Simulation method for tomographic imaging of coaxial heterostructure with potential continuous constraint

Abstract

The present application relates to the technical field of nondestructive testing imaging, in particular to a tomographic imaging simulation calculation method for coaxial heterogeneous structure potential continuous constraint, comprising: constructing a coaxial heterogeneous structure refined model, determining the dielectric constant and conductivity of each layer of material, dividing finite element grid units, identifying the interface of heterogeneous materials and applying potential continuous and flux balance constraints, and solving to obtain the potential value of all nodes; extracting the electric field intensity at the centroid of each unit, and constructing a sensitivity matrix; combining the measured capacitance data, obtaining the dielectric constant vector through inverse problem solving, mapping back to the grid unit to complete image reconstruction, and displaying the defect position. The present application significantly improves the electric field simulation accuracy and defect image reconstruction resolution by constructing a coaxial heterogeneous structure refined model and applying potential continuous constraints.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing imaging technology, and in particular to a tomographic imaging simulation calculation method for potential continuity constraints of coaxial heterostructures. Background Technology

[0002] This invention addresses the problem of model simplification in existing capacitance tomography (ECT) techniques when inspecting coaxial heterogeneous structures (such as the "metal core-inner shield-insulation layer-outer shield" multilayer system of high-voltage cables). Traditional methods often simplify the inspection area to a single dielectric or two-layer structure, ignoring the significant differences in dielectric constants between the layers and their impact on the electric field distribution. This results in an inability to accurately reconstruct the step-like attenuation and refraction characteristics of the electric field between different dielectric layers. Furthermore, existing technologies lack effective boundary constraints at heterogeneous interfaces with abrupt changes in dielectric constant, easily leading to pseudo-oscillations in the electric field gradient and non-convergence in calculations. This results in low signal-to-noise ratio of the sensitivity matrix and poor image reconstruction resolution during the inverse problem solution process, making it difficult to accurately locate and reconstruct the contours of minute defects (such as air gaps and inclusions) within the insulation layer. Consequently, this restricts the engineering application of ECT in the non-destructive testing of complex coaxial heterogeneous structures. Summary of the Invention

[0003] This invention provides a tomographic imaging simulation calculation method for continuous potential constraints in coaxial heterostructures, which solves the problems of electric field simulation distortion, numerical calculation instability, and low imaging resolution of small defects caused by the simplification of models and lack of boundary constraints in the detection of coaxial heterostructures in existing capacitance tomography technology.

[0004] The objective of this invention can be achieved through the following technical solutions:

[0005] The first aspect of this invention is to provide a tomographic imaging simulation calculation method for potential continuity constraints in coaxial heterostructures, comprising:

[0006] A refined model of the coaxial heterostructure is constructed; the parameters of each independent material layer in the refined model of the coaxial heterostructure are determined; the parameters include dielectric constant and conductivity;

[0007] A refined model of the coaxial heterostructure is used to divide the coaxial heterostructure into several finite element meshes. All heterogeneous material interfaces are identified through these meshes. Two types of boundary constraints are applied to the interfaces to obtain the potential values ​​of all nodes in the entire solution domain. Each mesh element contains several nodes.

[0008] Based on the potential values ​​of all nodes in the entire solution domain, a forward simulation is performed using the finite element method to extract the electric field intensity at the centroid of each mesh element; a sensitivity matrix is ​​then constructed based on the electric field intensity.

[0009] The capacitance data of the coaxial heterostructure is obtained through an electrode capacitance sensor and a capacitance measurement value vector is formed.

[0010] The dielectric constant vector is obtained by inversely solving the capacitance measurement vector and the sensitivity matrix;

[0011] The image is reconstructed by mapping the dielectric constant vector back to the finite element mesh, and the location of the defect is displayed.

[0012] Furthermore, the refined model of the coaxial heterostructure includes a conductor layer, a conductor semiconducting shielding layer, an insulating layer, and an insulating semiconducting shielding layer.

[0013] Furthermore, the process of identifying all heterogeneous material interfaces is as follows:

[0014] In a finite element method for a multi-layered coaxial heterogeneous structure, the interface between heterogeneous materials is identified by determining whether the material numbers of adjacent mesh elements are different.

[0015] Furthermore, the process of obtaining the potential values ​​of all nodes within the entire solution domain is as follows:

[0016] At the interface of heterogeneous materials, two types of boundary constraints are explicitly applied; the two types of boundary constraints include potential continuity constraints and flux balance constraints.

[0017] The initial global stiffness matrix and right-hand vector are obtained by assembling using the finite element method, and then corrected by degree-of-freedom coupling or penalty function method to obtain the corrected global stiffness matrix and right-hand vector after applying constraints.

