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In this paper, we propose a novel reconstruction scheme for the low-frequency near-field electromagnetic imaging of high-contrast conductivity distributions inside shielded regions using the system of Maxwell's equations in 3D. In our novel scheme, we focus on estimating the shape characteristics of the electrical conductivity profile inside these regions from low-frequency electromagnetic data measured at external locations for a single frequency. We introduce a colour level set regularization scheme which is a shape-based approach focusing on the simultaneous reconstruction of several shape-like distributions of different conductivity values in the same region of interest. Using two numerical experiments addressing a three-value reconstruction problem related to the imaging of shielded boxes or cargo containers, we compare this novel approach with results obtained from standard voxel-based reconstruction schemes on the one hand and the more established two-value shape-based approach on the other hand. We demonstrate that, depending on the particular situation of the imaging setup, this three-value (or in general multiple-value) shape-based reconstruction technique has the potential to provide superior reconstruction results in many situations, in particular regarding reconstruction of the correct shapes. We also discuss particular challenges of this novel methodology. [ABSTRACT FROM AUTHOR]

In this paper, we assess the reliability of explicit formulas introduced by Pham et al. [Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers. Wave Motion. 2015;54:134–144] to compute the propagation of one-component waves through a stack of homogeneous layers, inserted between two half-planes, as a surrogate model of wave propagation in functionally graded materials (FGM). Afterwards, we use the model reliability assessment as diagnostics prior to solving the associated inverse problem. We have used both the Legendre continuous nodal Galerkin method with Gauss–Lobatto quadratures (LCNG) and the Thomson–Haskell (TH) method as reference approaches to approximate the solution of the continuous problem. Consequently, we have compared computationally the output of the surrogate model, the TM method and the LCNG method through sensitivity analysis; and secondly, we have used the surrogate model and the Bayesian inferential framework to estimate the FGM shear modulus given measurements of the amplitude of the reflected wave. We have found that if we know the structure of noise in the data and the signal to noise ratio, then we can reliably infer the FGM shear modulus. [ABSTRACT FROM AUTHOR]

In this paper, a novel inversion method is proposed for jointly robust estimation of parameters and variance components from disjunctive groups of observations affected by outliers. This method, named robust non-negative variance component estimation (RVCE), is a coupling of variance component estimation (VCE) technique with a robust estimation method, developed to cope with outliers and to avoid negative variance, leading thus, to an estimation reliable enough. The principle of RVCE method is based on the refinement of the stochastic model via an equivalent weight matrix established from the original measurement weight matrix and an adapted full weight matrix with hard rejection to outliers. This last one is derived from the robust standardized residuals, using a highly robust estimator, as an initial solution of the inverse problem, and a cut-off value adapted to sort out the good observations from the bad ones. Furthermore, because the original weight matrix is partly known, the integration of the VCE technique plays a key role to reach an optimal solution and to provide valuable information on the precision of the estimates. The performance of the proposed method is demonstrated by considering a rockfill dam as an example, where the material parameters and variance components are jointly estimated from geotechnical and geodetic measurements. The results of comparison study between RVCE method with other methods such as the classical NN-VCE, RIMCO, least squares and the combined Huber’s M-estimator with VCE (HVCE) for various configuration options have highlighted the pertinence of the proposed method. [ABSTRACT FROM PUBLISHER]

We are concerned with the inverse spectral problem for a quadratic pencil operator. We show that one given spectrum is enough for its reconstruction in the case of one analytic potential. To do so we first prove few identities between the Taylor coefficients of the sought function and the Taylor coefficients of the characteristic function of the operator, whose zeros are the given eigenvalues. The method leads to solving an upper triangular nonlinear algebraic system, which is easily solved by Gaussian elimination. Convergence of the algorithm is proven in case p is a polynomial and several examples are used at the end to illustrate the accuracy and speed of the algorithm. [ABSTRACT FROM AUTHOR]

