Expansion Debye model parameter identification method based on dynamic mode decomposition

Abstract

The invention relates to the technical field of insulation dielectric response characteristic identification and aging state evaluation of capacitive power equipment, in particular to an extended Debye model parameter identification method based on dynamic modal decomposition, which comprises the following steps of: acquiring time-varying data of depolarization current, constructing the time-varying data into a Hankel matrix, and taking front N columns and rear N columns to form a matrix A and a matrix B; carrying out economic SVD decomposition on the matrix A, setting a singular value threshold value, abandoning singular values smaller than the singular value threshold value, and reconstructing an SVD decomposition matrix; solving X = A-1B, and then solving a characteristic value and a characteristic vector of X; solving modals of the X and sorting the X according to an energy decreasing sequence; the modes are screened, the screened modes are selected to restore the depolarization current, the effect of dynamic mode decomposition is judged, and whether the singular value threshold value is adjusted or not is judged according to the restoration effect; and calculating the number of branches, a time constant and a relaxation intensity coefficient of the insulation expansion Debye model. The parameter identification result obtained through the method is clear in physical significance.

Description

Technical Field

[0001] The present invention relates to the technical field of insulating dielectric response characteristic recognition and aging state assessment of capacitive power equipment, and in particular to an extended Debye model parameter identification method based on dynamic mode decomposition. Background Art

[0002] Serious accidents of large capacitive power equipment (such as generators, transformers, etc.) will not only cause damage to themselves, but also interrupt power supply, causing huge economic losses to society. With the increase of operating years and the complexity of operating conditions, the insulation system of large capacitive power equipment faces the synergistic effect of electrical, thermal, mechanical and environmental stresses. The insulation aging problem is becoming increasingly serious, and shutdown failures are prone to occur, which brings huge hidden dangers to the stable operation of the power system.

[0003] The amount of dielectric response information obtained by traditional insulation state assessment methods (such as insulation resistance test, power frequency dielectric loss test, partial discharge test, breakdown voltage test, etc.) is small, and it is easily affected by on-site noise, and may even cause damage to power equipment. Compared with traditional insulation state assessment methods, the time domain dielectric response method - Polarization and Depolarization Current (PDC) method has gradually gained popularity due to its non-destructive and high-precision advantages. At present, the research on the PDC method to characterize the insulation state is mainly to conduct PDC tests on power equipment, obtain polarization / depolarization currents, fit current data to the extended Debye model, obtain circuit branch parameters and characteristic parameters, and thus realize the state assessment of power equipment. Therefore, how to quickly and accurately obtain the circuit parameters of the extended Debye model is the key to the on-site application of the PDC method for state assessment of power equipment.

[0004] The extended Debye model is a classic dielectric response model, which treats the insulation of power equipment as equivalent to insulation resistance branches, geometric capacitance branches and multiple RC series branches. The PDC test data is fitted to the extended Debye model, and the insulation status of the power equipment can be diagnosed using the model parameters. Regarding the extended Debye model branch identification method of the PDC method, the current research is mainly divided into the following aspects: ① Preset the number of branches, substitute the polarization / depolarization current into the parameter matrix of each branch, and use the optimization algorithm to obtain the optimal solution of the equation to achieve the purpose of branch identification and parameter extraction. However, this method is prone to fall into the local optimal solution, the polarization / depolarization current data needs to be filtered in advance, and different filtering algorithms have a great influence on the branch identification results. ② Use the dominant mode parameter identification method for branch identification. Among the common methods, the Prony algorithm is too sensitive to the noise in the input data, and interference inevitably exists in the PDC test data, resulting in less than ideal model identification effect; the TLS-ESPRIT algorithm is robust to the noise in the input data, but the algorithm usually assumes that the signal satisfies rotational invariance, but the complex extended Debye model may not meet this assumption; the CMIF algorithm is also sensitive to the noise in the input data, and the Debye model will have dense modes in complex scenarios, which makes the algorithm unable to perform effective identification.

