Electromagnetic field momentum-based electrical capacitance tomography method and gradient signal detection device

Abstract

The application discloses a kind of based on electromagnetic field momentum's electrical capacitance tomography method and gradient signal detection device, the method is based on electromagnetic field momentum reciprocity theorem, reconstructs dielectric constant by the gradient signal of capacitance.It steps are, first, solve boundary value problem under voltage source excitation, construct sensitivity matrix or the gradient of sensitivity matrix;Second, construct ECT-EMM linear equation under suitable coordinate system;Then, obtain the gradient signal of sensor receiving electrode's capacitance by signal detection part;Again, reconstruct dielectric constant distribution using sensitivity matrix or the gradient of sensitivity matrix, coordinate system related coefficient vector and the gradient signal of capacitance.It gradient signal detection device includes: signal generating part, sensor, signal detection part, signal amplification part and signal acquisition and imaging algorithm part.The imaging method proposed in the application has the advantages of high imaging resolution and can meet the needs of different industrial environments.

Description

Technical Field

[0001] This invention relates to the field of capacitance tomography, and more specifically to a capacitance tomography method and gradient signal detection device based on electromagnetic field momentum. Background Technology

[0002] Electrical capacitance tomography (ECT) is a process imaging technique based on the principle of capacitance sensitivity. It reflects the distribution of dielectric constant within the imaging region by detecting changes in the capacitance value on electrodes. Due to its wide applicability, fast response speed, simple sensor structure, low cost, and good safety, ECT is widely used in the industrial process detection of insulating media in petroleum, chemical, power, and metallurgical industries.

[0003] The electromagnetic reciprocity of current capacitance tomography (ECT) can be described by Green's reciprocity theorem. Excitation electrode A and detection electrode B constitute a reciprocal process, where process I involves applying a voltage u to electrode A. A The detection capacitance value C is obtained through electrode B. AB Process II involves applying a voltage u to electrode B. B The detection capacitance value C is obtained through electrode A. BA Since capacitance is only a function of the dielectric distribution and electrode positions, then C AB With C BA Equal, uniformly denoted as C AB Then, the voltage source and the sensing capacitor it generates in a reciprocal process satisfy the following relationship:

[0004]

[0005] In the formula, V is the volume of the imaging region, r is the spatial position coordinate, ε(r) is the spatial distribution of the dielectric constant, E1(r) is the spatial distribution of the electric field intensity in process I, and E2(r) is the spatial distribution of the electric field intensity in process II.

[0006] The electromagnetic reciprocity relationship in capacitance tomography (ECT) can be described by Green's reciprocity theorem, an energy reciprocity theorem that describes the relationship between a charge source and its generated electric field, and is related to the energy of the electromagnetic field. The spatial resolution of ECT is related to the amount of independent measurement data, which in turn is related to the number of electrodes. Therefore, increasing the number of electrodes can improve the imaging resolution to some extent. However, due to limitations in hardware systems and imaging areas, the number of electrodes cannot be arbitrarily increased. Overall, the ECT method has low spatial resolution and poor image quality.

[0007] Electromagnetic fields possess both energy and momentum, meaning that a reciprocal relationship between two electromagnetic systems can be established from either an energy or momentum perspective. In 2020, Liu et al. derived the electromagnetic momentum reciprocity theorem for homogeneous media, and in 2022, they derived it for inhomogeneous media. This relationship, like the energy reciprocity theorem, can be used for capacitance tomography. The electromagnetic reciprocity relationship in electrical capacitance tomography based on electromagnetic momentum (ECT-EMM) can be described by the momentum reciprocity theorem, satisfying the electromagnetic momentum reciprocity relationship, i.e., a set of charge sources and the electric field intensity they generate satisfy a reciprocal relationship. Under charge source excitation, ECT measures potential; under voltage source excitation, ECT measures capacitance. The measurement data in both excitation modes are scalar data. Under charge source excitation, ECT-EMM measures electric field intensity; under voltage source excitation, it measures capacitance gradient signals. Both excitation modes produce vector data. Vector data contains scalar information in different directions, thus ECT-EMM is more capable of reconstructing high-resolution images than ECT.

[0008] In summary, electrostatic capacitance tomography (ECT), based on the energy reciprocity theorem, is a scalar imaging method with low spatial resolution and poor image quality. Electromagnetic field momentum-based electrostatic capacitance tomography (ECT-EMM), on the other hand, is a vector imaging method with high resolution and high image reconstruction quality, thus overcoming the low resolution limitation of existing ECT imaging methods. Summary of the Invention

[0009] To address the aforementioned technical problems, this invention provides a capacitance tomography (ECT-EMM) method based on electromagnetic field momentum and a gradient signal detection device. This method is an ECT-EMM method under voltage source excitation, which reconstructs the dielectric constant distribution by measuring the gradient signal of the capacitor. The gradient signal detection device can acquire the gradient signal of the dielectric constant imaging method of this invention. Its signal detection unit can measure the gradient signal of the capacitor.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A capacitance tomography method based on electromagnetic field momentum includes the following steps:

[0012] Step 1: Under voltage source excitation, solve the analytical or numerical solution of ECT for the boundary value problem of the imaging region to obtain the electric field intensity E of the imaging region, and construct the sensitivity matrix or the gradient of the sensitivity matrix; ECT stands for capacitance tomography.

[0013] Step 2: Select a suitable coordinate system and construct the ECT-EMM linear equation; ECT-EMM represents capacitance tomography based on electromagnetic field momentum.