[0018] A new system of algebraic equations is formed using the potential vector to be determined, the global stiffness matrix corrected after applying constraints, and the right-hand side vector; the new algebraic equations are specifically expressed as follows:

[0019]

[0020] In the formula, This represents the global stiffness matrix after constraints are applied. This represents the vector of potential values ​​to be determined for all nodes. This represents the right-hand vector that has been modified after the constraint has been applied;

[0021] The potentials of all nodes in the entire solution domain are determined by using the vector of potential values ​​to be determined for all nodes.

[0022] Furthermore, the process of constructing the sensitivity matrix includes:

[0023] The sensitivity coefficient of each grid cell is obtained by performing a vector dot product based on the electric field intensity; the sensitivity matrix is ​​then constructed using the sensitivity coefficients of all grid cells.

[0024] Furthermore, the process of obtaining the capacitance measurement value vector includes:

[0025] The capacitance data of the coaxial heterostructure is acquired by using an electrode capacitance sensor and a multi-electrode rotation excitation mode, and the capacitance measurement values ​​of all independent electrode pairs are obtained. The capacitance measurement values ​​of all electrode pairs are then combined into a capacitance measurement value vector.

[0026] Furthermore, the process of solving for the dielectric constant vector is as follows:

[0027] The specific process of inversely solving for the dielectric constant vector is as follows: the dielectric constant is solved using the Tikhonov regularization method to obtain the initial dielectric constant vector; based on the initial dielectric constant vector, the Tikhonov quasi-Newton iterative algorithm is used for fine-tuning to obtain the final dielectric constant vector.

[0028] Furthermore, the process of obtaining the sensitivity coefficient of each grid cell includes:

[0029]

[0030] In the formula, This represents the sensitivity coefficient of the k-th grid cell under the combination of excitation electrode i and measurement electrode j. This represents the integral area of ​​the k-th grid cell. Denotes an integral infinitesimal element. This represents the coordinates of the center point of the k-th grid cell. This represents the vector mean of the electric field intensity within the k-th grid cell when only the excitation electrode i is subjected to a voltage. This represents the vector mean of the electric field intensity within the k-th grid cell when only electrode j is subjected to voltage. This represents the voltage amplitude of the excitation electrode i. This represents the voltage amplitude of the measuring electrode j.

[0031] A second aspect of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures.

[0032] A third aspect of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the tomographic simulation calculation method for potential continuity constraints of coaxial heterostructures.

[0033] Compared with existing technologies, the beneficial effects of this invention are: constructing a refined model of a coaxial heterostructure; determining the parameters of each independent material layer in the refined model of the coaxial heterostructure; the parameters include dielectric constant and conductivity; realistically restoring the step dielectric properties of the multilayer dielectric, laying the foundation for accurate electric field calculation; dividing the coaxial heterostructure into several mesh elements of the finite element method using the refined model of the coaxial heterostructure, and identifying all heterostructure material interfaces using these mesh elements; applying two types of boundary constraints on the interfaces to obtain the potential values ​​of all nodes in the entire solution domain; each mesh element contains several nodes; and eliminating spurious oscillations in the electric field at the interfaces. To ensure numerical calculation stability and physical consistency, the finite element method is used for forward simulation based on the potential values ​​of all nodes in the entire solution domain, extracting the electric field intensity at the centroid of each mesh element. A sensitivity matrix is ​​constructed based on the electric field intensity. Actual capacitance data is obtained and a capacitance measurement vector is formed. The dielectric constant vector is obtained by inverse solution based on the capacitance measurement vector and the sensitivity matrix. A high signal-to-noise ratio sensitivity matrix is ​​obtained, improving the accuracy of inverse problem solution and defect identification capability. The dielectric constant vector is mapped back to the mesh element of the finite element method to complete image reconstruction and display the defect location. High-resolution imaging of small-sized defects is achieved, intuitively displaying the defect location and contour. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 A flowchart illustrating the steps of the tomographic imaging simulation calculation method for potential continuity constraints of coaxial heterostructures provided by this invention.

[0036] Figure 2 An image of a refined model of a coaxial heterostructure;

[0037] Figure 3 A schematic diagram of a cuboid defect in a refined model of a coaxial heterostructure;

[0038] Figure 4 Image of a cuboid defect representing 10% of its area using the Tikhonov regularization method;

[0039] Figure 5 Image of a rectangular defect representing 10% of its area, created using the Tikhonov quasi-Newton iterative algorithm.