[0005] For example, in the prior art, a Chinese invention patent document with publication number CN113779914A and publication date December 10, 2021, is proposed. The technical solution disclosed in the patent document is as follows: A method for identifying parameters of an extended Debye equivalent circuit of transformer oil-paper insulation based on TLS-ESPRIT. This method is based on the physical property that the depolarization current is a superposition of exponential functions in the extended Debye equivalent model. By performing singular value decomposition on the Hankel matrix constructed from the sample data, the number of polarization branches is determined according to the singular value change rate, and then the relaxation coefficient and time constant of each polarization branch are obtained by using the total least squares-rotating vector invariant technology (TLS-ESPRIT) algorithm, and the parameters of the resistance and capacitance of each polarization branch are identified by substituting them into the Debye equivalent circuit parameter identification formula.

[0006] In the above technical solution, by solving the singular value change rate, the singular value change rate of 0 is used as the truncation standard, and the number of singular values ​​after truncation is the number of Debye model branches, and the physical meaning is not clear enough. Summary of the invention

[0007] In order to solve the above technical problems, the present invention proposes a parameter identification method of an extended Debye model based on dynamic mode decomposition. After solving the eigenvalue of X, DMD modes representing different frequency components are constructed, and modes that conform to exponential decay are screened from all modes. The physical meaning of the modes is consistent with the response characteristics of each branch of the Debye model. Therefore, the parameter identification results obtained by this method have clear physical meanings.

[0008] The present invention is achieved by adopting the following technical solutions:

[0009] A method for identifying parameters of an extended Debye model based on dynamic mode decomposition comprises the following steps:

[0010] Step S1. Obtain the data of the depolarization current changing with time, construct it into a Hankel matrix, and take the first N columns and the last N columns to form matrix A and matrix B;

[0011] Step S2. Perform economical SVD decomposition on matrix A, set a singular value threshold, discard singular values ​​less than the singular value threshold, and reconstruct the SVD decomposition matrix;

[0012] Step S3. Solve X=A -1 B, then solve the eigenvalues ​​and eigenvectors of X;

[0013] Step S4. Solve the modes of X and sort them in order of decreasing energy;

[0014] Step S5. Screening the modes, selecting the screened modes to restore the depolarization current, judging the effect of dynamic mode decomposition, and judging whether to adjust the singular value threshold according to the restoration effect;

[0015] Step S6. Calculate the branch number, time constant and relaxation strength coefficient of the insulation extended Debye model.

[0016] The step S1 specifically includes the following steps:

[0017] Step S 11 . Obtain two vectors of depolarization current current(i) (i=1,2,3,…,n) and time t(i) (i=1,2,3,…,n);

[0018] Step S 12 . Change step S 11 The length of the depolarization current vector in becomes an even number n. If the vector length is an odd number, the last element of the depolarization current vector is discarded;

[0019] Step S 13 .Use step S 12 The depolarization current data in constructs the Hankel matrix shown below;

[0020]

[0021] Step S 14 .Extract the first N columns and the last N columns from the Hankel matrix to form matrix A and matrix B.

[0022] The value of N is n / 2.

[0023] The step S2 specifically includes the following steps:

[0024] Step S 21 . Perform economical SVD decomposition on matrix A and extract all singular values;

[0025] Step S 22 .Set the singular value threshold and discard all singular values ​​smaller than the singular value threshold;

[0026] Step S 23 .Reconstruct the SVD decomposition matrix based on the retained singular values.

[0027] The step S3 specifically comprises the following steps:

[0028] Step S 31 .Use the reconstructed SVD decomposition matrix and B matrix to solve X = A -1 B;

[0029] Step S 32 .Find the eigenvalues ​​and eigenvectors of matrix X.

[0030] The step S4 specifically comprises the following steps:

[0031] Step S 41 .Use the eigenvalues ​​of X, SVD decomposition results and B matrix to solve the mode;

[0032] Step S 42 .Solve the energy of each mode and sort the modes in order from high to low energy.

[0033] The mode screening in step S5 specifically refers to: based on the extended Debye equivalent circuit model of stator bar insulation, the mode is screened, when the modal slope is non-negative and the initial value is positive, the exponential decay requirement is met, the mode that meets the exponential decay requirement is retained, and the mode with a negative slope or a non-positive initial value is removed.

