An image reconstruction method for detecting industrial two-phase flow

Abstract

The application discloses an image reconstruction method for detecting industrial two-phase flow, and specifically comprises the following steps: constructing a 16-electrode electrical impedance tomography measurement system model; obtaining a sensitivity matrix A by calculating the sensitivity matrix A according to relative boundary voltage measurement data combined with sensitivity theory; converting a nonlinear problem of image reconstruction into a linear problem; obtaining initial population information; biological population initialization; iteratively updating the biological population through hunting behavior, defense behavior and jumping behavior to obtain a new biological population; after the iteratively updating of the biological population, judging whether the new biological population satisfies v>V or not; if yes, stopping iteration and outputting a global optimal solution; if not, continuing iteration by setting v=v+1; and obtaining the global optimal solution of the biological population, that is, the global optimal solution is an optimal conductivity distribution to complete image reconstruction. The application has higher resolution, clearer background and better robustness.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electrical tomography, and particularly relates to an image reconstruction method for detecting industrial two-phase flow. BACKGROUND

[0002] Electrical impedance tomography (EIT) is a non-destructive functional imaging technology that presents the internal conductivity changes of an object in real time through images based on the boundary voltage measurement data of the object. The working principle of the electrical impedance tomography technology is that different structural organizations inside a measured conductive object have different electrical response characteristics to an electrical excitation signal. A certain number of electrodes are attached to the surface of the measured electric field, an electrical excitation signal is applied on different electrode pairs, the electrical response signal is measured on other electrode pairs in turn, and finally, a corresponding inverse problem image reconstruction algorithm is used to image the internal conductivity changes of the measured object. Due to the advantages of EIT such as non-invasiveness, non-destructiveness, low cost, simple hardware structure and the like, the technology has been widely applied to many fields such as medical imaging, industrial process detection, material damage detection and the like.

[0003] Image reconstruction is an important part of an EIT system, however, the process of image reconstruction is a complex nonlinear and ill-posed inverse problem, which poses a great challenge to the research of EIT. In order to further improve the accuracy of image reconstruction, it is very important to design an effective method to ensure the accurate reconstruction of the conductivity distribution. In recent years, with the in-depth research on the EIT image reconstruction technology, many image reconstruction methods have been proposed, such as traditional methods such as Landweber method, Tikhonov regularization method, D-bar method, conjugate gradient (CG) method and the like. In addition, commonly used intelligent methods include a deep learning method based on convolutional neural network, a genetic algorithm and the like. The Newton-Raphson method is one of the commonly used methods for solving the EIT inverse problem, which can effectively improve the quality of image reconstruction through iteration, but has the problem of local convergence, and a large amount of time is required to calculate the sensitivity matrix for each iteration. In view of the local convergence defect of the Newton-Raphson method, an intelligent bionic swarm optimization algorithm is introduced. The swarm algorithm is an algorithm proposed for the collaborative mechanism formed by the clustering activities of individuals with common characteristics, and has the remarkable characteristics of simplicity, fast convergence speed and ability to jump out of local convergence. It is a high-efficiency parallel optimization method and can be used to solve a large number of nonlinear and non-differentiable problems. Through in-depth research and analysis, the application proposes an EIT image reconstruction method based on an improved biological population optimization algorithm, which introduces an adaptive adjustment of the jump interval parameter, so that the method has strong global optimization ability in the initial stage and strong local optimization ability in the later stage, can effectively improve the quality of the reconstructed image, and solves the problem that the Newton-Raphson method is easy to fall into local optimization. SUMMARY

[0004] The application provides an image reconstruction method for detecting industrial two-phase flow, compared with a traditional image reconstruction method, the method provided by the application is improved by optimizing the conductivity distribution obtained by iterating once the Newton-Raphson method through a biological population optimization algorithm, in the optimization process, local optimization is performed through the hunting behavior or defense behavior of the biological population, a self-adaptive adjustment jump parameter is introduced to jump out of local optimization and global optimization is performed through the jump behavior, the method can have strong global optimization ability in the initial stage and strong local optimization ability in the later stage, the global optimal solution obtained through optimization is the optimal conductivity distribution, the obtained solution is closer to the real conductivity distribution, and image reconstruction is completed.