[0040] Figure 6 Image of a rectangular defect representing 5% of its area using the Tikhonov regularization method;

[0041] Figure 7 The image is an image created using the Tikhonov quasi-Newton iterative algorithm for a cuboid defect representing 5% of its area. Detailed Implementation

[0042] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0043] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0044] To address the problems existing in the background technology, a tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures has been designed, which has important practical significance.

[0045] like Figure 1 As shown, the first aspect of the present invention is to provide a tomographic imaging simulation calculation method for potential continuity constraints of coaxial heterostructures, comprising the following steps:

[0046] Step S1: Construct a refined model of the coaxial heterostructure; determine the parameters of each independent material layer in the refined model of the coaxial heterostructure; the parameters include dielectric constant and conductivity.

[0047] It should be noted that, in order to accurately reproduce the distribution characteristics of the electric field between different dielectric layers under actual working conditions, a four-layer geometric structure covering the conductor layer, the conductor semiconducting shielding layer, the insulating layer, and the insulating semiconducting shielding layer is established. Based on the actual electrical parameters of each layer, independent dielectric constants and conductivity are assigned. This breaks the assumption of traditional single dielectric or simplified models and lays a geometric and material foundation that conforms to physical reality for the subsequent accurate application of interface constraints, calculation of electric field distribution, and high signal-to-noise ratio sensitivity matrix.

[0048] Specifically, taking high-voltage cables as an example, a four-layer coaxial geometric model is established: "conductor layer - conductor semiconducting shield layer - insulation layer - insulation semiconducting shield layer"; denoted as the refined coaxial heterostructure model; the imaging diagram of the refined coaxial heterostructure model is shown below. Figure 2 As shown.

[0049] The parameters of each independent material layer in the refined model of the coaxial heterostructure were determined; these parameters include dielectric constant and electrical conductivity.

[0050] In this simulation, the conductor layer is made of metallic copper or aluminum, which has very high conductivity and is usually assumed to be an equipotential body. The relative permittivity of the metallic conductor can be set to a maximum value (e.g., 10000), and the conductivity is approximately 5.8 × 10⁻⁶. 7 S / m (copper);

[0051] The conductor semiconducting shielding layer has a relative permittivity of 10 and a conductivity of 1 S / m.

[0052] Insulating layer: relative permittivity is set to 2.3, and conductivity is 0;

[0053] Insulating semiconductive shielding layer: relative permittivity is set to 10, and conductivity is set to 1 S / m;

[0054] The unit of conductivity is Siemens per meter.

[0055] This completes the construction of the refined model of the coaxial heterogeneous structure and the setting of its corresponding parameters.

[0056] Step S2: Divide the coaxial heterostructure into several finite element meshes using the refined model of the coaxial heterostructure, and identify all heterostructure material interfaces using the several meshes of the finite element; apply two types of boundary constraints on the interfaces to obtain the potential values ​​of all nodes in the entire solution domain; each mesh element contains several nodes.

[0057] It should be noted that, in order to eliminate the pseudo-oscillation of the electric field gradient and the non-convergence of numerical calculation caused by the abrupt change in dielectric constant at the interface of heterogeneous materials, the potentials on both sides of the interface are forced to be equal (potential continuity) and the normal components of the electric displacement vector are equal (flux balance). This ensures that the simulation results strictly conform to the physical laws of the electrostatic field at the interface of the medium, thereby obtaining a real and smooth electric field distribution. This provides a reliable physical field input for subsequent high-precision sensitivity matrix calculation and high-quality image reconstruction.

[0058] Specifically, a number of mesh elements of the finite element method for the multi-layer coaxial heterogeneous structure are divided by a refined model of the coaxial heterogeneous structure. All heterogeneous material interfaces are identified through the mesh elements of the finite element method. The specific process is as follows: in the mesh elements of the finite element method for the multi-layer coaxial heterogeneous structure, the heterogeneous material interfaces are identified by judging whether the material numbers of adjacent mesh elements are different.

[0059] Two types of boundary constraints are applied at the interface to obtain the potential values ​​of all nodes in the entire solution domain. The specific process of applying constraints and obtaining the potential values ​​of all nodes in the entire solution domain is as follows: At the interface of the heterogeneous materials, two types of boundary constraints are explicitly applied; these constraints include potential continuity constraints and flux balance constraints. Each mesh element contains several nodes.

[0060] Among them, the potential continuity constraint is that the potentials at both ends of the interface are equal; the flux balance constraint is that the normal component of the electric displacement vector is continuous.

[0061] The potential continuity constraint is specifically expressed by the following formula:

[0062]

[0063] In the formula, This indicates the electrical potential value on one side of the interface. This indicates the potential value on the other side of the interface.

