A Grey Level Fitting Mechanism based on Gompertz Function for Two Phase Flow Imaging using Electrical Capacitance Tomography Measurement Systems

Electrical Capacitance Tomography (ECT) is an image generating system based on soft field sensory system. The preferred Linear Back Projection (LPB) reconstruction algorithm for multi-phase measurement has blurring effect on the image generated. These two inherent factors, among others, affect the quality of image generated from ECT systems. Introducing fitting in the image generation process is one the solutions to improving its quality. In this article an alternative fitting mechanism based on the Gompertz function has been developed and evaluated. Comparative analysis results shows improvement on the spatial quality of images generated, in terms of minimum relative image and distribution errors, maximum correlation coefficient, and at relatively no additional computational cost. The mechanism is more effective for annular than stratified flow data hence complimenting the weakness of Xie method for annular flow. General Terms Industrial Process Tomography, Image Reconstruction Algorithms.

[1]  G. A. Johansen,et al.  The use of entropic thresholding methods in reconstruction of capacitance tomography data , 1997 .

[2]  M. S. Beck,et al.  8-electrode capacitance system for two-component flow identification. I. Tomographic flow imaging , 1989 .

[3]  Åke Björck,et al.  Numerical methods for least square problems , 1996 .

[4]  P. Franses.  Fitting a Gompertz Curve , 1994 .

[5]  Ø. Isaksen,et al.  A review of reconstruction techniques for capacitance tomography , 1996 .

[6]  E. Bradley,et al.  A theory of growth , 1976 .

[7]  J. Navarro-Pedreño.  Numerical Methods for Least Squares Problems , 1996 .

[8]  Geir Anton Johansen,et al.  Multiphase Flow Component Volume Fraction Measurement: Experimental Evaluation of Entropic Thresholding Methods Using an Electrical Capacitance Tomography System , 2001 .

[9]  N. Zabaras,et al.  Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective , 2013 .

[10]  Lihui Peng,et al.  Image reconstruction using a genetic algorithm for electrical capacitance tomography , 2005 .

[11]  Clifford H. Thurber,et al.  Parameter estimation and inverse problems , 2005 .

[12]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[13]  A. Kirsch.  An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[14]  Tomasz Dyakowski,et al.  Applications of electrical tomography for gas-solids and liquid-solids flows : a review , 2000 .

[15]  Shi Liu,et al.  An image reconstruction algorithm based on the extended Tikhonov regularization method for electrical capacitance tomography , 2009 .

[16]  Brian S. Hoyle,et al.  Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors , 1992 .

[17]  Maurice Beck,et al.  Tomographic imaging of two-component flow using capacitance sensors , 1989 .

[18]  David P. Smith,et al.  On the Nature of the Function Expressive of the Law of Human Mortality , 2013 .

[19]  Lihui Peng,et al.  Image reconstruction algorithms for electrical capacitance tomography , 2003 .

[20]  Jiamin Ye,et al.  Evaluation of Effect of Number of Electrodes in ECT Sensors on Image Quality , 2012, IEEE Sensors Journal.

[21]  Miljenko Marušić,et al.  Generalized two-parameter equation of growth , 1993 .

[22]  Zhao Jinchuang,et al.  An image reconstruction algorithm based on a revised regularization method for electrical capacitance tomography , 2002 .

[23]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[24]  Maurice Beck,et al.  Experimental evaluation of capacitance tomographic flow imaging systems using physical models , 1994 .

[25]  Kwang Youn Kim,et al.  Modified iterative Landweber method in electrical capacitance tomography , 2006 .