[0005] The technical implementation scheme of the application is that: the method provided by the application firstly uses the initial conductivity distribution obtained by iterating once the Newton-Raphson method as the initial population of the biological population, initializes the parameters of the biological population, then updates the position of the initial population through the hunting behavior, defense behavior and jump behavior of the biological population, in the optimization process, the biological population is easy to fall into local optimization, the self-adaptive adjustment jump interval parameter is introduced to jump out of local optimization and perform global optimization, and the global optimization ability of the biological population is improved. Evaluate all the biological populations, wherein H is the fitness value, A is the sensitivity matrix, is the updated conductivity distribution, and U is the measured voltage. The fitness values of all the biological populations are calculated, then the minimum fitness values obtained in all the cycles are compared, the minimum fitness value in all the cycle processes is obtained, the solution represented by the biological population with the minimum fitness value is the global optimal solution, and finally the global optimal solution is the optimal conductivity distribution.

[0006] A method for image reconstruction for detecting industrial two-phase flow, characterized by the following specific process: (1) Constructing a 16-electrode electrical impedance tomography measurement system model, using adjacent electrode current injection and adjacent electrode voltage measurement modes. For a complete measurement cycle, firstly, the first and second electrodes are excited, and the voltage signals between adjacent electrodes 3-4, 4-5...15-16 are measured. Next, the second and third electrodes are excited, and the voltage signals between adjacent electrodes 4-5, 5-6...16-1 are measured. The measurement cycle continues until a complete cycle is completed, and a total of 208 sets of independent voltage data are obtained. When there are no inclusions in the field, the empty field voltage measured is U1, and when there are inclusions, the full field voltage measured is U2. Further, the relative boundary voltage measurement value U can be obtained; (2) Based on the relative boundary voltage measurement data and combined with sensitivity theory, the sensitivity matrix A is calculated; (3) The nonlinear problem of image reconstruction is transformed into a linear problem; (4) Obtaining initial population information: the conductivity approximate distribution obtained by one iteration of the Newton-Raphson algorithm. (5) Initialize the biological population as the initial population for the biological population optimization algorithm; (6) Iterate and update the biological population through predation behavior, defense behavior and jumping behavior to obtain a new biological population; (7) After iterative update of the biological population, a new biological population is obtained. Propose a fitness function Evaluate the quality of each organism in the new biological population, compare the minimum fitness values ​​obtained in all cycles, and obtain the solution represented by the organism with the minimum fitness value in all cycles, that is, the solution represented by the organism with the minimum fitness value; (8) Determine whether v satisfies v>V. If yes, stop the iteration and output the global optimal solution; if no, v=v+1 and continue the iteration; (9) Obtain the global optimal solution of the biological population, that is, the global optimal solution is the optimal conductivity distribution. Complete the image reconstruction.

[0007] The beneficial effects of this invention are as follows: The method proposed in this invention, by introducing an adaptive adjustment of the jump interval parameter, can guide biological populations to escape local optimization, thereby improving the global optimization ability of biological populations. This can effectively improve the quality of reconstructed images, resulting in clearer backgrounds and better noise resistance. This invention has conducted qualitative and quantitative analysis of the performance of this image reconstruction method. The results show that the image reconstruction method proposed in this invention for detecting industrial two-phase flow has higher imaging quality, clearer backgrounds, more accurate placement of inclusions in the reconstructed image, and inclusion sizes closer to the actual target. Attached Figure Description

[0008] Figure 1 This is a flowchart of the image reconstruction method for detecting industrial two-phase flow according to the present invention;

[0009] Figure 2The 16-electrode sensor array of the present application;

[0010] Figure 3 The result images of the image reconstruction of six different models by using the Landweber method, the Newton-Raphson method and the method of the present application respectively;

[0011] Figure 4 The result images of the image reconstruction of six different models by using the Landweber method, the Newton-Raphson method and the method of the present application respectively; DETAILED DESCRIPTION

[0012] The image reconstruction method for detecting industrial two-phase flow of the present application is described in detail in combination with the drawings and examples.