[0064] The flux balance constraint is specifically expressed by the following formula:

[0065]

[0066] In the formula, This represents the electric displacement vector on one side of the interface. This represents the electric displacement vector on the other side of the interface. This represents the geometric normal vector (i.e., the unit vector perpendicular to the interface) defined on the heterogeneous interface. Represents the dot product of vectors.

[0067] The initial global stiffness matrix and right-hand side vector are obtained by assembling using the finite element method. These are then corrected using degree-of-freedom coupling or the penalty function method to obtain the corrected global stiffness matrix and right-hand side vector after applying constraints. The finite element method, degree-of-freedom coupling, and penalty function method are all well-known techniques and will not be elaborated upon here.

[0068] In this process, the element stiffness matrix of each mesh element is calculated based on its geometry, material properties (such as dielectric constant), and interpolation function. The element stiffness matrices of all mesh elements are superimposed on the corresponding positions of the global stiffness matrix according to the node number to obtain the global stiffness matrix. Interface constraints are embedded through degree-of-freedom coupling or penalty function method to ensure that the solution satisfies potential continuity and flux balance, thus obtaining the global stiffness matrix and the right-hand vector after applying constraints.

[0069] The data values ​​in the initial right-hand vector are determined by the excitation source (such as the voltage applied to the electrode) and boundary conditions (such as grounding or floating). During the finite element discretization process, the excitation voltage is transformed into an equivalent "source term" on the corresponding node and assembled into the corresponding position of the right-hand vector. For nodes without excitation, the corresponding component of the right-hand vector is 0.

[0070] It should be noted that when coupling degrees of freedom in constraints, if it is necessary to unify two boundary data into one data, the positions of the two data should be overlapped and the data value should be set as an unknown.

[0071] Specifically, the above constraints are embedded into the global stiffness matrix and the right-hand side vector to obtain the global stiffness matrix and the right-hand side vector after applying the constraints; a new system of algebraic equations is formed using the potential value vector to be determined, the global stiffness matrix after applying the constraints, and the right-hand side vector; the new algebraic equations are specifically expressed as follows:

[0072]

[0073] In the formula, This represents the global stiffness matrix after constraints are applied. This represents the vector of potential values ​​to be determined for all nodes. This represents the right-hand side vector corrected after applying constraints (containing contributions from the excitation source and interface flux terms); where the global stiffness matrix has a size of... The vector of potential values ​​to be determined is The column vector, with the right-hand vector as... Column vectors; where The number of nodes.

[0074] By using the potential vectors of all nodes, the potential values ​​of all nodes in the entire solution domain can be determined.

[0075] Step S3: Based on the potential values ​​of all nodes in the entire solution domain, perform forward simulation using the finite element method to extract the electric field intensity at the centroid of each mesh element; construct a sensitivity matrix based on the electric field intensity; acquire the capacitance data of the coaxial heterostructure through an electrode capacitance sensor and form a capacitance measurement vector; perform inverse solution based on the capacitance measurement vector and the sensitivity matrix to obtain the dielectric constant vector.

[0076] It should be noted that, in order to establish a quantitative mapping relationship between the measured capacitance value and the change in the internal dielectric constant, finite element simulation was performed on the model after applying boundary constraints to obtain the actual electric field distribution under excitation of each electrode pair. The contribution weight of each element to the measured value (i.e., the sensitivity coefficient) was calculated based on the vector electric field dot product, thereby constructing a high signal-to-noise ratio sensitivity matrix, which provides a core mathematical model for subsequently retrieving defect images from the measured capacitance data.

[0077] It should be further explained that, based on the potential value vector to be determined, a continuous potential distribution is constructed within the cell using an interpolation function to obtain the potential function; the components of the electric field intensity on the three axes are obtained by taking the partial derivative of the potential function; the calculation based on the vector electric field dot product is to multiply the components of the electric field intensity on the three axes separately and then superimpose them to obtain the final result.

[0078] Specifically, capacitance data of the coaxial heterostructure is acquired by using an electrode capacitance sensor and a multi-electrode rotation excitation mode to obtain capacitance measurements of all independent electrode pair combinations; wherein, the capacitance measurements of all electrode pair combinations are combined into a capacitance measurement value vector.

[0079] In this embodiment, the number of multiple electrodes is represented by G, and the number of combination pairs of capacitance measurements for all independent electrode pairs is: In this embodiment, the number of electrodes G is 8. The specific number of electrodes is not limited and can be determined by the implementer according to specific circumstances. Specifically, this means that an 8-electrode rotating excitation mode is used to collect capacitance data, obtaining 28 independent capacitance measurements.

