Microwave Measurements for Metal Vessels

We present two different measurement techniques intended for closed metal vessels, where the objective is to measure the permittivity inside the metal vessel. This problem is relevant for many applications found in e.g. process industry. The first approach exploits the measurement of resonance frequencies, where the metal vessel is used as a microwave resonator. In the second approach, we let the boundary of the metal vessel be equipped with aperture antennas, where the aperture antennas are implemented in terms of rectangular waveguides. The waveguide apertures loads the cavity significantly and we exploit the scattering matrix parameters for the solution of the inverse problem

Global monitoring of fluidized-bed processes by means of microwave cavity resonances

We present an electromagnetic measurement system for monitoring of the effective permittivity in closed metal vessels, which are commonly used in the process industry. The measurement system exploits the process vessel as a microwave cavity resonator and the relative change in its complex resonance frequencies is related to the complex effective permittivity inside the vessel. Also, thermal expansion of the process vessel is taken into account and we compensate for its influence on the resonance frequencies by means of a priori information derived from a set of temperature measurements. The sensitivities, that relate the process state to the measured resonance frequencies, are computed by means of a detailed finite element model. The usefulness of the proposed measurement system is successfully demonstrated for a pharmaceutical fluidized-bed process, where the water and solid contents inside the process vessel is of interest

System Identification and Tuning of Wireless Power Transfer Systems with Multiple Magnetically Coupled Resonators

We present a procedure for system identification and tuning of a wireless power transfer (WPT) system with four magnetically coupled resonators, where each resonator consists of a coil and a capacitor bank. The system-identification procedure involves three main steps: 1) individual measurement of the capacitor banks in the system; 2) measurement of the frequency-dependent two-port impedance matrix of the magnetically coupled resonators; and 3) determining the inductance of all coils and their corresponding coupling coefficients using a Bayesian approach. The Bayesian approach involves solving an optimization problem where we minimize the mismatch between the measured and simulated impedance matrix together with a penalization term that incorporates information from a direct measurement procedure of the inductance and losses of the coils. This identification procedure yields an accurate system model which we use to tune the four capacitance values to recover high system-performance and account for, e.g., manufacturing tolerances and coil displacement. For a prototype WPT system, we achieve 3.3 kW power transfer with 91 % system efficiency over an air-gap distance of approximately 20 cm

Microwave Measurement Systems for Parameter Estimation and Classification

Microwave measurement systems are attractive for diagnostics and monitoring purposes in a number of important applications. For example, the strong interaction between microwaves and water make microwaves well-suited for moisture measurements. Moreover, the power used in microwave measurements is often sufficiently low such that the measurement can be classified as non-destructive. As such, microwave measurements systems are appropriate for applications in, for example, biomedical imaging and monitoring of pharmaceutical processes.In this thesis, parameter estimation methods are employed for two microwave measurement systems with application in the pharmaceutical industry. Additionally, we present a numerical study of a simplified microwave measurement system for the localization of intracranial bleedings via classification. In order to achieve good agreement between measured and simulated data, we utilize accurate electromagnetic models by means of the finite element method and calibration methods using a reference case measurement. In addition, we utilize a priori information to mitigate problems associated with parameter ambiguity, where the a priori information may be incorporated by means of regularization. First, we consider a transmission/reflection tomography measurement system. Here, the parameter estimation method involves a goal function that corresponds to the misfit between the measured and simulated scattering data, where a non-linear gradient-based optimization method is used to determine the parameters. The gradients are computed by means of continuum sensitivity expressions based on an adjoint field problem. The tomography system is used to estimate the effective permittivity of densely packed microcrystalline cellulose (MCC) pellets and we find that the estimated permittivity depends on the moisture content of the MCC pellets. Second, we solve a minimization problem for resonance measurements in a pharmaceutical process vessel, which acts as a metal cavity. Here, we estimate parameters using a quadratic minimization problem with a regularization term, which incorporates a priori information provided from other sensors. The physical model is linearized and small perturbations of the resonant frequencies are related to small variations in the permittivity. During operation, the vessel is loaded with MCC pellets that are fluidized and circulated by injection of air, which yields a dilute MCC/air mixture. The measured resonant frequencies are used to estimate the effective complex permittivity of three different sub-regions inside the process vessel as a function of process time