[0013] The image reconstruction method for detecting industrial two-phase flow of the present application can enhance the global search ability of the biological population by improving the biological population optimization algorithm to solve the problem that the Newton-Raphson algorithm is easy to fall into local optimum when solving the inverse problem, and can jump out of the local optimum to search the global optimum solution. The image reconstructed by the method has less artifacts, clear background and is closer to the real target.

[0014] As shown in Figure 1 , it is a flow chart of the image reconstruction method for detecting industrial two-phase flow of the present application.

[0015] As shown in Figure 2 , it is a 16-electrode sensor array of the present application. In the sensor array, 16 electrode arrays are closely attached to the pipe wall and are installed at equal intervals outside the measured pipeline filled with conductive medium. AC is injected on a pair of adjacent electrodes, and the boundary voltage is measured on other adjacent electrode pairs. For adjacent data acquisition mode, a total of 208 sets of boundary voltage measurement data can be obtained.

[0016] The traditional image reconstruction method has low image quality and poor real-time performance when detecting two-phase flow. The EIT image reconstruction method based on the improved biological population optimization algorithm of the present application has high real-time performance, small image artifacts, clear background, and better reconstructed target position and size when used for detecting industrial two-phase flow. The specific implementation steps are as follows:

[0017] Step one: Construct a 16-electrode electrical impedance tomography measurement system model, using adjacent electrode current injection and adjacent electrode voltage measurement mode. For a complete measurement cycle, first excite the 1st and 2nd electrodes, measure the voltage signals between adjacent electrodes 3-4, 4-5…15-16, then excite the 2nd and 3rd electrodes, measure the voltage signals between adjacent electrodes 4-5, 5-6…16-1, and the measurement cycle continues until a complete cycle is measured, a total of 208 independent voltage data are obtained. The empty field voltage measured when there is no inclusion in the field is U1, the full field voltage measured when there is an inclusion is U2, and the relative boundary voltage measurement value U can be further obtained, i.e. U = U2-U1.

[0018] Step two: According to the relative boundary voltage measurement data obtained in step one, the sensitivity matrix A is calculated by combining the sensitivity theory, and the calculation formula is:

[0019]

[0020] In the formula, φ i and φ j are the field potential distributions of the i th electrode group and the j th electrode group when the excitation currents are I i and I j , respectively, and represent the gradient operators of φ i and φ j , respectively, A i,j is the sensitivity coefficient of the j th electrode group to the i th electrode group, and all the calculated sensitivity coefficients A i,j together constitute the sensitivity matrix A. Among them, 1≤i≤16, 1≤j≤16.

[0021] Step three: After the calculation of the sensitivity is completed, in the image reconstruction process, the relationship between the relative boundary voltage measurement data and the conductivity distribution is nonlinear, which is expressed as f(σ) = U, wherein σ represents the conductivity. Since the conductivity distribution changes little, the change of the boundary measurement voltage can be simplified as a linear form: ΔU = AΔσ. In the formula, ΔU is the change of the boundary voltage measurement value, and Δσ is the change of the conductivity distribution. In order to facilitate the representation, the above linear form is expressed as: U = Ag, wherein g is the conductivity change value.

[0022] Step four: (1) Obtain initial population information: the approximate conductivity distribution g obtained by iterating once using the Newton-Raphson algorithm is used as the initial population of the biological population optimization algorithm. The expression for solving is

[0023] (2) biological population initialization: each biological in the biological population is regarded as a particle without weight and volume in the M-dimensional search space, where M is the number of finite element subdivision meshes in the EIT forward problem, the number of the population is N, the initial population is g, the maximum jump interval parameter is FI max , the minimum jump interval parameter is FI min , the hunting probability is a constant P (P ∈ (0, 1)), the maximum iteration number is V, the current iteration number is v, let v = 0, and iteration is performed.

