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Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of electrical capacitance tomography. Two known computational bottlenecks are the assembly of the FE equation system as well as the computation of the Jacobian. Here, existing computation techniques like adjoint field approaches require additional simulations. This paper aims to present fast numerical techniques for the sensor simulation and computations with the Jacobian matrix.

For the FE equation system, a solution strategy based on Green’s functions is derived. Its relation to the solution of a standard FE formulation is discussed. A fast stiffness matrix assembly based on an eigenvector decomposition is shown. Based on the properties of the Green’s functions, Jacobian operations are derived, which allow the computation of matrix vector products with the Jacobian for free, i.e. no additional solves are required. This is demonstrated by a Broyden–Fletcher–Goldfarb–Shanno-based image reconstruction algorithm.

MATLAB-based time measurements of the new methods show a significant acceleration for all calculation steps compared to reference implementations with standard methods. E.g. for the Jacobian operations, improvement factors of well over 100 could be found.

The paper shows new methods for solving known computational tasks for solving inverse problems. A particular advantage is the coherent derivation and elaboration of the results. The approaches can also be applicable to other inverse problems.

The purpose of this paper is to present a model to describe the nonlinear and hysteretic properties of ferromagnetic materials.

The energetic model of ferromagnetic hysteresis evolved from some well‐known concepts in ferromagnetism in the last years. The magnetisation process is calculated from energy balance and statistical domain behaviour. Based on vectorial, anisotropic, multi‐domain considerations an isotropic, scalar model is derived, which gives quite simple equations to describe the nonlinear, hysteretic magnetisation process.

The presented simulations for steel samples and ferrite samples show very nice correspondence with measurements.

The scalar model seems to be especially suited for integration into finite element modelling or into simulations of electro‐magnetic circuits.

The investigation of the influence of the modeling error on the solution of the inverse problem given uncertain measured data in electrical capacitance tomography (ECT).

The solution of the nonlinear inverse problem in ECT and hence, the obtainable accuracy of the reconstruction result, highly depends on the numerical modeling of the forward map and on the required regularization. The inherent discretization error propagates through the forward map, the solution of the inverse problem, the subsequent calculation of process parameters and properties and may lead to a substantial estimation error. Within this work different finite element meshes are compared in terms of obtainable reconstruction accuracy. In order to characterize the reconstruction results, two error measures are introduced, a relative integral error and the relative error in material fraction. In addition, the influence of the measurement noise given different meshes is investigated from the statistical point of view using repeated measurements.

The modeling error, the degree of regularization, and measurement uncertainties are the determining and limiting factors for the obtainable reconstruction accuracy of electrical tomography systems. The impact of these key influence factors on the calculation of process properties given both synthetic as well as measured data is quantified. Practical implications – The obtained results show that especially for measured data, the variability in calculated parameters strongly depends on the efforts put on the forward modeling, i.e. on an appropriate finite element mesh size. Hence, an investigation of the modeling error is highly recommended when real‐world tomography problems have to be solved.

The results presented in this work clearly show how the modeling error as well as inherent measurement uncertainties influence the solution of the inverse problem and the posterior calculation of certain parameters like void fraction in process tomography.

The purpose of this paper is to investigate the achievable improvement in reconstruction accuracy in electrical tomography through the incorporation of physical bound constraints as prior knowledge in the inverse problem solution.

The structure of the nonlinear least squares inverse problem formulation and the importance of prior knowledge are addressed. Several different methods for the incorporation of bound constraints are discussed. The methods are compared by means of reconstructions from simulated and measured data and the computational demands.

The inclusion of bound constraints on the material values in the inverse problem solution results in a considerable improvement of the reconstructions. The occurrence of artefacts and blurring can be reduced. Among the investigated constraint handling methods, the logarithmic parameter reconstruction approach can be implemented with minimal additional computational effort.

The study is performed with discrete two‐phase material distributions as occurring in industrial problems. A further step would be the extension to multiple phases.

The logarithmic transform method is a novel approach for the incorporation of bound constraints in tomography. It outperforms other constraint handling approaches and may be of interest for electrical tomography systems in various applications.

This paper aims to propose an energetic model parameter calculation method for predicting the materials’ symmetrical static hysteresis loop and asymmetrical minor loop to improve the accuracy of electromagnetic analysis of equipment.

For predicting the symmetrical static hysteresis loop, this paper deduces the functional relationship between magnetic flux density and energetic model parameters based on the materials’ magnetization mechanism. It realizes the efficient and accurate symmetrical static hysteresis loop prediction under different magnetizations. For predicting the asymmetrical minor loop, a new algorithm is proposed that updates the energetic model parameters of the asymmetrical minor loop to consider the return-point memory effect.

The comparison of simulation and experimental results verifies that the proposed parameters calculation method has high accuracy and strong universality.

The proposed parameter calculation method improves the existing parameter calculation method’s problem of relying on too much experimental data and inaccuracy. Consequently, the presented work facilitates the application of the finite element electromagnetic field analysis method coupling the hysteresis model.

