A highly robust charge inversion method and related device based on B-spline function

Abstract

The present invention belongs to the technical field of insulation structure design for power equipment, and discloses a highly robust charge inversion method and related device based on B-spline functions: calculating the potential distribution of an epoxy core electric field finite element simulation model; extracting the potentials of preset observation points on the epoxy core surface and forming a potential distribution matrix; using B-spline functions to form a basis function group for discretizing and analyzing the epoxy core, calculating the potentials of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function and forming a response matrix; combining the potential distribution matrix and the response matrix into an overdetermined linear equation, regularizing the equation and solving it using the least squares method to obtain a coefficient matrix; using each item in the coefficient matrix as the coefficient of the corresponding basis function in the B-spline function and performing a sum operation to obtain the surface charge distribution of the epoxy core. The present invention can improve the robustness of charge inversion while ensuring computational efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of insulation structure design of power equipment, and in particular relates to a high-robustness charge inversion method based on B-spline function and related devices. Background Art

[0002] Under the long-term action of DC voltage, charges easily accumulate on the surface of solid insulation. The accumulated charges will cause local electric field distortion, which in turn affects its insulation performance. In experimental research on the charge accumulation characteristics of solid insulation surfaces, applying DC voltage, measuring surface potential, inverting and calculating surface charge distribution, and analyzing the charge distribution law are common research methods. Among them, the key to the performance of charge inversion methods lies in the setting and implementation of basis functions, inversion methods, and robustness improvement measures. In current charge inversion methods, the charge distribution basis functions mostly use sine functions or binary functions, which have a low degree of fit to the actual distribution. In addition, when there are errors in charge measurement, the inversion results are easily disturbed, and the robustness of the inversion calculation is insufficient. Summary of the Invention

[0003] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a highly robust charge inversion method and related device based on B-spline function. The present invention can realize the rapid inversion of the charge distribution on the surface of epoxy core, while ensuring the computational efficiency, and can also improve the robustness of charge inversion.

[0004] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0005] A highly robust charge inversion method based on B-spline function, comprising:

[0006] Calculate the potential distribution for a pre-established, parameterized, and meshed epoxy core electric field finite element simulation model;

[0007] The potential distribution of the epoxy core electric field finite element simulation model is used to extract the potential of the preset observation point on the epoxy core surface;

[0008] Combining the potentials of the observation points into a potential distribution matrix;

[0009] The B-spline function is used to form a basis function group for discretizing the epoxy core. The potential of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function is calculated, and the potential of each observation point at this time is combined into a response matrix.

[0010] The potential distribution matrix and the response matrix are combined into an overdetermined linear equation, which is regularized and solved using the least squares method to obtain a coefficient matrix.

[0011] The surface charge distribution of the epoxy core is obtained by taking each item in the coefficient matrix as the coefficient of the corresponding basis function in the B-spline function and performing a sum operation.

[0012] Preferably, the parameters set for the electric field finite element simulation model of the epoxy core include the electrical performance parameters of the material and the constraints required for the analysis and calculation of the electric field finite element simulation model of the epoxy core.

[0013] Preferably, the electrical performance parameters of the material include dielectric constant and conductivity, and the constraints include: the potential of each conductor, the capacitor plate structure, the grounding structure, and the initial potential of each structure.

[0014] Preferably, a plurality of observation points are preset on the surface of the epoxy core, and the plurality of observation points are evenly distributed on the surface of the epoxy core, wherein the spacing between the observation points on the surface of the epoxy core in the circumferential direction is the same and the spacing in the axial direction is the same.

[0015] Preferably, the B-spline function adopts a third-order B-spline function.

[0016] Preferably, the basis function group is composed of n The third-order B-spline function is composed of three third-order B-spline functions, each of which is generated by the Cox-de-Boor recursive formula and satisfies the smooth continuity condition; the third-order B-spline function as follows:

[0017]

[0018] in, is the axial coordinate. On the surface of the epoxy core, the minimum axial coordinate is 0 and the maximum axial coordinate is ; is the circumferential coordinate. On the surface of the epoxy core, the minimum circumferential coordinate is 0 and the maximum circumferential coordinate is ; is the third-order quasi-uniform B-spline basis function; is the third-order cyclic B-spline basis function; k is the order of the third-order quasi-uniform B-spline basis function, l is the order of the third-order cyclic B-spline basis function.

