Abstract: A method for determining an electrical property of interest of material(s) in a target region confined by a boundary surface comprises receiving measured values of a measurable electrical quantity; providing simulated values of the measurable electrical quantity for an initial approximation of the electrical property conditions; determining an objective function comprising observation difference between the measured and the simulated values as well a prior model, and determining an adjusted approximation; and providing, on the basis of the adjusted approximation, an estimation of the electrical property of interest. Simulated statistics of a position deviation in the observations is provided, caused by a difference of an effective position of the measurement probe from a predetermined reference position; and by providing the observation model to define the observations of the measurable electrical quantity to correspond to measurements made with the measurement probe in the reference position.

Abstract: An apparatus for determining, by electrical tomography, vertical profile of an electrical property of interest of material(s) in a target volume comprises a measurement probe to be positioned at a plurality of different measurement levels in a target volume and comprising a plurality of measurement elements each having an interface surface. Each interface surface has a size, shape, and rotational position. A measurement path is formed between two interface surfaces as dependent on the sizes, shapes, and rotational positions of the two interface surfaces, and the distance between the two interface surfaces. The locations, rotational positions, shapes, and sizes of the interface surfaces are selected to provide at least two different measurement paths differing from each other in one or more of said sizes of, shapes of, rotational positions of, and distances between the associated interface surfaces.

Abstract: A method for determining a quantity of interest in a target comprises: providing simulated statistics of a deviation, caused by a boundary distortion in observations of the physical quantity; providing an approximate mathematical model of observations of the physical quantity, the approximate mathematical model defining the physical quantity to be dependent on the quantity of interest in the target domain, and on a deviation a boundary distortion causes in the observations, said deviation being determined to behave in accordance with the simulated statistics; receiving measured values of the physical quantity; determining an observation difference between the measured values of the physical quantity and corresponding observations according to the approximate mathematical model, and adjusting the approximate mathematical model to reduce the observation difference; and determining an estimate of the quantity of interest in the target domain on the basis of the adjusted approximate mathematical model.

Abstract: A method for determining an electrical property of interest of material(s) in a target region confined by a boundary surface comprises receiving measured values of a measurable electrical quantity; providing simulated values of the measurable electrical quantity for an initial approximation of the electrical property conditions; determining an objective function comprising observation difference between the measured and the simulated values as well a prior model, and determining an adjusted approximation; and providing, on the basis of the adjusted approximation, an estimation of the electrical property of interest. Simulated statistics of a position deviation in the observations is provided, caused by a difference of an effective position of the measurement probe from a predetermined reference position; and by providing the observation model to define the observations of the measurable electrical quantity to correspond to measurements made with the measurement probe in the reference position.

Abstract: An apparatus for determining, by electrical tomography, vertical profile of an electrical property of interest of material(s) in a target volume comprises a measurement probe to be positioned at a plurality of different measurement levels in a target volume and comprising a plurality of measurement elements each having an interface surface. Each interface surface has a size, shape, and rotational position. A measurement path is formed between two interface surfaces as dependent on the sizes, shapes, and rotational positions of the two interface surfaces, and the distance between the two interface surfaces. The locations, rotational positions, shapes, and sizes of the interface surfaces are selected to provide at least two different measurement paths differing from each other in one or more of said sizes of, shapes of, rotational positions of, and distances between the associated interface surfaces.

Abstract: A method for determining the location of an interface of interest in a target domain, between a free volume of a flowable material and a solid material limiting said free volume, the method involves the steps of providing a mathematical model of the target domain determining, for a plurality of pairs of electrode groups, a characteristic electrical quantity proportional to the capacitance of a capacitor formed by a pair of electrode groups; receiving measurements of the characteristic electrical quantity for a plurality of pairs of electrode groups; adjusting the mathematical model by varying the location of the boundary surface in order to take into account possible wear of the boundary surface so as to reduce the differences between the measured characteristic electrical quantities and those defined by the mathematical model; and determining the location of the interface of interest on the basis of the adjusted mathematical model.

Abstract: A method for investigating permittivity within a target domain comprises a step of measuring, for a plurality of pairs of contact element groups, the contact elements of the contact element groups being arranged in capacitance measurement connection with the target domain, an electrical quantity of interest proportional to the capacitance of a capacitor formed by a pair of contact element groups; the contact elements comprising a plurality of electrodes supported between the target domain and an electrically conductive background body limiting the capacitance measurement zone of the electrodes. The contact elements may further comprise the electrically conductive background body.

Abstract: A method for determining a quantity of interest in a target comprises: providing simulated statistics of a deviation, caused by a boundary distortion in observations of the physical quantity; providing an approximate mathematical model of observations of the physical quantity, the approximate mathematical model defining the physical quantity to be dependent on the quantity of interest in the target domain, and on a deviation a boundary distortion causes in the observations, said deviation being determined to behave in accordance with the simulated statistics; receiving measured values of the physical quantity; determining an observation difference between the measured values of the physical quantity and corresponding observations according to the approximate mathematical model, and adjusting the approximate mathematical model to reduce the observation difference; and determining an estimate of the quantity of interest in the target domain on the basis of the adjusted approximate mathematical model.

Abstract: A method for investigating permittivity within a target domain comprises a step of measuring, for a plurality of pairs of contact element groups, the contact elements of the contact element groups being arranged in capacitance measurement connection with the target domain, an electrical quantity of interest proportional to the capacitance of a capacitor formed by a pair of contact element groups; the contact elements comprising a plurality of electrodes supported between the target domain and an electrically conductive background body limiting the capacitance measurement zone of the electrodes. The contact elements may further comprise the electrically conductive background body.

Abstract: A method for determining the location of an interface of interest in a target domain, between a free volume of a flowable material and a solid material limiting said free volume, the method involves the steps of providing a mathematical model of the target domain determining, for a plurality of pairs of electrode groups, a characteristic electrical quantity proportional to the capacitance of a capacitor formed by a pair of electrode groups; receiving measurements of the characteristic electrical quantity for a plurality of pairs of electrode groups; adjusting the mathematical model by varying the location of the boundary surface in order to take into account possible wear of the boundary surface so as to reduce the differences between the measured characteristic electrical quantities and those defined by the mathematical model; and determining the location of the interface of interest on the basis of the adjusted mathematical model.

Abstract: A method for determining the electrical conductivity of a mass flow in a three dimensional target volume including the steps of placing electrodes in a measuring connection with the target volume; supplying alternating voltage or alternating current to the tar-get volume between two of the electrodes and measuring the current or the voltage between the electrodes; determining a state space model which defines the relationships between the electrical conductivity, the voltage and the current in the target volume and the evolution of the electrical conductivity as a function of time; comparing the currents and/or the voltages according to the state space model with the supplied and the measured ones; and modifying the state space model to decrease any differences. The electrodes are placed substantially within one plane; and the state space model is determined so as to the time-dependent flow field of the mass flow within the target volume.