[0034] The step S6 specifically includes the following steps: assuming that the eigenvalues ​​of X are λ1, λ2, ..., λ m , then the amplitude, time constant and relaxation intensity coefficient of each branch of the extended Debye model are:

[0035]

[0036] A i =|a i |,

[0037]

[0038] Where Ts is the sampling time interval.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] 1. This method is highly robust to the noise of field tests. It does not require high-order filtering of the PDC test data and has low computational complexity. It only needs to set the decomposition threshold according to the magnitude of the PDC test data to achieve modal decomposition of the PDC test data, accurately identify the branch parameters of the extended Debye model, and then diagnose the insulation status.

[0041] The present invention is different from the conventional method for determining the number of branches of the Debye model.

[0042] Conventional methods for determining the number of branches of the Debye model include solving the rate of change of singular values, taking the rate of change of singular values ​​to be 0 as the truncation criterion, and the number of singular values ​​after truncation is the number of branches of the Debye model, or solving the sparse enhanced amplitude vector and determining the number of branches of the extended Debye model according to the number of non-zero elements therein. The above methods are not intuitive enough and the physical meaning is not clear enough.

[0043] On the contrary, in the present invention, after solving the eigenvalue of X, DMD modes representing different frequency components are constructed, and modes that conform to exponential decay are screened from all modes. The physical meaning of these modes is consistent with the response characteristics of each branch of the Debye model, so the parameter identification results obtained by this method have clear physical meanings.

[0044] Moreover, compared with the traditional optimal fitting method, the present invention does not require the preset number of branches of the extended Debye model, will not fall into the problem of local optimal solution, and the input data does not require high-order filtering, which is convenient for the maintenance site to quickly identify the branch parameters of the extended Debye model and then diagnose the insulation status.

[0045] 2. In the prior art, conventional designs only delete smaller singular values, which can only remove smaller noise. However, the generator maintenance test site usually has large interference, and the noise level may be the same as the depolarization current level. The method of deleting smaller singular values ​​cannot effectively remove larger noise, which may cause greater interference to the solution results. The prior art also eliminates the false modes introduced by noise interference by adding a sparsity penalty function, but this process requires multiple iterations to achieve the purpose of noise resistance.

[0046] On the contrary, in the present invention, a singular value threshold for deleting smaller singular values ​​is set to prevent computational divergence. In this step, smaller singular values ​​represented by smaller noise are deleted, thereby improving the algorithm's anti-noise performance. Then, by screening each order mode, retaining the mode that conforms to exponential decay, and eliminating the oscillation mode caused by noise, the algorithm's anti-noise performance is further improved. Through the cooperation of these two steps, and without the need for iteration, excellent anti-noise performance can be achieved with a smaller amount of calculation, which is more suitable for on-site maintenance testing.

[0047] Furthermore, the singular value threshold is not a completely fixed value and can be updated during the identification process to make the identification result more accurate.

[0048] Furthermore, since the present invention removes the modes that do not conform to the exponential decay, mode screening can be performed without other complicated calculations. This can not only avoid excessive algorithm calculations and long time consumption, but also ensure the parameter identification effect, with low equipment and instrument requirements, and is more suitable for on-site maintenance testing.

[0049] 3. The present invention aims to solve the dielectric response information contained in the time series obtained from the PDC test. Based on the principle of the dynamic mode decomposition (DMD) algorithm, the depolarization current data is constructed as a Hankel matrix, and the first N columns are set as matrix A, and the last N columns are set as matrix B. Matrix A and matrix B are in an advance and lag relationship on the time scale, and then there is the following mapping relationship: B = AX, where X is a mapping matrix containing the dielectric response information of the test system. Solve the eigenvalue of the X matrix, separate the eigenvalue representing the dielectric response information from the eigenvalue representing the noise, and further solve the Debye model. Through this step, the lead-lag state information contained in the PDC test data is fully considered. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, wherein:

[0051] Figure 1 It is a schematic diagram of the process of the present invention;

[0052] Figure 2 This is a diagram showing the meaning of each branch of the expanded Debye model in the present invention;

[0053] Figure 3 It is a schematic diagram of performing PDC test on the stator bar of the generator in the present invention;

[0054] Figure 4 Schematic diagram of unfiltered depolarization current data input in the present invention;

[0055] Figure 5 It is a schematic diagram of the distribution of characteristic roots obtained by decomposition in the present invention;

[0056] Figure 6 This is a diagram showing the effect of using the screened modal restoration depolarization current in the present invention. DETAILED DESCRIPTION

[0057] Example 1

[0058] As a basic implementation mode of the present invention, the present invention includes a method for identifying parameters of an extended Debye model based on dynamic mode decomposition, comprising the following steps:

[0059] Step S1. Obtain the data of the depolarization current changing with time, construct it into a Hankel matrix, and take the first N columns and the last N columns to form matrix A and matrix B.