[0019] Preferably, the relationship between the epoxy core surface charge distribution, the coefficient matrix and the basis function group is as follows:

[0020]

[0021] in, Epoxy core surface The charge density at is the coefficient matrix j item, is the firstj basis functions.

[0022] The present invention also provides a highly robust charge inversion system based on a B-spline function, comprising:

[0023] Potential distribution calculation module: used to calculate the potential distribution of the pre-established epoxy core electric field finite element simulation model with set parameters and meshing;

[0024] Observation point potential extraction module: used to extract the potential of the preset observation point on the epoxy core surface using the potential distribution of the epoxy core electric field finite element simulation model;

[0025] A potential distribution matrix building module is used to form a potential distribution matrix from the potentials of the observation points;

[0026] Response matrix construction module: used to use B-spline functions to form a basis function group for discretizing and analyzing the epoxy core, calculate the potential of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function, and form the potential of each observation point into a response matrix;

[0027] Coefficient matrix calculation module: used to combine the potential distribution matrix and the response matrix into an overdetermined linear equation, regularize the overdetermined linear equation and solve it using the least squares method to obtain the coefficient matrix;

[0028] Calculation module: used to take each item in the coefficient matrix as the coefficient of the corresponding basis function in the B-spline function and perform summation operation to obtain the surface charge distribution of the epoxy core.

[0029] The present invention also provides an electronic device, comprising:

[0030] one or more processors;

[0031] a storage device having one or more programs stored thereon;

[0032] When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the highly robust charge inversion method based on the B-spline function as described above in the present invention.

[0033] The present invention further provides a storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the highly robust charge inversion method based on the B-spline function as described above is implemented in the present invention.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention is a highly robust charge inversion method based on B-spline functions. It comprehensively considers the calculation rate and robustness when inverting the surface charge distribution. It uses third-order B-spline basis functions to generate a basis function group for discretely analyzing the surface potential distribution of the epoxy core, calculates the response matrix, and regularizes the overdetermined linear equation consisting of the response matrix and the surface potential distribution matrix and solves it using the least squares method. This greatly improves the discrete analytical capability of the basis function group, effectively increases the calculation efficiency, and improves the robustness of the algorithm under random perturbations. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0037] Figure 1 Flowchart of a highly robust charge inversion method based on B-spline function in an embodiment of the present invention;

[0038] Figure 2 (a) shows the quasi-uniform B-spline basis function used in the embodiment of the present invention. The function graph of ;

[0039] FIG2( b ) is a cyclic B-spline basis function used in an embodiment of the present invention. The function graph of ;

[0040] Figure 3 The position of the observation point used for inversion in Example 1 of the present invention on the expanded image of the epoxy core surface;

[0041] FIG4 (a) shows the charge inversion error when there is no potential measurement error in Example 1 of the present invention;

[0042] FIG4( b ) shows the charge inversion error when the potential measurement error is 1% in Example 1 of the present invention;

[0043] FIG4( c ) shows the charge inversion error when the potential measurement error is 10% in Example 1 of the present invention. DETAILED DESCRIPTION

[0044] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0045] See also Figure 1 The highly robust charge inversion method based on the B-spline function in this embodiment includes the following steps:

[0046] Step 1): Establish an electric field finite element simulation model of the epoxy core and mesh the electric field finite element simulation model of the epoxy core (the meshing should be detailed enough to ensure that the basis function used in the finite element method has sufficient analytical ability, so that the selected basis function can be effectively characterized in the simulation calculation). Set the electrical performance parameters of the material required for the analysis and calculation of the electric field finite element simulation model of the epoxy core, where the electrical performance parameters of the material include dielectric constant and conductivity;

[0047] Step 2): Determine the constraints required for the electric field finite element simulation model analysis and calculation of the epoxy core, the constraints include: the potential of each conductor, the capacitor plate structure, the grounding structure, the initial potential of each structure, and a certain distribution of charge on the surface of the epoxy core;

