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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]

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]

Pretouch sensors are capable to classify objects and estimate their position prior to touching and thus close the gap between vision- and contact-based sensing. This will be particularly useful for robotics applications not only just for manipulation of objects but also with respect to safety. As robots will more and more operate in “open environments” where there is little prior knowledge, it will be important to gather as much information on the environment as possible. However, although there are many measurement principles that might be applied, only a few can cope with the requirements, e.g., limitations with respect to spatial dimensions, weight, and power consumption. In this paper, we investigate a measurement system for two types of materials. Dielectric and ferromagnetic materials, which are common in many industrial applications, can be located and distinguished in the vicinity of a robot grasper. Inspired by magnetic field tomography, we use a permanent magnet and apply giant magnetic resistor sensors to measure the magnetic field deformation caused by ferromagnetic objects. Furthermore, we use an electrical capacitance tomography approach to measure the change of the electric field by dielectric objects. Based on the measurement results, we solve an inverse problem with respect to the object position and spatial permittivity distribution. We present experimental results for a prototype implementation and provide a description of the calibration method. [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]