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The reconstruction of the spatial complex conductivity σ + j ω ε 0 ε r from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. However, the necessary computation of the Jacobian is known to be computationally expensive, as standard techniques such as adjoint field methods require additional simulations. In this work, we show a more efficient way to computationally access the Jacobian matrix. In particular, the presented techniques do not require additional simulations, making the use of the Jacobian, free of additional computational costs. [ABSTRACT FROM AUTHOR]

Dielectric sensing based on capacitive measurement technology is a favourable measurement approach in many industries and fields of application. From an electrical point of view, a coupling capacitance must be measured in the presence of stray capacitances. Different receiver circuit structures have been proposed for the underlying displacement current measurement. Ideally, the sensor assembly is directly connected to the sensor circuitry to minimize the influence with respect to these parasitic capacitances. However, under harsh operating conditions, e.g., at high temperatures, the sensor and the receiver circuit must be separated in order to protect the electronics. Consequently, the receiver circuit and the sensor have to be connected by cables, e.g., coaxial cables. The measurement setup differs significantly from the ideal design with a direct connection. In this paper, we investigate the behaviour of three common measurement circuits for capacitive measurements in instrumentations with cables. We study the interaction between the sensor and the electronics and analyse the operating behaviour of the circuit, as well as the operating states of the amplifiers used. We also address cross-sensitivities in the sensor design due to stray capacitances. The analyses are carried out for different cable lengths and measuring frequencies, and conditions for the usability of the circuit are deduced. In addition to the operational behaviour, we also evaluate the circuits by means of a noise analyses. Based on this analysis, we show a direct comparison of the circuits. The analysis is based on simulation studies, as well as collaborative measurements on test circuits where all circuit parameters are provided. The test circuits are realized with dedicated state-of-the-art circuit elements and, together with the analysis approach and the results, thus provide a basis for future developments. [ABSTRACT FROM AUTHOR]

Capacitive sensing has become a favorable measurement technology for flow metering in pneumatic conveying systems. Multielectrode sensing structures and tomographic signal evaluations enable spatially resolved flow parameter estimation, which is of particular interest for pneumatically conveyed solids due to inhomogeneous particle distributions within the pipeline. The noninvasive working principle of capacitive sensors is an important feature for the application in industrial processes with harsh environments. However, cross sensitivities of the capacitive probe cause effects, such as temperature drifts of the measurements. For a reliable operation of capacitive flow meters in harsh environments, induced drifts have to be compensated. In this article, we present the detailed analyses of thermal effects within capacitive sensors. Based on the findings, a model-based temperature compensation approach is developed within the Bayesian framework. The performance of the proposed compensation approach is analyzed by a measurement-based validation within a climate chamber and by a simulation-based uncertainty quantification. The capability to obtain temperature-independent estimates with calibration measurements acquired at room temperature is demonstrated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Atmospheric ice accretion is considered a severe safety issue for technical systems such as communication infrastructure, power lines, blades of wind turbines, and so on in cold climate regions. Among different sensing systems to detect and provide reliable information about the state of ice, capacitive sensing has been reported as a suitable technique. In capacitive sensing, measured capacitances are influenced due to ice accretion. Signal processing for ice sensors requires to estimate parameters for the state of ice from the data. In this paper, we present a model-based estimation approach for capacitive ice sensors. We analyze different electrode topologies for ice sensing and provide a statistical analysis of the sensor behavior. We hereby consider the random nature of natural ice accretion. From simulations, we show how a statistical model for the measurement process can be derived and demonstrate the construction of estimation algorithms within the Bayesian framework. We will demonstrate the capability of our approach for automated ice detection by means of long-term field data showing the ability to estimate ice layers with a precision better than 1 mm. [ABSTRACT FROM AUTHOR]