[0014] Step 3: Obtain the gradient signal of the capacitance of the sensor receiving electrode through the signal detection unit;

[0015] Step 4: Reconstruct the dielectric constant distribution using the sensitivity matrix, the coordinate system-related coefficient vector, and the gradient signal of the capacitance; or reconstruct the dielectric constant distribution using the gradient of the sensitivity matrix, the coordinate system-related coefficient vector, and the gradient signal of the capacitance.

[0016] Further, step one includes:

[0017] Considering the imaging region V, with boundary Γ, the electromagnetic field boundary value problem corresponding to ECT is:

[0018]

[0019] In formula (2) Let r be the Nabla operator, r be the spatial coordinates, ε(r) be the spatial distribution of dielectric constant, u(r) be the spatial distribution of potential, A be the electrode position, and u be the position of the electrode. A Γ / A represents the voltage applied to electrode A, where Γ / A is the region boundary excluding electrode A.

[0020] From equation (1), if a small perturbation is applied to the working fluid, the linear equation of ECT is:

[0021] Sg=λ (3)

[0022] In equation (3), This is the normalized sensitivity matrix. The normalized dielectric constant is The capacitance is the normalized value, M is the number of independent measurements, and N is the number of pixels in the imaging region.

[0023] Define the dielectric constant distribution ε(r) within the imaging region, and apply a voltage u at electrode A. A The spatial distribution of the electric field intensity E(r) is solved through numerical calculation; the matrix elements of the sensitivity matrix constructed from E(r) are:

[0024] S ij (r)=E i (r)·E j (r) (4a)

[0025] In equation (4a), i and j are electrode numbers, E i (r) represents the spatial distribution of the electric field intensity when excitation is applied to electrode i, E j(r) represents the spatial distribution of the electric field intensity when excitation is applied to electrode j, S ij (r) represents the spatial distribution of the sensitivity matrix of the electromagnetic reciprocal process formed by electrodes i and j, where i ≠ j.

[0026] The matrix elements of the gradient of the sensitivity matrix constructed from E(r) are:

[0027]

[0028] In equation (4b) Let be the spatial distribution of the gradient of the sensitivity matrix of the electromagnetic reciprocal process formed by electrodes i and j, where i ≠ j.

[0029] Furthermore, step two includes:

[0030] The suitable coordinate system includes a two-dimensional rectangular coordinate system, a two-dimensional polar coordinate system, a three-dimensional rectangular coordinate system, or a cylindrical coordinate system, etc.

[0031] Find e in equation (3) l Taking the directional derivative, we obtain two forms of the ECT-EMM equations. The first form of the ECT-EMM linear equations is:

[0032]

[0033] In formula (5a) For normalized capacitance at e l directional derivative of direction, For the normalized dielectric constant in e l The directional derivative of the direction, Q and H are coefficient vectors, which are related to the specific expansion of the gradient in the selected coordinate system.

[0034] The second form of the ECT-EMM linear equation is:

[0035]

[0036] In equation (5b) For the sensitivity matrix in e l The directional derivative of the direction.

[0037] Furthermore, step three includes:

[0038] According to the gradient formula, the gradient signal of a capacitor is obtained by measuring the capacitance derivative along the coordinate axes of an orthogonal coordinate system.

[0039] Furthermore, step four includes:

[0040] The two forms of ECT-EMM linear equations correspond to two different reconstruction methods.

[0041] The reconstruction method corresponding to the first form of ECT-EMM linear equation is as follows: The dielectric constant distribution is reconstructed by applying the algorithm according to equation (5a) based on the sensitivity matrix S, the coefficient vector related to the coordinate system and the gradient signal of the capacitance; the dielectric constant of the outermost pixel in the imaging region is taken as a known quantity, and the dielectric constant of the remaining pixels is taken as an unknown quantity. An equation is established between the dielectric constant of adjacent pixels and the gradient of the dielectric constant of the pixel. The dielectric constant distribution is obtained by solving the equation.

[0042] The reconstruction method corresponding to the second form of the ECT-EMM linear equation is: based on the gradient of the sensitivity matrix. The coefficient vectors related to the coordinate system and the gradient signal of the capacitance are used to reconstruct the dielectric constant distribution according to equation (5b).

[0043] The present invention also provides a gradient signal detection device using the above-described capacitance tomography method based on electromagnetic field momentum, comprising: a signal generating unit, a sensor, a signal detection unit, a signal amplification unit, and a signal acquisition and imaging algorithm unit; the output end of the signal generating unit is connected to the transmitting electrode of the sensor, the receiving electrode of the sensor is connected to the input end of the signal detection unit, the output end of the signal detection unit is connected to the input end of the signal amplification unit, and the output end of the signal amplification unit is connected to the signal acquisition and imaging algorithm unit.

[0044] Furthermore, the signal detection unit is used to measure the gradient signal of the capacitance of the sensor receiving electrode. The electrode can be arranged at two positions close to each other along the coordinate axes of the orthogonal coordinate system, or it can be moved along the coordinate axes of the orthogonal coordinate system. The electrode can be selected to be attached to the imaging area or not attached to the imaging area as required. The electrode not attached to the imaging area is fixed by the electrode bracket.

[0045] Furthermore, the sensor includes a measuring chamber and electrodes; the electrodes include a transmitting electrode and a receiving electrode; the outer wall of the measuring chamber is grounded to shield the measurement signal from external electromagnetic interference; the dielectric constant sample to be measured is placed inside the sensor.