[0048] Step 3): Calculate the overall potential distribution of the epoxy core and select uniformly on the surface of the epoxy core m observation points (the circumferential and axial coordinates of the selected observation points are evenly distributed on the surface of the epoxy core, where the number of observation points per unit length in the axial direction is m 1. The number of observation points per unit length in the ring is m 2, m equal m 1 and m 2), extract the potential of each observation point and form a potential distribution matrix as follows:

[0049]

[0050] in, The epoxy core surface i The potential of the observation point, m is the number of observation points;

[0051] Step 4): Considering the random interference (white noise) in the actual potential measurement, the potential distribution matrix Perform random perturbation processing to simulate the random interference in potential measurement. The maximum amplitude of the perturbation signal is 1% to 10% of the maximum potential to simulate the random interference (white noise) in potential measurement.

[0052] Step 5): Use the third-order B-spline basis function to form a basis function group for discrete analysis of the epoxy core surface charge distribution, calculate the potential of each observation point under zero input response when the epoxy core surface charge distribution is equal to each basis function, and form a response matrix , wherein each third-order B-spline function is generated by the Cox-de-Boor recursive formula and satisfies the smooth continuity condition; the third-order B-spline function ,in, is the axial coordinate. On the surface of the epoxy core, the minimum axial coordinate is 0 and the maximum axial coordinate is ; is the circumferential coordinate. On the surface of the epoxy core, the minimum circumferential coordinate is 0 and the maximum circumferential coordinate is ; is a 3rd order quasi-uniform B-spline basis function, and its function graph is shown in Figure 2(a); is a 3rd order cyclic B-spline basis function, and its function graph is shown in Figure 2(b).

[0053] The specific operations of this step are as follows:

[0054] Let the charge distribution on the epoxy core surface be the basis function ( j =1,…, n ), calculate the potential of each observation point under zero input response , and the response matrix is ​​obtained by combining ,in, is the surface charge distribution and basis function When the epoxy core surface is completely consistent, i Observation locations The potential at the epoxy core is an axisymmetric structure. is a block circulant matrix, so The response can be The actual number of simulations can be reduced from 360 to 30 times.

[0055] Step 6): The potential distribution matrix With the response matrix Combining into overdetermined linear equations , with respect to this equation, the response matrix and potential distribution matrix Overdetermined linear equations Convert it into a least squares problem and add regularization terms to solve the coefficient matrix , so that the response matrix The product of the coefficient matrix is ​​equal to the potential distribution matrix , where the least squares problem is , is the regularization coefficient;

[0056] Step 7): The coefficient matrix Each item in the equation is used as the coefficient of the corresponding basis function in the B-spline basis function group and the sum is calculated to obtain the surface charge distribution of the epoxy core. Then compare the inverted charge distribution with the test function of charge distribution and calculate the inversion error of surface charge distribution, where the surface charge distribution is expressed as Calculate, where Epoxy core surface The charge density at is the coefficient matrix Middle j item, is the first j The test function of the charge distribution on the epoxy core surface is to first give the epoxy core surface a certain charge distribution, invert the potential distribution under the charge distribution, and compare the calculated charge distribution on the epoxy core surface with the test function to verify the accuracy and efficiency of the method.

[0057] Example 1

[0058] This embodiment uses the above method to perform charge inversion calculation on the surface potential distribution under a certain charge distribution on the epoxy core surface, and compares the inversion result with the test function, including the following steps:

[0059] Step 1): Establish a finite element analysis model of the epoxy core, mesh the electric field finite element simulation model of the epoxy core, and set the electrical performance parameters of the materials required for calculation, including the dielectric constant and conductivity of each component required for calculating the potential.

[0060] Step 2): Set the constraints required for the calculation, including the potential of each conductor, the capacitor plate structure, the grounding structure, and the initial potential of each structure.

[0061] Step 3): Add a test function for charge distribution and set the charge distribution on the epoxy core surface to ,in, is the axial coordinate, is the circumferential coordinate. On the surface of the epoxy core, the minimum axial coordinate is 0 and the maximum axial coordinate is , the minimum circumferential coordinate is 0, and the maximum axial coordinate is .

