Single-section electrical tomography flow velocity measurement method based on electromagnetic parameter space-time distribution

Abstract

The application discloses a single-section electrical tomography flow velocity measurement method based on electromagnetic parameter space-time distribution. The method utilizes an electrical tomography imaging device to continuously sample multiphase fluid on a single measurement section, acquires boundary measurement signals and reconstructs electromagnetic parameter distribution in the section, respectively performs time dimension derivative operation and space dimension gradient operation, establishes a convection transport constraint relationship based on the physical mechanism that electromagnetic parameters in the multiphase flow are transported with fluid movement, combines constraint equations of each pixel point in the section into an over-determined equation group, and obtains flow velocity vector distribution by solving the over-determined equation group through a least square method. Finally, the flow velocity distribution is subjected to weighted average based on sensitivity to obtain overall flow velocity. The application realizes flow velocity measurement under the single-section condition, does not need experience calibration and double-section cross-correlation time delay estimation, reduces measurement complexity, and can be widely applied to resistive tomography imaging, capacitive tomography imaging and electromagnetic tomography imaging devices.

Description

Technical Field

[0001] This invention relates to the field of fluid measurement technology, and in particular to a single-section electrical tomography velocity measurement method based on the spatiotemporal distribution of electromagnetic parameters. Background Technology

[0002] Electrical tomography (EMT) is a process detection technique that reconstructs cross-sectional distribution based on differences in the electromagnetic properties of a medium. It has been widely used for visualization and parameter measurement of multiphase flow processes, including gas-solid, liquid-solid, and gas-liquid processes. Depending on the physical parameters used, EMT mainly includes resistive tomography (using conductivity as the sensitive parameter), capacitive tomography (using dielectric constant as the sensitive parameter), and electromagnetic tomography (using magnetic permeability as the sensitive parameter).

[0003] In the field of flow velocity measurement using electro-tomography, existing technologies mainly include three types of methods: First, the dual-section cross-correlation velocimetry method, which obtains the time delay by performing correlation analysis between signals or images of multiple measurement sections to calculate the flow velocity. However, this method depends on the sensor spacing and synchronization accuracy, and is prone to errors when there is lateral flow or changes in flow pattern. Second, the single-section feature calibration method, which achieves velocity measurement by extracting the cross-sectional distribution features and establishing an empirical relationship between them and the flow velocity. However, this method relies on a large amount of calibration data and has poor generalization ability. Third, the indirect derivation method based on fluid mechanics, which calculates physical quantities such as density through electromagnetic parameters and combines them with fluid equations to calculate the flow velocity. However, this method relies on multiple intermediate parameters, is computationally complex, and has limited real-time performance and stability.

[0004] Therefore, existing technologies cannot achieve a flow velocity measurement method that is calibration-free and highly adaptable under single-section conditions, and there is an urgent need to propose a new technical solution to overcome the above problems. Summary of the Invention

[0005] Therefore, the purpose of this invention is to provide a single-section electrical tomography flow velocity measurement method based on the spatiotemporal distribution of electromagnetic parameters. By utilizing the rate of change of electromagnetic parameter images in time and the gradient in space within the same cross section, the flow velocity can be directly deduced through physical equations, achieving single-section flow velocity measurement and eliminating empirical calibration and time delay errors.

[0006] To achieve the above objectives, this invention provides a single-section electrical tomography velocity measurement method based on the spatiotemporal distribution of electromagnetic parameters, comprising the following steps: S1. Using an electrical tomography device, the multiphase fluid is continuously sampled on a single measurement section to obtain the boundary measurement signal that changes with time, forming time series measurement data; S2. Based on the time-series measurement data, an image reconstruction algorithm is used to obtain the electromagnetic parameter distribution within the cross-section. ,in Represents the spatial coordinates of the cross section. Indicates time; S3. Calculate the derivative of the electromagnetic parameters in the time dimension; S4. Calculate the gradient of the electromagnetic parameter distribution in the spatial dimension; S5. Based on the obtained derivatives and gradients, and considering the physical mechanism of electromagnetic parameter transport in multiphase flow, establish convective transport constraints. Where v represents the velocity vector to be solved; S6. Based on the aforementioned convection transport constraints, construct a least-squares model for solving the velocity problem; S7. Based on the obtained flow velocity distribution, perform a sensitivity-based weighted average on the sensor cross-section to obtain the final flow velocity.