[0060] Step S2: Perform economical SVD decomposition on matrix A, set a singular value threshold, discard singular values ​​less than the singular value threshold, and reconstruct the SVD decomposition matrix.

[0061] Step S3. Solve X=A -1 B, then solve for the eigenvalues ​​and eigenvectors of X.

[0062] Step S4. Solve the modes of X and sort them in order of decreasing energy.

[0063] Step S5. Filter the modes, select the filtered modes to restore the depolarization current, judge the effect of dynamic mode decomposition, and judge whether to adjust the singular value threshold according to the restoration effect.

[0064] Step S6. Calculate the branch number, time constant and relaxation strength coefficient of the insulation extended Debye model.

[0065] Example 2

[0066] As a preferred embodiment of the present invention, the present invention includes a method for identifying parameters of an extended Debye model based on dynamic mode decomposition, comprising the following steps:

[0067] Step S1. Obtain the data of the depolarization current changing with time, construct it into a Hankel matrix, and take the first N columns and the last N columns to form a matrix A and a matrix B. Specifically, the steps include:

[0068] Step S 11 . Obtain two vectors of depolarization current current(i) (i=1,2,3,…,n) and time t(i) (i=1,2,3,…,n).

[0069] Step S 12 . Change step S 11 The length of the depolarization current vector in becomes an even number n. If the vector length is an odd number, the last element of the polarization current vector is discarded.

[0070] Step S 13 .Use step S 12 Construct the Hankel matrix from the depolarization current data in .

[0071] Step S 14.Extract the first N columns and the last N columns from the Hankel matrix to form matrix A and matrix B.

[0072] Step S2: Perform economical SVD decomposition on matrix A, set a singular value threshold, discard singular values ​​less than the singular value threshold, and reconstruct the SVD decomposition matrix.

[0073] Step S3. Solve X=A -1 B, then solve for the eigenvalues ​​and eigenvectors of X.

[0074] Step S4. Solve the modes of X and sort them in order of decreasing energy.

[0075] Step S5. Filter the modes, select the filtered modes to restore the depolarization current, judge the effect of dynamic mode decomposition, and judge whether to adjust the singular value threshold according to the restoration effect. Filtering the modes specifically refers to: based on the extended Debye equivalent circuit model of stator bar insulation, filter the modes, and when the modal slope is non-negative and the initial value is positive, the exponential decay requirement is met, and the modes that meet the exponential decay requirement are retained, and the modes with negative slopes or non-positive initial values ​​are removed.

[0076] Step S6. Calculate the branch number, time constant and relaxation strength coefficient of the insulation extended Debye model.

[0077] Example 3

[0078] As another preferred embodiment of the present invention, the present invention includes a method for identifying parameters of an extended Debye model based on dynamic mode decomposition, comprising the following steps:

[0079] Step S1. Obtain the data of the depolarization current changing with time, construct it into a Hankel matrix, and take the first N columns and the last N columns to form matrix A and matrix B.

[0080] Step S2. Perform economical SVD decomposition on matrix A, set a singular value threshold, discard singular values ​​less than the singular value threshold, and reconstruct the SVD decomposition matrix. Specifically, the following steps are included:

[0081] Step S 21 . Perform economical SVD decomposition on matrix A and extract all singular values;

[0082] Step S 22 .Set the singular value threshold and discard all singular values ​​smaller than the singular value threshold;

[0083] Step S 23 .Reconstruct the SVD decomposition matrix based on the retained singular values.

[0084] Step S3. Solve X=A -1B, then solve the eigenvalues ​​and eigenvectors of X. Specifically, the following steps are included:

[0085] Step S 31 .Use the reconstructed SVD decomposition matrix and B matrix to solve X = A -1 B;

[0086] Step S 32 .Find the eigenvalues ​​and eigenvectors of matrix X.

[0087] Step S4. Solve the modes of X and sort them in order of decreasing energy.