Inverse and optimization problems in electromagnetics -- a finite-element method perspective

In this thesis, a selection of inverse and optimization problems are studied where the finite element method (FEM) serves as a comprehensive tool to solve electromagnetic field problems that lack an analytic solution. The inverse problems are typically formulated in terms of an optimization problem where the misfit between a measurement and the corresponding result of a computational model is minimized. The optimization problems are solved by a combination of techniques that involve gradient-based methods, stochastic methods and parameter studies.The first contribution of the thesis is a new higher-order hybrid FEM for Maxwell\u27s equations that combines (i) brick-shaped elements for large homogeneous regions with (ii) tetrahedrons for regions where local refinement is necessary. The tangential continuity of the electric field at the interface between the different element types is enforced in the weak sense using Nitsche\u27s method.\ua0This yields a flexible and efficient computational method that is free of spurious solutions and features a low dispersion error. We employ a stable implicit-explicit time-stepping scheme using an implicitness parameter associated with the tetrahedrons and the hybrid interface. No late-time instabilities are observed in the solution for computations with up to 300 000 time steps.The second contribution of this thesis deals with four inverse scattering problems: (i) gradient-based estimation of the dielectric properties of moist micro-crystalline cellulose in terms of a Debye model; (ii) detection and positioning of multiple scatterers inside a metal vessel using compressed sensing; (iii) monitoring of the material perturbations in a pharmaceutical process vessel using a linearized model around an operation point that varies with the process state; and (iv) a subspace-based classification method for the detection of intracranial bleedings in a simulated data set. The third contribution of the thesis explores stochastic optimization for an inductive power transfer (IPT) system consisting of four magnetically coupled resonance circuits, which is intended for power transfer distances on the order of the coils\u27 radius. A genetic algorithm is employed to compute the Pareto front that contrast the maximum efficiency and power transfer. Results are presented for both linear and non-linear circuits: (i) a time-harmonic model for magnetically coupled resonance circuits with a resistive load; and (ii) a transient model for an IPT system with square-wave excitation, rectifier, smoothing filter and battery

Inverse and optimization problems in electromagnetics -- a finite-element method perspective

In this thesis, a selection of inverse and optimization problems are studied where the finite element method (FEM) serves as a comprehensive tool to solve electromagnetic field problems that lack an analytic solution. The inverse problems are typically formulated in terms of an optimization problem where the misfit between a measurement and the corresponding result of a computational model is minimized. The optimization problems are solved by a combination of techniques that involve gradient-based methods, stochastic methods and parameter studies.The first contribution of the thesis is a new higher-order hybrid FEM for Maxwell\u27s equations that combines (i) brick-shaped elements for large homogeneous regions with (ii) tetrahedrons for regions where local refinement is necessary. The tangential continuity of the electric field at the interface between the different element types is enforced in the weak sense using Nitsche\u27s method.\ua0This yields a flexible and efficient computational method that is free of spurious solutions and features a low dispersion error. We employ a stable implicit-explicit time-stepping scheme using an implicitness parameter associated with the tetrahedrons and the hybrid interface. No late-time instabilities are observed in the solution for computations with up to 300 000 time steps.The second contribution of this thesis deals with four inverse scattering problems: (i) gradient-based estimation of the dielectric properties of moist micro-crystalline cellulose in terms of a Debye model; (ii) detection and positioning of multiple scatterers inside a metal vessel using compressed sensing; (iii) monitoring of the material perturbations in a pharmaceutical process vessel using a linearized model around an operation point that varies with the process state; and (iv) a subspace-based classification method for the detection of intracranial bleedings in a simulated data set. The third contribution of the thesis explores stochastic optimization for an inductive power transfer (IPT) system consisting of four magnetically coupled resonance circuits, which is intended for power transfer distances on the order of the coils\u27 radius. A genetic algorithm is employed to compute the Pareto front that contrast the maximum efficiency and power transfer. Results are presented for both linear and non-linear circuits: (i) a time-harmonic model for magnetically coupled resonance circuits with a resistive load; and (ii) a transient model for an IPT system with square-wave excitation, rectifier, smoothing filter and battery

