Method and apparatus for acquiring electrical capacitance tomography results

Abstract

The application discloses the technical field of capacitance tomography, and discloses a capacitance tomography result acquisition method and device. The application comprises the following steps: constructing a negative correlation physical model based on the electrostatic field boundary condition, the energy minimization principle and the electric field refraction law of the pipe wall-medium interface; performing global space discretization processing on the pipe wall area and the pipe medium area to obtain a calculation grid model; performing dielectric constant disturbance simulation and response feature extraction on each pixel unit, generating sensitivity feature data and constructing a global coverage sensitivity matrix; establishing a linear forward mapping model of the medium distribution and the capacitance measurement value; combining the global sensitivity matrix and the forward model to perform inversion calculation and imaging reconstruction on the measured capacitance data, and obtaining the capacitance tomography result. The application effectively compensates the pipe wall shielding loss, improves the resolution and boundary restoration accuracy of the capacitance tomography under the thick pipe wall working condition, and is suitable for medium distribution detection of industrial thick wall pipelines.

Description

Technical Field

[0001] This application relates to the field of capacitance tomography technology, and in particular to a method and apparatus for acquiring capacitance tomography results. Background Technology

[0002] With the rapid development of industries such as petroleum, chemical, and power, thick-walled pipelines are widely used for fluid transportation and process monitoring under high pressure, high temperature, and strong corrosion conditions. Capacitive tomography, as a non-invasive, radiation-free, and fast-response process imaging technology, has become an important means of detecting the distribution of media within pipelines.

[0003] Current capacitance tomography methods typically construct sensitivity matrices only for the dielectric region inside the pipe, neglecting the significant impact of the thick pipe wall on the electric field distribution. While this method achieves good imaging results with thin pipe walls, under thick-walled, high-resistivity shielding conditions, the pipe wall, as a high-dielectric-constant medium, exerts a strong electric field constraint, confining most electric field lines within the pipe wall. This results in a significant reduction in the electric field intensity in the central region of the pipe, leading to highly uneven sensitivity distribution. Furthermore, existing methods do not consider the negative correlation between capacitance and the dielectric constant of the internal dielectric under thick pipe walls, which can easily lead to polarity errors, resulting in distorted imaging reconstructions that fail to accurately reflect the true dielectric distribution inside the pipe.

[0004] Therefore, how to effectively overcome the electric field shielding effect of thick tube walls, construct an accurate sensitivity matrix covering the entire tube wall and interior, and improve the resolution and accuracy of capacitance tomography under thick tube wall conditions is an urgent problem to be solved. Summary of the Invention

[0005] In view of this, the method and apparatus for acquiring capacitance tomography results provided in this application can effectively overcome the electric field shielding effect of thick tube walls, construct an accurate sensitivity matrix covering the entire tube wall and interior, and improve the resolution and accuracy of capacitance tomography under thick tube wall conditions. The method and apparatus for acquiring capacitance tomography results provided in this application are implemented as follows: This application provides a method for obtaining capacitance tomography results, comprising: Based on the electrostatic field boundary conditions, the principle of energy minimization, and the electric field refraction law at the tube wall-dielectric interface, a physical model of the negative correlation between capacitance and dielectric constant of the internal dielectric under thick tube wall conditions is constructed. Based on the negative correlation physical model, the pipe wall region and the internal medium region are discretized in the whole domain space to obtain a computational grid model. The dielectric constant perturbation simulation and response feature extraction are performed on each pixel unit in the computational grid model to obtain sensitivity feature data; The sensitivity feature data are processed by matrix construction to obtain a global sensitivity matrix covering the pipe wall region and the medium region inside the pipe; Based on the global sensitivity matrix, a linear forward mapping model between dielectric distribution and capacitance measurement is established. Based on the global sensitivity matrix and the linear forward mapping model, a regularized imaging algorithm is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data to obtain capacitance tomography results under thick pipe wall conditions.

[0006] In some embodiments, the construction of a negative correlation physical model between capacitance and dielectric constant of the internal dielectric under thick-wall conditions, based on electrostatic boundary conditions, the principle of energy minimization, and the electric field refraction law at the tube wall-dielectric interface, includes: The electrostatic field boundary conditions, the energy minimization principle, and the electric field refraction law at the pipe wall-dielectric interface are analyzed and processed to obtain the electric field path distribution and transmission loss characteristics under the thick pipe wall condition. By analyzing the electric field path distribution, the transmission loss characteristics, and the dielectric constant of the internal medium, the variation law of the total effective electric flux density is obtained. The variation law of the total effective electric flux density was correlated and derived to obtain a negative correlation trend; The negative correlation trend was verified by finite element simulation, and a physical model of the negative correlation between capacitance and dielectric constant of internal medium under thick pipe wall conditions was obtained.

[0007] In some embodiments, the step of performing global spatial discretization processing on the pipe wall region and the internal medium region based on the negative correlation physical model to obtain a computational grid model includes: The computational domain of the negatively correlated physical model is defined to obtain a global computational domain that includes both the pipe wall region and the internal medium region. The global computational domain is divided into grid cells to obtain multiple independent pixel cells; The initial parameters of the dielectric constants of the multiple independent pixel units are uniformly set to obtain the basic calculation parameters; The global computational domain, the multiple independent pixel units, and the basic computational parameters are integrated to obtain a computational grid model.

[0008] In some embodiments, the step of performing dielectric constant perturbation simulation and response feature extraction on each pixel unit in the computational grid model to obtain sensitivity feature data includes: The dielectric constant increment is applied to each pixel unit in the computational grid model to obtain the pixel perturbation simulation model; Finite element simulation and difference calculation are performed on the pixel perturbation simulation model to obtain the capacitance response difference corresponding to each pixel unit; The polarity of the capacitance response difference corresponding to each pixel unit is distinguished and marked to obtain sensitivity feature data.

[0009] In some embodiments, the matrix construction processing of the sensitivity feature data to obtain a global sensitivity matrix covering the pipe wall region and the internal medium region includes: The sensitivity feature data is matched with each pixel unit in the computational grid model to obtain a set of sensitivity coefficients with spatial coordinate labels. The set of sensitivity coefficients with spatial coordinate markings is arranged according to a preset matrix dimension to obtain an initial sensitivity matrix covering the pipe wall region and the medium region inside the pipe. The dielectric distribution-capacitance measurement mapping relationship of the initial sensitivity matrix is ​​subjected to consistency verification processing to obtain the verified sensitivity matrix; The verified sensitivity matrix is ​​then format-normalized to obtain the global sensitivity matrix.

[0010] In some embodiments, establishing a linear forward mapping model between the dielectric distribution and the capacitance measurement value based on the global sensitivity matrix includes: The global sensitivity matrix is ​​analyzed to obtain the mapping parameters; The correspondence between the medium distribution vector inside the pipe and the electrode capacitance measurement vector is defined and processed to obtain the input and output parameters of the forward model; The global sensitivity matrix, the mapping relationship parameters, and the input and output parameters are integrated to obtain an initial linear forward mapping model. The linear correlation and physical consistency of the initial linear forward mapping model are verified to obtain the linear forward mapping model.

[0011] In some embodiments, the step of performing inversion calculations and imaging reconstruction processing on measured capacitance data using a regularized imaging algorithm based on the global sensitivity matrix and the linear forward mapping model to obtain capacitance tomography results under thick-walled conditions includes: The measured capacitance data is denoised and standardized to obtain standardized measured capacitance data. The standardized measured capacitance data, the global sensitivity matrix, and the linear forward mapping model are processed to construct inversion equations, resulting in capacitance tomography inversion equations. The capacitance tomography inversion equation is solved using a regularized imaging algorithm to obtain initial medium distribution data. The initial medium distribution data and the positive and negative weights of the global sensitivity matrix are subjected to polarity correction and pipe wall shielding loss compensation to obtain the corrected medium distribution data. The corrected medium distribution data is subjected to imaging rendering and sharpness optimization processing to obtain capacitance tomography results under thick pipe wall conditions.

