High-robustness charge inversion method based on B-spline function and related device

Abstract

The invention belongs to the technical field of power equipment insulation structure design, and discloses a high-robustness charge inversion method based on a B spline function and a related device. The method comprises the following steps: calculating potential distribution for an epoxy core electric field finite element simulation model; extracting potentials of preset observation points on the surface of the epoxy core and forming a potential distribution matrix; forming a primary function group for discretely analyzing the epoxy core by adopting B spline functions, calculating potentials of observation points under zero input response when the surface charge distribution of the epoxy core is equal to the primary functions, and forming a response matrix; combining the potential distribution matrix and the response matrix into an overdetermined linear equation, carrying out regularization processing on the equation, and solving by adopting a least square method to obtain a coefficient matrix; and taking each item in the coefficient matrix as a coefficient of a corresponding primary function in the B-spline function, and performing summation operation to obtain surface charge distribution of the epoxy core. According to the method, the robustness of charge inversion can be improved while the calculation efficiency is ensured.

Description

Technical Field

[0001] The 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 a related device. Background Art

[0002] Under the long-term action of DC voltage, charges are easily accumulated on the surface of solid insulation, which will cause local electric field distortion and affect its insulation performance. In the experimental study of charge accumulation characteristics on the surface of solid insulation, 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 the current charge inversion methods, the charge distribution basis functions mostly use sine functions or binary functions, which have a low fit to the actual distribution, and when there are errors in charge measurement, the inversion results are also 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, which can realize the rapid inversion of charge distribution on the surface of epoxy core, while ensuring the calculation efficiency, it can also improve the robustness of charge inversion.

[0004] In order to achieve the above object, the present invention is implemented by adopting the following technical solutions: A highly robust charge inversion method based on B-spline function, comprising: Calculate the potential distribution for the pre-established, parameterized and meshed epoxy core electric field finite element simulation model; The potential distribution of the finite element simulation model of the epoxy core electric field is used to extract the potential of the preset observation point on the epoxy core surface; The potentials of the observation points are formed into a potential distribution matrix; The B-spline function is used to form a basis function group for discretizing and analyzing the epoxy core, and 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 formed into a response matrix; The potential distribution matrix and the response matrix are combined into an overdetermined linear equation, the overdetermined linear equation is regularized and solved by the least square method to obtain a coefficient matrix; The various items in the coefficient matrix are used as the coefficients of the corresponding basis functions in the B-spline function and the summation operation is performed to obtain the surface charge distribution of the epoxy core.

[0005] Preferably, the parameters set in 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.

[0006] 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.

[0007] 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.

[0008] Preferably, the B-spline function adopts a third-order B-spline function.

[0009] 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:

[0010] 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.

[0011] Preferably, the relationship between the epoxy core surface charge distribution and the coefficient matrix and basis function group is as follows:

[0012] in, Epoxy core surface The charge density at is the coefficient matrix j item, is the first j basis functions.

[0013] The present invention also provides a highly robust charge inversion system based on B-spline function, comprising: 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 surface of the epoxy core using the potential distribution of the epoxy core electric field finite element simulation model; A potential distribution matrix building module: used for forming a potential distribution matrix from the potentials of the observation points; Response matrix construction module: used to form a basis function group for discrete analysis of epoxy cores using B-spline functions, 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 a response matrix with the potential of each observation point at this time; 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 use 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.

[0014] The present invention also provides an electronic device, comprising: 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 implement the highly robust charge inversion method based on the B-spline function as described above in the present invention.

[0015] 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 in the present invention is implemented.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The highly robust charge inversion method based on B-spline function of the present invention comprehensively considers the calculation rate and robustness when inverting the surface charge distribution, generates a basis function group for discrete analysis of the surface potential distribution of the epoxy core by adopting the third-order B-spline basis function, calculates the response matrix, and regularizes the overdetermined linear equation composed of the response matrix and the surface potential distribution matrix and solves it by the least squares method, which greatly improves the discrete analysis capability of the basis function group, effectively increases the calculation efficiency, and improves the robustness of the algorithm under random disturbance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. 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 creative work.