Measurement systems operating in cold climate regions are directly affected by harsh atmospheric conditions. Under severe conditions, e.g. ice accretion on a sensor surface can lead to a degraded performance or even a breakdown of the measurement system. In order to avoid such critical conditions, measures to prevent even partial icing of the sensor system have to be applied. E.g. weather and radiation shields are equipped with heating elements to maintain ice free conditions of a critical sensor surface. However, the control of the heating functionality is often based on little knowledge about the actual conditions on the surface. This leads to unnecessarily high power consumption of the heating module in case of a pessimistic control strategy. Hence a further sensing modality is of interest, which lowers the uncertainty in the icing prediction, eventually leading to a minimum of heating periods. In this work we present a general concept of a combined sensor and thermal actuator structure, which allows for a reliable detection and prevention of critical icing conditions on surfaces. The concept exploits a shared front-end structure for both sensing and heating to achieve space constraints comparable to traditional shields. We discuss the design of the front-end topology and the different modes of operation of the sensor and actuator system. The functionality of the approach is experimentally investigated by means of laboratory tests. [ABSTRACT FROM AUTHOR]

Pneumatic conveying is a widely applied technique for the transportation of powders. Dense phase conveying such as slug flow is the preferable operating condition of such transport systems. Advantages are the reduced energy and conveying gas consumption and reduced material wear. The design and the operation of dense phase conveyors is a challenging task due to complex flow dynamics and the lack of reliable flow meters, which are crucial for process control. In this work the capabilities of electrical capacitance tomography (ECT) for slug flow parameter estimation are analysed. The estimation of flow parameters is addressed and demonstrated by means of laboratory experiments. Amongst other parameters it is shown that mass concentration distributions as well as particle velocity fields can be obtained from tomographic image reconstruction results, which are substantial parameters for potential mass flow metering. Additionally, the proposed estimation techniques are applied to signals provided by an ECT system, which is installed within a large-scale pneumatic conveyor of an industrial process plant. It is observed that also Geldart group A powders with Archimedes numbers in the scale of A r ≈ 1 e 0 are conveyable in slug-like structures which can be separated by stationary or non-stationary layers. Furthermore, various slug flow properties of powders with A r > 1 e 2 reported in literature are confirmed but also deviating properties are observed, leading to novel insights into horizontal dense phase flow processes of powders with A r ≈ 1 e 0. The results demonstrated in this work are pointing out the capabilities of ECT for flow analyses, which are enabling further insights into flow mechanisms and future developments of flow meters for dense phase flow processes. [Display omitted] • Electrical capacitance tomography-based slug flow parameter estimation. • Tomographic imaging of mass concentration distributions. • Differentiation between slug velocity and particle velocity. • Application within an industrial-scale pneumatic conveyor with a length of 2 km. • Novel insights into dense phase conveying of Geldart group A powders with A r ≈ 1 e 0. [ABSTRACT FROM AUTHOR]

Pneumatic conveying is a standard transportation technique for bulk materials in various industrial fields. Flow metering is crucial for the efficient and reliable operation of such systems and for process control. Capacitive measurement systems are often proposed for this application. In this method, electrodes are placed on the conveyor systems transport line and capacitive signals are sensed. The design of the sensor with regard to the arrangement and the number of electrodes as well as the evaluation of the capacitive sensor signals can be divided into two categories. Calibration-based flow meters use regression methods for signal processing, which are parametrized from calibration measurements on test rigs. Their performance is limited by the extend of the calibration measurements. Electrical capacitance tomography based flow meters use model-based signal processing techniques to obtain estimates about the spatial material distribution within the sensor. In contrast to their calibration-based counterparts, this approach requires more effort with respect to modeling and instrumentation, as typically a larger number of measurement signals has to be acquired. In this work we present a comparative analysis of the two approaches, which is based on measurement experiments and a holistic system model for flow metering. For the model-based analysis Monte Carlo simulations are conducted, where randomly generated pneumatic conveying flow patterns are simulated to analyze the sensor and algorithm behavior. The results demonstrate the potential benefit of electrical capacitance tomography based flow meters over a calibration-based instrument design. [ABSTRACT FROM AUTHOR]

