Purpose: 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. Design/methodology/approach: 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. Findings: 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. Practical implications: 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. Originality/value: 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.

Knowledge about the dielectric properties of materials, i.e., the relative permittivity and the conductivity, is important for various sensing applications and engineering. In pneumatic conveying systems, the dielectric properties of the transported good are affected by the transport gas, which aerates the pulverized material, effectively decreasing the permittivity. Traditional probe designs such as the open-ended coaxial probe are well suited for the dielectric characteristics of liquids, gels, and pulverized materials. However, to measure the dielectric properties for aerated materials, the probe has to provide measures to create an aerated state. In this paper, we present a probe design to measure the dielectric properties of aerated pulverized materials. The probe maintains a coaxial design with a dedicated gas injection, enabling the analysis of diluted materials. We discuss the design of the probe, show the modeling of the probe, and present suitable calibration techniques. Furthermore, we analyze the uncertainty of the probe design by means of a statistical analysis of the calibration approach.

Electrical capacitance tomography (ECT) is a well-established technique for process monitoring, which enables the visualization of spatial material distributions within a region of interest, e.g. a pipeline. Switched capacitor (SC) circuits or continuous displacement current measurements are used to measure the coupling capacitances within the ECT sensor. In order to measure the coupling capacitances with high accuracy, the circuit concepts make use of fast excitation signals, e.g. fast transients in SC circuits or high excitation frequency signals in continuous displacement current measurements. For industrial process tomography in harsh environments a spatial separation between the sensor and the front-end circuitry is favorable. Consequently, the measurement circuitry and the sensor are connected by means of coaxial cables. For high excitation frequencies, transmission line effects like standing waves, reflections, or impedance transformation effects appear, leading to undefined signal conditions in the measurement system. It can be shown that the undefined signal propagation can lead to significant measurement errors. In this paper we present an impedance matched front-end circuitry, i.e. the source impedance of the excitation source and the input impedance of the measurement circuitry are matched to the wave impedance of the transmission lines. Due to the matching the signal propagation becomes defined, allowing the use of arbitrary cable lengths and excitation signals. We present the design of an impedance matched front-end for ECT and study the behavior of the excitation system and the measurement system. Comparative measurements from a demonstrator are presented. Finally we study the measurement error of the system and show the validity of the impedance matched system approach.

The design and realization of capacitive measurement systems requires a variety of prior knowledge of the system, to achieve the intended performance. Electrical capacitance tomography (ECT) is a high end application of capacitive sensing. The required electronics is usually tailored to specific application constraints. To compare suitable circuit structures, a holistic design framework is required considering all components and their mutual interactions to derive appropriate figures of merit. We present an analysis framework and exemplary compare two different ECT circuit structures with respect to their sensitivity. The framework incorporates real world sensor conditions, for the application of the system.

Knowledge about the dielectric properties of materials, i.e. the relative permittivity and the conductivity, is important for various sensing applications and engineering. In pneumatic conveying systems the dielectric properties of the transported good are affected by the transport gas, which aerates the pulverized material, effectively decreasing the permittivity. Traditional probe designs like the open ended coaxial probe are well suited for the dielectric characteristics of liquids, gels and pulverized materials. Yet this probes show shortcomings for diluted materials as the probes do not allow a manipulation of the material. In this work we present a probe design to measure the dielectric properties of aerated pulverized materials. The probe maintains a coaxial design with a dedicated gas injection, enabling the analysis of diluted materials.

The determination and differentiation of various materials is of great interest in numerous applications. For this purpose, spectroscopic impedance measurement systems are applied. The frequency dependent impedance analysis enables a detailed material investigation and an assessment of its composition e. g. the moisture content. By applying impedance measurement systems in industrial environments conditions as high temperatures, high pressures or vibrations have to be considered. In this paper we present a front-end topology intended to be used for frequency spectroscopic based measurement systems, deployed in industrial environments. The impedance measurement capability of the proposed system is investigated by means of a realized prototype. We present results obtained for measurement frequencies up to 50MHz and address calibration strategies, which improve the robustness. The measurement electronics is also characterized over the environmental temperature range.