[0046] Furthermore, the signal generating unit includes a signal generator connected to the transmitting electrode of the sensor;

[0047] The signal detection unit includes a signal conversion circuit that converts the voltage signal of the electrode into a capacitance signal;

[0048] The input terminal of the signal amplification unit is connected to the output terminal of the signal detection unit to amplify the capacitance signal;

[0049] The signal acquisition and imaging algorithm unit includes a computer with signal acquisition capabilities and image reconstruction algorithms, used to process the acquired data from the signal detection unit and apply the reconstruction algorithm to perform image reconstruction.

[0050] It should be noted that other methods that utilize the principle of electromagnetic field momentum reciprocity imaging to reconstruct the dielectric constant distribution by measuring the gradient signal of the capacitor are also within the scope of protection of this invention.

[0051] Beneficial effects:

[0052] This invention proposes a capacitance tomography method and gradient signal detection device based on the electromagnetic field momentum reciprocity theorem. While imaging methods based on the energy reciprocity theorem are scalar imaging methods, those based on the electromagnetic field momentum reciprocity theorem are vector imaging methods. This improves the imaging system's sensitivity to dielectric constants in different directions, which is beneficial for obtaining higher resolution dielectric constant images. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the gradient signal detection device of the present invention;

[0054] Figure 2 This is a schematic diagram of electrode movement located outside the tube wall and not in contact with the tube wall;

[0055] Figure 3 This is a schematic diagram of the movement of an electrode located inside the tube wall but not in contact with the tube wall.

[0056] Figure 4 This is a schematic diagram of a multi-electrode system that is attached to the tube wall. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0058] The present invention provides a capacitance tomography method based on electromagnetic field momentum, comprising the following steps:

[0059] Step 1: Under voltage source excitation, solve the analytical or numerical solution of ECT for the boundary value problem of the imaging region, obtain the electric field intensity E of the imaging region, and construct the sensitivity matrix or the gradient of the sensitivity matrix.

[0060] Step 2: Select a suitable coordinate system and construct the ECT-EMM linear equations;

[0061] Step 3: Obtain the gradient signal of the capacitance of the sensor receiving electrode through the signal detection unit;

[0062] Step 4: Reconstruct the dielectric constant distribution using the sensitivity matrix, the coordinate system-related coefficient vector, and the gradient signal of the capacitance; or reconstruct the dielectric constant distribution using the gradient of the sensitivity matrix, the coordinate system-related coefficient vector, and the gradient signal of the capacitance.

[0063] Specifically, step one includes:

[0064] Considering the imaging region V, with boundary Γ, the electromagnetic field boundary value problem corresponding to ECT is:

[0065]

[0066] In formula (2) Let r be the Nabla operator, r be the spatial position coordinates, ε(r) be the spatial distribution of the dielectric constant, and u(r) be the spatial distribution of the potential. A Γ / A represents the voltage applied to electrode A, and Γ / A represents the portion of the imaging region boundary excluding electrode A.

[0067] From equation (1), if a small perturbation is applied to the working fluid, the linear equation of ECT is:

[0068] Sg=λ (3)

[0069] In equation (3), This is the normalized sensitivity matrix. The normalized dielectric constant is Here, M represents the normalized capacitance, M represents the number of independent measurements, and N represents the number of pixels in the imaging region.

[0070] Define the spatial distribution of the dielectric constant ε(r) within the imaging region, and apply a voltage u to electrode A. A The spatial distribution of the electric field intensity, E(r), is solved numerically. The matrix elements of the sensitivity matrix constructed from E(r) are:

[0071] S ij (r)=E i (r)·E j (r) (4a)

[0072] In equation (4a), i and j are electrode numbers, E i (r) represents the spatial distribution of the electric field intensity when excitation is applied to electrode i, E j (r) represents the spatial distribution of the electric field intensity when excitation is applied to electrode j, S ij (r) represents the spatial distribution of the sensitivity matrix of the electromagnetic reciprocal process formed by electrodes i and j, where i ≠ j.

[0073] The matrix elements of the gradient of the sensitivity matrix constructed from E(r) are:

[0074]

[0075] In equation (4b) Let be the spatial distribution of the gradient of the sensitivity matrix of the electromagnetic reciprocal process formed by electrodes i and j, where i ≠ j.

[0076] Specifically, step two includes:

[0077] The linear equation of ECT-EMM is equivalent to finding the gradient of the linear equation of ECT.

[0078] Choose a suitable coordinate system, such as a two-dimensional rectangular coordinate system, a two-dimensional polar coordinate system, a three-dimensional rectangular coordinate system, or a cylindrical coordinate system.

[0079] Find e in equation (3) l Taking the directional derivative, we obtain two forms of the ECT-EMM equations. The first form of the ECT-EMM linear equations is:

[0080]

[0081] In formula (5a) For normalized capacitance at e l directional derivative of direction, For the normalized dielectric constant in e l The directional derivative of the direction, Q and H are coefficient vectors, which are related to the specific expansion of the gradient in the selected coordinate system.

[0082] The second form of the ECT-EMM linear equation is:

[0083]

[0084] In equation (5b) For the sensitivity matrix in e l The directional derivative of the direction.

[0085] S is the sensitivity matrix. Note that theoretically, e l The direction can be arbitrary, therefore any method for finding the directional derivative along any direction is within the scope of protection of this invention.