[0062] Step 4): Calculate the overall potential distribution of the epoxy core. Select 72,000 observation points (2,000 in the axial direction and 36 in the circumferential direction) evenly on the surface of the epoxy core. The positions of the selected observation points on the expanded diagram of the epoxy core surface are as follows: Figure 3 As shown, the potential of each observation point is extracted and the potential distribution matrix is ​​formed .

[0063] Step 5): Potential distribution matrix Random perturbation processing is performed, and the maximum amplitude of the perturbation signal is 1% and 10% of the maximum potential respectively.

[0064] Step 6): Let the basis function group be , calculate the potential of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function And form the response matrix .

[0065] Step 7): Solve the least squares problem , so that the response matrix With the coefficient matrix The product is equal to the potential distribution matrix ,in, is the regularization coefficient.

[0066] Step 8): Through the expression Solve the surface charge distribution of the epoxy core, compare the inverted charge distribution with the test function of the charge distribution, and calculate the inversion error of the surface charge distribution, where: is the coefficient matrix Middle j item, is the first j basis functions.

[0067] The charge inversion error of the epoxy core in the absence of potential measurement error (as shown in Figure 4 (a)), the charge inversion error under a random potential perturbation of 1% (as shown in Figure 4 (b)), and the charge inversion error under a random potential perturbation of 10% (as shown in Figure 4 (c)). When there is no potential measurement error, the charge inversion result is in good agreement with the actual charge distribution, with the maximum error being less than 0.2% of the maximum charge density; when the potential measurement error is small, the inversion error increases with the increase of the regularization coefficient; when the potential measurement error is large, the inversion error first decreases and then increases with the increase of the regularization coefficient. When the regularization coefficient When the potential measurement error is large, the accuracy of the inversion calculation can be effectively improved, and the inversion calculation can be highly accurate when the potential measurement error is small. Therefore, the selection of this regularization coefficient has strong robustness to random disturbances, which verifies the rationality and accuracy of the method of the present invention.

[0068] The present invention also provides a system based on the highly robust charge inversion method based on the B-spline function as described above, comprising:

[0069] Potential distribution calculation module: used to calculate the potential distribution of the pre-established epoxy core electric field finite element simulation model with set parameters and meshing;

[0070] Observation point potential extraction module: used to extract the potential of the preset observation point on the epoxy core surface using the potential distribution of the epoxy core electric field finite element simulation model;

[0071] A potential distribution matrix building module is used to form a potential distribution matrix from the potentials of the observation points;

[0072] Response matrix construction module: used to use B-spline functions to form a basis function group for discretizing and analyzing the epoxy core, calculate the potential of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function, and form the potential of each observation point into a response matrix;

[0073] Coefficient matrix calculation module: used to combine the potential distribution matrix and the response matrix into an overdetermined linear equation, regularize the overdetermined linear equation and solve it using the least squares method to obtain the coefficient matrix;

[0074] Calculation module: used to take each item in the coefficient matrix as the coefficient of the corresponding basis function in the B-spline function and perform summation operation to obtain the surface charge distribution of the epoxy core.

[0075] The embodiments of the present invention also provide corresponding electronic devices and computer-readable storage media for implementing the solutions provided by the embodiments of the present invention.

[0076] The device includes a memory and a processor, the memory is used to store instructions or codes, and the processor is used to execute the instructions or codes, so that the device executes the high-robustness charge inversion method based on B-spline function described in any embodiment of the present application.

[0077] The storage medium stores a computer program, wherein when the computer program is executed by the processor, the highly robust charge inversion method based on the B-spline function described in any embodiment of the present application is implemented.

[0078] The above describes in detail the specific embodiments of the present invention. It should be understood that numerous modifications and variations based on the concepts of the present invention can be made by those skilled in the art without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art based on the concepts of the present invention through logical analysis, reasoning, or limited experimentation based on the existing technology should be within the scope of protection of the claims of the present invention.