[0012] This application provides an apparatus for acquiring capacitance tomography results, comprising: The processing module is used to construct a physical model of the negative correlation between capacitance and dielectric constant of the internal medium under thick pipe wall conditions, based on electrostatic boundary conditions, the principle of energy minimization, and the electric field refraction law at the pipe wall-dielectric interface. The processing module is also used to perform global spatial discretization processing on the pipe wall region and the pipe medium region based on the negative correlation physical model to obtain a computational grid model; The processing module is also used to perform dielectric constant perturbation simulation and response feature extraction on each pixel unit in the computational grid model to obtain sensitivity feature data; The processing module is also used to perform matrix construction processing on the sensitivity feature data to obtain a global sensitivity matrix covering the pipe wall region and the medium region inside the pipe. The module is used to establish a linear forward mapping model between the dielectric distribution and the capacitance measurement value based on the global sensitivity matrix; The imaging module is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data based on the global sensitivity matrix and the linear forward mapping model, using a regularized imaging algorithm to obtain capacitance tomography results under thick pipe wall conditions.

[0013] The computer device provided in this application includes a memory and a processor. The memory stores a computer program that can run on the processor. When the processor executes the program, it implements the method described in this application.

[0014] The computer-readable storage medium provided in this application embodiment stores a computer program thereon, which, when executed by a processor, implements the method described in this application embodiment.

[0015] The present application provides a method and apparatus for acquiring capacitance tomography results. This method constructs a negatively correlated physical model based on electrostatic boundary conditions, the principle of energy minimization, and the electric field refraction law at the tube wall-dielectric interface. A computational grid model is obtained by discretizing the tube wall region and the internal dielectric region across the entire spatial domain. Dielectric constant perturbation simulation and response feature extraction are performed on each pixel unit to generate sensitivity feature data and construct a sensitivity matrix covering the entire domain. A linear forward mapping model between dielectric distribution and capacitance measurements is established. The measured capacitance data is inverted and reconstructed using the global sensitivity matrix and the forward model to obtain the capacitance tomography results. This effectively overcomes the electric field shielding effect of thick tube walls, constructs an accurate sensitivity matrix covering both the tube wall and the entire internal domain, improves the resolution and accuracy of capacitance tomography under thick tube wall conditions, and solves the technical problems mentioned in the background art. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A schematic diagram illustrating the implementation process of a method for obtaining capacitance tomography results provided in an embodiment of this application; Figure 2 A schematic diagram illustrating the implementation process of obtaining a negatively correlated physical model, provided in an embodiment of this application; Figure 3 A schematic diagram of the structure of a device for acquiring capacitance tomography results provided in an embodiment of this application; Figure 4 A schematic diagram showing the direction of electric field lines with a dielectric constant of 1 inside a pipe, provided in an embodiment of this application; Figure 5 A schematic diagram showing the direction of electric field lines with a dielectric constant of 2 inside a pipe, provided in an embodiment of this application; Figure 6 A schematic diagram illustrating the relationship between the electric field strength, capacitance value, and dielectric constant of the medium inside the pipe between the excitation electrode and the adjacent measuring electrode provided in this embodiment of the application. Figure 7 A single medium distribution location diagram provided for an embodiment of this application; Figure 8 A schematic diagram illustrating imaging of different media sizes provided in an embodiment of this application; Figure 9 This is a schematic diagram of an imaging medium with a resolution of 7% provided for an embodiment of this application. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0020] Figure 1 This is a schematic flowchart illustrating the implementation of a method for obtaining capacitance tomography results according to an embodiment of this application, including steps 101 to 106. Wherein, Figure 1 This is merely one execution order shown in the embodiments of this application and does not represent the only execution order of a method for obtaining capacitance tomography results. Where the final result can be achieved, Figure 1 The steps shown can be performed in parallel or in reverse order.

[0021] Step 101: Based on the electrostatic field boundary conditions, the principle of energy minimization, and the electric field refraction law at the pipe wall-dielectric interface, a physical model of the negative correlation between capacitance and dielectric constant of the internal dielectric under thick pipe wall conditions is constructed.

[0022] In this embodiment, the refraction characteristics of electric field lines at the pipe wall-dielectric interface are analyzed based on the electrostatic field boundary conditions and the principle of energy minimization. The electrostatic field is applied in two different isotropic media (with dielectric constants of [insert dielectric constants here]). and At the interface between the two sides, the boundary conditions of Maxwell's equations must be satisfied:

[0023] in, and These are the tangential and normal components of the electric field intensity, respectively. Let be the free charge density at the interface. Without considering the interface charge... When the electric field line is zero, it will refract when it passes through the interface, and its angle of incidence will be zero. With the angle of refraction The angle between the angle and the normal satisfies the law of refraction:

[0024] Therefore, it can be seen that when electric field lines enter a medium with a high dielectric constant from a medium with a low dielectric constant ( ),but The electric field lines deviate from the normal. According to the principle of minimizing electrostatic energy, the total energy of the system tends to be at a minimum. Since high-dielectric-constant media store energy more efficiently per unit volume, the electric field lines will spontaneously converge towards the high-dielectric-constant region. Based on this distribution law, the electric field confinement effect generated by the thick tube wall as a high-dielectric-constant medium is analyzed. The working principle of capacitance tomography is based on the quasi-static electromagnetic field theory, and the electric field distribution inside the sensor can be represented by the Poisson equation:

[0025] in, It is the dielectric constant distribution at spatial location r; This refers to the spatial potential distribution. The boundary condition is that in a sensor with N electrodes, a voltage of magnitude U is applied to the excitation electrode, while no voltage is applied to the other electrodes, and all electrodes except the detection electrode are grounded. An ECT sensor with N electrodes can be obtained... A capacitor. Under the condition of a thick tube wall (assuming the tube wall material is PEEK (Poly Ether Ether Ketone), with a dielectric constant of 3.2), the tube wall is not only a physical support but also an important guiding channel for the electric field. The paths of the electric field lines generated by the excitation electrode to the adjacent measuring electrode are divided into two types: one where the vast majority of electric field lines are completely closed inside the thick tube wall, with a short geometric path and high coupling strength; and the other where a few electric field lines penetrate the tube wall and pass through the internal medium, with a long geometric path. Distinguish between the closed electric field line paths within the tube wall region and the electric field line paths penetrating the tube wall-medium interface and entering the internal medium region, and calculate the difference in electric field transmission loss between the two paths. Based on path loss analysis, the competing mechanism between the shielding effect and the dielectric effect caused by changes in the dielectric constant of the internal medium is analyzed: The first is the shielding effect, where enhanced interface refraction forces high-density electric field lines, originally closed by the thick pipe wall, to detach from the wall and enter the central region with a longer geometric path. The second is the dielectric effect, where although the number of electric field lines entering the pipe increases, these lines must pass through a three-layer structure of "pipe wall-dielectric-pipe wall" to reach the measuring electrode. The variation law of the total effective current flux density on the measuring electrode surface as the dielectric constant of the internal medium increases is derived. Combining the integral relationship between induced charge and effective current flux, and the definition of capacitance, the negative correlation trend of the capacitance values ​​of adjacent electrodes with changes in the dielectric constant of the internal medium is derived. The essence of induced charge is the integral of the effective current flux on the measuring electrode surface, and its expression is as follows:

[0026] The definition of capacitance is:

[0027] Where Q is the total free charge on the surface of the measuring electrode; S is any closed integral surface of the measuring electrode; D is the electric displacement vector; and E is the electric field intensity vector. Let be the dielectric constant of the medium inside the pipe; dA is the area vector of a infinitesimal element on the closed surface S. The trend of capacitance variation is consistent with the trend of induced charge variation. Finite element simulation was used to verify the electric field distribution and electrode capacitance variation under different dielectric constants of the internal medium, confirming the correctness of the negative correlation trend. Figure 4 and Figure 5 As shown. Figure 4 The dielectric constant inside the pipe is 1. Figure 5 The dielectric constant inside the pipe is 2. It can be observed that when the dielectric constant of the internal medium increases, the electric field lines that were originally highly concentrated inside the PEEK pipe wall decrease and shift and converge towards the central axis of the pipe. This reduces the effective electric flux density that reaches the surface of the measuring electrode only through the pipe wall. Although the electric field line density of the medium entering the pipe increases, the effective electric flux density of the electric field lines entering the pipe will still decrease after long-distance transmission and secondary penetration of the thick pipe wall, due to the attenuation of the point charge field strength with the square of the distance.

[0028] This application uses finite element simulation to analyze the relationship between the electric field intensity at the center of the measuring electrode adjacent to the excitation electrode, the capacitance value of the adjacent electrodes, and the dielectric constant of the medium inside the pipe. Figure 6 As shown, it can be observed that as the dielectric constant of the medium increases, the electric field strength gradually decreases, and the amount of charge accumulated on the surface of the measuring electrode gradually decreases. Therefore, the capacitance value exhibits a gradually decreasing negative correlation trend. Finally, a physical model of the negative correlation between capacitance and the dielectric constant of the internal medium under thick pipe wall conditions is constructed.

[0029] Step 102: Based on the negative correlation physical model, the pipe wall region and the medium inside the pipe are discretized in a global spatial manner to obtain a computational grid model.

[0030] In this embodiment, a global computational domain is defined, encompassing both the pipe wall region and the internal medium region, based on the electric field range determined by the negative correlation physical model. The global computational domain is meshed using triangular or quadrilateral elements to obtain multiple independent pixel units. The initial dielectric constant parameter for each pixel unit is uniformly set: the dielectric constant of the pipe wall region pixel units is set to the dielectric constant value of the pipe wall material (e.g., 3.2 for PEEK material), and the dielectric constant of the internal medium region pixel units is set to the dielectric constant value of the reference medium. The global computational domain, the partitioned pixel units, and the set initial dielectric constant parameters are integrated to obtain a computational mesh model suitable for thick pipe wall conditions.

[0031] Step 103: Perform dielectric constant perturbation simulation and response feature extraction on each pixel unit in the computational grid model to obtain sensitivity feature data.

[0032] In this embodiment, individual pixel units in the computational grid model are selected sequentially, and a preset dielectric constant increment is applied to them while keeping the dielectric constant parameters of all other pixel units unchanged, thus constructing a single-pixel perturbation simulation model. Finite element electrostatic field simulation is performed on this single-pixel perturbation simulation model to extract the capacitance response data of all adjacent probe electrode pairs. The difference between this capacitance response data and the reference capacitance data without dielectric constant perturbation is calculated to obtain the capacitance response difference corresponding to the pixel unit. Based on perturbation theory, the sensitivity of a spatial pixel can be expressed as the partial derivative of the capacitance with respect to the dielectric constant:

[0033] in, This represents the sensitivity coefficient for the corresponding spatial pixel k. This is the change in the dielectric constant of the medium; To increase the dielectric constant of the medium The capacitance value at that time; The dielectric constant of the medium is The capacitance value.

[0034] According to electrostatic field theory, the capacitance between adjacent electrodes can be characterized by the total electrostatic energy within the field:

[0035] in, To measure the mutual capacitance between electrode i and excitation electrode j; Let r be the dielectric constant distribution at spatial location r.

[0036] Let be the magnitude of the space potential gradient; U be the excitation voltage; This refers to the internal region of the pipe. When the distribution of the medium inside the pipe is slightly disturbed, the change in capacitance can be derived using the variational principle of energy:

[0037] in, This represents the change in capacitance. The initial electric field vector magnitude when no dielectric disturbance occurs; Let be the vector representing the change in electric field due to the change in dielectric (i.e., the new electric field minus the old electric field). Extending this formula to discrete space, defining the sensitivity of a spatial pixel as the partial derivative of the capacitance with respect to the permittivity, it can be expressed as:

[0038] The inner wall of the tube near the electrode, The modulus is extremely high and its sensitivity to changes in the medium is low; the first term dominates, resulting in positive sensitivity. In the core region of the pipe, due to the "flow-limiting effect" of the thick pipe wall and dilution over long distances, the square-order attenuation of the field strength modulus—the second term—masks the medium polarization gain on a massive scale. This causes a reversal of the sensitivity polarity in the central region, forming a negative sensitivity zone. The above process of applying incremental dielectric constants, finite element simulation, and calculating the capacitance response difference is repeated for all pixel units in the computational mesh model to obtain a set of full-pixel capacitance response differences. Each difference in the full-pixel capacitance response difference set is then polarized and labeled to obtain polarized sensitivity feature data.

[0039] Step 104: Perform matrix construction processing on the sensitivity feature data to obtain the global sensitivity matrix covering the pipe wall region and the medium region inside the pipe.

[0040] In this embodiment, the polarity-marked sensitivity feature data is matched one-to-one with the spatial location of each pixel unit in the computational grid model, and a corresponding spatial coordinate marker is added to each sensitivity coefficient, resulting in a set of sensitivity coefficients with spatial coordinate markers. The dimension of the sensitivity matrix is ​​determined based on the number of electrode pairs and the number of pixel units. The set of sensitivity coefficients with spatial coordinate markers is arranged according to the preset matrix dimension to obtain an initial sensitivity matrix covering the pipe wall region and the pipe internal medium region. The consistency of the medium distribution-capacitance measurement mapping relationship of the initial sensitivity matrix is ​​verified, abnormal sensitivity coefficients are removed and corrected, resulting in a verified sensitivity matrix. The verified sensitivity matrix is ​​then standardized to meet the requirements of subsequent forward modeling and inverse calculations, ultimately yielding the global sensitivity matrix.

[0041] Step 105: Based on the global sensitivity matrix, establish a linear forward mapping model between the dielectric distribution and the capacitance measurement value.

[0042] In this embodiment, the physical meaning and dimensional information of the elements of the global sensitivity matrix are analyzed to clarify the influence of the dielectric constant change of a specific pixel unit on the capacitance value of a specific electrode pair for each matrix element. A dielectric distribution vector within the tube is defined, whose elements are the dielectric constant values ​​of each pixel unit; an electrode capacitance measurement vector is defined, whose elements are the capacitance measurement values ​​of each adjacent electrode pair. The global sensitivity matrix, dielectric distribution vector, and electrode capacitance measurement vector are integrated to establish an initial linear forward mapping model.

[0043] in, = The normalized capacitance vector g is the required dielectric constant distribution vector, i.e., the pixel grayscale value of the image; S is the sensitivity matrix. This model describes the linear relationship between the dielectric distribution vector and the electrode capacitance measurement vector through the global sensitivity matrix. The linearity and physical consistency of the initial linear forward mapping model are verified to ensure that the model can accurately reflect the correspondence between the dielectric distribution and capacitance measurement values ​​under thick pipe wall conditions, thus obtaining the final linear forward mapping model.