[0024] (3) the biological population is iteratively updated, and the process is specifically as follows:

[0025] (3.1) first update the jump interval parameter: the population optimization algorithm is easy to fall into a local optimal solution in the local optimization process, in order to jump out of the local optimal solution and improve the global search ability of the biological population, the application introduces an adaptive adjustment jump interval parameter FI, which jumps out of the local extreme value by adjusting the value of FI, and the adaptive adjustment jump interval parameter is:

[0026]

[0027] In the formula, FI max and FI min are the maximum jump interval parameter and the minimum jump interval parameter respectively, and the adaptive adjustment jump interval parameter FI is updated in real time with the change of the iteration number each time.

[0028] (3.2) calculate the value of the adaptive adjustment jump interval parameter FI, and judge whether FI is equal to V, if the two are equal, go to step (3.5); if the two are not equal, generate an independent uniformly distributed random number between 0 and 1, if the random number is less than the hunting probability constant P, go to step (3.3), otherwise, go to step (3.4).

[0029] (3.3) hunting behavior: each biological will record and update its own experience and the experience of the whole population in the process of hunting behavior, which can be used to search for food and update the position of the biological population, and the position update is as follows:

[0030]

[0031] In the formula, rand (0, 1) is an independent uniformly distributed random number between 0 and 1, C and S are the biological individual perception coefficient and the biological population evolution coefficient respectively, p i，j and G j are the optimal position of the i-th biological and the current optimal position of the population in the j-th dimension. represents the value of the i-th biological in the j-th dimension at the iteration number v+1, represents the value of the i-th biological in the j-th dimension at the iteration number v.

[0032] After completion, perform (4).

[0033] (3.4) Defense behavior: the biological population will feel the danger of the external environment into the defense behavior, each biological will try to move to the center of the population, due to the influence of the competition between groups when jumping, each biological will not directly move to the center of the population. Defense behavior can be expressed as:

[0034]

[0035]

[0036]

[0037] In the formula, k ∈ [1, 2, 3,... N], (k ≠ i), a1 and a2 are constants between 0 and 2, mean j The jth element representing the average position of the entire population, pFit i The best fitness value of the ith biological, pFit k The best fitness value of the kth biological, sumFit represents the sum of the best fitness values of the population, ε is a very small constant to avoid zero division error, D1 and D2 are two variables affected by the environment directly and indirectly, respectively.

[0038] After completion, perform (4).

[0039] (3.5) Jumping behavior: the biological population reaches a new position through jumping behavior, and the population will hunt again. Some biologicals will search for food, acting as laborers; others will forage in the food area found by the laborers, acting as beggars. The behavior of laborers and beggars can be described mathematically as:

[0040]

[0041]

[0042] In the formula, randn(0, 1) represents a Gaussian distribution random number with a mean of 0 and a standard deviation of 1, and FL (FL ∈ [0, 2]) represents the jumping coefficient of the laborer following the beggar.

[0043] After completion, perform (4).

[0044] (4) After the biological population is iteratively updated, a new biological population is obtained Propose fitness function The evaluation of the advantages and disadvantages of each organism in the biological population is the fitness value H. The fitness value of each organism in the current biological population is calculated, and the minimum fitness value obtained by calculation is recorded. Then, the minimum fitness values obtained in all cycles are compared to obtain the minimum fitness value in all cycles, that is, the solution represented by the organism with the minimum fitness value is the global optimal solution.

[0045] (5) judging whether v satisfies v>V, if yes, stopping iteration and outputting the global optimal solution, if no, v=v+1, returning to (3) to continue iteration.

[0046] Step five: obtaining the global optimal solution of the biological population according to step four, that is, the global optimal solution is the optimal conductivity distribution The reconstruction of the image is completed.

[0047] As Figure 3 shown, the present application selects six different models for the reconstruction of the conductivity distribution. The Landweber method, the Newton-Raphson method and the method of the present application are used for the image reconstruction of the six different models, and the reconstructed images are compared and analyzed. The results show that the image quality reconstructed by the Landweber method is the worst, the reconstructed target object is too large, and the boundary of the target object is relatively fuzzy. The image reconstructed by the Newton-Raphson method is improved compared with the Landweber method, the reconstructed target object artifact is smaller, and the quality is a little better, but the overall imaging quality is not high. In comparison, the image reconstructed by the image reconstruction method of the present application is greatly improved, the target object boundary is clear, the artifact in the background is smaller, and the size of the target object is more accurate.