[0007] Furthermore, the electromagnetic parameters include conductivity, dielectric constant, and magnetic permeability; in S2, the step of obtaining the distribution of electromagnetic parameters within the cross-section based on the time-series measurement data using an image reconstruction algorithm includes the following steps: S201. Discretize the cross section to be measured into multiple pixel units, and perform sensitivity calculation on the electrical tomography device to establish a sensitivity matrix; the sensitivity matrix is ​​used to characterize the degree of influence of electromagnetic parameter changes in each pixel unit on the boundary measurement signal; S202. Based on the single-frame boundary measurement vector in the time series measurement data and the sensitivity matrix, establish a linear reconstruction model; S203. Solve the linear reconstruction model using a reconstruction algorithm to obtain the cross-sectional electromagnetic parameter distribution corresponding to the frame measurement data; S204. Repeat steps S202 to S203 for each frame of data in the time series measurement data to obtain the distribution of electromagnetic parameters in the cross section that changes with time.

[0008] Furthermore, the reconstruction algorithm can employ a linear back-projection algorithm, with the calculation formula being: ,in This represents the sensitivity matrix of an electrical tomography device. express transpose, This represents the boundary measurement data of the electrical tomography device. The electromagnetic parameter distribution within the reconstructed cross section.

[0009] Furthermore, in S3, the derivatives of the electromagnetic parameters distributed over time are calculated using the difference calculation formula shown below: ; in, The electromagnetic parameter distribution for reconstruction; For time intervals.

[0010] Furthermore, in S4, when calculating the gradient of the electromagnetic parameter distribution in the spatial dimension, the central difference formula shown below is used. in, This represents the gradient of magnetic permeability in the x-direction; This represents the gradient of magnetic permeability in the y-direction; Indicates the interval in the x-direction. This indicates the interval in the y-direction.

[0011] Furthermore, in S5, during the convective transport modeling process, the changes in electromagnetic parameters are dominated by the convection term, while the diffusion and source terms are ignored.

[0012] Furthermore, in S6, based on the aforementioned convection constraint relationship, the least squares model for solving the flow velocity includes: For all pixels ,make , , The convective transport constraint relationship can be expressed as follows: The above equations are solved using the least squares method.

[0013] Furthermore, the objective function to be solved is constructed as follows: in, Here is the regularization parameter; the analytical solution of the above objective function is...

[0014] Furthermore, in S7, based on the obtained flow velocity distribution, a sensitivity-based weighted average is performed on the sensor cross-section to obtain the final flow velocity, including: Based on the sensitivity matrix, the sensitivity of each pixel is normalized to obtain the weight distribution; The formula for calculating the sensitivity-based weights is as follows: The formula for calculating the overall flow velocity is: , in, Let N be the sensitivity matrix, and N be the matrix dimension; i and j are the row and column indices of the sensitivity matrix, respectively. The obtained flow velocity distribution.

[0015] The beneficial effects of this invention are: 1. It realizes single-section velocity measurement, reducing system complexity; 2. It eliminates the need for empirical calibration, improving generalization ability; 3. It avoids time delay estimation errors and does not rely on cross-correlation or time window processing; 4. It has good real-time performance and can realize online flow velocity measurement; 5. The physical mechanism is clear and has clear engineering interpretability. Attached Figure Description

[0016] Figure 1 This is an overall flowchart of the single-section electrical tomography velocity measurement method based on the spatiotemporal distribution of electromagnetic parameters of the present invention. Figure 2 This is a schematic diagram of a single-section electromagnetic tomography velocimetry device. Figure 3 This is a schematic diagram of the internal structure of the sensor module; Figure 4 A schematic diagram of the image reconstructed from the image of magnetic permeability distribution; Figure 5 This is a schematic diagram showing the trend of magnetic permeability distribution over time. Figure 6 This is a schematic diagram of the spatial gradient distribution of magnetic permeability. Figure 7 This is a schematic diagram of the fluid velocity distribution across the sensor cross-section.