[0044] Step 106: Based on the global sensitivity matrix and the linear forward mapping model, a regularized imaging algorithm is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data to obtain capacitance tomography results under thick pipe wall conditions.

[0045] In this embodiment, the measured capacitance data acquired by the capacitance tomography system is denoised and standardized to eliminate noise interference and system errors, resulting in standardized measured capacitance data. Based on a linear forward mapping model, the standardized measured capacitance data and the global sensitivity matrix are substituted into the inversion equation to construct the capacitance tomography inversion problem. The inversion equation is solved using regularized imaging algorithms such as Tikhonov regularization or L1 regularization to obtain initial dielectric distribution data. The polarity of the initial dielectric distribution data is corrected using the positive and negative weights in the global sensitivity matrix, while simultaneously compensating for the electric field shielding loss caused by the thick pipe wall, resulting in corrected dielectric distribution data. The corrected dielectric distribution data is then subjected to imaging rendering and sharpness optimization processing, converting it into a visualized grayscale or pseudo-color image, ultimately yielding the capacitance tomography results under thick pipe wall conditions.

[0046] This application utilizes a finite element simulation platform to establish a pipeline model for verification. The model has an outer diameter of 57 mm, an inner diameter of 31 mm, and a wall thickness of 26 mm. The pipe wall is made of PEEK material with a dielectric constant of 3.2. Several typical media distribution conditions were set up, including an empty pipe condition (the pipe is completely filled with air) and a full pipe condition (the pipe is completely filled with the medium under test) as a reference. In addition, other conditions were also set up... Figure 7 The typical non-uniform distribution condition shown is that a single high dielectric constant medium is placed at different radial positions inside the pipe to illustrate the effect of the above sensitivity matrix on image reconstruction.

[0047] according to Figure 7 Operating conditions: Different sizes of media are used, assuming the ratio of the media radius to the pipe inner diameter is... ,set up With sensitivity values ​​of 20%, 15%, and 10%, the common Tikhonov regularization method was used to image the medium using the aforementioned sensitivity matrix. The imaging results are as follows: Figure 8 As shown.

[0048] pass Figure 8 It can be observed that the high dielectric response region in the reconstructed image has a high degree of consistency with the set dielectric distribution. Through comparison... , , The image, along with As the medium size decreases, the image contrast exhibits a non-linear decay, with the pixel saturation in the red core region gradually decreasing. This intuitively defines the effective detection resolution threshold. While artifacts gradually appear at the edges as the medium size decreases, the location of the medium can still be discerned. This demonstrates that using the aforementioned sensitivity matrix and common non-iterative algorithms, image reconstruction of the medium distribution inside the pipe is still possible.

[0049] Repeating the image reconstruction process, it was found that the resolution of the above sensitivity matrix under the Tikhonov regularization method was 7%, as shown below. Figure 9 As shown. (Through) Figure 9 It can be observed that there are many artifacts in the image reconstruction. The high dielectric constant region cannot present red, which represents a high value, but can only reach a yellow-green tone. The distinction between it and the dark blue background is reduced to an extremely low level, indicating that it is close to the limit of detection sensitivity. However, it can still distinguish the approximate location of the high dielectric constant medium and has basic localization ability. This result shows that the minimum resolution of the above sensitivity matrix under the Tikhonov regularization method is about 7%.

[0050] This application introduces a sensitivity matrix with negative weights to establish a polarity correction mechanism for the negative correlation characteristics of thick pipe walls during image reconstruction. Addressing the physical phenomenon of capacitance decrease due to increased medium in the pipe center, the negative weight terms in the matrix are logically mapped to the negative measurement vector, ensuring that the imaging algorithm accurately reconstructs "capacitance decrease" as "medium increase." This fundamentally corrects the bias of traditional positive definite matrices that incorrectly identify negative responses as medium deficiency, thus eliminating false low-value holes in the central region of the reconstructed image. Simultaneously, it enables spatial quantization compensation for pipe wall shielding effects and path stretching losses, significantly improving the accuracy of thick-walled sensors in reconstructing the geometric boundaries of internal targets. This ensures high fidelity imaging results under complex conditions. Simulations show that the minimum resolution of the global sensitivity matrix under the common Tikhonov regularization method is approximately 7%, and the resolution can be further improved by refining the imaging algorithm.

[0051] This application embodiment establishes a complete capacitance tomography imaging scheme adapted to thick pipe wall conditions, overcoming the limitations of traditional methods that only model the medium inside the pipe and ignore the electric field constraint and dielectric negative correlation characteristics of the thick pipe wall. Through global modeling, global sensitivity solving, and polarity-compensated inversion imaging, it corrects the imaging distortion caused by the shielding of the thick pipe wall from the physical mechanism level, significantly improving the imaging accuracy and resolution of the medium at the pipe wall boundary and the central region inside the thick pipe, and expanding the applicability of capacitance tomography in the medium detection scenarios of high temperature and high pressure thick-walled industrial pipelines.

[0052] In the above Figure 1 Based on the above, this application embodiment also provides a schematic diagram of the implementation process for obtaining a negatively correlated physical model. For example... Figure 2 As shown, steps 201 to 204 are included: Step 201 involves analyzing the electrostatic field boundary conditions, the principle of energy minimization, and the electric field refraction law at the pipe wall-dielectric interface to obtain the electric field path distribution and transmission loss characteristics under the thick pipe wall condition.

[0053] In this embodiment, based on the continuous boundary conditions of the normal electric displacement and the tangential electric field intensity of the electrostatic field, and combined with the principle of energy minimization, the refraction formula of electric field lines at the interface of media with different dielectric constants is derived, clarifying the basic law of electric field lines deflecting and converging towards the high dielectric constant region. For the thick-walled condition, the binding effect of the pipe wall material as a high dielectric constant medium on the electric field is analyzed, and all electric field line paths are divided into two categories: one is the electric field line path that is closed only within the pipe wall region and does not penetrate the pipe wall-medium interface; the other is the effective electric field line path that penetrates the pipe wall-medium interface and enters the internal medium region. The electric field energy loss and transmission efficiency of the two types of paths are calculated respectively, obtaining the electric field path distribution and transmission loss characteristics under the thick-walled condition.

[0054] Step 202 involves analyzing the electric field path distribution, transmission loss characteristics, and dielectric constant of the internal medium to obtain the variation law of the total effective electric flux density.

[0055] In this embodiment, based on the aforementioned electric field path distribution and transmission loss characteristics, two effects caused by changes in the dielectric constant of the internal medium are analyzed: first, the dielectric effect, i.e., when the dielectric constant of the internal medium increases, the electric field energy stored per unit volume increases, theoretically increasing the electric flux density on the surface of the measuring electrode; second, the shielding effect, i.e., when the dielectric constant of the internal medium increases, the electric field lines will further converge towards the pipe wall region, resulting in a decrease in the number of effective electric field lines penetrating the pipe wall into the internal medium region, and a decrease in the effective electric flux density on the surface of the measuring electrode. By quantitatively analyzing the competing relationship between the two effects, it is determined that the shielding effect dominates under the thick pipe wall condition, and thus the trend of decreasing total effective electric flux density on the surface of the measuring electrode when the dielectric constant of the internal medium increases is derived.

[0056] Step 203: The variation law of total effective electric flux density is correlated and deduced to obtain a negative correlation trend.