[0080] In this system, the excitation electrode and the measurement electrode are a pair of electrodes in the multi-electrode rotating excitation mode. The electrode that applies voltage in the combination is called the excitation electrode, and the electrode that detects capacitance in the combination is called the measurement electrode.

[0081] The capacitance data acquisition process based on the multi-electrode rotary excitation mode is as follows:

[0082] This invention employs an 8-electrode capacitive sensor tightly bonded to the outer layer of a cable, constructing a four-layer refined geometric model. During sensor operation, a single-electrode rotary excitation mode is used to acquire raw capacitance data. The specific process is as follows:

[0083] (1) Excitation process: Starting with any one of the 8 electrodes (defined as electrode 1), apply an excitation voltage of a preset amplitude to electrode 1. At this time, the other electrodes are numbered in sequence. The excitation voltage applied in this invention is 1V.

[0084] (2) Measurement combination: When the excitation electrode 1 is excited, electrodes 2 to 8 are used as measuring electrodes in sequence to measure and record the capacitance values ​​between electrodes 1-2, 1-3, 1-4, ..., 1-8; then, the excitation voltage is moved to electrode 2 and the capacitance values ​​between 2-3, 2-4, ..., 2-8 are measured.

[0085] (3) Data completeness: The process continues until the last set of measurements of excitation electrode 7 and measurement electrode 8 is completed. Through this cycle, the system obtains a total of 28 independent capacitance measurement values, which constitute a capacitance measurement value vector.

[0086] Based on the potential values ​​of all nodes in the entire solution domain, a forward simulation is performed using the finite element method to extract the electric field intensity at the centroid of each mesh element; where the electric field intensity is a vector.

[0087] The sensitivity coefficient of each grid cell is obtained by performing a vector dot product of the electric field intensity. A sensitivity matrix is ​​then constructed using the sensitivity coefficients of all grid cells. The specific formula for calculating the sensitivity coefficient of each grid cell is as follows:

[0088]

[0089] In the formula, This represents the sensitivity coefficient of the k-th grid cell under the combination of excitation electrode i and measurement electrode j. This represents the integral area of ​​the k-th grid cell. Denotes an integral infinitesimal element. This represents the coordinates of the center point of the k-th grid cell. This represents the vector mean of the electric field intensity within the k-th grid cell when only the excitation electrode i is subjected to a voltage. This represents the vector mean of the electric field intensity within the k-th grid cell when only electrode j is subjected to voltage. This represents the voltage amplitude of the excitation electrode i. This represents the voltage amplitude of the measuring electrode j.

[0090] The sensitivity coefficients of all grid cells are used to form a sensitivity matrix of H×M, where M is the total number of grid cells. H represents the number of electrode pair combinations, which is determined by the number of electrodes under test, i.e., by the pairwise combinations of electrodes. For example, if the total number of electrodes under test is G, then... ; This indicates pairwise combinations from G data points.

[0091] Thus, the capacitance measurement vector and sensitivity matrix are obtained through the above method.

[0092] Step S4: Map the dielectric constant vector back to the finite element mesh to complete image reconstruction.

[0093] It should be noted that in order to invert the dielectric constant distribution within the measured region from the measured capacitance data, and thus identify the location and size of defects, the inverse problem of ECT (Electrical Capacitance Tomography) is underdetermined and ill-conditioned, and cannot be solved directly. Therefore, a regularization method (such as Tikhonov regularization) is needed to transform the problem into an optimization problem. By iteratively solving the problem, the true distribution is approximated, and finally, the inversion result is mapped back to the finite element mesh to achieve visual imaging of defects.

[0094] Specifically, the dielectric constant vector is obtained by inversely solving the capacitance measurement vector and the sensitivity matrix; the formula for inversely solving the dielectric constant vector is as follows:

[0095]

[0096] In the formula, Represents the sensitivity matrix. Represents a vector of capacitance measurements. This represents the dielectric constant vector.

[0097] It should be noted that the ECT inverse problem is underdetermined and ill-conditioned, therefore it is solved iteratively using optimization methods. The number of data points in the capacitance measurement vector is much smaller than the number of data points in the unknown dielectric constant vector, the number of equations is less than the number of unknowns, and the solution is not unique, thus exhibiting underdeterminism. The sensitivity matrix is ​​non-invertible and has a very large condition number. This means that even small errors (noise) in the capacitance measurement vector can cause huge oscillations and distortions in the dielectric constant vector solution, making direct solution extremely unstable, thus exhibiting ill-conditioned behavior.