Microwave Measurement Systems for Parameter Estimation and Classification

Microwave measurement systems are attractive for diagnostics and monitoring purposes in a number of important applications. For example, the strong interaction between microwaves and water make microwaves well-suited for moisture measurements. Moreover, the power used in microwave measurements is often sufficiently low such that the measurement can be classified as non-destructive. As such, microwave measurements systems are appropriate for applications in, for example, biomedical imaging and monitoring of pharmaceutical processes.In this thesis, parameter estimation methods are employed for two microwave measurement systems with application in the pharmaceutical industry. Additionally, we present a numerical study of a simplified microwave measurement system for the localization of intracranial bleedings via classification. In order to achieve good agreement between measured and simulated data, we utilize accurate electromagnetic models by means of the finite element method and calibration methods using a reference case measurement. In addition, we utilize a priori information to mitigate problems associated with parameter ambiguity, where the a priori information may be incorporated by means of regularization. First, we consider a transmission/reflection tomography measurement system. Here, the parameter estimation method involves a goal function that corresponds to the misfit between the measured and simulated scattering data, where a non-linear gradient-based optimization method is used to determine the parameters. The gradients are computed by means of continuum sensitivity expressions based on an adjoint field problem. The tomography system is used to estimate the effective permittivity of densely packed microcrystalline cellulose (MCC) pellets and we find that the estimated permittivity depends on the moisture content of the MCC pellets. Second, we solve a minimization problem for resonance measurements in a pharmaceutical process vessel, which acts as a metal cavity. Here, we estimate parameters using a quadratic minimization problem with a regularization term, which incorporates a priori information provided from other sensors. The physical model is linearized and small perturbations of the resonant frequencies are related to small variations in the permittivity. During operation, the vessel is loaded with MCC pellets that are fluidized and circulated by injection of air, which yields a dilute MCC/air mixture. The measured resonant frequencies are used to estimate the effective complex permittivity of three different sub-regions inside the process vessel as a function of process time

Higher-order brick-tetrahedron hybrid method for Maxwell\u27s equations in time domain

We present a higher-order brick-tetrahedron hybrid method for Maxwell\u27s equations in time domain. Brick-shaped elements are used for large homogeneous parts of the computational domain, where we exploit mass-lumping and explicit time-stepping. In regions with complex geometry, we use an unstructured mesh of tetrahedrons that share an interface with the brick-shaped elements and, at the interface, tangential continuity of the electric field is imposed in the weak sense by means of Nitsche\u27s method. Implicit time-stepping is used for the tetrahedrons together with the interface. For cavity resonators, the hybrid method reproduces the lowest non-zero eigenvalues with correct multiplicity and, for geometries without field singularities from sharp corners or edges, the numerical eigenvalues converge towards the analytical result with an error that is approximately proportional to h^2p, where h is the cell size and p is the polynomial order of the elements. For a rectangular waveguide, a layer of tetrahedrons embedded in a grid of brick-shaped elements yields a low reflection coefficient that scales approximately as h^2p. Finally, we demonstrate hybrid time-stepping for a lossless closed cavity resonator, where the time-domain response is computed for 300,000 time steps without any signs of instabilities

Higher-order hybrid method for curl-conforming elements on tetrahedrons and bricks

We present a brick-tetrahedron hybrid finite-element method with higher-order basis functions for solving electromagnetic field problems. For the brick-shaped elements, we use mass lumping for interpolatory basis-functions of incomplete order, which yields a diagonal mass-matrix. Hierarchical basis functions of incomplete and/or complete order are used for the tetrahedral elements. We enforce tangential continuity at the brick-tetrahedron interface in the weak sense. Our hybrid method correctly reproduces the lowest eigenvalues with correct multiplicity for a closed cavity-resonator. For tests in a rectangular waveguide, we demonstrate that the hybrid interface yields a low reflection coefficient

Estimating Scatterer Positions using Sparse Approximation

We present a convex optimization method for a class of inverse scattering problems. The method is based on three steps: (i) compute a database of scattering data for the measurement situations of interest; (ii) find a sparse approximation of a measured response in terms of the database; and (iii) estimate a representative description from the sparse approximation as a weighted average.We use the method to estimate the position of multiple scatters inside a microwave measurement system