[0057] In this embodiment, based on Gauss's law, an integral relationship between the induced charge on the surface of the measuring electrode and the total effective current flux density is established, leading to the conclusion that a decrease in the total effective current flux density results in a decrease in the induced charge on the surface of the measuring electrode. Combining this with the basic definition of capacitance—that the capacitance value equals the ratio of the induced charge on the electrode surface to the voltage between the electrodes—under the condition of a constant voltage applied between the electrodes, a decrease in the induced charge directly leads to a decrease in the capacitance value between adjacent electrodes. Through the above correlation derivation, a negative correlation trend is finally obtained where the capacitance value of adjacent electrodes decreases as the dielectric constant of the internal medium increases.

[0058] Step 204: Perform finite element simulation verification on the negative correlation trend to obtain a physical model of the negative correlation between capacitance and dielectric constant of the internal medium under thick pipe wall conditions.

[0059] In this embodiment, a three-dimensional finite element simulation model including electrodes, pipe walls, and internal dielectric is established. Different pipe wall thickness parameters and internal dielectric dielectric constant parameters are set. A constant excitation voltage is applied between the electrodes, and the capacitance values ​​of adjacent electrode pairs under different parameter combinations are simulated and calculated. The capacitance value variation curves obtained from the simulation are compared and analyzed with the negative correlation trend derived above to verify the correctness and applicability of the negative correlation trend. Based on the verified negative correlation trend, combined with the electric field path distribution, transmission loss characteristics, and the variation law of total effective current flux density, a physical model of the negative correlation between capacitance and internal dielectric dielectric constant under thick pipe wall conditions is constructed.

[0060] This application's embodiments, by combining electrostatic field boundaries, energy minimization, and the refraction law at the interface of the medium, derive a physical model of the negative correlation between capacitance and dielectric constant from the electric field transmission mechanism. This model accurately characterizes the objective law of the competition between the bound electric field of thick-walled high-dielectric materials and the dual effects of the inner and outer media, thus overcoming the shortcomings of existing technologies that neglect the negative correlation effect of thick-walled materials and suffer from physical model distortion. The model is verified by relying on finite element simulation to ensure the physical authenticity of the model, providing a reliable underlying physical basis for subsequent global mesh generation and sensitivity calculation, and avoiding sensitivity solution deviations caused by missing mechanisms from the source.

[0061] In some embodiments, based on the negative correlation physical model, the pipe wall region and the pipe internal medium region are subjected to global spatial discretization to obtain a computational grid model, including: delineating the computational domain range of the negative correlation physical model to obtain a global computational domain including the pipe wall region and the pipe internal medium region.

[0062] Specifically, based on the electric field boundary determined in the negative correlation physical model—that is, the maximum spatial range where electric field lines can reach and generate an effective capacitive response—the geometric boundary of the global computational domain is defined. This computational domain completely covers the entire radial thickness range of the pipe wall and the entire flow area of ​​the medium inside the pipe, while reserving sufficient boundary buffer areas to eliminate boundary truncation errors, ensuring that the complete distribution of the electric field in the pipe wall and the medium inside the pipe can be accurately simulated.

[0063] Furthermore, the global computational domain is divided into grid cells to obtain multiple independent pixel cells.

[0064] Specifically, based on the pipeline's geometry and electric field distribution characteristics, triangular or quadrilateral elements are used to perform unstructured meshing of the global computational domain. Mesh refinement is applied at the pipe-medium interface to improve computational accuracy in areas with large electric field gradients; in areas with relatively uniform electric field distribution, the mesh size is appropriately increased to balance computational accuracy and efficiency. After meshing, the global computational domain is decomposed into multiple independent, non-overlapping pixel units, each corresponding to a unique spatial location.

[0065] Furthermore, the initial parameters of the dielectric constants of multiple independent pixel units are uniformly set to obtain the basic calculation parameters.

[0066] Specifically, the initial dielectric constant values ​​are set according to the region type to which the pixel unit belongs: the dielectric constant of all pixel units belonging to the pipe wall region is set to the dielectric constant value of the actual pipe wall material; the dielectric constant of all pixel units belonging to the inner medium region is set to the dielectric constant value of the reference medium. By uniformly setting the initial parameters, a consistent reference state is provided for subsequent dielectric constant perturbation simulations, ensuring the comparability and accuracy of the sensitivity calculation results.

[0067] Furthermore, the global computational domain, multiple independent pixel units, and basic computational parameters are integrated to obtain a computational grid model.

[0068] Specifically, the geometric boundary information of the entire computational domain, the spatial coordinates and geometric dimensions of each pixel unit, and the initial dielectric constant parameters of all pixel units are integrated and mapped to the corresponding electric field boundary conditions. All of the above information is organized and stored according to the standard format of finite element simulation to form a complete computational mesh model that can be directly used for subsequent dielectric constant perturbation simulation and electric field calculation.

[0069] This application embodiment defines a global computational domain including the pipe wall and the internal medium by relying on a negatively correlated physical model. This differs from the traditional discrete method that only divides the internal region of the pipe. It realizes integrated mesh modeling of the pipe wall and the medium, which fully covers the entire space where the electric field acts. It unifies the initial dielectric parameters of the pixel units and integrates them to generate a computational mesh, and unifies the benchmark simulation conditions to ensure that the calculation benchmarks for subsequent pixel perturbation simulation and sensitivity extraction are consistent, effectively reducing the system calculation errors caused by missing computational domains and inconsistent parameters.

[0070] In some embodiments, dielectric constant perturbation simulation and response feature extraction processing are performed on each pixel unit in the computational grid model to obtain sensitivity feature data, including: applying dielectric constant increment processing to each pixel unit in the computational grid model to obtain a pixel perturbation simulation model.

[0071] Specifically, following the spatial order of pixel units in the computational grid model, individual pixel units are selected sequentially as perturbation objects. A preset small increment of the dielectric constant is applied to each pixel. The value of this increment must ensure that the change in dielectric constant remains within the linear response range to avoid introducing nonlinear errors. While applying the dielectric constant increment, the dielectric constant parameters of all other pixel units are kept consistent with the basic calculation parameters, thus constructing a single-pixel perturbation simulation model for each individual pixel unit. This process is repeated until the dielectric constant increment has been applied to all pixel units in the computational grid model, resulting in a set of pixel perturbation simulation models corresponding to all pixels.

[0072] Furthermore, finite element simulation and difference calculation are performed on the pixel perturbation simulation model to obtain the capacitance response difference corresponding to each pixel unit.

[0073] Specifically, firstly, a finite element electrostatic field simulation is performed on the original computational mesh model without any dielectric constant perturbation to extract the reference capacitance data for all probe electrode pairs, which serves as a unified benchmark for subsequent difference calculations. Then, a finite element electrostatic field simulation under the same conditions is performed on each single-pixel perturbation simulation model, extracting the capacitance response data for all probe electrode pairs under that perturbation state. The capacitance response data obtained from each single-pixel perturbation simulation model is then compared with the reference capacitance data for each electrode pair, resulting in the capacitance response difference for all electrode pairs corresponding to that pixel unit. This simulation and difference calculation process is repeated to obtain the set of capacitance response differences corresponding to all pixel units in the computational mesh model.

[0074] Furthermore, the polarity of the capacitance response difference corresponding to each pixel unit is distinguished and marked to obtain sensitivity feature data.

[0075] Specifically, based on the constructed physical model of the negative correlation between capacitance and the dielectric constant of the internal medium under thick-walled conditions, the polarity of the capacitance response difference is clarified: when the dielectric constant of the pixel unit in the internal medium region increases, the corresponding capacitance response difference is negative; when the dielectric constant of the pixel unit in the pipe wall region increases, the corresponding capacitance response difference is positive. Polarity is identified for each difference data point in the capacitance response difference set, and a corresponding polarity marker is added to the data, preserving both the magnitude and polarity information of the difference. Finally, sensitivity feature data containing spatial location correspondence, numerical magnitude, and polarity information is obtained, which is used for the subsequent construction of the global sensitivity matrix.