[0086] Specifically, step three includes:

[0087] The gradient signal of the capacitor is obtained through a signal detection unit. According to the gradient formula, the gradient signal of the capacitor can be obtained by measuring the capacitance derivative along the coordinate axes of an orthogonal coordinate system.

[0088] Specifically, step four includes:

[0089] The reconstruction method corresponding to the first form of the ECT-EMM linear equation is as follows: The dielectric constant distribution is reconstructed by applying the algorithm according to equation (5a) based on the sensitivity matrix S, the coefficient vector related to the coordinate system and the gradient signal of the capacitance. Since the boundary conditions of the imaging region are known, the dielectric constant of the outermost pixel of the imaging region can be taken as a known quantity, and the dielectric constant of the remaining pixels can be taken as an unknown quantity. An equation is established between the dielectric constant of adjacent pixels and the gradient of the dielectric constant of the pixel. The dielectric constant distribution is obtained by solving the equation.

[0090] The reconstruction method corresponding to the second form of the ECT-EMM linear equation is: based on the gradient of the sensitivity matrix. The coefficient vectors related to the coordinate system and the gradient signal of the capacitance are used to reconstruct the dielectric constant distribution according to equation (5b).

[0091] The gradient signal detection device using the imaging method of the present invention includes: a signal generating unit, a sensor, a signal detecting unit, a signal amplifying unit, and a signal acquisition and imaging algorithm unit. The output terminal of the signal generating unit is connected to the transmitting electrode of the sensor, the receiving electrode of the sensor is connected to the input terminal of the signal detecting unit, the output terminal of the signal detecting unit is connected to the input terminal of the signal amplifying unit, and the output terminal of the signal amplifying unit is connected to the signal acquisition and imaging algorithm unit.

[0092] The signal detection unit is used to measure the gradient signal of the capacitance of the sensor receiving electrode. The electrode can be arranged at two positions close to each other along the coordinate axes of the orthogonal coordinate system, or it can be moved along the coordinate axes of the orthogonal coordinate system. The electrode can be selected to be attached to the imaging area or not, depending on the requirements. For electrodes not attached to the imaging area, they can be fixed by an electrode bracket. This invention lists three specific embodiments based on different sensor structures and measurement methods. The sensor includes a measuring chamber and electrodes. The electrodes include a transmitting electrode and a receiving electrode. The outer wall of the measuring chamber is grounded to shield the measurement signal from external electromagnetic interference. The dielectric constant sample to be measured is placed inside the sensor.

[0093] The core component of the signal generating unit is a signal generator, which is connected to the transmitting electrode of the sensor.

[0094] The signal detection unit is a signal conversion circuit that converts the voltage signal from the electrodes into a capacitance signal. The input terminal of the signal amplification unit is connected to the output terminal of the signal detection unit to amplify the capacitance signal.

[0095] The main body of the signal acquisition and imaging algorithm unit is a computer with signal acquisition capabilities and image reconstruction algorithms. This computer can process the data acquired by the sensor and apply the reconstruction algorithm to reconstruct the image.

[0096] Example 1

[0097] In this embodiment, such as Figure 2 As shown, the imaging region is the cross-section inside the cylindrical pipe, i.e., the xoy plane. The electrodes are not attached to the imaging region but are fixed to the outside of the pipe wall by an electrode support. The steps of the capacitance tomography method based on electromagnetic field momentum in this embodiment are as follows:

[0098] Step one: Consider a two-dimensional imaging region V, where the boundary of V is Γ. For example... Figure 2 The sensor shown has 12 electrodes. Solve the electromagnetic field boundary value problem corresponding to equation (2) to calculate the spatial distribution E(r) of the electric field intensity. Establish a linear equation based on equation (3), with 66 independent measurements and 32×32 pixels in the imaging region. Solve for the sensitivity matrix S according to equation (4a) or the gradient of the sensitivity matrix according to equation (4b).

[0099] Step two: Select a rectangular coordinate system and construct the ECT-EMM linear equations; for Figure 2 The sensor moves the electrode via an electrode support movement control device, measuring the capacitance before and after the electrode movement to obtain the capacitance gradient signal. The electrode before movement is represented by 1-12, and the gradient signal is obtained along e. x The moved electrode is denoted by 1'-12', along e y The moved electrode is represented by 1"-12". In the rectangular coordinate system, Q and H in the linear equations of equations (5a) and (5b) are both unit vectors. Let the two coordinate axes of the rectangular coordinate system be e. x axis and e y The axis is selected, and the electrode movement direction is e. x With e y Direction. Along e x The first form of the ECT-EMM linear equation during electrode movement is:

[0100]

[0101] Along e y The first form of the ECT-EMM linear equation during electrode movement is:

[0102]

[0103] In equations (6a) and (7a) For normalized capacitance at e x directional derivative of direction, For normalized capacitance at e y directional derivative of direction, For the normalized dielectric constant in e x directional derivative of direction, For the normalized dielectric constant in e y The directional derivative of the direction.

[0104] Along e x The second form of the ECT-EMM linear equation when the electrode is moved is:

[0105]

[0106] Along e y The second form of the ECT-EMM linear equation when the electrode is moved is:

[0107]

[0108] In equations (6b) and (7b) To normalize the sensitivity matrix in e x directional derivative of direction, To normalize the sensitivity matrix in e y The directional derivative of the direction.