[0017] In the diagram: 1. Sensor module; 2. Data acquisition module; 3. Imaging module. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 1 As shown, one embodiment of the present invention provides a single-section electrical tomography velocity measurement method based on the spatiotemporal distribution of electromagnetic parameters, which includes the following steps: S1, using an electrical tomography device, continuous sampling of a multiphase fluid is performed on a single measurement cross-section to acquire time-varying boundary measurement signals, forming time-series measurement data; wherein, the electrical tomography device includes: a resistance tomography device, a capacitance tomography device, and an electromagnetic tomography device. This embodiment uses an electromagnetic tomography device for reconstructing the permeability distribution as an example for description, but the present invention is also applicable to capacitance tomography devices for reconstructing the dielectric constant distribution and resistance tomography devices for reconstructing the conductivity distribution. The single-section electromagnetic tomography velocimetry device used in the present invention, such as... Figure 2 As shown, it includes a sensor module 1, a data acquisition module 2, and an imaging module 3. The electromagnetic tomography imaging device continuously samples the multiphase fluid at a single measurement cross-section to acquire boundary measurement signals that vary over time, forming time-series measurement data. During operation, boundary measurement signals under different combinations are acquired through excitation-measurement switching. Among them, boundary measurement signals The measurement includes the following process, according to Figure 3The sensor module shown has 8 excitation coils numbered ah surrounding it. When one excitation coil responds, the other excitation coils do not work. At this time, 16 TMRs collect data simultaneously. When the next excitation coil works, the magnetic field signals of the 16 TMRs are acquired. This process continues in sequence. One frame of signal, or one cycle, is a one-dimensional magnetic field signal B composed of 8*16=128 data points, which constitute the boundary measurement signal matrix B.

[0020] S2, Based on the time-series measurement data, an image reconstruction algorithm is used to obtain the magnetic permeability distribution within the cross-section. ,in Represents the spatial coordinates of the cross section. To express time, the following steps are involved: S201. Discretize the cross section to be measured into multiple pixel units, and perform sensitivity calculation on the electromagnetic tomography device to establish a sensitivity matrix; the sensitivity matrix is ​​used to characterize the degree of influence of the change in magnetic permeability within each pixel unit on the boundary measurement signal. The electromagnetic tomography sensor adopts a structure combining arrayed coils and magnetically sensitive detection elements. Multiple excitation coils are uniformly arranged circumferentially along the same cross section of the outer wall of the pipe being measured, and the axial direction of each excitation coil is perpendicular to the pipe cross section, which is used to apply an alternating magnetic field to the measured area. The magnetically sensitive element is set at the corresponding position of each coil, which is used to detect the magnetic field response signal caused by the change of the magnetic permeability of the medium in the measured area.

[0021] During the measurement process, a sinusoidal AC constant current source sequentially excites individual coils in the array. While any excitation coil is active, the remaining magnetically sensitive detection elements synchronously acquire the induced signal at the corresponding position, thereby obtaining the boundary measurement response under that excitation state. Subsequently, each excitation coil is excited one by one according to a preset scanning sequence, and the above synchronous detection process is repeated until one round of excitation scanning of the entire array coils is completed, ultimately obtaining the electromagnetic tomography boundary measurement data. For the electromagnetic tomography system, the sensitivity matrix is ​​constructed based on the following steps: The finite element model is used to solve the problem. The circular cross section to be measured is divided into N pixel units. The perturbation is achieved by changing the relative permeability of each unit in the model in turn, and the boundary measurement data under the perturbation of each unit is obtained.

[0022] The formula for calculating the sensitivity of an electromagnetic tomography system is as follows: Where (x, y) represents the unit position, m represents the excitation coil number, and n represents the detection element number. This represents the boundary magnetic flux density when the perturbation element is located at (x, y). This represents the boundary magnetic field strength when there is no disturbance. This represents the change in permeability of the element at (x,y) before and after the perturbation. By traversing all N elements, the final sensitivity matrix S used for image reconstruction can be obtained.

[0023] S202. Based on the single-frame boundary measurement vector in the time-series measurement data and the sensitivity matrix, establish a linear reconstruction model; it should be noted that the single-frame boundary measurement vector used for image reconstruction The magnetic flux density is not the directly measured absolute magnetic field strength, but rather the change relative to the measured data of the reference field boundary. Similarly, the reconstructed permeability μ is also the change relative to the permeability of the reference field. Under the linearization approximation, the relationship between the two can be expressed as: The image reconstruction process is based on the known S and Under the premise of , solve for μ.

[0024] S203. Solve the linear reconstruction model using a reconstruction algorithm to obtain the cross-sectional permeability distribution corresponding to the frame measurement data; The boundary measurement data obtained in S1 is input into the image reconstruction module, and a reconstruction algorithm is used to reconstruct the magnetic permeability distribution image within the cross section. ,like Figure 4 As shown, the left side is the magnetic permeability distribution image at time t before reconstruction, and the right side is the reconstructed magnetic permeability distribution image at time t+Δt. This figure intuitively reflects the spatial distribution of different media (such as magnetic particles, bubbles, etc.) in the fluid, and the changes over time reflect the fluid motion; red / orange areas indicate higher magnetic permeability; blue / green areas indicate lower magnetic permeability.