[0076] This application embodiment can accurately separate the capacitance response corresponding to the dielectric change at each spatial location through a single-pixel successive perturbation simulation method, ensuring the accuracy of sensitivity data points; relying on the negative correlation model to mark the polarity of the capacitance difference, it distinguishes the positive and negative attributes of the sensitivity of the tube wall and the inner medium, solving the data defect of traditional sensitivity being uniformly treated as a positive value, which violates the law of electric field change in thick tube walls, and ensuring that the sensitivity data fits the real electric field response characteristics.

[0077] In some embodiments, matrix construction processing is performed on the sensitivity feature data to obtain a global sensitivity matrix covering the pipe wall region and the medium region inside the pipe. This includes: performing spatial position matching processing on the sensitivity feature data and each pixel unit in the computational grid model to obtain a set of sensitivity coefficients with spatial coordinate labels.

[0078] Specifically, the unique spatial coordinates and cell number of each pixel unit in the computational grid model are extracted. Each sensitivity feature data is then matched one-to-one with its corresponding pixel unit to ensure that each sensitivity coefficient accurately corresponds to its spatial location. During the matching process, the numerical value and polarity labeling information of the sensitivity feature data are fully preserved to avoid spatial misalignment in subsequent matrix construction due to matching errors. The final result is a set of sensitivity coefficients with spatial coordinate labels, where each element contains spatial coordinates, a sensitivity value, and polarity information.

[0079] Furthermore, the set of sensitivity coefficients with spatial coordinate markings is arranged according to a preset matrix dimension to obtain the initial sensitivity matrix covering the pipe wall region and the medium region inside the pipe.

[0080] Specifically, the number of rows in the sensitivity matrix is ​​determined based on the number of electrodes in the capacitance tomography system; the number of rows equals the total number of all adjacent detector electrode pairs. The number of columns in the sensitivity matrix is ​​determined based on the total number of pixel units in the computational grid model; the number of columns equals the sum of the number of pixel units in the tube wall region and the tube internal medium region. Following the preset electrode pair numbering order and pixel unit spatial arrangement order, the sensitivity coefficients with spatial coordinate markings are sequentially filled into the corresponding positions in the matrix. The element in the i-th row and j-th column of the matrix represents the degree of influence of the dielectric constant change of the j-th pixel unit on the capacitance value of the i-th electrode pair. After arrangement, an initial sensitivity matrix containing sensitivity information for both the tube wall region and the tube internal medium region is obtained.

[0081] Furthermore, the consistency verification process is performed on the dielectric distribution-capacitance measurement mapping relationship of the initial sensitivity matrix to obtain the verified sensitivity matrix.

[0082] Specifically, based on the constructed negative correlation physical model and electric field distribution law, the initial sensitivity matrix is ​​physically consistent with the following checks: The polarity of the sensitivity coefficients in the tube wall region and the inner medium region is checked to ensure they conform to expectations (i.e., the sensitivity coefficients in the tube wall region are positive, and those in the inner medium region are negative); the numerical distribution of the sensitivity coefficients is checked to ensure they conform to the electric field attenuation law (i.e., the sensitivity coefficients near the electrodes are larger, and those in the central region of the tube are smaller); and any abnormal sensitivity coefficients that deviate significantly from the physical laws are checked. For any abnormal coefficients found during the checks, the sensitivity data of the corresponding pixel units is recalculated for correction, invalid data is removed, and finally, a verified sensitivity matrix conforming to the physical laws is obtained.

[0083] Furthermore, the format of the verified sensitivity matrix is ​​standardized to obtain the global sensitivity matrix.

[0084] Specifically, following the unified data format requirements for subsequent linear forward mapping model construction and inversion calculations, the verified sensitivity matrix undergoes format conversion and standardization: the data type of matrix elements is unified to double-precision floating-point; the matrix storage order is adjusted to row-major; and metadata information is added to the matrix, including the number of electrode pairs, the total number of pixel units, the pixel unit division boundary between the tube wall region and the inner medium region, and the matrix construction time. The standardized global sensitivity matrix can be directly used in subsequent steps without additional format conversion, ensuring the consistency and accuracy of the calculation process.

[0085] This application embodiment binds and matches sensitivity data with pixel spatial coordinates to ensure a one-to-one correspondence between matrix coefficients and spatial positions, avoiding spatial misalignment of the sensitivity matrix; through matrix arrangement, physical consistency verification and standardization processing, a sensitivity matrix containing the entire pipe wall is constructed, overcoming the drawbacks of traditional methods that discard the pipe wall region and lack key information in the sensitivity matrix, thereby improving the integrity and reliability of the input data of the forward model.

[0086] In some embodiments, a linear forward mapping model between dielectric distribution and capacitance measurement is established based on the global sensitivity matrix, including: performing analytical processing on the global sensitivity matrix to obtain mapping relationship parameters.

[0087] Specifically, the dimensional information of the global sensitivity matrix is ​​analyzed. It is determined that the number of rows in the matrix equals the total number of all adjacent detector electrode pairs in the capacitance tomography system, and the number of columns equals the sum of the total number of pixel units in the tube wall region and the tube internal medium region in the computational grid model. The physical meaning of each element in the matrix is ​​analyzed; that is, the element in the i-th row and j-th column represents the change in capacitance of the i-th electrode pair when the dielectric constant of the j-th pixel unit changes by one unit. Through the above analysis, the mapping relationship parameter from the change in medium distribution to the change in capacitance measurement value is obtained, i.e., the sensitivity weight of each pixel unit to each electrode pair.

[0088] Furthermore, the correspondence between the medium distribution vector inside the pipe and the electrode capacitance measurement vector is defined and processed to obtain the input and output parameters of the forward model.

[0089] Specifically, a dielectric distribution vector within the tube is defined, with the same dimension as the number of columns in the global sensitivity matrix. Each element in the vector corresponds to the dielectric constant value of a pixel unit in the computational mesh model. An electrode capacitance measurement vector is also defined, with the same dimension as the number of rows in the global sensitivity matrix. Each element in the vector corresponds to the capacitance measurement value of an adjacent probe electrode pair. The input to the forward model is clearly defined as the dielectric distribution vector within the tube, and the output is the electrode capacitance measurement vector, establishing a framework for the correspondence between the input and output.

[0090] Furthermore, the global sensitivity matrix, mapping parameters, and input / output parameters are integrated to obtain the initial linear forward mapping model.

[0091] Specifically, based on the principle of linear superposition—that is, the total capacitive response generated by the combined effect of the dielectric constant changes of multiple pixel units is equal to the sum of the capacitive responses generated by the individual effects of each pixel unit—the global sensitivity matrix is ​​used as the linear transformation matrix to establish a mathematical expression that the electrode capacitance measurement vector is equal to the product of the global sensitivity matrix and the in-tube dielectric distribution vector. Integrating the global sensitivity matrix, mapping parameters, and predefined input / output parameters into this mathematical expression yields an initial linear forward mapping model. This model can describe the linear mapping relationship between the dielectric distribution and capacitance measurement values ​​under thick-walled conditions.

[0092] Furthermore, the linear correlation and physical consistency of the initial linear forward mapping model are verified to obtain the linear forward mapping model.