[0109] Step three: Move the electrode in a rectangular coordinate system. The electrode before movement is represented by Arabic numerals 1-12. Along the e... x The electrodes after directional movement are represented by Arabic numerals with a ', along e y The electrodes after directional movement are represented by Arabic numerals with "+". Let C be the capacitance before and after the electrode movement, and convert it to a normalized capacitance λ. Specifically, let λ be the normalized capacitance vector before the electrode movement. b The electrode along e x The normalized capacitance vector after directional electrode movement is λ ax The electrode along e y The normalized capacitance vector after directional electrode movement is λ ay Assuming along e x Directional movement distance dx and along e y If the directional movement distance dy is equal, denoted as d, then the normalized capacitance at e x Directional derivative For (λ) ax -λ b ) / d, normalized capacitance at e y Directional derivative For (λ) ay -λ b If ) / d, then equations (6a) and (7a) become:

[0110]

[0111]

[0112] Equations (6b) and (7b) become:

[0113]

[0114]

[0115] Step four: Reconstruct the dielectric constant distribution using the sensitivity matrix and the gradient signal of the capacitance;

[0116] For the first form of the ECT-EMM linear equation, according to equations (8a) and (9a), the sensitivity matrix S and the directional derivative of the capacitance in the electrode movement direction are used. and The dielectric constant in e is reconstructed using the Tikhonov regularization algorithm. x and e y The directional derivative of the direction is the dielectric constant gradient. Since the boundary conditions of the imaging region are known, the dielectric constant of the outermost pixel in the imaging region can be taken as a known quantity. The dielectric constants of the remaining pixels are taken as unknown quantities. An equation is established between the dielectric constants of adjacent pixels and the gradient of the pixel's dielectric constant. The dielectric constant distribution in the xoy plane is solved using the Tikhonov regularization algorithm.

[0117] For the second form of the ECT-EMM linear equation, the dielectric constant distribution is reconstructed using the gradient of the sensitivity matrix and the gradient signal of the capacitance; according to equations (8b) and (9b), the directional derivative of the sensitivity matrix in the electrode movement direction is used. and and the directional derivative of the capacitor in the direction of electrode movement and The dielectric constant was reconstructed using the Tikhonov regularization algorithm.

[0118] like Figure 1 As shown, the gradient signal detection device using the dielectric constant imaging method includes: a signal generation unit A1, a sensor B1, a signal detection unit C1, a signal amplification unit D1, and a signal acquisition and imaging algorithm unit E1. The output terminal of the signal generation unit A1 is connected to the transmitting electrode of the sensor B1, the receiving electrode of the sensor B1 is connected to the input terminal of the signal detection unit C1, the output terminal of the signal detection unit C1 is connected to the input terminal of the signal amplification unit D1, and the output terminal of the signal amplification unit D1 is connected to the signal acquisition and imaging algorithm unit E1.

[0119] The sensor B1 includes a measuring chamber and electrodes. The electrodes are located outside the tube wall but not in contact with it, and are fixed by an electrode support. The electrode support is connected to an electrode support movement control device. The electrode support movement control device controls the electrode support to move along e... x Direction and e yDirectional movement. Two factors need to be considered when selecting the electrode movement distance: first, the capacitance measured by the signal detection unit before and after the electrode movement should be distinguishable at that distance; second, the electrode movement distance should be as small as possible within the sensor size. The measurement chamber is located outside the electrode, and its outer wall is grounded to shield against external electromagnetic interference. The dielectric constant sample to be measured is placed inside the tube wall.

[0120] The signal detection unit C1 is a signal conversion circuit that converts the voltage signal from the electrodes into a capacitance signal. The signal amplification unit D1 amplifies the capacitance signal. The main body of the signal acquisition and imaging algorithm unit E1 is a computer, which processes the acquired capacitance data and performs image reconstruction using the Tikhonov regularization algorithm.

[0121] Example 2

[0122] In this embodiment, the electrode is not attached to the imaging area, along e z The electrodes are arranged in two layers and fixed inside the tube wall by electrode supports, constituting an invasive measurement method. Figure 3 As shown, the imaging region is the side surface of a cylinder, which unfolds into surface ABCD. The steps of the capacitance tomography method based on electromagnetic field momentum in this embodiment are as follows:

[0123] Step one includes: [The following is a description of the process] Figure 3 For a sensor containing 16 electrodes located inside the tube wall, considering the imaging region V, with the boundary of V being Γ, solve the electromagnetic field boundary value problem corresponding to equation (2) to calculate the spatial distribution E(r) of the electric field intensity. Solve the sensitivity matrix S of the cylindrical side surface according to equation (4a) or the gradient of the sensitivity matrix according to equation (4b). The unfolded surface of the cylinder's lateral side is surface ABCD.

[0124] Step two includes: selecting a cylindrical coordinate system and constructing the ECT-EMM linear equations;

[0125] for Figure 3 The sensor moves the electrode via an electrode support movement control device, measuring the capacitance before and after the electrode movement to obtain the capacitance gradient signal. A cylindrical coordinate system is chosen, and a linear equation as shown in equation (5a) is constructed. The two coordinate axes of the cylindrical coordinate system are denoted as e. φ axis and e z The axis is selected, and the electrode movement direction is e. φ With e z The direction is along e φ The first form of the ECT-EMM linear equation during electrode movement is:

[0126]

[0127] In formula (10a) Let be the coefficient vector in the cylindrical coordinate system, with vector elements of 1 / k, where k is the radius of the circle enclosed by the electrodes on the roφ surface. This is a coefficient vector in cylindrical coordinates, with each element being 1 / r, where r is the distance between the pixel and the center of the pipe. For normalized capacitance at e φ directional derivative of direction, For the normalized dielectric constant in e φ The directional derivative of the direction.

