Electrical capacitance tomography three-dimensional image reconstruction method based on class sensitivity equation

Abstract

The invention designs an electrical capacitance tomography three-dimensional image reconstruction method based on a sensitivity-like equation, and belongs to the technical field of electrical capacitance tomography. The method comprises the following steps: firstly, according to an electrostatic boundary differential equation and a capacitance calculation formula of an ECT detection system, constructing a class sensitivity equation by utilizing a Gaussian divergence theorem so as to describe a relationship between dielectric constant distribution in a pipeline and multiple groups of capacitance measurement values; performing wavelet threshold de-noising processing on the acquired multiple groups of capacitance measurement values to remove noise caused by electromagnetic interference and measurement errors; then designing and training a back propagation neural network optimized based on a double-chain quantum genetic algorithm to solve the sensitivity-like equation to obtain an approximate solution of dielectric constant distribution in the pipeline; and finally, outputting a three-dimensional dielectric constant distribution image according to the trained neural network model. According to the method, the sensitivity-like equation model, waveform denoising and the quantum optimization neural network are combined, and the accuracy and robustness of ECT three-dimensional image reconstruction are effectively improved. Experimental results show that compared with a traditional reconstruction algorithm, the method can obtain images with higher quality, and the reconstruction precision and the signal-to-noise ratio are remarkably improved.

Description

Technical Field

[0001] The present invention relates to electrical capacitance tomography (ECT) technology, and more specifically, to a three-dimensional image reconstruction method based on a sensitivity-like equation. This method establishes a mathematical model between the internal permittivity distribution of a pipeline and the measured capacitance value. Combined with signal preprocessing and optimization algorithms, the method processes the capacitance measurement data from the ECT system to ultimately produce a three-dimensional permittivity distribution image. Background Art

[0002] Electrical capacitance tomography (ECT) is a method for imaging two-phase / multi-phase fluids based on an array of capacitance sensors. Because different fluid media have different relative dielectric constants, the ECT system reflects the internal fluid distribution by measuring the capacitance changes between multiple pairs of electrodes surrounding the pipe. Currently, traditional ECT image reconstruction algorithms mainly use linear backprojection, iterative Landweber, or Gauss-Newton methods. These methods rely on a sensitivity matrix to approximate the linear relationship between the dielectric constant distribution within the pipe and the electrode capacitance response. However, in practical applications, factors such as the limited number of electrodes, capacitance measurement noise, and the number of measurements being less than the number of grid cells often affect this problem, resulting in a highly ill-posed state, low reconstruction accuracy, and the susceptibility to artifacts. To improve the accuracy of ECT three-dimensional reconstruction, nonlinear reconstruction methods based on optimization algorithms and neural networks have been developed in recent years. However, these methods still suffer from high computational complexity and a tendency to fall into local optimality. Therefore, a technical solution that can accurately and efficiently complete ECT three-dimensional image reconstruction is urgently needed. Summary of the Invention

[0003] In response to the shortcomings of the existing technology, the present invention provides a three-dimensional image reconstruction method for electrical capacitance tomography based on a quasi-sensitivity equation. The core idea of ​​this method is: first, using the ECT electrostatic boundary differential equation and the electrostatic energy storage formula, a quasi-sensitivity equation between the dielectric constant distribution inside the pipeline and the measured capacitance value is derived to establish a mathematical model for three-dimensional imaging; then, the measured capacitance data is subjected to wavelet threshold denoising to reduce the impact of environmental noise and measurement error on the reconstruction accuracy; then, a back propagation (BP) neural network optimized by a double-chain quantum genetic algorithm is used to solve the above equation, and the optimal network weight is obtained through a global optimization algorithm, thereby avoiding the network training from falling into a local optimum; finally, the denoised capacitance value is mapped to a three-dimensional dielectric constant distribution image using the trained network model. The method of the present invention can effectively improve the quality and stability of ECT three-dimensional image reconstruction.

[0004] Effects of the Invention

[0005] 1. By establishing a quasi-sensitivity equation based on electrostatic field theory, the relationship between the three-dimensional dielectric constant distribution and capacitance response is accurately described, providing a theoretical basis for three-dimensional imaging;

[0006] 2. Introducing wavelet threshold denoising technology to pre-process the capacitance measurement sequence, significantly improving the signal-to-noise ratio of the data, thereby improving the quality of the final image reconstruction;

[0007] 3. Using a double-chain quantum genetic algorithm to optimize the BP neural network, the global search capability of quantum evolution improves the network training effect and avoids the local convergence problem of the traditional BP algorithm;

[0008] 4. This method can accurately reconstruct the dielectric constant distribution of the measured area even when the measurement data is insufficient and there is noise, thus improving the application performance of the ECT system. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 ; Peak signal-to-noise ratio of different filtering methods

[0010] Figure 2 ;Calculation flow chart of BP neural network optimized by DCQGA

[0011] Figure 3 ; Comparison of expected imaging and actual imaging Specific implementation methods

[0012] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to illustrate the present invention and are not intended to limit the present invention. The present invention is described in detail below in conjunction with the accompanying drawings and examples.