[0048] Table 1

[0049]

[0050] Table 1 is a comparison table of the absolute error (Relative Error, RE) and the correlation coefficient (Correlation Coefficient, CC) calculated when the three methods are used for image reconstruction. In electrical tomography, the relative error (Relative error, RE) and the correlation coefficient (Correlation Coefficient, CC) are usually used to evaluate the algorithm to quantitatively evaluate the image reconstruction quality. The absolute error and the correlation coefficient expressions are as follows:

[0051]

[0052]

[0053] In the formula, is the calculated conductivity of the reconstruction region, g is the actual conductivity, and δ represents the number of pixels. and g δ denotes and the δth element of g, and denotes and the average value of g. The smaller the image absolute error is, the larger the correlation coefficient is, which indicates that the image reconstruction quality is better. As can be seen from the table, the RE value of the image reconstruction method provided in the present application is obviously smaller than that of other methods, and the CC value is larger, which further verifies that the present application has obvious advantages in image reconstruction.

[0054] As Figure 4 shown, the results of image reconstruction by three methods under the condition of a signal-to-noise ratio of 25 dB for six different models. The image reconstructed by the method provided in the present application is obviously better than the other two methods, Landweber method and Newton-Raphson method, and the images reconstructed by the two methods are severely deformed and have a large number of artifacts. The target object reconstructed by the method provided in the present application is the most accurate, the background is the clearest, and the robustness to noise is the strongest.

[0055] Table 2

[0056]

[0057] Table 2 is a comparison table of the absolute error (Relative Error, RE) and the correlation coefficient (Correlation Coefficient, CC) calculated when the three methods are used to perform image reconstruction under the condition of a signal-to-noise ratio of 25 dB. As can be seen from the table, the RE value of the image reconstruction method provided in the present application is the smallest and the CC value is the largest, which further proves that the method provided in the present application has strong anti-noise performance.

[0058] The above examples describe the basic principles, main features and advantages of the present application. It should be understood by those skilled in the art that the present application is not limited by the above examples. The above examples and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the scope of the principles of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of protection of the present application.