[0098] Specifically, the reverse process for solving the dielectric constant vector is as follows: The dielectric constant is solved using the Tikhonov regularization method to obtain an initial dielectric constant vector; based on the initial dielectric constant vector, a fine-tuning process is performed using the Tikhonov quasi-Newton iterative algorithm to obtain the final dielectric constant vector. Both the Tikhonov regularization method and the Tikhonov quasi-Newton iterative algorithm are well-known techniques and will not be elaborated upon here.

[0099] The process of solving for the initial dielectric constant using the Tikhonov regularization method is as follows:

[0100] The first step is to define the objective function to be minimized, which can be expressed by the following formula:

[0101]

[0102] In the formula, Represents the sensitivity matrix. Represents a vector of capacitance measurements. Represents the dielectric constant vector. Represents the 2-norm symbol. Represents the square of the L2 norm. This represents the function that takes the minimum value. This represents a regularization matrix (usually an identity matrix or some kind of difference matrix). Represents the regularization parameter. This represents minimizing the objective function, i.e., taking the dielectric constant vector corresponding to the minimum objective function.

[0103] in, Represents the residual vector. This represents the data fidelity term, calculates the sum of squared residuals, and ensures that the solved image matches the measurement data. This represents a regularization term (penalty term) that penalizes certain characteristics of the solution (such as the degree of non-smoothness) to guide the solution to conform to the expected prior information. The regularization matrices are all pre-defined; in this embodiment, the regularization parameters... The maximum singular value in the Singular Value Decomposition (SVD) of the sensitivity matrix; Singular value decomposition is a well-known technique and will not be described in detail here.

[0104] The initial dielectric constant vector is determined by minimizing the objective function; the derivation process for obtaining the initial dielectric constant vector is as follows:

[0105] The first step is to expand the objective function to its squared form; the formula is as follows:

[0106]

[0107] In the formula, the superscript T in the parentheses indicates the transpose symbol.

[0108] The second step is to expand the parentheses. The specific formula is as follows:

[0109]

[0110]

[0111] The third step is... Taking the derivative and setting it to zero, we obtain the following formula:

[0112]

[0113] The fourth step is to simplify and combine like terms, resulting in the following formula:

[0114]

[0115] Finally obtained

[0116] At this point, As the initial dielectric constant vector.

[0117] Based on the initial dielectric constant vector, the Tikhonov quasi-Newton iterative algorithm is used for fine-tuning to obtain the final dielectric constant vector; the derivation process for obtaining the final dielectric constant vector is as follows:

[0118] The direction of the fastest descent of the function value is the negative gradient direction at the current point (i.e., the direction of the fastest descent of the function is the negative gradient direction). Therefore, the iterative formula can be written as:

[0119]

[0120] Will be The result after differentiation, substituted into the equation, is:

[0121]

[0122] In the formula, This represents the dielectric constant vector calculated during the r-th iteration. This represents the dielectric constant vector calculated during the (r+1)th iteration. It should be noted that, in this embodiment... The Laplace operator or difference operator (not the difference or change) is used to represent the expression for the solution. A second-order smoothing constraint (i.e., a penalty curvature) is applied. In this embodiment, the maximum number of iterations is set to 100; however, no specific limit is imposed, and implementers can adjust it according to specific circumstances.

[0123] It's important to note that the main purpose of introducing second-order iterative algorithms (such as the quasi-Newton method) in solving the inverse problem of capacitance tomography (ECT) is to accelerate convergence and improve image reconstruction accuracy. Compared to first-order gradient methods (such as the steepest descent method), second-order methods utilize the curvature information of the objective function (Hessian matrix or its approximation) to construct a better update direction, enabling them to approximate the true solution in fewer iterations and effectively overcome the ill-conditioned and underdetermined nature of the ECT inverse problem. The benefits are: firstly, a significantly improved convergence speed, especially suitable for high-resolution imaging or real-time detection scenarios; secondly, higher spatial resolution and clearer edges in the reconstructed image, allowing for more accurate identification of defect locations and shapes; and thirdly, the addition of a regularization term reduces detail loss caused by excessive smoothing while maintaining stability.

[0124] Thus, the final dielectric constant vector is obtained through the above method.

[0125] After iterative convergence, the final dielectric constant vector is mapped back to the finite element mesh to complete image reconstruction and identify regions with abnormal dielectric constants.

[0126] Step S5: Defect identification and verification.

[0127] It should be noted that, in order to evaluate the effectiveness and accuracy of the proposed simulation calculation method and image reconstruction algorithm in actual defect detection, typical defects (such as air gaps) with known locations, shapes and sizes are preset in the refined model. The imaging results of different reconstruction algorithms (such as the Tikhonov regularization method and the Tikhonov quasi-Newton iterative algorithm) are compared to verify the method's ability to identify small-sized defects, thereby proving the feasibility and superiority of the method in non-destructive testing of coaxial heterostructures.