[0093] Specifically, a linear correlation check is performed by analyzing the rank of the global sensitivity matrix and eliminating linearly correlated rows or columns to avoid ill-conditioned problems in the model. A physical consistency check is then performed by substituting the known uniform dielectric distribution into the initial model and comparing the calculated theoretical capacitance value with the baseline capacitance value obtained from actual simulation or measurement to verify the physical correctness of the model. Any unreasonable parameters discovered during the check are corrected, ultimately resulting in a linear forward mapping model that meets both linear correlation and physical consistency requirements.

[0094] This application embodiment relies on the global sensitivity matrix to analyze the mapping parameters and standardize the input and output vectors, and builds a forward model based on the principle of linear superposition to accurately quantify the mapping relationship between the global dielectric distribution and the electrode capacitance. The initial model is subjected to both linear and physical verification to eliminate ill-conditioned parameters and erroneous terms that violate the physical laws of thick pipe walls, ensuring the mathematical stability and physical rationality of the forward model, and providing accurate and reliable forward constraints for the back-end inversion solution.

[0095] In some embodiments, based on the global sensitivity matrix and the linear forward mapping model, a regularized imaging algorithm is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data to obtain capacitance tomography results under thick pipe wall conditions, including: denoising and standardizing the measured capacitance data to obtain standardized measured capacitance data.

[0096] Specifically, in industrial thick-walled pipeline inspection scenarios, the measured capacitance data collected on-site is susceptible to environmental electromagnetic interference, system hardware errors, pipeline vibration, and other factors, resulting in noise and data deviation. Therefore, it is necessary to filter and denoise the raw measured capacitance data to remove high-frequency interference noise and abrupt changes, retaining accurate and valid capacitance change information. Simultaneously, the denoised capacitance data is standardized in amplitude and dimension by incorporating system baseline parameters. This eliminates system errors caused by hardware gain differences and measurement baseline offsets, ensuring that the format and amplitude range of the measured capacitance data fully adapt to the calculation requirements of the linear forward mapping model, ultimately yielding standardized measured capacitance data.

[0097] Furthermore, the standardized measured capacitance data, the global sensitivity matrix, and the linear forward mapping model are processed to construct inversion equations, resulting in capacitance tomography inversion equations.

[0098] Specifically, based on the established linear forward modeling framework, the problem of solving the dielectric distribution problem is transformed into an inverse problem. Standardized measured capacitance data are used as the constraint output of the equation, the global sensitivity matrix is ​​used as the fixed linear transformation weight matrix, and the dielectric distribution vector to be solved is used as the unknown. These are substituted into the forward model to complete the initial construction of the inversion equation. This inversion equation fully incorporates the global sensitivity weights of both the tube wall region and the internal dielectric region. Unlike traditional inversion equations that only target the internal region, this equation can adapt to the special physical characteristics of electric field shielding in thick tube walls and negative correlation changes in capacitance. It accurately addresses the dielectric imaging solution requirements under thick tube wall conditions, resulting in a complete capacitance tomography inversion equation.

[0099] Furthermore, the capacitance tomography inversion equation is solved using a regularized imaging algorithm to obtain the initial medium distribution data.

[0100] Specifically, due to the typical ill-conditioned characteristics of capacitance tomography inversion problems, direct solutions are prone to non-uniqueness and numerical divergence. Therefore, a regularized imaging algorithm is used to constrain the inversion equations. By introducing regularization constraints, numerical oscillations and ill-conditioned biases in the solution process are effectively suppressed. Based on the weight distribution law of the global sensitivity matrix, the dielectric constant distribution of each pixel unit is iteratively solved. After the iteration converges, preliminary global dielectric distribution information is output, yielding initial dielectric distribution data without error correction.

[0101] Furthermore, polarity correction and pipe wall shielding loss compensation are performed on the positive and negative weights of the initial medium distribution data and the global sensitivity matrix to obtain the corrected medium distribution data.

[0102] Specifically, considering the negative correlation between capacitance and dielectric constant under thick pipe wall conditions, and relying on the pre-defined positive and negative weighting rules of the global sensitivity matrix, the initial dielectric distribution data is polarized to correct the polarity inversion problem caused by the neglect of the negative correlation characteristics of the pipe wall in traditional imaging algorithms. Simultaneously, addressing the sensitivity attenuation and imaging signal loss in the central region of the pipe caused by the electric field shielding of the thick pipe wall, quantitative compensation is performed for the imaging loss caused by the pipe wall shielding based on the weighting attenuation law of the global sensitivity matrix. This corrects the calculated dielectric constant values ​​of each pixel unit, eliminates the imaging distortion problem caused by the electric field constraint of the thick pipe wall, and yields corrected dielectric distribution data with accurate physical laws and true numerical values.

[0103] Furthermore, the corrected medium distribution data is subjected to imaging rendering and sharpness optimization processing to obtain capacitance tomography results under thick pipe wall conditions.

[0104] Specifically, the corrected global dielectric distribution numerical data is visualized and rendered according to the spatial coordinates of each pixel unit, transforming the abstract dielectric constant distribution values ​​into corresponding grayscale or pseudo-color images to intuitively present the dielectric distribution state across the entire pipeline. Simultaneously, edge optimization, noise smoothing, and detail enhancement are performed on the imaging images to improve the imaging clarity of the pipe wall boundaries and the layered regions of the internal dielectric, mitigating image noise and blurring issues caused by numerical calculations. Ultimately, high-precision, high-fidelity capacitance tomography results suitable for the special conditions of thick pipe walls are obtained.

[0105] This application's embodiments eliminate on-site noise and system baseline errors through measured capacitance preprocessing, improving the reliability of measured data; build inversion equations based on a complete forward model, fully incorporating the sensitivity information of the entire pipe wall; improve the ill-conditioning problem of CT inversion by using regularization algorithms, and complete polarity correction and pipe wall shielding loss compensation by combining positive and negative sensitivity weights, specifically offsetting the imaging distortion caused by the electric field shielding and negative correlation characteristics of thick pipe walls; finally, imaging optimization further improves image clarity, ultimately achieving high-precision reconstruction imaging of pipe wall contour and multiphase medium distribution inside the pipe under thick pipe wall conditions.

[0106] While this application provides the method operation steps as described in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in this embodiment is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the methods shown in this embodiment or the accompanying drawings can be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0107] like Figure 3 As shown in the illustration, this application also provides a device 300 for acquiring capacitance tomography results. The device includes: Processing module 301 is used to construct a physical model of the negative correlation between capacitance and dielectric constant of internal medium under thick pipe wall conditions, based on electrostatic boundary conditions, the principle of energy minimization, and the electric field refraction law at the pipe wall-dielectric interface.

[0108] The processing module 301 is also used to perform global spatial discretization processing on the pipe wall region and the medium region inside the pipe based on the negative correlation physical model to obtain a computational grid model.

[0109] The processing module 301 is also used to perform dielectric constant perturbation simulation and response feature extraction on each pixel unit in the computational grid model to obtain sensitivity feature data.

[0110] The processing module 301 is also used to perform matrix construction processing on the sensitivity feature data to obtain a global sensitivity matrix covering the pipe wall region and the medium region inside the pipe.

[0111] Module 302 is used to establish a linear forward mapping model between dielectric distribution and capacitance measurement based on the global sensitivity matrix.

[0112] The imaging module 303 is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data based on the global sensitivity matrix and the linear forward mapping model, and to obtain capacitance tomography results under thick pipe wall conditions.

[0113] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0114] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0115] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, such as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module that implements the method or a structure within a hardware component.

[0116] This application also provides an apparatus, the apparatus comprising: a processor; a memory for storing processor-executable instructions; wherein, when the processor executes the executable instructions, it implements the method described in this application.

