Research On Image Reconstruction Iterative Algorithm For Electrical Capacitance Tomography System Based On Self-scaling Variable Metric

Electrical capacitance tomography is referred to as ECT.ECT detects the capacitance signal detected by the electrode plate placed outside the target by a specific capacitance detecting sensor,collects and returns it to the computer through the data acquisition system,and then restores the multiphase fluid inside the target by a suitable image reconstruction algorithm.The distribution of dielectric constants.In this paper,a better ECT image reconstruction is studied.By analyzing the basic principles of ECT image reconstruction,an ECT image reconstruction algorithm based on self-adjusting ratio scale correction method and an ECT image reconstruction algorithm based on sparse quasi-Newton BFGS correction method are proposed.Simulation experiments show that these two algorithms provide new ideas for solving the inverse problem of electrical capacitance tomography.This article is divided into the following sections:(1)Explain the equipment used in the simulation experiment of the ECT system.Then,the working principle of ECT image reconstruction is analyzed in detail,and the mathematical model of ECT inverse problem is deduced.The reasons for the current difficulty in applying ECT technology in practical industrial production and environmental protection are illustrated.Finally,several common classical algorithms in the field of ECT image reconstruction are introduced.For example:polynomial acceleration method,steepest descent method,landweber iteration method,Gauss-Nowton method,conjugate gradient method.The above classical algorithm is simulated together with the proposed algorithm,and the experimental results of each algorithm are compared and analyzed.(2)An ECT image reconstruction algorithm based on self-adjusting ratio scale correction is proposed for reducing iterations in ECT image reconstruction.Based on the study of the mathematical model of ECT image reconstruction,the formula for solving the ECT image reconstruction problem is derived.A description of the selection of the scaling factor and the convergence analysis of the algorithm are given.In order to verify the effectiveness of the algorithm in the field of ECT image reconstruction,the ECT image reconstruction simulation experiments were carried out on four different flow patterns of oil-water two-phase flow.From the experimental results,the algorithm greatly reduces the number of trial iterations on the basis of ensuring the accuracy of image reconstruction.Most of the flow patterns can obtain optimal imaging within ten iterations.In the low-level laminar flow and small-radius core flow patterns,the image quality and error rate of the image reconstruction are better than LBP,Landweber,CQ and SD algorithms.(3)In view of the morbidity of seneitivity matrix in ECT,a sparse quasi-Newton BFGS correction image reconstruction for Electrical Capacitance Tomography is proposed on basis of the analysis of the principle of quasi-Newton algorithm.The algorithm thins out the ill-conditioned sensitivity matrix and constructs the Hesse inverse approximation matrix in the ECT image reconstruction objective function.Combined with the solution principle of quasi-Newton algorithm,the iterative solution formula finally applied to ECT image reconstruction is derived,and the convergence proof is given.Through simulation experiments,the image quality of image reconstruction is better than LBP,Landweber and SD algorithms in low-level laminar flow,mid-level laminar flow and small-radius core flow.And the number of iterations is better than the Landweber and SD algorithms.Compared with the self-adjusting ratio scaling algorithm,the algorithm performs better in imaging images in the median laminar flow,not only the image is closest to the original image,but also the image error rate is kept lowest in all algorithms.