Application of Simulated Annealing and Genetic Algorithms to the Reconstruction of Electrical Permittivity Images

in Capacitance Tomography

C Ortiz-Alemán, R Martin, J C Gamio and A Nicolas

Instituto Mexicano del Petróleo, Eje Central L Cárdenas 152, México, DF, 07730, México jcortiz@imp.mx

ABSTRACT

In this work we apply the simulated annealing (SA) and genetic algorithms (GA) inversion methods to the reconstruction of permittivity images from electrical capacitance tomography (ECT) measurements. The forward problem (i.e., to find the mutual capacitance data for a given permittivity distribution in the sensor) is calculated by using a finite-volume space discretization method in order to avoid singularity problems at the centre of the pipe (as occurs with the finite difference method), and to take advantage from the conservative formulation of finite element methods. We test the GA and SA inversion methods using static physical models simulating the typical distribution patterns of two- component flow. The GA and SA-based permittivity inversions have some advantages over other approaches based on damped least-squares inversion: they can find good solutions starting with poor initial models, can more easily implement complex a priori information, and do not introduce smoothing effects in the final permittivity distribution model. A major disadvantage comes from the fact that GA and SA are computationally intensive and lead to relatively slow reconstructions.

Keywords Simulated annealing, Genetic algorithms, Capacitance tomography, Global optimisation, Finite volumes.