Iterative re-weighted least square (IRLS) algorithms for-minimization problems require to select proper value of regularization parameter, for which Stein’s unbiased risk estimate (SURE) – an unbiased estimate of prediction error – is often used as a criterion for this selection. In this paper, we propose a recursive SURE to estimate the prediction error during the IRLS iterations. Particularly, we derive the recursion of Jacobian matrix by incorporating matrix splitting scheme into IRLS algorithms. Numerical examples demonstrate that minimizing SURE consistently leads to the nearly optimal reconstructions in terms of prediction error. Theoretical derivations in this work related to the evaluation of Jacobian matrix can be extended, in principle, to other types of regularizers and regularized iterative reconstruction algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust inversion method for correlated observations (RIMCO) is proposed to determine the material parameters from correlated observations under the effect of outliers and leverage points. This method is based on a full equivalent weight matrix established from the original measurement weight matrix and an adapted full weight matrix with hard rejection to outliers. This equivalent weight matrix plays key role to refine the stochastic model, while keeping the original correlation of measurements unchanged on the one hand, and ensuring simultaneously high robustness and statistical efficiency of the proposed method, on the other hand. The performance of the proposed method is demonstrated by considering a rockfill dam as an example, where the material parameters are identified from geotechnical and geodetic measurements after achievement of the construction, and during the first filling up of reservoir. Results of comparison of RIMCO with least squares and M Huber methods concerning their robustness and efficiency are presented for various configuration options. [ABSTRACT FROM AUTHOR]

A common approach to solve an inverse problem, i.e. to single out the model parameters that explain the observed phenomena, is to iteratively minimize a residual function, which expresses the difference between the observations (measured data) and the forward response of the estimated model (recalculated data). The convergence properties of the solver can be difficult to control and to analyse, especially when dealing with global optimizers applied to non-linear inverse problems. In this paper, we plot the residual vs. a single scalar, the Euclidian distance in the variable space. We show how this can be used to avoid misleading solutions given by the local minima. The performance of this approach is investigated in three examples with increasing complexity (in terms of dimensions). Moreover, we propose to exploit the distance indicator in a new hybrid inversion strategy that combines a simulated annealing algorithm and a local approach and that reduces the computational cost of the optimization. [ABSTRACT FROM AUTHOR]

A novel approach to diagnostics of transformer winding deformations, caused by mechanical forces from short-circuit currents, is presented. We employ a simple model of a transformer as a two-dimensional parallel plate waveguide. The upper plate represents the transformer tank wall and the lower plate represents the iron core which carries the magnetic flux. Between the two plates, we model the transformer winding by a set of parallel conductors. We utilize commercial simulation software to simulate the generation and measurement of microwave radiation at both ends of the winding structure. The radiation interacts with the metallic structures in the model waveguide. The measured responses from the model waveguide are expected to be sensitive to mechanical deformations of the transformer winding. We use conventional waveguide theory to solve the direct propagation problem, and an optimization method to solve the inverse problem. In particular, we determine the locations of winding segments, and obtain a good agreement between reconstructed and true conductor positions. [ABSTRACT FROM PUBLISHER]

We consider the problem of guaranteed estimation of unknown right-hand sides of the equations entering the statement of the exterior Neumann problems for the Helmholtz equation from indirect observations of their solutions. A method is developed for the determination of guaranteed a posteriori estimates of this right-hand sides which are compatible with measurement data. It is shown that such estimates can be expressed via solutions of a uniquely solvable system of the Helmholtz equations. [ABSTRACT FROM AUTHOR]

The global material properties and boundary conditions of Fibre Reinforced Plastics (FRP) plates can change substantially from their initial values after prolonged use. Since composite plates use different materials in different layers, a method for determination of layerwise material parameters can be useful for structural health monitoring. Vibration responses being sensitive to material properties, an inverse material identification methodology using experimental modal testing and finite element model updating can be a reasonable option. Most of the existing inverse techniques are limited to the determination of average homogenized material constants only. The current two-staged technique, supplemented by information from specially fabricated 'Characteristic plates' having material properties same as those of the 'Actual plate' but different stacking sequences, is proposed as an effective solution. Modal testing has been conducted on a rectangular FRP plate under various boundary conditions and the difficulties associated with the implementation of such technique have been critically judged. [ABSTRACT FROM AUTHOR]

We devise a fast and reliable computational framework for the elasticity imaging inverse problem of detecting cancerous tumors in the human body using an output least-squares (OLS) approach. From a mathematical standpoint, this inverse problem requires identifying a parameter in a mixed variational problem. We develop, in a continuous setting, a first-order adjoint method and two second-order adjoint methods. The continuous formulae are then used to devise a scheme for an efficient computation of the gradient and the Hessian of the OLS objective. We give detailed numerical examples. [ABSTRACT FROM PUBLISHER]

We discuss computational aspects of the inverse and ill-posed problem of identifying residual stresses in steel structures under thermal loading. This corresponds to an inverse source problem in linear thermo-elasticity. The studies aim in investigating whether thermal loadings for the excitation of structures are sufficient in order to detect reliably inherent residual stresses. These stresses may result from the construction process or later thermal or mechanical treatment of the structure-like welding. By answering the raised question positively, our method provides an important basis for successful thermal straightenings. The quality of the solution of the inverse problem depends on a series of parameters, like material parameters, noise in the measurements, and the experimental setup. We numerically study the effects of these parameters and quantify the uncertainties in the results of the inverse problems by means of Sobol indices. [ABSTRACT FROM AUTHOR]

