth-order Runge-Kutta method is used to numerically solve the first-order differential equations, with the initial condition (x0, y0) = (0.1, 0), the time step h = 0.0125 s, the total calculation time of 750 s, and the data length N = 60000; Among them, the iterative formulas of x and y based on the numerical solution of the fourth-order Runge-Kutta method are: Among them, k 1x , k 2x , k 3x , k 4x , k 1y , k 2y , k 3y and k 4y is the intermediate variable, t n is the time, and the calculation formula is:

2. The causal verification method for cross-convergence mapping of state parameters of large deformation plates according to claim 1 is characterized in that: The constant parameter phase space reconstruction method is used to obtain two constant parameter phase space reconstruction attractors according to two state parameters, including the following steps: Select the phase space reconstruction constant parameters, where the delay time τ = 1 and the embedding dimension m = 2; Construct and reconstruct attractors based on state parameters X As shown below: in, represents the coordinates of the i-th phase point, and M represents the number of phase points; Computational reconstruction attractor The autocorrelation matrix of is: Perform eigenvalue decomposition on the autocorrelation matrix: C=FLF -1 ; Among them, Λ is the eigenvalue matrix, Φ represents the eigenvector; Project the reconstructed attractor along the direction of the main eigenvector to obtain the constant parameter phase space reconstructed attractor M' x : Normalize the reconstructed attractor to the interval [-1,1] to obtain the final normalized constant parameter reconstructed attractor M x ; Solve the state parameter Y according to the above steps to obtain the normalized constant parameter phase space reconstruction attractor M y .

3. The causal verification method for cross-convergence mapping of state parameters of large deformation plates according to claim 1 is characterized in that: The method uses two constant parameter phase space reconstructed attractors as shadow manifolds and solves the cross-convergence mapping correlation coefficient between the real value and the predicted value of the system state parameters through a cross-convergence mapping algorithm, including the following steps: Solve the normalized constant parameter phase space to reconstruct the attractor M y The Euler distance between each phase point is sorted from small to large, denoted by M y The i-th phase point in and The first m+1=3 points with the smallest distance are in Indicates phase point The corresponding time is calculated as follows: and Distance The operator D(a,b) represents the Euler distance between vectors a and b; Calculate phase point The weight coefficient of: in, is the standardized coefficient; Extract the reconstructed attractor M y The obtained state parameter X at time t i Predicted value: Further solve the cross-convergence mapping correlation coefficient between the true value and the predicted value of the state parameter X: Among them, the operator ρ(A,B) represents the standard Pearson correlation coefficient between variables A and B; The reconstructed attractor M x Repeat the above steps to obtain the cross-convergence mapping correlation coefficient between the true value and the predicted value of the state parameter Y: C YX =[ρ(Y,YM x )] 2 。 4. The causal verification method for cross-convergence mapping of state parameters of large deformation plates according to claim 3 is characterized in that: The calculation formula of the causal test index is as follows: Δ=C YX -C XY ; Among them, Δ is the causality test indicator.

5. The causal verification method for cross-convergence mapping of state parameters of large deformation plates according to claim 4 is characterized in that: The method of determining the ability of the constant parameter phase space to reconstruct the attractor cross-prediction state parameter according to the positive and negative values ​​of the causal test index, and testing the causal relationship between different state parameters, includes the following steps: If the causality test index Δ>0, it indicates that the reconstructed attractor M x The state parameter Y can be accurately predicted, that is, the state parameter Y drives the state parameter X; If the causality test index Δ<0, it means that the reconstructed attractor M y The state parameter X can be accurately predicted, that is, the state parameter X drives the state parameter Y; If the causality test index Δ=0, it means that the reconstructed attractor M y The ability to predict the state parameter X is related to the reconstructed attractor M y The ability to predict state parameter X is consistent, that is, there is no significant causal relationship between state parameter X and state parameter Y.

6. A causal verification system for cross-convergence mapping of state parameters of large deformation plates, characterized in that: include: processor; a memory having stored thereon a computer program executable on the processor; Wherein, when the computer program is executed by the processor, the steps of the causal verification method of cross-convergence mapping of state parameters of a large deformation plate as described in any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a data processing program, which, when executed by a processor, implements the steps of the causal verification method for cross-convergence mapping of state parameters of a large deformation plate according to any one of claims 1 to 5.

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