[0128] Specifically, a cuboid air gap defect was set in the insulating layer (dielectric constant was set to 3, normally 2.3); the imaging effects of the Tikhonov regularization method and the Tikhonov quasi-Newton iterative algorithm were compared to verify the method's ability to identify small-sized defects (minimum recognition area ratio of 5%).

[0129] Specific implementation examples are as follows:

[0130] (1) Four-layer refined discretization of geometric structure: This invention breaks through the limitation of traditional detection models that simplify cables into a single insulating medium. Based on the actual physical distribution of high-voltage cables, a four-layer coaxial heterogeneous geometric model is constructed in the three-dimensional simulation domain. The model is set from the inside out as follows: conductor layer, conductor semi-conductive shielding layer, XLPE main insulation layer, and insulating semi-conductive shielding layer. The radius of the conductor layer is 3.05cm, the radius of the conductor semi-conductive shielding layer is 3.244cm, the radius of the XLPE main insulation layer is 6.044cm, and the radius of the insulating semi-conductive shielding layer is 6.174cm. The geometric radii of each layer strictly follow the actual production standards of cables to ensure that the model has full-scale characteristics, thereby accurately simulating the electric field coupling effect between the shielding layer (millimeter-level thin layer) and the insulation layer (centimeter-level thick layer) in a large span space. Among them, XLPE (Cross-linked Polyethylene) is a thermosetting plastic. It is made by transforming the linear molecular structure of polyethylene into a three-dimensional network structure through chemical or radiation methods, so that it does not melt at high temperatures. It has excellent electrical insulation properties, heat resistance and mechanical strength, and is widely used as the main insulation material for high-voltage cables.

[0131] (2) Physical parameter mapping of heterogeneous materials: According to the electrical characteristics of each layer of material, the present invention independently assigns electromagnetic field simulation parameters to them: the main insulating layer is set with a relative permittivity of 2.3, and for the conductor semiconducting shielding layer and the insulating semiconducting shielding layer, according to their semiconducting polymer characteristics, the relative permittivity is uniformly set to 10, and a non-zero conductivity of 1S / m is assigned.

[0132] Image reconstruction using cable insulation defects as an example:

[0133] To verify the effectiveness of the method proposed in this invention in actual detection, this embodiment takes a typical early insulation defect of a high-voltage cable as an example and demonstrates the decisive role of the accuracy of the forward model on the quality of the reverse imaging through comparative analysis.

[0134] Defect model setup and operating condition simulation;

[0135] In the fully detailed model of "conductor layer - conductor semiconducting shielding layer - insulating layer - insulating semiconducting shielding layer" constructed in this invention, specifically as follows: Figure 3 As shown, a typical fault was designed for the section between the inner shielding layer and the insulation layer, where defects are most likely to occur in the cable insulation structure. A cuboid air gap defect was created, and the dielectric constant of the defect area was set to 3, compared with the normal XLPE dielectric constant of 2.3. The location of the insulation defect is shown in the figure. Figure 3 As shown. First, the length of the cuboid defect is set to 2.5cm and the width to 1.5cm, and its area accounts for approximately 9.84% of the total cable cross-sectional area. Then, inverse problem image reconstruction is performed.

[0136] Comparison of inverse problem image reconstruction algorithms;

[0137] Based on the sensitivity matrix extracted in this invention, Tikhonov regularization and Tikhonov quasi-Newton iterative algorithm were used for image reconstruction, and their defect recognition capabilities at coaxial heterogeneous interfaces were compared.

[0138] 1) Tikhonov regularization: Although it can initially identify the location of defects, it is limited by the "smoothing effect" of the regularization term, resulting in a diffuse phenomenon at the edges of the reconstructed target, such as... Figure 4 As shown.

[0139] 2) Tikhonov Quasi-Newton Iterative Algorithm: This algorithm demonstrates superior imaging performance compared to the former. Through multiple rounds of residual approximation, the reconstructed energy is highly focused on the defect center, restoring the cuboid contour of the defect, as shown below. Figure 5 As shown.

[0140] Then, by reducing the size of the aforementioned cuboid insulation defect, and after multiple simulations, it was found that the smallest recognizable cuboid air gap defect, with an area ratio of only 5%, was imaged as follows. Figure 6 , 7 As shown.

[0141] This concludes the embodiment.

[0142] A second aspect of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a tomographic imaging simulation calculation method for potential continuity constraints of coaxial heterostructures.