This article proposes an approach for reconstructing physical parameters of a sample in a rectangular resonator during microwave radiation, knowing a priori, its electric field distribution. The inverse problem was solved using two global optimization algorithms and the peak signal-to-noise ratio (PSNR) criterion. First, the Self-regulated Fretwidth Harmony Search algorithm (SFHS) identified suitable resonant frequencies for a given configuration. Next, the unified Particle Swarm Optimization (UPSO) optimized said configuration. Together, they became a maximization strategy of the PSNR through a dual optimization process. Results showed the ability of the approach for estimating the height of each sample block and the resonating frequency of the cavity. This process takes longer to finish as a higher PSNR is demanded (mainly due to the aforementioned dual optimization). Even so, it allows for more similar electric field distributions between both, the direct and inverse problems. [ABSTRACT FROM AUTHOR]

The non-destructive control of steam generators is an essential task for the safe and failure-free operation of nuclear power plants. Due to magnetite particles in the cooling water of the plants, a frequent source for failures are magnetic deposits in the cooling loop of steam generators. From eddy current signals measured inside a U-tube in the steam generator, we propose and analyze a regularized shap optimization algorithm to identify magnetic deposits outside the U-tube with either known or unknown physical properties. Motivated by the cylindrical geometry of the U-tubes we assume an axisymmetric problem setting, reducing Maxwell’s equations to a 2-D elliptic eddy current problem. The feasibility of the proposed algorithms is illustrated via numerical examples demonstrating in particular the stability of the method under noise. [ABSTRACT FROM PUBLISHER]

There are a wide range of applications involving laser propagation through a scattering medium. Very often, a measurement of the scattered light will be taken with the intent of learning some information about the medium. On the contrary, the present work seeks to extract a description of the source of light and its location. A phenomenological model for off-axis intensity is presented which employs a Mie scattering aerosol database. The model is extended to predict the off-axis polarized light described by the Stokes vector. Several inversion techniques are given and analysed as well as example problems are detailed which can recover the range, direction, power and polarization of the laser source. [ABSTRACT FROM AUTHOR]

The parameter recovery problem for cancellous bone by acoustic interrogation is investigated numerically. Biot’s equations coupled with boundary integral equations are used to model ultrasound propagation through a bone sample immersed in a water tank. The mathematical formulation for two-dimensional orthotropic bone is presented, but numerical results are only discussed in the isotropic case. The inversion procedure consists in minimizing some error on the pressure at measurement points located outside the bone sample. For this purpose, two different minimization algorithms are considered. A number of numerical tests are performed for a range of frequencies, which demonstrate the model’s ability to recover some bone parameters with satisfactory accuracy. [ABSTRACT FROM AUTHOR]

In this study, the necessary and sufficient conditions for solvability of an inverse spectral problem about eigenvalues and normalizing numbers for finite-order real Jacobi matrices with zero diagonal elements are established. An explicit procedure of reconstruction of the matrix from the spectral data consisting of the eigenvalues and normalizing numbers is given. Numerical examples and error analysis are provided to demonstrate the solution technique of the inverse problem. The results obtained are used to justify the solving procedure of the finite Langmuir lattice by the method of inverse spectral problem. [ABSTRACT FROM AUTHOR]

A system of ground movement measurements under a highway in an Upper Silesia (Poland, Europe) mining damage area has been presented. The objective of the research was to develop a numerical analysis of such slumps occurring under a highway, carried out by a reliable and fast method of converting the results of relevant experimental measurements into ground displacements under the road. For engineering purposes, the results of both monitoring and analysis should be proceeded online, in a fast, sufficiently accurate and reliable way. [ABSTRACT FROM AUTHOR]

An explicit guidance law that maximizes terminal velocity is developed for a re-entry vehicle to a fixed target. Motion is constrained to an optimal, 3D Bezier curve. Acceleration commands are derived by solving an inverse problem related to Bezier parameters. An optimal Bezier curve is determined by solving a real-coded genetic algorithm. For online trajectory generation, optimal trajectory is approximated by fixing the second control point of the Bezier curve. The near optimal trajectory is compared with the genetic solution and with a form of proportional navigation. The near optimal terminal velocity solution compares very well with the genetic solution and is superior to the proportional navigation one. The approach robustness is examined by Monte Carlo simulation. [ABSTRACT FROM AUTHOR]