[0128] Along e z The linear equation for the first form of ECT-EMM during electrode movement is:

[0129]

[0130] In formula (11a) For normalized capacitance at e z directional derivative of direction, For the normalized dielectric constant in e z The directional derivative of the direction.

[0131] Along e φ The second form of the ECT-EMM linear equation when the electrode is moved is:

[0132]

[0133] In equation (10b) To normalize the sensitivity matrix in e φ The directional derivative of the direction.

[0134] Along e z The linear equation for the second form of ECT-EMM during electrode movement is:

[0135]

[0136] In equation (11b) To normalize the sensitivity matrix in e z The directional derivative of the direction.

[0137] Step three includes: moving the electrode in a cylindrical coordinate system, selecting the electrode movement direction as e. φ With e z Direction, denoted by Arabic numerals for the electrode before movement, along e φ The electrodes after directional movement are represented by Arabic numerals with a ', along e z The electrodes after directional movement are represented by Arabic numerals with "+". Let C be the capacitance before and after the electrode movement, and convert it to a normalized capacitance λ. Specifically, let λ be the normalized capacitance vector before the electrode movement. b The electrode along eφ The normalized capacitance vector after directional electrode movement is λ aφ The electrode along e z The normalized capacitance vector after directional electrode movement is λ az Assuming along e φ Directional movement distance dφ and along e z If the directional movement distance dz is equal, denoted as d, then the normalized capacitance at e φ Directional derivative For (λ) aφ -λ b ) / d, normalized capacitance at e z Directional derivative For (λ) az -λ b If ) / d, then equations (10a) and (11a) become:

[0138]

[0139]

[0140] Equations (10b) and (11b) become:

[0141]

[0142]

[0143] Step four includes: reconstructing the dielectric constant distribution using the sensitivity matrix, the coefficient vector of the cylindrical coordinate system, and the gradient signal of the capacitance;

[0144] The reconstruction method corresponding to the first form of the ECT-EMM linear equation is as follows: According to equations (12a) and (13a), the sensitivity matrix S and the directional derivative of the capacitance in the electrode movement direction are used to construct the ECT-EMM linear equation. and The dielectric constant in e is reconstructed using the Tikhonov regularization algorithm. φ and e z The directional derivative of the direction is the dielectric constant gradient. Since the boundary conditions of the imaging region are known, the dielectric constant of the outermost pixel in the imaging region can be taken as a known quantity. The dielectric constants of the remaining pixels are taken as unknown quantities. An equation is established between the dielectric constants of adjacent pixels and the gradient of the pixel's dielectric constant. The dielectric constant distribution on the side surface of the cylinder is solved using the Tikhonov regularization algorithm.

[0145] The reconstruction method corresponding to the second form of the ECT-EMM linear equation is as follows: The dielectric constant distribution is reconstructed using the gradient of the sensitivity matrix, the coefficient vector of the cylindrical coordinate system, and the gradient signal of the capacitance; according to equations (12b) and (13b), the directional derivative of the sensitivity matrix in the electrode movement direction is used... and and the directional derivative of the capacitor in the direction of electrode movement and The dielectric constant is reconstructed using the Tikhonov regularization algorithm. It should be noted that the imaging area of ​​this method is the side surface of the cylinder where the electrodes are located. Multiple layers of electrodes can be arranged according to actual needs to obtain more images of the dielectric constant distribution on the side surface of the cylinder, thereby obtaining the dielectric constant distribution inside the tube wall.

[0146] Gradient signal detection device using dielectric constant imaging method, such as Figure 1 As shown, except for sensor B1, the detection device is the same as in Example 1.

[0147] The sensor B1 includes a measuring chamber and electrodes. The electrodes are located inside the tube wall but not in contact with it, and are fixed by an electrode support. The electrode support is connected to an electrode support movement control device. The electrode support movement control device controls the electrode support to move along e... φ Direction and e z Directional movement.

[0148] Example 3

[0149] In this embodiment, as Figure 4 As shown, the imaging area is the cross-section inside a square pipe, i.e., the xoy plane. The sensor electrodes are fixed to the outside of the pipe wall. Let the three axes of the rectangular coordinate system be e. x axis, e y axis and e z Axis, due to its relationship with e x A pipe wall with a parallel direction is not convenient for running along e y Electrodes are arranged in a specific direction, in relation to e y A pipe wall with a parallel direction is not convenient for running along e x The electrodes are arranged in a specific direction, therefore, the following method is adopted: Figure 4 The arrangement method is as follows. The steps of the capacitance tomography method based on electromagnetic field momentum in this embodiment are as follows:

[0150] Step one includes: Figure 4 For electrodes that are in contact with the tube wall, the electrode numbers are indicated by lowercase English letters. Figure 4 Only some electrode numbers (aj) are marked. The electrode spacing is approximately 1 / 30 of the side length of the square tube wall. The electrode size is basically the same as the electrode spacing. For the imaging region V, the boundary of V is Γ. Solve the electromagnetic field boundary value problem corresponding to equation (2) to calculate the spatial distribution E(r) of the electric field intensity. Solve the sensitivity matrix S according to equation (4a) or solve the gradient of the sensitivity matrix according to equation (4b).