[0018] Figure 1 Flow chart of a highly robust charge inversion method based on B-spline function in an embodiment of the present invention; FIG. 2 (a) is a quasi-uniform B-spline basis function used in an embodiment of the present invention. The function graph of ; FIG. 2( b ) is a cyclic B-spline basis function used in an embodiment of the present invention. The function graph of ; Figure 3 is the position of the observation point used for inversion in Example 1 of the present invention on the surface development diagram of the epoxy core; FIG4 (a) shows the charge inversion error when there is no potential measurement error in Example 1 of the present invention; FIG4( b ) is a charge inversion error when the potential measurement error is 1% in Example 1 of the present invention; FIG4( c ) shows the charge inversion error when the potential measurement error is 10% in Example 1 of the present invention. DETAILED DESCRIPTION

[0019] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0020] See also Figure 1 The highly robust charge inversion method based on the B-spline function in this embodiment includes the following steps: 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; 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 the surface charge of the epoxy core; Step 3): Calculate the overall potential distribution of the epoxy core and select uniformly on the surface of the epoxy core mobservation points (the circumferential coordinates and axial coordinates of the selected observation points are evenly distributed on the surface of the epoxy core, among which 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:

[0021] in, The epoxy core surface i The potential of the observation point, m is the number of observation points; Step 4): Considering the random interference (white noise) in the actual potential measurement, the potential distribution matrix Perform random disturbance processing to simulate the random interference in potential measurement, where the maximum amplitude of the disturbance signal is 1% to 10% of the maximum potential to simulate the random interference (white noise) in potential measurement; Step 5): Use the third-order B-spline basis function to form a basis function group for discrete analysis of the surface charge distribution of the epoxy core, calculate the potential of each observation point under the zero input response when the surface charge distribution of the epoxy core 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 third-order quasi-uniform B-spline basis function, and its function graph is shown in Figure 2 (a); is a third-order cyclic B-spline basis function, and its function graph is shown in Figure 2(b).

[0022] The specific operations of this step are as follows: 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 location 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. 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 equation Transform it into a least squares problem, add a regularization term, and solve to get 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; Step 7): Convert the coefficient matrix Each item in is used as the coefficient of the corresponding basis function in the B-spline basis function group and summed to obtain the surface charge distribution of the epoxy core Then, the inverted charge distribution is compared with the test function of charge distribution to calculate the inversion error of surface charge distribution, where the surface charge distribution is expressed by 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.

[0023] Example 1 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: 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.

[0024] Step 2): Set the constraints required for calculation, including the potential of each conductor, the capacitor plate structure, the grounding structure, and the initial potential of each structure.

[0025] Step 3): Add a test function for charge distribution, and let the charge distribution on the epoxy core surface be ,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 .

[0026] 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, and 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 .

[0027] 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.

[0028] Step 6): Let the basis function group be , respectively 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 .

[0029] 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.

[0030] 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 jbasis functions.

[0031] The charge inversion error of the epoxy core mentioned above when there is no potential measurement error (as shown in Figure 4 (a)), the charge inversion error when the random potential perturbation is 1% (as shown in Figure 4 (b)), and the charge inversion error when the random potential perturbation is 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, and the maximum error is 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 when the potential measurement error is small can have high accuracy. 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.

[0032] 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: 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 surface of the epoxy core using the potential distribution of the epoxy core electric field finite element simulation model; A potential distribution matrix building module: used for forming a potential distribution matrix from the potentials of the observation points; Response matrix construction module: used to form a basis function group for discrete analysis of epoxy cores using B-spline functions, 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 a response matrix with the potential of each observation point at this time; 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 use 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.

[0033] 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.

[0034] 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.

[0035] The storage medium stores a computer program, wherein the computer program, when executed by the processor, implements the highly robust charge inversion method based on B-spline function described in any embodiment of the present application.

[0036] The specific embodiments of the present invention are described in detail above. It should be understood that ordinary technicians in the field can make many modifications and changes based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by technicians in the technical field through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art 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 the pre-established, parameterized and meshed epoxy core electric field finite element simulation model; The potential distribution of the finite element simulation model of the epoxy core electric field is used to extract the potential of the preset observation point on the epoxy core surface; The potentials of the observation points are formed into a potential distribution matrix; The B-spline function is used to form a basis function group for discretizing and analyzing the epoxy core, and 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 formed into a response matrix; The potential distribution matrix and the response matrix are combined into an overdetermined linear equation, the overdetermined linear equation is regularized and solved by the least square method to obtain a coefficient matrix; The various items in the coefficient matrix are used as the coefficients of the corresponding basis functions in the B-spline function and the summation operation is performed to obtain the surface charge distribution of the epoxy core.

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. A 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. A 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 charge distribution on the epoxy core surface 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 surface of the epoxy core using the potential distribution of the epoxy core electric field finite element simulation model; A potential distribution matrix building module: used for forming a potential distribution matrix from the potentials of the observation points; Response matrix construction module: used to form a basis function group for discrete analysis of epoxy cores using B-spline functions, 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 a response matrix with the potential of each observation point at this time; 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 use 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 implement the highly robust charge inversion method based on B-spline function as described in 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, a highly robust charge inversion method based on a B-spline function as claimed in any one of claims 1 to 7 is implemented.

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