Quadrupole method: A new approach for solving the direct problem of electrical resistance tomography

Abstract

An inverse problem was considered to estimate electrical conductivity distribution for the electrical resistance tomography. This technique allows to control the internal parameters by reconstructing the distribution of electrical conductivity of liquid/solid suspension. As an analytical tool, the quadrupole method was used to solve the forward problem in order to simulate the sensors voltage evolution. The inverse problem is solved using the Levenberg–Marquardt method. A major source of uncertainty in tomographic inversion is the data error. The effect of the measurement errors on the stability of the solution was investigated. In order to find the current injection strategy which gives more information about the electrical conductivity, sensitivity analysis was carried out. The effect of Levenberg–Marquardt coefficient and initial value of the conductivity on the stability of the scheme was analyzed. The developed algorithm can be employed to rebuild the electrical conductivity which permits to go back to the physical parameters of the suspension.

Keywords

• Inverse problem
• Electrical resistance tomography
• Electrical conductivity
• Estimation
• Quadrupole method
• Levenberg–Marquardt