[0117] This application also provides a non-volatile computer-readable storage medium storing a computer program or instructions thereon, which, when executed, enables the method described in this application embodiment to be implemented.

[0118] Furthermore, in the various embodiments of the present invention, each functional module can be integrated into a processing module, or each module can exist independently, or two or more modules can be integrated into a single module.

[0119] The aforementioned storage media include, but are not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Cache, Hard Disk Drive (HDD), or Memory Card. The memory can be used to store computer program instructions.

[0120] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0121] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0122] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A method for acquiring capacitance tomography results, characterized in that, include: Based on the electrostatic field boundary conditions, the principle of energy minimization, and the electric field refraction law at the tube wall-dielectric interface, a physical model of the negative correlation between capacitance and dielectric constant of the internal dielectric under thick tube wall conditions is constructed. Based on the negative correlation physical model, the pipe wall region and the internal medium region are discretized in the whole domain space to obtain a computational grid model. The dielectric constant perturbation simulation and response feature extraction are performed on each pixel unit in the computational grid model, and the polarity differentiation and labeling are performed on the capacitance response difference corresponding to each pixel unit to obtain sensitivity feature data. The sensitivity feature data is processed by matrix construction to obtain a global sensitivity matrix covering the pipe wall region and the medium region inside the pipe. The global sensitivity matrix is ​​a global sensitivity matrix that includes negative weights. Based on the global sensitivity matrix, a linear forward mapping model between dielectric distribution and capacitance measurement is established. Based on the global sensitivity matrix and the linear forward mapping model, a regularized imaging algorithm is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data. Polarity correction and pipe wall shielding loss compensation are performed by combining the positive and negative weights of the global sensitivity matrix to obtain capacitance tomography results under thick pipe wall conditions.

2. The method according to claim 1, characterized in that, The physical model for the negative correlation between capacitance and dielectric constant of the internal dielectric under thick-wall conditions is constructed based on electrostatic boundary conditions, the principle of energy minimization, and the electric field refraction law at the pipe wall-dielectric interface. This model includes: The electrostatic field boundary conditions, the energy minimization principle, and the electric field refraction law at the pipe wall-dielectric interface are analyzed and processed to obtain the electric field path distribution and transmission loss characteristics under the thick pipe wall condition. By analyzing the electric field path distribution, the transmission loss characteristics, and the dielectric constant of the internal medium, the variation law of the total effective electric flux density is obtained. The variation law of the total effective electric flux density was correlated and derived to obtain a negative correlation trend; The negative correlation trend was verified by finite element simulation, and a physical model of the negative correlation between capacitance and dielectric constant of internal medium under thick pipe wall conditions was obtained.

3. The method according to claim 1, characterized in that, Based on the negative correlation physical model, the pipe wall region and the internal medium region are discretized in a global spatial manner to obtain a computational grid model, including: The computational domain of the negatively correlated physical model is defined to obtain a global computational domain that includes both the pipe wall region and the internal medium region. The global computational domain is divided into grid cells to obtain multiple independent pixel cells; The initial parameters of the dielectric constants of the multiple independent pixel units are uniformly set to obtain the basic calculation parameters; The global computational domain, the multiple independent pixel units, and the basic computational parameters are integrated to obtain a computational grid model.

4. The method according to claim 1, characterized in that, The process of performing dielectric constant perturbation simulation and response feature extraction on each pixel unit in the computational grid model, and performing polarity differentiation and labeling on the capacitance response difference corresponding to each pixel unit, to obtain sensitivity feature data includes: The dielectric constant increment is applied to each pixel unit in the computational grid model to obtain the pixel perturbation simulation model; Finite element simulation and difference calculation are performed on the pixel perturbation simulation model to obtain the capacitance response difference corresponding to each pixel unit; The polarity of the capacitance response difference corresponding to each pixel unit is distinguished and marked to obtain sensitivity feature data.

5. The method according to claim 1, characterized in that, The step of performing matrix construction processing on the sensitivity feature data to obtain a global sensitivity matrix covering the pipe wall region and the internal medium region includes: The sensitivity feature data is matched with each pixel unit in the computational grid model to obtain a set of sensitivity coefficients with spatial coordinate labels. The set of sensitivity coefficients with spatial coordinate markings is arranged according to a preset matrix dimension to obtain an initial sensitivity matrix covering the pipe wall region and the medium region inside the pipe. The dielectric distribution-capacitance measurement mapping relationship of the initial sensitivity matrix is ​​subjected to consistency verification processing to obtain the verified sensitivity matrix; The verified sensitivity matrix is ​​then format-normalized to obtain the global sensitivity matrix.

6. The method according to claim 1, characterized in that, The establishment of a linear forward mapping model between dielectric distribution and capacitance measurement based on the global sensitivity matrix includes: The global sensitivity matrix is ​​analyzed to obtain the mapping parameters; The correspondence between the medium distribution vector inside the pipe and the electrode capacitance measurement vector is defined and processed to obtain the input and output parameters of the forward model; The global sensitivity matrix, the mapping relationship parameters, and the input and output parameters are integrated to obtain an initial linear forward mapping model. The linear correlation and physical consistency of the initial linear forward mapping model are verified to obtain the linear forward mapping model.

7. The method according to claim 1, characterized in that, Based on the global sensitivity matrix and the linear forward mapping model, a regularized imaging algorithm is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data. Polarity correction and tube wall shielding loss compensation are then performed using the positive and negative weights of the global sensitivity matrix to obtain capacitance tomography results under thick tube wall conditions, including: The measured capacitance data is denoised and standardized to obtain standardized measured capacitance data. The standardized measured capacitance data, the global sensitivity matrix, and the linear forward mapping model are processed to construct inversion equations, resulting in capacitance tomography inversion equations. The capacitance tomography inversion equation is solved using a regularized imaging algorithm to obtain initial medium distribution data. The initial medium distribution data and the positive and negative weights of the global sensitivity matrix are subjected to polarity correction and pipe wall shielding loss compensation to obtain the corrected medium distribution data. The corrected medium distribution data is subjected to imaging rendering and sharpness optimization processing to obtain capacitance tomography results under thick pipe wall conditions.

8. A device for acquiring capacitance tomography results, characterized in that, include: The processing module is used to construct a physical model of the negative correlation between capacitance and dielectric constant of the internal medium under thick pipe wall conditions, based on electrostatic boundary conditions, the principle of energy minimization, and the electric field refraction law at the pipe wall-dielectric interface. The processing module is also used to perform global spatial discretization processing on the pipe wall region and the pipe medium region based on the negative correlation physical model to obtain a computational grid model; The processing module is also used to perform dielectric constant perturbation simulation and response feature extraction on each pixel unit in the computational grid model, and to perform polarity differentiation and marking on the capacitance response difference corresponding to each pixel unit to obtain sensitivity feature data. The processing module is further configured to perform matrix construction processing on the sensitivity feature data to obtain a global sensitivity matrix covering the pipe wall region and the medium region inside the pipe, wherein the global sensitivity matrix is ​​a global sensitivity matrix containing negative weights. The module is used to establish a linear forward mapping model between the dielectric distribution and the capacitance measurement value based on the global sensitivity matrix; The imaging module is used to perform inversion calculation and imaging reconstruction processing on the measured capacitance data based on the global sensitivity matrix and the linear forward mapping model, using a regularized imaging algorithm. It combines the positive and negative weights of the global sensitivity matrix to perform polarity correction and tube wall shielding loss compensation, thereby obtaining capacitance tomography results under thick tube wall conditions.

9. A computer device comprising a memory and a processor, the memory storing a computer program executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

Images