Research On Image Reconstruction Algorithms And Design Of Semi-physical Simulation System For Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) is mainly applied to visualization measurement for multiphase flow. It attempts to image the permittivity distribution of the dielectric in the measured field by measuring the electrical capacitances. Due to its advantages such as non-intrusive, non-radioactive, low-cost, visualization, and easy installation, etc., ECT is considered as a promising detection technology with broad application prospects. Image reconstruction algorithm plays a significant role in the successful application of ECT technology. Firstly, this paper has intensively studied the model and computational method of the sensitivity field in ECT sensor. Based on this, in order to make up the negative effects on image reconstruction caused by "soft field" characteristic, two new image reconstruction algorithms were proposed, which are DPSCO algorithm and ECT-CS image reconstruction algorithm. And the classic Landweber’s Algorithm was improved to address its semi-convergence problem. At last, a semi-physical simulation system for ECT was designed. The main contents are as follow:(1) The principle of ECT system was expounded, and the classic algorithms for image reconstruction were derived, analyzed and simulated. The common problem of the classic algorithms was summed up, and the half convergence problem of Landweber’s method was solved. At first, the paper discussed compositions and working principle of ECT system, then analyzed the mathematical basis of ECT technology. Secondly, the sensitivity distribution, the key factor involved in the solution of inverse problem, is analyzed. Thirdly, five kinds of classical algorithm for image reconstruction are discussed. They are linear back projection, Tikhonov regularization method, Landweber’s method Newton-Raphson method, and conjugate gradient method. The principle, the advantages and disadvantages of various algorithms are deduced and analyzed respectively. The simulation results are also given. Finally, the common problem of the classical algorithms was pointed out. Moreover, the mathematical cause for the unstable convergence of Landweber’s method was analyzed; a compression operator was constructed to achieve the stable convergence. The stable convergence of the improved Landweber’s method was proved by simulation.(2) To solve the problem of the solution of the important prior condition (i.e. the sensitivity distribution) for image reconstruction, the calculation model of potential distribution of electrostatic field in ECT was established based on finite element method, and the numerical solution of the sensitivity distribution was obtained. The calculation process of sensitivity distribution was described in the sense of finite element method, and its graphical results were given.(3) For the problem that the accuracy of reconstructed image is restricted by "soft field" characteristic, based on the principle of particle swarm optimization (PSO), an image reconstruction algorithm with dual particle swarm collaborative optimization was presented, and named as DPSCO. Firstly, the mechanism of "soft field" characteristic is explored, and its physical performance was described. And then the way on which "soft field" characteristic affects image reconstruction was analyzed. On the basis, DPSCO algorithm was proposed. In the algorithm, the image samples were trained by the least square support vector machine, and then a prior condition was obtained to describe influence degree of "soft field" characteristic. Based on the prior condition, the fitness function of particle swarm optimization was constructed, and it compensated the influence of "soft field" characteristic on the image reconstruction. Secondly, since standard particle swarm optimization used in ECT image reconstruction has the problem of premature convergence, to make PSO have a stronger global convergence, Lotka-Volterra equation was introduced to describe the species competition; and the competition strategy of dual particle swarm was designed. At last, simulation results showed that despite more calculating time, DPSCO algorithm can increase the image accuracy by 20%-50%, compared with Landweber’s method and Newton-Raphson method. Meanwhile, DPSCO algorithm is more likely than standard PSO to converge to the global optimum.(4) For the universal problem of the classical algorithms, especially the problem that the reconstructed image accuracy is low for the complex flow regimes, ECT-CS image reconstruction algorithm was put forward based on compressed sensing theory. In the algorithm, the species of two-phase flow regimes are classified reasonably, and a sample subset for each flow regime was established. All the subsets consist of a complete space or over-complete space of permittivity distribution vector, and then the sparse decomposition of an arbitrary permittivity distribution vector is achieved. By using compressed sensing theoretical framework and its mature signal reconstruction algorithm, the image reconstruction was converted to a convex optimization problem. Meanwhile, considering the deviation of image reconstruction caused by "soft field" characteristic, the discrete phase component in permittivity distribution signal was solved separately. So the compensation for influence caused by "soft field" characteristic was achieved. At last, simulation results showed that, compared with classical algorithms, ECT-CS algorithm can increase image accuracy by more than 60%. So it can meet the needs of high-precision detection in non-real time.(5) To research, design capacitance sensor and verify image reconstruction algorithms on the same platform, the method of semi-physical simulation was introduced. And a semi-physical simulation system for ECT was developed. On one hand, the sensor and data acquisition were designed as virtual instrument in Lab VIEW platform. The virtual measurement of capacitance sensor was completed by MATLAB. The design of the virtual instrument and its graphical implementation were given. On the other hand, the image reconstruction unit was physically implemented in DSP embedded processing system. At last, the hardware and software of the main modules of the DSP system were presented.