Nonlinear Electrical Impedance Tomography Method Using a Complete Electrode Model for the Characterization of Heterogeneous Domains

This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electrodemodel(CEM),which seeks the electric potential within the domain and at surface electrodes considering the contact impedance between them.The finite element solution of the electric potential has been validated using a commercial code.The inverse medium problem for reconstructing the unknown electrical conductivity profile is formulated as an optimization problem constrained by the CEM.The method seeks the optimal solution of the domain’s electrical conductivity to minimize a Lagrangian functional consisting of a least-squares objective functional and a regularization term.Enforcing the stationarity of the Lagrangian leads to state,adjoint,and control problems,which constitute the Karush-Kuhn-Tucker(KKT)first-order optimality conditions.Subsequently,the electrical conductivity profile of the domain is iteratively updated by solving the KKT conditions in the reduced space of the control variable.Numerical results show that the relative error of the measured and calculated electric potentials after the inversion is less than 1%,demonstrating the successful reconstruction of heterogeneous electrical conductivity profiles using the proposed EIT method.This method thus represents an application framework for nondestructive evaluation of structures and geotechnical site characterization.

Network Lifetime Global Optimization for Multi-Source and Single-Sink Topology in Wireless Sensor Networks

The multi-source and single-sink(MSSS) topology in wireless sensor networks(WSNs) is defined as a network topology,where all of nodes can gather,receive and transmit data to the sink.In energy-constrained WSNs with such a topology,the joint optimal design in the physical,medium access control(MAC) and network layers is considered for network lifetime maximization(NLM).The problem of integrating multi-layer information to compute NLM,which involves routing flow,link schedule and transmission power,is formulated as a nonlinear optimization problem.Specially under time division multiple access(TDMA) scheme,this problem can be transformed into a convex optimization problem.To solve it analytically we make use of the property that local optimization is global optimization in convex problem.This allows us to exploit the Karush-Kuhn-Tucker (KKT) optimality conditions to solve it and obtain analytical solution expression,i.e.,the globally optimal network lifetime(NL).NL is derived as a function of number of nodes,their initial energy and data rate arrived at them. Based on the analysis of analytical approach,it takes the influence of data rates,link access and routing method over NLM into account.Moreover,the globally optimal transmission schemes are achieved by solution set during analytical approach and applied to algorithms in TDMA-based WSNs aiming at NLM on OMNeT++ to compare with other suboptimal schemes.