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The purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.

The method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.

In this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.

The current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

Eddy current testing (ECT) is a nondestructive testing method for the detection of flaws that uses electromagnetic induction to find defects in conductive materials. In this method, eddy currents are generated in a conductive material by a changing magnetic field. A defect is detected when there is a disruption in the flow of the eddy current. The purpose of this paper is to develop a new noniterative inversion methodology for detecting degradation (defect characterization) such as cracking, corrosion and erosion from the measurement of the impedance variations.

The methodology is based on multi-output support vector machines (SVM) combined with the adaptive database schema design method (SDM). The forward problem was solved numerically using finite element method (FEM), with its accuracy experimentally verified. The multi-output SVM is a statistical learning method that has good generalization capability and learning performance. FEM is used to create the adaptive database required to train the multi-output SVM and the genetic algorithm is used to tune the parameters of multi-output SVM model.

The results show the applicability of multi-output SVM to solve eddy current inverse problems instead of using traditional iterative inversion methods which can be very time-consuming. With the experimental results the authors demonstrate the accuracy which can be provided by the multi-output SVM technique.

The work allows extending the capability of the experimentation ECT defect characterization system developed at LGEP.

A new inversion method is developed and applied to ECT defect characterization. This new concept introduces multi-output SVM in the context of ECT. The real data together with estimated one obtained by multi-output SVM model are compared in order to evaluate the effectiveness of the developed technique.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.

The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.

The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.

A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.

From the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.

As the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.

The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

The purpose of this paper is to propose a new aerodynamic parameter estimation methodology based on neural network and output error method, while the output error method is improved based on particle swarm algorithm.

Firstly, the algorithm approximates the dynamic characteristics of aircraft based on feedforward neural network. Neural network is trained by extreme learning machine, and the trained network can predict the aircraft response at (k + 1)th instant given the measured flight data at kth instant. Secondly, particle swarm optimization is used to enhance the convergence of Levenberg–Marquardt (LM) algorithm, and the improved LM method is used to substitute for the Gauss Newton algorithm in output error method. Finally, the trained neural network is combined with the improved output error method to estimate aerodynamic derivatives.

Neither depending on the initial guess of the parameters to be estimated nor requiring numerical integration of the aircraft motion equation, the proposed algorithm can be used for unstable aircraft and is successfully applied to extract aerodynamic derivatives from both simulated and real flight data.

The proposed method requires iterative calculation and can only identify parameters offline.

The proposed method is successfully applied to estimate aircraft aerodynamic parameters and can also be used as a new algorithm for other optimization problems.

In this study, the output error method is improved to reduce the dependence on the initial value of parameters and expand its application scope. It is applied in aircraft aerodynamic parameter identification together with neural network.

This paper aims to investigate the usability of the non-iterative monotonicity approach for electrical capacitance tomography (ECT)-based object detection. This is of particular importance with respect to object detection in robotic applications.

With respect to the detection problem, the authors propose a precomputed threshold value for the exclusion test to speed up the algorithm. Furthermore, they show that the use of an inhomogeneous split-up strategy of the region of interest (ROI) improves the performance of the object detection.

The proposed split-up strategy enables to use the monotonicity approach for robotic applications, where the spatial placement of the electrodes is constrained to a planar geometry. Additionally, owing to the improvements in the exclusion tests, the selection of subregions in the ROI allows for avoiding self-detection. Furthermore, the computational costs of the algorithm are reduced owing to the use of a predefined threshold, while the detection capabilities are not significantly influenced.

The presented simulation results show that the adapted split-up strategies for the ROI improve significantly the detection performance in comparison to the traditional ROI split-up strategy. Thus, the monotonicity approach becomes applicable for ECT-based object detection for applications, where only a reduced number of electrodes with constrained spatial placement can be used, such as in robotics.