Pneumatic conveying systems have become a standard technique for the transport of bulk materials such as powdery or granulates. The spatial dependence of the material density and the stream velocity in such transport systems require a volumetric measurement principle for flow measurement. In this paper we analyse the capability to estimate the volume fraction from capacitive sensing data using electrical capacitance tomography (ECT). In particular, we investigate the capability of back-projection type imaging algorithms. The ill-posed nature of the imaging problem of ECT require the incorporation of prior knowledge in the design of the estimator. We analyse the different flow profiles in pneumatic conveying in order to generate specific sample-based prior information to improve the estimation performance and robustness. We discuss the construction of different linear image reconstruction algorithms and present a framework, which allows a detailed statistical analysis of the estimator performance. Simulation studies show the estimation behaviour of different algorithms with respect to the incorporated prior information. We demonstrate, that the incorporation of specific prior knowledge leads to an improved estimator behaviour; for example, reduced variance and unbiased estimates. We implemented laboratory experiments in order to analyse the presented approach for the application in real pneumatic conveying processes. We demonstrate the improved robust estimation behaviour by means of comparative reconstruction results obtained with different algorithms and priors. Furthermore, the uncertainty of the estimated volume fraction is analysed in steady state conveying processes. Hereby, it is demonstrated, that appropriate prior information improves the estimation performance also for measurements coming from real pneumatic conveying processes, making ECT a suitable tool for the volume fraction estimation in such transport systems. [ABSTRACT FROM AUTHOR]

This paper considers the problem of determining and comparing the quality of nonlinear sensor systems concerning a measurement task in a data-driven way. Due to various noise sources and nonlinear characteristics, physical sensor and measurement systems, in general, exhibit an intractable random input-to-output behavior. In practice, this makes it impossible to describe the exact stochastic system model analytically. Nevertheless, such a description is required if one wishes to formulate efficient processing algorithms and to draw rigorous conclusions about the fundamental performance limits of the sensor system. After determining the mean and covariance of a set of user-defined statistics at the sensor output in a calibrated environment, the unknown probabilistic model of the physical measurement system can be approximated by an equivalent model within the exponential family. Such an approximation features a mathematically tractable model description and is guaranteed to be conservative in the sense that it exhibits a lower Fisher information than the exact data-generating model. By considering measurement tasks with nonlinear amplifiers and capacitive sensors, we here outline how to use the presented data-driven model replacement strategy to compare the parameter uncertainty level which is achievable with different sensor layouts. [ABSTRACT FROM AUTHOR]

Measuring the state of batteries and their change over time is essential during research and development. A number of standard test methods are available to determine specific cell parameters, such as capacitance, internal resistance, coulombic efficiency, etc. Although these methods have been in use for a long time, a thorough analysis of the uncertainties associated with them – especially when using high-precision measuring equipment – is still lacking. Therefore, a primary goal of this work is to close this gap. For each method, the results of the uncertainty analysis are divided into a variable part (noise, jitter) and a constant part (absolute accuracy). In addition, the theoretical analysis is accompanied by practical measurement results from a high-precision measurement hardware, demonstrating what is currently possible with state-of-the-art equipment. The constant part of the uncertainty is mainly limited by the used calibration equipment. For the variable part of uncertainty, the situation is somewhat more varied. Using a battery temperature control with a variability of only ± 0. 1 ∘ C , capacity, capacity change and coulombic efficiency still show a strong influence on the prevailing small temperature variations. For the voltage analysis methods (differential capacity and voltage analysis) the predominate factor is voltage noise and drift. • Ratiometric quantities, e.g. Δ C or CE, reach uncertainties in the low ppm range. • Non-ratiometric quantities, e.g. capacitance, are much worse at several 100 ppm. • The value-to-value jitter is very low, ranging from a few to a few tens of ppm. • For low uncertainty, a highly stable temperature control (few mK) is necessary. [ABSTRACT FROM AUTHOR]