Matrix Properties of Data From Electrical Capacitance Tomography

Some properties of the matrix of capacitance-data collected by the electrical capacitance tomography (ECT) technique are studied. These data are used to extract information in various industrial process applications and, in particular, about flows in pipelines. The features in the eigenvalue distribution of normalized capacitance matrices for three practical classes of permittivity distributions, namely core flows, annular flows, and stratified flows, are investigated and compared by numerical solution. It is shown that the leading eigenvalue is strongly related to the area ratio of permittivity contrast in the cross-section of the flow, while the next two eigenvalues provide a basis for distinguishing among these three classes of flows. In particular, for core and annular flows, the difference between the second and third eigenvalues is shown to be related to the eccentricity of permittivity profile. Numerical examples are presented to illustrate how the area ratio for some permittivities that do not belong to these classes can be effectively estimated.