Claims

1. An image reconstruction method for detecting industrial two-phase flow, characterized in that The specific steps are: Step one: Construct a 16-electrode electrical impedance tomography measurement system model, adopt adjacent electrode current injection and adjacent electrode voltage measurement mode, for a complete measurement cycle, first excite the 1st and 2nd electrodes, measure the voltage signals between adjacent electrodes 3-4, 4-5…15-16, then excite the 2nd and 3rd electrodes, measure the voltage signals between adjacent electrodes 4-5, 5-6…16-1, the measurement cycle continues until a complete cycle is measured, a total of 208 independent voltage data are obtained, the empty field voltage measured when there is no inclusion in the field is U1, the full field voltage measured when there is an inclusion is U2, and the relative boundary voltage measurement value U is further obtained, that is, U=U2-U1; Step two: according to the relative boundary voltage measurement data obtained in step one, the sensitivity matrix A is calculated by combining the sensitivity theory, and the calculation formula is: In the formula, φ i and φ j For the i-th electrode group and the j-th electrode group, the excitation currents are respectively I i I j electric potential distribution in the field at that time and φ i and φ j The gradient operator, A i,j It is the sensitivity coefficient of the j-th electrode group to the i-th electrode group. All calculated sensitivity coefficients A i,j Together they form the sensitivity matrix A, where 1≤i≤16, 1≤j≤16; Step three: after the calculation of the sensitivity is completed, in the image reconstruction process, the relationship between the relative boundary voltage measurement data and the conductivity distribution is nonlinear, which is expressed as f(σ)=U, wherein σ represents the conductivity, and since the conductivity distribution changes little, the change of the boundary measurement voltage can be simplified as a linear form: ΔU=AΔσ, wherein ΔU is the change of the boundary voltage measurement value, and Δσ is the change of the conductivity distribution, in order to facilitate representation, the above linear form is expressed as: U=Ag, wherein g is the conductivity change value; Step four: (1) Obtain initial population information: the conductivity approximation distribution obtained by iterating once using the Newton-Raphson algorithm As the initial population of the biological population optimization algorithm, the expression of solving is: (2) biological population initialization: each biological in the biological population is regarded as a particle without weight and volume in M-dimensional search space, where M is the number of finite element mesh in EIT forward problem, the number of population is N, and the initial population is The maximum jump interval parameter is FI max The minimum jump interval parameter is FI min The hunting probability is a constant P (P ∈ (0, 1)), the maximum iteration number is V, the current iteration number is v, let v = 0, and iteration is performed. (3) iteratively update the biological population, the process is as follows: (3.1) first update the jump interval parameter: the population optimization algorithm is easy to fall into a local optimal solution in the local optimization process, in order to jump out of the local optimal solution and improve the global search ability of the biological population, an adaptive adjustment jump interval parameter FI is introduced, which jumps out of the local extreme value by adjusting the FI value, and the adaptive adjustment jump interval parameter is: In the formula, FI max and FI min are the maximum and minimum jump interval parameters, respectively, and the adaptive jump interval parameter FI is updated in real time with each change in the number of iterations. (3.2) calculate the value of the adaptive adjustment jump interval parameter FI, judge whether FI and V are equal, if both are equal, go to step (3.5); if both are not equal, generate an independent uniform distribution random number between 0 and 1, if the random number is less than the hunting probability constant P, go to step (3.3), otherwise, go to step (3.4); (3.3) hunting behavior: each biological will record and update its own experience and the experience of the entire population in the hunting behavior process, which is used to search for food or update the position of the biological population, and the position update is as follows: where rand(0,1) is a random number independently and uniformly distributed between 0 and 1, C and S are the individual perception coefficient and the species evolution coefficient respectively, p i，j and G j are the optimal position of the i-th individual and the current optimal position of the population respectively in the j-th dimension, denotes the value of the i-th individual in the j-th dimension at iteration v+1, denotes the value of the i-th individual in the j-th dimension at iteration v; After completion, execute (4); (3.4) defense behavior: the biological population will feel the danger of the external environment and enter the defense behavior, each biological will try to move to the center of the population, and due to the mutual competition between groups when jumping, each biological will not directly move to the center of the population, and the defense behavior is expressed as: where k ∈ [1, 2, 3,... N], (k ≠ i), a1 and a2 are constants between 0 and 2, mean j the jth element representing the average position of the entire population, pFit i the ith element representing the best fitness value of the ith organism, pFit k the kth element representing the best fitness value of the kth organism, sumFit represents the sum of the best fitness values of the population, ε is a very small constant to avoid zero division error, D1 and D2 are two variables directly and indirectly affected by the environment, respectively; After completion, execute (4); (3.5) jumping behavior: the biological population reaches a new position through jumping behavior, and the population will hunt again, some biologicals will search for food and act as laborers; other biologicals will forage in the food area found by the laborers and act as beggars, and the behaviors of the laborers and beggars are described by mathematical methods as: In the formula, randn(0, 1) represents a Gaussian distribution random number with a mean of 0 and a standard deviation of 1, and FL (FL ∈ [0, 2]) represents a jump coefficient of a laborer following a beggar; After completion, (4) is executed; (4) after the biological population iterative update, a new biological population is obtained fitness function is proposed evaluate the advantages and disadvantages of each organism in the biological population, H is the fitness value, calculate the fitness value of each organism in the current biological population, record the minimum fitness value obtained by calculation; then, compare the minimum fitness values obtained in all cycles to obtain the minimum fitness value in all cycles, that is, the solution represented by the organism with the minimum fitness value is the global optimal solution; (5) determining whether v satisfies v>V, if yes, stopping iteration and outputting a global optimal solution; if no, v=v+1, returning to (3) to continue iteration; Step five: Obtain the global optimal solution of the biological population according to step four, that is, the global optimal solution is the optimal conductivity distribution The reconstruction of the image is completed.

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