[0013] (1) For 3D image reconstruction, the ECT boundary differential equation is used to construct a sensitivity-like function expression, and the sensitivity is calculated in conjunction with the Gaussian divergence theorem. Regarding the construction and definition of the sensitivity-like equation: First, according to the physical model of the ECT system, the dielectric constant distribution ε(x, y, z) inside the pipe affects the capacitance C between the electrodes. Furthermore, the electrostatic field of the ECT system satisfies the boundary differential equation and the electrostatic energy storage calculation formula. The integral formula for calculating the charge within the volume V of the ECT system is as follows.

[0014]

[0015] Combining the capacitance calculation equation C = Q / U and introducing electrostatic boundary conditions, the volume integral is converted into the electrode surface integral through the Gaussian divergence theorem, and the expression between the capacitance value and the dielectric constant distribution can be obtained as follows.

[0016]

[0017] Rearranging the equation yields:

[0018]

[0019] Among them, D xy represents the projection of the ECT detection system's outer surface onto the xoy plane; S(x,y,z) is the ECT detection system's sensitivity. The constructed quasi-sensitivity equation formally links the pipeline's internal permittivity distribution vector, φ, with the capacitance measurement vector, C. Specifically, when z = 0, it becomes the ECT two-dimensional capacitance calculation equation, equivalent to generalizing the traditional two-dimensional sensitivity matrix to three dimensions. This equation provides the mathematical foundation for solving the permittivity distribution.

[0020] (2) Wavelet threshold denoising: Since the capacitance signal in actual measurement is affected by environmental electromagnetic noise and sensor errors, the present invention performs wavelet threshold denoising on the collected multiple sets of capacitance measurement sequences before reconstruction. The recursive equation for the wavelet transform of the capacitance measurement signal is as follows.

[0021] Sf(j+1,k)=Sf(j,k)×h(j,k)

[0022] Wf(j+1,k)=Sf(j,k)×g(j,k)

[0023] Here, functions h and g are the low-pass and high-pass filters of the wavelet transform, respectively; j determines the scaling, and k determines the translation amplitude; Sf(0,k) is the true value of the capacitance at time 0, and Sf(j,k) and Wf(j,k) are the scale coefficient and wavelet coefficient, respectively. Specifically, the capacitance measurement signal is treated as a continuous signal that varies over time, and a multi-layer wavelet decomposition is performed on it to obtain a set of scale coefficients and detail coefficients. Since signal components correspond to larger coefficients in the transform domain and noise corresponds to smaller coefficients, a threshold is set for the decomposition coefficients at each layer. Coefficients less than the threshold are set to zero, and coefficients greater than the threshold are retained. The remaining coefficients are then subjected to an inverse wavelet transform to reconstruct the denoised capacitance signal. The inverse wavelet transform equation for the reconstructed capacitance measurement signal after thresholding is as follows.

[0024]

[0025] according to Figure 1 Experiments show that after wavelet threshold denoising, the peak signal-to-noise ratio (PSNR) of the obtained capacitance signal is greatly improved (from about 17dB of the original signal to more than 54dB), significantly eliminating the influence of random noise on the reconstruction effect. The denoised capacitance data is used as the input of the subsequent BP neural network, which improves the stability of network training and reconstruction accuracy.

[0026] (2) Double-chain quantum genetic algorithm optimizes BP neural network: Under the sensitivity equation model, since the number of actual measurable capacitance values ​​is often less than the number of segmentation units, it is an underdetermined problem. Therefore, BP neural network is used for approximate solution. The optimized BP calculation process is as follows: Figure 2As shown. First, a BP network is constructed. The number of input nodes is equal to the number of sensors, the number of output nodes is equal to the number of cross-section segmentation grid units, and the output value corresponds to the dielectric constant of each grid unit. Considering the problem that the traditional BP algorithm is prone to falling into local optimality, the present invention adopts a double-chain quantum genetic algorithm (DCQGA) to optimize the weights and threshold parameters of the neural network. In DCQGA, the initial parameter sequence composed of the initial weights and biases of the BP neural network is usually encoded by quantum bit probability coding. The double-chain coding method is as follows.

[0027]

[0028] Where m is the population size of the initial parameter sequence; p i is the i-th data in the population, i=1,2,…,m; n is the number of qubits, j=1,2,…,n; α ij , β ij is the amplitude of the jth qubit in the i-th data of the population; t ij =2π×rand, where rand is a random number between 0 and 1. DCQGA uses qubit amplitude encoding to encode the chromosome into a quantum state and divides the quantum chromosome into two sub-chains to search for the optimal solution simultaneously. The quantum rotation gate operation iteratively updates the amplitude parameters of the qubit, allowing the two sub-chains to co-evolve and quickly converge to the global optimal solution. The qubit amplitude is mapped to the solution space, then p i The solution space variable formula is as follows.

[0029]

[0030] In the specific implementation, the initial weights of the BP network are quantum encoded, and quantum individual updates and classical selection crossover mutations are cyclically performed during the training process to obtain the optimal network parameters in a global optimization manner.