[0151] Step two includes: selecting a rectangular coordinate system and constructing the ECT-EMM linear equation;

[0152] In a rectangular coordinate system, Q and H in the linear equations (5a) and (5b) are both unit vectors. Along e x The first form of the ECT-EMM linear equation when the electrode is moved in a certain direction is:

[0153]

[0154] Along e y The first form of the ECT-EMM linear equation when the electrode is moved in a certain direction is:

[0155]

[0156] In equations (14a) and (15a) For normalized capacitance at e x directional derivative of direction, For normalized capacitance at e y directional derivative of direction, For the normalized dielectric constant in e x directional derivative of direction, For the normalized dielectric constant in e y The directional derivative of the direction.

[0157] Along e x The second form of the ECT-EMM linear equation when the electrode is moved in a certain direction is:

[0158]

[0159] Along e y The second form of the ECT-EMM linear equation when the electrode is moved in a certain direction is:

[0160]

[0161] In equations (14b) and (15b) To normalize the sensitivity matrix in e x directional derivative of direction, To normalize the sensitivity matrix in e y The directional derivative of the direction.

[0162] Step three includes:

[0163] Figure 4 The sensor has a small electrode spacing, allowing the electrodes to be arranged at two locations close to each other along the coordinate axes of an orthogonal coordinate system. This enables the signal detection unit to measure the capacitance gradient signal. Electrodes are arranged on planes ABCD, DCFE, DCFE, and DCFE. Figure 4Only the electrodes on planes ABCD and DCFE are shown. A rectangular coordinate system is chosen, and the capacitance before and after electrode movement is denoted as C, which is then converted to a normalized capacitance λ. The electrode spacing on the same plane is the same, denoted as d. Specifically, for electrodes arranged on plane ABCD, the capacitance is measured along e... x With e z Directional derivative of the direction; for electrodes arranged on the plane DCFE, the measured capacitance along e y With e z The directional derivative. Let λ be the normalized capacitance of electrodes m and n. mn Taking a labeled electrode as an example, for an electrode on plane ABCD, the capacitance is along e x The directional derivative of the direction is (λ) cb -λ ba ) / d, capacitance along e z The directional derivative of the direction is (λ) ed -λ da ) / d; For an electrode on a plane DCFE, the capacitance is along e y The directional derivative of the direction is (λ) gf -λ fi ) / d, capacitance along e z The directional derivative of the direction is (λ) jh -λ hi ) / d. Capacitance along e x e y With e z The directional derivatives are correlated, therefore, the directional derivative of the capacitance along another direction can be calculated from any two directions, thus obtaining the capacitance along the electrode plane. x With e y The directional derivative of the capacitance along the direction. x With e y The directional derivative of the xoy plane forms the gradient of the capacitance.

[0164] Step four includes: reconstructing the dielectric constant distribution using the sensitivity matrix and the gradient signal of the capacitance.

[0165] For the first form of the ECT-EMM linear equation, the sensitivity matrix S and the capacitance along e x With e y The directional derivative of the direction, according to equations (14a) and (15a), is used to reconstruct the dielectric constant in the direction of e using the Tikhonov regularization algorithm. x and e yThe directional derivative of the direction is the dielectric constant gradient. Since the boundary conditions of the imaging region are known, the dielectric constant of the outermost pixel in the imaging region can be taken as a known quantity. The dielectric constants of the remaining pixels are taken as unknown quantities. An equation is established between the dielectric constants of adjacent pixels and the gradient of the pixel's dielectric constant. The dielectric constant distribution in the xoy plane is solved using the Tikhonov regularization algorithm.

[0166] For the second form of the ECT-EMM linear equation, the dielectric constant distribution is reconstructed using the gradient of the sensitivity matrix and the gradient signal of the capacitance; according to equations (14b) and (15b), the directional derivative of the sensitivity matrix in the electrode movement direction is used. and and the directional derivative of the capacitor in the direction of electrode movement and The dielectric constant was reconstructed using the Tikhonov regularization algorithm.

[0167] Gradient signal detection device using dielectric constant imaging method, such as Figure 1 As shown, except for sensor B1, the detection device is the same as in Example 1.

[0168] The sensor B1 includes a measuring chamber and electrodes. The electrodes are arranged outside and in contact with the tube wall. The electrode spacing needs to consider two factors: first, the directional derivative of the capacitance measured by the signal detection unit must be distinguishable at this electrode spacing; second, the electrode spacing should be as small as possible within the sensor's dimensions. The measuring chamber is located outside the tube wall, and its outer wall is grounded to shield against external electromagnetic interference. The dielectric constant sample to be measured is placed inside the tube wall.

[0169] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A capacitance tomography method based on electromagnetic field momentum, characterized in that, Includes the following steps: Step 1: Under voltage source excitation, solve the analytical or numerical solution of the ECT for the boundary value problem of the imaging region to obtain the electric field intensity of the imaging region. Construct the sensitivity matrix or the gradient of the sensitivity matrix; ECT represents capacitance tomography. Step 2: Select a suitable coordinate system and construct the ECT-EMM linear equations; ECT-EMM represents capacitance tomography based on electromagnetic field momentum, including: The suitable coordinate system includes a two-dimensional rectangular coordinate system, a two-dimensional polar coordinate system, a three-dimensional rectangular coordinate system, or a cylindrical coordinate system; Pair beg The directional derivative of the direction yields two forms of the ECT-EMM equation; The first form of the ECT-EMM linear equation is: （5a） in, This is the normalized sensitivity matrix. The normalized dielectric constant is The normalized capacitance. For independent measurements, The number of pixels in the imaging region; in equation (5a) For normalized capacitance directional derivative of direction, For the normalized permittivity in directional derivative of direction, and This is a coefficient vector, which is related to the specific expansion of the gradient in the selected coordinate system; The second form of the ECT-EMM linear equation is: （5b） In equation (5b) For the sensitivity matrix in Directional derivative of the direction; Step 3: Obtain the gradient signal of the capacitance of the receiving electrode of the sensor through the signal detection unit; Step 4: Reconstruct the dielectric constant distribution using the sensitivity matrix, the coordinate system-related coefficient vector, and the gradient signal of the capacitance.