Inverse problems are often marked by highly dimensional state vectors. The high dimension affects the quality of the estimation result as well as the computational complexity of the estimation problem. This paper aims to present a state reduction technique based on prior knowledge.

Ill-posed inverse problems require prior knowledge to find a stable solution. The prior distribution is constructed for the high-dimensional data space. The authors use the prior distribution to construct a reduced state description based on a lower-dimensional basis, which they derive from the prior distribution. The approach is tested for the inverse problem of electrical capacitance tomography.

Based on a singular value decomposition of a sample-based prior distribution, a reduced state model can be constructed, which is based on principal components of the prior distribution. The approximation error of the reduced basis is evaluated, showing good behavior with respect to the achievable data reduction. Owing to the structure, the reduced state representation can be applied within existing algorithms.

The full state description is a linear function of the reduced state description. The reduced basis can be used within any existing reconstruction algorithm. Increased noise robustness has been found for the application of the reduced state description in a back projection-type reconstruction algorithm.

The paper presents the construction of a prior-based state reduction technique. Several applications of the reduced state description are discussed, reaching from the use in deterministic reconstruction methods up to proposal generation for computational Bayesian inference, e.g. Markov chain Monte Carlo techniques.

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.

The purpose of this paper is to reduce the artifacts in fast Bayesian reconstruction images in electrical tomography. This is in particular important with respect to object detection in electrical tomography applications.

The authors suggest to apply the Box-Cox transformation in Bayesian linear minimum mean square error (BMMSE) reconstruction to better accommodate the non-linear relation between the capacitance matrix and the permittivity distribution. The authors compare the results of the original algorithm with the modified algorithm and with the ground truth in both, simulation and experiments.

The results show a reduction of 50 percent of the mean square error caused by artifacts in low permittivity regions. Furthermore, the algorithm does not increase the computational complexity significantly such that the hard real time constraints can still be met. The authors demonstrate that the algorithm also works with limited observations angles. This allows for object detection in real time, e.g., in robot collision avoidance.

This paper shows that the extension of BMMSE by applying the Box-Cox transformation leads to a significant improvement of the quality of the reconstruction image while hard real time constraints are still met.

Optimization of light-emitting diodes’ (LEDs’) design together with long-term reliability is directly correlated with their photometric, electric and thermal characteristics. For a given thermal layout of the LED system, the maximum luminous flux occurs at an optimal electrical input power and can be determined using a photo-electro-thermal (PET) theory. The purpose of this study is to extend the application of the luminous flux equation in PET theory for low-power (LP) LEDs.

LP surface-mounted device LEDs were mounted on substrates of different thermal resistances. Three LEDs were attached to substrates which were flame-retardant fiberglass epoxy (FR4) and two aluminum-based metal core printed circuit boards (MCPCBs) with thermal conductivities of about 1.0 W/m.K, 2.0 W/m.K and 5.0 W/m.K, respectively. The conjunction of thermal transient tester and thermal and radiometric characterization of LEDs system was used to measure the thermal and optical parameters of the LEDs at a certain range of input current and temperature.

The validation of the extended application of the luminous flux equation was confirmed via a good agreement between the practical and theoretical results. The outcomes show that the optimum luminous flux is 25.51, 31.91 and 37.01 lm for the LEDs on the FR4 and the two MCPCBs, respectively. Accordingly, the stipulated maximum electrical input power in the LED datasheet (0.185 W) is shifted to 0.6284, 0.6963 and 0.8838 W between the three substrates.

Using a large number of LP LEDs is preferred than high-power (HP) LEDs for the same system power to augment the heat transfer and provide a higher luminous flux. The PET theory equations have been applied to HP LEDs using heatsinks with various thermal resistances. In this work, the PET theory luminous flux equation was extended to be used for Indium Gallium Aluminum Phosphide LP LEDs attached to the substrates with dissimilar thermal resistances.

Proper thermal management is a key to improve the efficiency and reliability of light-emitting diodes (LEDs). This paper aims to report the influence of applying thermally conductive materials on thermal performance of indium gallium aluminum phosphide (InGaAlP)-based thin-film surface-mounted device (SMD) LED.

The LED thermal and optical parameters were determined using the combination of thermal transient tester (T3Ster) and thermal and radiometric characterization of power LEDs (TeraLED) instruments. The LED was mounted on FR4, 2W and 5W aluminum (Al) package substrates. Measurements were carried out by setting different boundary conditions: air between LED package and substrate and using thermally conductive epoxy (TIM A) and adhesive (TIM B) of thermal conductivity 1.67 and 1.78 W/mK, respectively.

For LED mounted on FR4 package, the total real thermal resistance is improved because of TIM B by 6 and 9 per cent at 50 and 100 mA, respectively. Likewise, the relative decrease in total thermal resistance of LED on 2W Al package is about 9 and 11 per cent. As well, for LED mounted on 5W Al package, the total real thermal resistance is reduced by 2 and 4 per cent.

No much work can be found in the literature on thermal interface material effects on thermal performance of low-power SMD LED. This work can assist in thermal management of low-power LEDs.