Claims

1. A highly robust charge inversion method based on B-spline function, characterized in that: include: Calculate the potential distribution for a pre-established, parameterized, and meshed epoxy core electric field finite element simulation model; The potential distribution of the epoxy core electric field finite element simulation model is used to extract the potential of the preset observation point on the epoxy core surface; Combining the potentials of the observation points into a potential distribution matrix; The B-spline function is used to form a basis function group for discretizing the epoxy core. The potential of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function is calculated, and the potential of each observation point at this time is combined into a response matrix. The potential distribution matrix and the response matrix are combined into an overdetermined linear equation, which is regularized and solved using the least squares method to obtain a coefficient matrix. The surface charge distribution of the epoxy core is obtained by taking each item in the coefficient matrix as the coefficient of the corresponding basis function in the B-spline function and performing a sum operation.

2. A highly robust charge inversion method based on B-spline function according to claim 1, characterized in that: The parameters set for the electric field finite element simulation model of the epoxy core include the electrical performance parameters of the material and the constraints required for the analysis and calculation of the electric field finite element simulation model of the epoxy core.

3. The highly robust charge inversion method based on B-spline function according to claim 2, characterized in that: The electrical performance parameters of the material include dielectric constant and conductivity, and the constraints include: the potential of each conductor, the capacitor plate structure, the grounding structure, and the initial potential of each structure.

4. The highly robust charge inversion method based on B-spline function according to claim 1, characterized in that: A plurality of observation points are preset on the surface of the epoxy core, and the plurality of observation points are evenly distributed on the surface of the epoxy core, wherein the spacing between the observation points in the circumferential direction and the axial direction of the epoxy core surface are the same.

5. The highly robust charge inversion method based on B-spline function according to claim 1, characterized in that: The B-spline function adopts a third-order B-spline function.

6. The highly robust charge inversion method based on B-spline function according to claim 5, characterized in that: The basis function group is composed of n The third-order B-spline function is composed of three third-order B-spline functions, each of which is generated by the Cox-de-Boor recursive formula and satisfies the smooth continuity condition; the third-order B-spline function as follows: in, is the axial coordinate. On the surface of the epoxy core, the minimum axial coordinate is 0 and the maximum axial coordinate is ; is the circumferential coordinate. On the surface of the epoxy core, the minimum circumferential coordinate is 0 and the maximum circumferential coordinate is ; is the third-order quasi-uniform B-spline basis function; is the third-order cyclic B-spline basis function; k is the order of the third-order quasi-uniform B-spline basis function, l is the order of the third-order cyclic B-spline basis function.

7. The highly robust charge inversion method based on B-spline function according to claim 1, characterized in that: The relationship between the surface charge distribution of the epoxy core and the coefficient matrix and basis function group is as follows: in, Epoxy core surface The charge density at is the coefficient matrix j item, is the first j basis functions.

8. A highly robust charge inversion system based on B-spline function, characterized in that: include: Potential distribution calculation module: used to calculate the potential distribution of the pre-established epoxy core electric field finite element simulation model with set parameters and meshing; Observation point potential extraction module: used to extract the potential of the preset observation point on the epoxy core surface using the potential distribution of the epoxy core electric field finite element simulation model; A potential distribution matrix building module is used to form a potential distribution matrix from the potentials of the observation points; Response matrix construction module: used to use B-spline functions to form a basis function group for discretizing and analyzing the epoxy core, calculate the potential of each observation point under zero input response when the charge distribution on the epoxy core surface is equal to each basis function, and form the potential of each observation point into a response matrix; Coefficient matrix calculation module: used to combine the potential distribution matrix and the response matrix into an overdetermined linear equation, regularize the overdetermined linear equation and solve it using the least squares method to obtain the coefficient matrix; Calculation module: used to take each item in the coefficient matrix as the coefficient of the corresponding basis function in the B-spline function and perform summation operation to obtain the surface charge distribution of the epoxy core.

9. An electronic device, characterized in that: include: one or more processors; a storage device having one or more programs stored thereon; When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the highly robust charge inversion method based on B-spline function according to any one of claims 1 to 7.

10. A storage medium, characterized in that: A computer program is stored thereon, wherein when the computer program is executed by a processor, the highly robust charge inversion method based on the B-spline function as claimed in any one of claims 1 to 7 is implemented.

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