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期刊论文

Determining the boundary of inclusions with known conductivities using a Levenberg-Marquardt algorithm by electrical resistance tomography

谭超Tan Chao Xu Yaoyuan and Dong Feng

Measurement Science and Technology, 2011, Vol.22, No.10, 104005 (13pp).,-0001,():

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摘要/描述

Electrical resistance tomography (ERT) is a non-intrusive technique to image the electrical conductivity distribution of a close vessel by injecting exciting current into the vessel and measuring the boundary voltages induced. ERT image reconstruction is characterized as a severely nonlinear and ill-posed inverse problem with many unknowns. In recent years, there are a growing number of papers published which aim to determine the locations and shapes of inclusions by assuming their conductivities are piece-wise constant and isotropic. In this work, the boundary of inclusions is reconstructed by ERT with Boundary Element Method. The Jacobian matrix of forward problem is firstly calculated with a direct linearization method basing on boundary element, and validated through comparison with that determined by Finite Element Method and Analytical Method. A boundary reconstruction algorithm is later presented based on Levenberg-Marquardt (L-M) method. Several numerical simulations and static experiments were conducted to study the reconstruction quality, where much importance is put on the smoothness of boundaries in the reconstruction, thus a restriction of the curve radius is introduced to adjust the damping parameter for L-M algorithm. Analytical results on the stability and precision of the boundary reconstruction demonstrate that stable reconstruction can be achieved when the conductivity of the objects much differs from that of background medium, and convex boundaries can also be precisely reconstructed. Contrarily, the reconstructions for inclusions with similar conductivities to the background medium are not stable. The situation of an incorrect initial estimation on inclusions’ number is numerically studied and the results show that the boundary of inclusions could be correctly reconstructed with a splitting/merging function under the aforementioned proper operation condition of the present algorithm.

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