[0143] A third aspect of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a tomographic imaging simulation calculation method oriented towards potential continuity constraints of coaxial heterostructures.

[0144] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0145] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0146] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0147] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A tomographic imaging simulation calculation method for potential continuity constraints in coaxial heterostructures, characterized in that, include: Construct a refined model of the coaxial heterogeneous structure; The parameters of each independent material layer in the refined model of the coaxial heterostructure were determined; these parameters include dielectric constant and electrical conductivity. A refined model of the coaxial heterostructure is used to divide the coaxial heterostructure into several finite element meshes. All heterogeneous material interfaces are identified through these meshes. Two types of boundary constraints are applied to the interfaces to obtain the potential values ​​of all nodes in the entire solution domain. Each mesh element contains several nodes. Based on the potential values ​​of all nodes in the entire solution domain, a forward simulation is performed using the finite element method to extract the electric field intensity at the centroid of each mesh element. Construct a sensitivity matrix based on the electric field strength; The capacitance data of the coaxial heterostructure is obtained through an electrode capacitance sensor and a capacitance measurement value vector is formed. The dielectric constant vector is obtained by inversely solving the capacitance measurement vector and the sensitivity matrix; The image is reconstructed by mapping the dielectric constant vector back to the finite element mesh, and the location of the defect is displayed.

2. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 1, characterized in that, The refined model of the coaxial heterostructure includes a conductor layer, a conductor semiconducting shielding layer, an insulating layer, and an insulating semiconducting shielding layer.

3. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 1, characterized in that, The process of identifying all heterogeneous material interfaces is as follows: In a finite element method for a multi-layered coaxial heterogeneous structure, the interface between heterogeneous materials is identified by determining whether the material numbers of adjacent mesh elements are different.

4. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 1, characterized in that, The process of obtaining the potential values ​​of all nodes in the entire solution domain is as follows: At the interface of heterogeneous materials, two types of boundary constraints are explicitly applied; the two types of boundary constraints include potential continuity constraints and flux balance constraints. The initial global stiffness matrix and right-hand vector are obtained by assembling using the finite element method, and then corrected by degree-of-freedom coupling or penalty function method to obtain the corrected global stiffness matrix and right-hand vector after applying constraints. A new system of algebraic equations is formed using the potential vector to be determined, the global stiffness matrix corrected after applying constraints, and the right-hand side vector; the new algebraic equations are specifically expressed as follows: In the formula, This represents the global stiffness matrix after constraints are applied. This represents the vector of potential values ​​to be determined for all nodes. This represents the right-hand vector that has been modified after the constraint has been applied; The potentials of all nodes in the entire solution domain are determined by using the vector of potential values ​​to be determined for all nodes.

5. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 1, characterized in that, The process of constructing the sensitivity matrix includes: The sensitivity coefficient of each grid cell is obtained by performing a vector dot product based on the electric field intensity; the sensitivity matrix is ​​then constructed using the sensitivity coefficients of all grid cells.

6. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 1, characterized in that, The process of obtaining the capacitance measurement value vector includes: The capacitance data of the coaxial heterostructure is acquired by using an electrode capacitance sensor and a multi-electrode rotation excitation mode, and the capacitance measurement values ​​of all independent electrode pairs are obtained. The capacitance measurement values ​​of all electrode pairs are then combined into a capacitance measurement value vector.

7. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 1, characterized in that, The process of solving for the dielectric constant vector is as follows: The specific process of inversely solving for the dielectric constant vector is as follows: the dielectric constant is solved using the Tikhonov regularization method to obtain the initial dielectric constant vector; based on the initial dielectric constant vector, the Tikhonov quasi-Newton iterative algorithm is used for fine-tuning to obtain the final dielectric constant vector.

8. The tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures according to claim 5, characterized in that, The process of obtaining the sensitivity coefficient of each grid cell includes: In the formula, This represents the sensitivity coefficient of the k-th grid cell under the combination of excitation electrode i and measurement electrode j. This represents the integral area of ​​the k-th grid cell. Denotes an integral infinitesimal element. This represents the coordinates of the center point of the k-th grid cell. This represents the vector mean of the electric field intensity within the k-th grid cell when only the excitation electrode i is subjected to a voltage. This represents the vector mean of the electric field intensity within the k-th grid cell when only electrode j is subjected to voltage. This represents the voltage amplitude of the excitation electrode i. This represents the voltage amplitude of the measuring electrode j.

9. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the tomographic imaging simulation calculation method for potential continuity constraint of coaxial heterostructures as described in any one of claims 1-8.

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