[0088] Step S5. Filter the modes, select the filtered modes to restore the depolarization current, judge the effect of dynamic mode decomposition, and judge whether to adjust the singular value threshold according to the restoration effect.

[0089] Step S6. Calculate the branch number, time constant and relaxation strength coefficient of the insulation extended Debye model.

[0090] Example 4

[0091] As another preferred embodiment of the present invention, the present invention includes a method for identifying parameters of an extended Debye model based on dynamic mode decomposition, referring to the attached specification. Figure 1 , including the following steps:

[0092] Step S1. Obtain the data of the change of depolarization current over time, construct it into a Hankel matrix, and take the first N columns and the last N columns to form matrix A and matrix B. Specifically, the following steps are included:

[0093] Step S 11 .Use the PDC test device to test the object to be tested and obtain two vectors of depolarization current current(i) (i=1,2,3,…,n) and time t(i) (i=1,2,3,…,n).

[0094] Step S 12 . Change step S 11 The length of the depolarization current vector in becomes an even number n. If the vector length is an odd number, the last element of the depolarization current vector is discarded.

[0095] Step S 13 .Use step S 12 The depolarization current data in constructs the Hankel matrix shown below;

[0096]

[0097] Step S 14. Extract the first N columns and the last N columns from the Hankel matrix to form matrices A and B. The value of N can be n / 2.

[0098] Step S2. Perform economical SVD decomposition on matrix A, set a singular value threshold, discard singular values ​​less than the singular value threshold, and reconstruct the SVD decomposition matrix. Specifically, the following steps are included:

[0099] Step S 21 .Perform an economical SVD decomposition on the matrix A and extract all singular values.

[0100] Step S 22 .Set the singular value threshold and discard all singular values ​​smaller than the singular value threshold.

[0101] Step S 23 .Reconstruct the SVD decomposition matrix based on the retained singular values.

[0102] Step S3. Solve X=A -1 B, then solve the eigenvalues ​​and eigenvectors of X. Specifically, the following steps are included:

[0103] Step S 31 .Use the reconstructed SVD decomposition matrix and B matrix to solve X = A -1 B;

[0104] Step S 32 .Find the eigenvalues ​​and eigenvectors of matrix X.

[0105] Step S4. Solve the modes of X and sort them in descending order of energy. Specifically, the following steps are included:

[0106] Step S 41 .Use the eigenvalues ​​of X, the SVD decomposition results and the B matrix to solve the mode.

[0107] Step S 42 .Solve the energy of each mode and sort the modes in order from high to low energy.

[0108] Step S5. Screen the modes, select the screened modes to restore the depolarization current, determine the effect of dynamic mode decomposition, and determine whether to adjust the singular value threshold according to the restoration effect. Specifically, the following steps are included:

[0109] Step S 51 .Based on the extended Debye equivalent circuit model of stator bar insulation, the modes are screened. When the modal slope is non-negative and the initial value is positive, the exponential decay requirement is met. The modes that meet the exponential decay requirement are retained, and the modes with negative slope or non-positive initial value are removed.

[0110] Step S 52.Select the filtered mode to reconstruct the signal, that is, use the filtered mode superposition to obtain the reconstructed data, and judge the difference between the reconstructed data and the original data.

[0111] Step S 53 If the difference between the reconstructed data and the original data is small, proceed to step S6. If the difference between the reconstructed data and the original data is large, return to step S6. 22 Adjust the singular value threshold and re-decompose the depolarization current data.

[0112] This method has been tested by introducing a quantitative restoration accuracy coefficient, and the restoration rate has reached 99%.

[0113] Step S6. Calculate the number of branches, time constants and relaxation strength coefficients of the insulation extension Debye model. Specifically, when the degree of reduction is high, the number of branches, time constants and relaxation strength coefficients of the insulation extension Debye model are solved using the screened first five modes, for example. Assume that the eigenvalues ​​of X are λ1,λ2,…,λ m , then the amplitude, time constant and relaxation intensity coefficient of each branch of the extended Debye model are:

[0114]

[0115] A i =|a i |,

[0116]

[0117] Where Ts is the sampling time interval.