[0031] (3) Image reconstruction experiment analysis: In a specific embodiment, the pipeline cross section was divided into 16×16 grid cells, and capacitance was measured using 12 ring electrodes to obtain a 12-dimensional capacitance value vector. The collected capacitance data was subjected to wavelet threshold denoising and then input into a BP neural network. The network adopts a two-hidden layer structure, and the number of hidden nodes in each layer can be adjusted according to the system scale. The scoring function formula of the BP neural network is as follows.

[0032]

[0033] DCQGA was used to optimize and train the BP neural network. After several iterations, the error met the accuracy requirements. Experimental results showed that the uniformity and edge clarity of the three-dimensional dielectric constant distribution image reconstructed using the proposed method significantly outperformed traditional linear iterative algorithms, significantly improving reconstruction accuracy. The image reconstruction accuracy, Acc, is calculated as follows.

[0034]

[0035] The comparison between the 3D image reconstructed by the optimized BP neural network and the standard image is as follows: Figure 3 shown.

[0036] In addition, compared with the reconstruction scheme without wavelet denoising, the BP neural network based on the sensitivity equation and DCQGA optimization has higher image reconstruction accuracy for four flow states: full water phase, stratified flow, annular flow, and full gas phase.

[0037] The present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of the present invention.

Claims

1. A three-dimensional image reconstruction method for electrical capacitance tomography based on a sensitivity-like equation, characterized in that: The steps include: Step 1: Construct a quasi-sensitivity equation. Based on the electrostatic boundary differential equation and capacitance calculation formula of the electrical capacitance tomography (ECT) system, and using the Gaussian divergence theorem, the relationship between the dielectric constant distribution inside the pipeline and the capacitance measurement value is derived to obtain a quasi-sensitivity equation for 3D image reconstruction. Step 2: Capacitance data acquisition and denoising: Collect multiple sets of capacitance measurement values ​​under the two-phase flow state of the pipeline, and perform wavelet threshold denoising on the capacitance measurement values ​​in the time domain. That is, a threshold strategy is applied to the coefficients after wavelet transformation to remove the noise coefficients, and the inverse wavelet transform is used to reconstruct the signal to obtain the denoised capacitance data. Step 3: A double-chain quantum genetic algorithm is used to optimize BP neural network training. A back-propagation (BP) neural network is established, where the number of input nodes is equal to the number of capacitance sensors and the number of output nodes is equal to the number of units divided into the pipe cross section. The double-chain quantum genetic algorithm is used to optimize the weights and thresholds of the neural network. Specifically, the chromosome is initialized using qubit amplitude encoding, the chromosome is divided into two sub-chains, and a global search is performed simultaneously. The qubit probability amplitude is iteratively updated through a quantum rotation gate to obtain the globally optimal network parameters. The BP neural network is trained using the denoised capacitance data until the error converges. Step 4: 3D image reconstruction: Using the trained BP neural network model, the dielectric constant distribution of each grid cell inside the pipeline is output based on the denoised capacitance measurement value to form a 3D dielectric constant image of the pipeline cross section.

2. The method according to claim 1, wherein: The wavelet threshold denoising step includes performing multi-layer wavelet decomposition on the capacitance measurement time series, setting an appropriate threshold to remove the noise component in the wavelet coefficients, and then performing an inverse transform. The peak signal-to-noise ratio (PSNR) of the obtained denoised signal is significantly higher than that of the unprocessed signal.

3. The method according to claim 1, wherein: In step (1), the specific operation of constructing the quasi-sensitivity equation is as follows: the volume charge integral formula of the ECT system and the capacitance definition formula are combined, and combined with the boundary conditions, the volume integral is converted into the integral of the electrode surface through the Gaussian divergence theorem to obtain a formalized sensitivity function expression.

4. A three-dimensional image reconstruction device for electrical capacitance tomography based on a sensitivity-like equation, characterized in that: include: (1) an acquisition module for collecting multiple sets of capacitance measurement values ​​of two-phase flow in a pipeline; (2) A sensitivity equation construction module, which is used to construct a sensitivity equation based on the boundary differential equation of the ECT system and the capacitance calculation formula using the Gaussian divergence theorem; (3) A denoising module, which is used to perform wavelet threshold denoising on the collected capacitance measurement value sequence and output the denoised capacitance data; (4) A network training module, which is used to construct a BP neural network and use a double-chain quantum genetic algorithm to optimize its weights and thresholds, and train the neural network using the denoised capacitance data; (5) A reconstruction module, which is used to use the trained BP neural network model to output the dielectric constant distribution image inside the pipeline based on the denoised capacitance value.

5. The device according to claim 4, characterized in that: The BP neural network includes an input layer, at least one hidden layer and an output layer. The number of nodes in the input layer is the same as the number of capacitance measurement values, the number of nodes in the output layer is the same as the number of grid units in the pipeline cross section, and the network parameters are obtained by global optimization of a double-chain quantum genetic algorithm.

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