[0025] The reconstruction algorithm can be a linear back-projection algorithm, and the calculation formula for the linear back-projection algorithm is as follows: ,in This represents the sensitivity matrix of the electromagnetic tomography system. express The transpose of .

[0026] S204. Repeat steps S202 to S203 for each frame of data in the time series measurement data to obtain the permeability distribution in the cross section that changes with time.

[0027] S3, calculate the derivative of the permeability distribution in the time dimension; based on the continuously sampled permeability distribution obtained in S2, perform discrete difference calculation in the time dimension to obtain the trend of permeability distribution changing with time, such as... Figure 5 The curves in different colored areas of the figure represent the temporal evolution of the permeability of pixels at different locations within the cross-section. For example, the red curve indicates a large permeability value over time, while the blue curve indicates a small value. The difference calculation formula is as follows: Preferably, multi-frame averaging can be used to improve noise resistance. Wherein, The reconstructed permeability distribution; For time intervals.

[0028] S4, calculate the gradient of the permeability distribution in the spatial dimension; based on the results obtained in S2... The gradient of the permeability distribution at time t is calculated in the spatial dimension to obtain... The spatial gradient distribution of magnetic permeability is as follows Figure 6 As shown, Figure 6 The left side shows the spatial gradient of magnetic permeability along the X direction, and the right side shows the spatial gradient of magnetic permeability along the Y direction. The colors in the figure represent the magnitude of the gradient in the corresponding direction. Warm colors (red / orange) indicate increasing magnetic permeability along that direction, with larger values ​​resulting in redder colors; cool colors (blue / purple) indicate decreasing magnetic permeability along that direction, with larger absolute values ​​resulting in darker blue colors. The color distribution reveals regions in the flow field where magnetic permeability changes drastically (such as the location of phase interfaces).

[0029] The calculation formula using the central difference formula is as follows: ; ; in, This represents the gradient of magnetic permeability in the x-direction; This represents the gradient of magnetic permeability in the y-direction; Indicates the interval in the x-direction. This indicates the interval in the y-direction.

[0030] S5, based on the physical mechanism of permeability transport in multiphase flow, establishes convective transport constraint relationships. For each pixel in the permeability distribution image The specific constraint form is as follows: In S5, during convective transport modeling, the change in permeability is dominated by the convection term, neglecting the diffusion and source terms. Since electromagnetic parameters possess fluid properties, the spatial distribution of permeability follows fluid advection or convection. Therefore, neglecting diffusion and source terms, the total change of the scalar field μ with time is zero. .

[0031] S6, based on the aforementioned convection transport constraints, a least-squares model for velocity calculation is constructed. Based on the constraints in S5, the temporal derivative and spatial gradient are aligned at the same time level, and the constraint equations for each discrete pixel are combined to form an overdetermined system of equations. The least-squares method is used to solve this system of equations to obtain the velocity vector distribution, such as... Figure 7As shown, the left side is a schematic diagram of the fluid velocity distribution across the sensor cross-section in the X direction, and the right side is a schematic diagram of the fluid velocity distribution across the sensor cross-section in the Y direction. The color differences in different areas reflect the non-uniformity of the flow field, allowing for intuitive identification of high-speed, low-speed, and recirculation regions; warm colors (red / orange) indicate fluid movement along the positive X direction, with larger values ​​indicating redder colors; cool colors (blue / purple) indicate fluid movement along the negative X direction, with larger absolute values ​​indicating darker blue colors. The specific implementation process is as follows: For all pixels ,make , , The constraint relationships in S5 can be expressed as follows: Using the least squares method When solving the above equation, it is preferable to introduce a regularization term to improve the stability and noise resistance of the solution, and construct the objective function to be solved as follows: ,in For regularization parameters, Let v be the square of the L2 norm of the velocity vector to be determined, i.e., v 2 x +v 2 y The sum; the analytical solution of the above objective function is .