[0118] Example 5

[0119] As another specific embodiment of the present invention, the specification is attached Figure 2 In order to expand the meaning of each branch of the Debye model, the instruction manual is attached. Figure 3 The present invention uses a PDC test device to test an object to be tested. Specifically, the present invention includes a method for identifying parameters of an extended Debye model based on dynamic mode decomposition, comprising the following steps:

[0120] 1. According to step S1 in any one of embodiments 1 to 4, refer to the attached manual. Figure 3 , a PDC test was conducted on a stator bar of a hydro-turbine generator that had been in operation for 17 years using a PDC test device. The depolarization voltage was 1 kV, the depolarization time was 90 s, and the sampling interval was 0.07 s. The data on the variation of depolarization current over time were obtained as shown in the attached manual. Figure 4 shown.

[0121] 2. Solve the steps S2 and S3 in any one of the embodiments 1 to 4 in sequence to obtain the characteristic value distribution as shown in the attached manual. Figure 5 shown.

[0122] 3. According to steps S4, S5, and S6 in any one of embodiments 1 to 4, the depolarization current signal is restored using the selected mode, and the restoration effect is as shown in the attached manual. Figure 6 shown.

[0123] In summary, after reading the present invention document, ordinary technicians in this field can make various other corresponding transformation schemes based on the technical scheme and technical concept of the present invention without creative mental labor, which all fall within the scope of protection of the present invention.

Claims

1. A method for identifying parameters of an extended Debye model based on dynamic mode decomposition, characterized in that: The following steps are involved: Step S1. Obtain the data of the depolarization current changing with time, construct it into a Hankel matrix, and take the first N columns and the last N columns to form matrix A and matrix B; Step S2. Perform economical SVD decomposition on matrix A, set a singular value threshold, discard singular values ​​less than the singular value threshold, and reconstruct the SVD decomposition matrix; Step S3. Solve X=A -1 B, then solve the eigenvalues ​​and eigenvectors of X; Step S4. Solve the modes of X and sort them in order of decreasing energy; Step S5. Screening the modes, selecting the screened modes to restore the depolarization current, judging the effect of dynamic mode decomposition, and judging whether to adjust the singular value threshold according to the restoration effect; Step S6. Calculate the branch number, time constant and relaxation strength coefficient of the insulation extended Debye model.

2. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 1, characterized in that: The step S1 specifically includes the following steps: Step S 11 . Obtain two vectors of depolarization current current(i) (i=1,2,3,…,n) and time t(i) (i=1,2,3,…,n); Step S 12 . Change step S 11 The length of the depolarization current vector in becomes an even number n. If the vector length is an odd number, the last element of the depolarization current vector is discarded; Step S 13 .Use step S 12 The depolarization current data in constructs the Hankel matrix shown below; Step S 14 .Extract the first N columns and the last N columns from the Hankel matrix to form matrix A and matrix B.

3. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 2, characterized in that: The value of N is n / 2.

4. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 1, characterized in that: The step S2 specifically includes the following steps: Step S 21 . Perform economical SVD decomposition on matrix A and extract all singular values; Step S 22 .Set the singular value threshold and discard all singular values ​​smaller than the singular value threshold; Step S 23 .Reconstruct the SVD decomposition matrix based on the retained singular values.

5. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 1, characterized in that: The step S3 specifically comprises the following steps: Step S 31 .Use the reconstructed SVD decomposition matrix and B matrix to solve X = A -1 B; Step S 32 .Find the eigenvalues ​​and eigenvectors of matrix X.

6. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 1, characterized in that: The step S4 specifically comprises the following steps: Step S 41 .Use the eigenvalues ​​of X, SVD decomposition results and B matrix to solve the mode; Step S 42 .Solve the energy of each mode and sort the modes in order from high to low energy.

7. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 1, characterized in that: The mode screening in step S5 specifically refers to: based on the extended Debye equivalent circuit model of stator bar insulation, the mode is screened, when the modal slope is non-negative and the initial value is positive, the exponential decay requirement is met, the mode that meets the exponential decay requirement is retained, and the mode with a negative slope or a non-positive initial value is removed.

8. The method for identifying parameters of an extended Debye model based on dynamic mode decomposition according to claim 7, characterized in that: The step S6 specifically includes the following steps: assuming that the eigenvalues ​​of X are λ1, λ2, ..., λ m , then the amplitude, time constant and relaxation intensity coefficient of each branch of the extended Debye model are: A i =|a i |, Wherein, Ts is the sampling time interval.

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