2. The capacitance tomography method based on electromagnetic field momentum according to claim 1, characterized in that, Step one includes: Considering the volume of the imaging region , The boundary is The electromagnetic boundary value problem corresponding to ECT is: （2） In formula (2) For the Nabla operator, Spatial location coordinates, The spatial distribution of dielectric constant, For potential spatial distribution, Electrode position, To provide electrodes The applied voltage, Remove electrodes from the imaging region boundary Part of it; Depend on If a small perturbation is applied to the working fluid, the linear equation of ECT is: （3） In equation (3), the excitation electrode With detection electrode This constitutes a set of reciprocal processes, where process I is performed at the excitation electrode. Apply voltage By detecting electrodes Obtain the detection capacitance value Process II involves the detection electrode. Apply voltage Through excitation electrodes Obtain the detection capacitance value , and Equal, uniformly recorded as ; The spatial distribution of electric field intensity in process I. The spatial distribution of electric field intensity in process II; Define the spatial distribution of dielectric constant within the imaging region. , for excitation electrode Apply voltage at The spatial distribution of electric field intensity is solved through numerical calculation. ;Depend on The matrix elements of the constructed sensitivity matrix are: （4a） In equation (4a) and Number the electrodes. For the electrode Spatial distribution of electric field intensity when excitation is applied. For the electrode Spatial distribution of electric field intensity when excitation is applied. Electrode With electrodes The spatial distribution of the sensitivity matrix constituting the electromagnetic reciprocal process, and ; Depend on The gradient matrix elements of the constructed sensitivity matrix are: （4b） In equation (4b) Electrode With electrodes The spatial distribution of the gradient of the sensitivity matrix constituting the electromagnetic reciprocal process, and .

3. The capacitance tomography method based on electromagnetic field momentum according to claim 2, characterized in that, Step three includes: According to the gradient formula, the gradient signal of a capacitor is obtained by measuring the directional derivative of the capacitor along the coordinate axes of an orthogonal coordinate system.

4. The capacitance tomography method based on electromagnetic field momentum according to claim 3, characterized in that, Step four includes: The two forms of ECT-EMM linear equations correspond to two different reconstruction methods; The reconstruction method corresponding to the first form of the ECT-EMM linear equation is as follows: Based on the sensitivity matrix... The dielectric constant distribution is reconstructed based on the coefficient vectors related to the coordinate system and the gradient signal of the capacitance according to equation (5a). Then, the dielectric constant of the outermost pixel in the imaging region is taken as a known quantity, and the dielectric constant of the remaining pixels is taken as an unknown quantity. An equation is established between the dielectric constant of adjacent pixels and the gradient of the dielectric constant of the pixel. The dielectric constant distribution is obtained by solving the equation. The reconstruction method corresponding to the second form of the ECT-EMM linear equation is: based on the gradient of the sensitivity matrix. The dielectric constant distribution is reconstructed using the coefficient vectors related to the coordinate system and the gradient signal of the capacitance, according to equation (5b).

5. A gradient signal detection device using the capacitance tomography method based on electromagnetic field momentum as described in any one of claims 1-4, characterized in that, include: The system comprises a signal generator, a sensor, a signal detection unit, a signal amplification unit, and a signal acquisition and imaging algorithm unit. The output of the signal generator is connected to the transmitting electrode of the sensor, the receiving electrode of the sensor is connected to the input of the signal detection unit, the output of the signal detection unit is connected to the input of the signal amplification unit, and the output of the signal amplification unit is connected to the signal acquisition and imaging algorithm unit.

6. The gradient signal detection device according to claim 5, characterized in that, The signal detection unit is used to measure the gradient signal of the capacitance of the receiving electrode of the sensor. This is achieved by placing two electrodes at close distances along the coordinate axes of an orthogonal coordinate system, or by moving the electrodes along the coordinate axes of an orthogonal coordinate system. The electrodes are selected to be attached to the imaging area or not attached to the imaging area as required. Electrodes not attached to the imaging area are fixed by an electrode bracket.

7. The gradient signal detection device according to claim 6, characterized in that, The sensor includes a measuring chamber and electrodes; the electrodes include a transmitting electrode and a receiving electrode; the outer wall of the measuring chamber is grounded to shield the measurement signal from external electromagnetic interference. The dielectric constant sample to be measured is placed inside the sensor.

8. The gradient signal detection device according to claim 5, characterized in that, The signal generating unit includes a signal generator connected to the transmitting electrode of the sensor; The signal detection unit includes a signal conversion circuit that converts the voltage signal of the electrode into a capacitance signal; The input terminal of the signal amplification unit is connected to the output terminal of the signal detection unit to amplify the capacitance signal; The signal acquisition and imaging algorithm unit includes a computer with signal acquisition capabilities and image reconstruction algorithms, used to process the acquired data from the signal detection unit and apply the reconstruction algorithm to perform image reconstruction.

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