[0032] S7. Based on the obtained flow velocity distribution, a sensitivity-based weighted average is performed on the sensor cross-section to obtain the final flow velocity. The flow velocity distribution obtained in S6 is then subjected to a weighted average based on the sensitivity matrix distribution to obtain the overall flow velocity. Specifically, the process is as follows: spatial weight coefficients are constructed based on the sensitivity matrix of the electromagnetic tomography system, and the sensitivity of each pixel is normalized to obtain a weight distribution. Based on these weights, the obtained flow velocity distribution is weighted and averaged to obtain the overall flow velocity. The formula for calculating the weights based on the sensitivity distribution is as follows: The formula for calculating the overall flow velocity is: ;in, Let N be the sensitivity matrix, and N be the matrix dimension; i and j are the row and column indices of the sensitivity matrix, respectively. The obtained flow velocity distribution.

[0033] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters, characterized in that, Includes the following steps: S1. Using an electrical tomography device, the multiphase fluid is continuously sampled on a single measurement section to obtain the boundary measurement signal that changes with time, forming time series measurement data; S2. Based on the time-series measurement data, an image reconstruction algorithm is used to obtain the electromagnetic parameter distribution within the cross-section. ,in Represents the spatial coordinates of the cross section. Indicates time; S3. Calculate the derivative of the electromagnetic parameters in the time dimension; S4. Calculate the gradient of the electromagnetic parameter distribution in the spatial dimension; S5. Based on the obtained derivatives and gradients, and considering the physical mechanism of electromagnetic parameter transport in multiphase flow, establish convective transport constraints. Where v represents the velocity vector to be solved; S6. Based on the aforementioned convective transport constraints, construct a least squares model to solve for the velocity distribution; S7. Based on the obtained flow velocity distribution, calculate the sensitivity-based weighted average on the sensor cross section to obtain the final flow velocity.

2. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 1, characterized in that, The electromagnetic parameters include conductivity, dielectric constant, and magnetic permeability; The process of obtaining the electromagnetic parameter distribution within the cross-section based on the time-series measurement data and using an image reconstruction algorithm includes the following steps: S201. Discretize the cross section to be measured into multiple pixel units, and perform sensitivity calculation on the electrical tomography device to establish a sensitivity matrix; the sensitivity matrix is ​​used to characterize the degree of influence of electromagnetic parameter changes in each pixel unit on the boundary measurement signal; S202. Based on the single-frame boundary measurement vector in the time series measurement data and the sensitivity matrix, establish a linear reconstruction model; S203. Solve the linear reconstruction model using a reconstruction algorithm to obtain the cross-sectional electromagnetic parameter distribution corresponding to the frame measurement data; S204. Repeat steps S202 to S203 for each frame of data in the time series measurement data to obtain the distribution of electromagnetic parameters in the cross section that changes with time.

3. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 2, characterized in that, The reconstruction algorithm can employ a linear back-projection algorithm, and the calculation formula is as follows: ,in This represents the sensitivity matrix of an electrical tomography device. express transpose, For boundary measurement data of the electrical tomography device, The electromagnetic parameter distribution within the reconstructed cross section.

4. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 1, characterized in that, In S3, the derivatives of the electromagnetic parameter distribution in the time dimension are calculated using the following difference calculation formula: ； in, The electromagnetic parameter distribution for reconstruction; For time intervals.

5. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 4, characterized in that, In S4, the gradient of the electromagnetic parameter distribution in the spatial dimension is obtained using the central difference formula shown below. in, This represents the gradient of magnetic permeability in the x-direction; This represents the gradient of magnetic permeability in the y-direction; Indicates the interval in the x-direction. This indicates the interval in the y-direction.

6. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 1, characterized in that, In S5, during the modeling of convective transport, the changes in electromagnetic parameters are dominated by the convection term, while the diffusion and source terms are ignored.

7. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 1, characterized in that, In S6, based on the aforementioned convection constraint relationship, the least squares model for solving the flow velocity includes: For all pixels ,make , The convective transport constraint relationship can be expressed as follows: The above equations are solved using the least squares method.

8. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 7, characterized in that, The objective function to be solved is constructed as follows: in, Here is the regularization parameter; the analytical solution of the above objective function is... .

9. The method for measuring single-section electrical tomography velocity based on the spatiotemporal distribution of electromagnetic parameters according to claim 7, characterized in that, In S7, based on the obtained flow velocity distribution, a sensitivity-based weighted average is performed on the sensor cross-section to obtain the final flow velocity, including: Based on the sensitivity matrix, the sensitivity of each pixel is normalized to obtain the weight distribution; The formula for calculating the sensitivity-based weights is as follows: The formula for calculating the overall flow velocity is: , in, Let N be the sensitivity matrix, and N be the matrix dimension; i and j are the row and column indices of the sensitivity matrix, respectively. The obtained flow velocity distribution.

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