State estimation in process tomography—Three‐dimensional impedance imaging of moving fluids

Seppänen, Aku; Vauhkonen, Marko; Vauhkonen, P J; Voutilainen, Arto; Kaipio, Jari P.

doi:10.1002/nme.2142

Cited by 23 publications

(40 citation statements)

References 24 publications

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“…The aim is to reconstruct the electrical conductivity (or admittivity, resistivity, or impedivity) inside the object. Applications of EIT include biomedical imaging [1], nondestructive testing [17], and process tomography [27]. The reconstruction task is an extensively studied inverse problem for which both direct and iterative methods have been proposed [16,22,30].…”

Section: Introductionmentioning

confidence: 99%

Smoothened Complete Electrode Model

Hyvönen¹,

Mustonen²

2017

SIAM J. Appl. Math.

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Abstract. This work reformulates the complete electrode model of electrical impedance tomography in order to enable more efficient numerical solution. The model traditionally assumes constant contact conductances on all electrodes, which leads to a discontinuous Robin boundary condition since the gaps between the electrodes can be described by vanishing conductance. As a consequence, the regularity of the electromagnetic potential is limited to less than two square-integrable weak derivatives, which negatively affects the convergence of, e.g., the finite element method. In this paper, a smoothened model for the boundary conductance is proposed, and the unique solvability and improved regularity of the ensuing boundary value problem are proven. Numerical experiments demonstrate that the proposed model is both computationally feasible and also compatible with real-world measurements. In particular, the new model allows faster convergence of the finite element method.

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Section: Introductionmentioning

confidence: 99%

Smoothened Complete Electrode Model

Hyvönen¹,

Mustonen²

2017

SIAM J. Appl. Math.

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“…The next section features a brief presentation of the basic equations and concepts. Indeed, Extended Kalman Filters (EKF) have been extensively employed for inverse problems related to a wide range of applications (see for example [21][22][23][24]) and, particularly relevant for the present work [25], in which the EKF was applied to crack detection.…”

Section: Hydraulic Fracture Monitoring As a Nonstationary Inverse Promentioning

confidence: 99%

Monitoring hydraulic fractures: state estimation using an extended Kalman filter

Rochinha

Peirce

2010

Inverse Problems

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There is considerable interest in using remote elastostatic deformations to identify the evolving geometry of underground fractures that are forced to propagate by the injection of high pressure viscous fluids. These so-called hydraulic fractures are used to increase the permeability in oil and gas reservoirs as well as to pre-fracture ore-bodies for enhanced mineral extraction. The undesirable intrusion of these hydraulic fractures into environmentally sensitive areas or into regions in mines which might pose safety hazards has stimulated the search for techniques to enable the evolving hydraulic fracture geometries to be monitored. Previous approaches to this problem have involved the inversion of the elastostatic data at isolated time steps in the time series provided by tiltmeter measurements of the displacement gradient field at selected points in the elastic medium. At each time step, parameters in simple static models of the fracture (e.g. a single displacement discontinuity) are identified. The approach adopted in this paper is not to regard the sequence of sampled elastostatic data as independent, but rather to treat the data as linked by the coupled elastic-lubrication equations that govern the propagation of the evolving hydraulic fracture. We combine the Extended Kalman Filter (EKF) with features of a recently developed implicit numerical scheme to solve the coupled free boundary problem in order to form a novel algorithm to identify the evolving fracture geometry. Numerical experiments demonstrate that, despite excluding significant physical processes in the forward numerical model, the EKF-numerical algorithm is able to compensate for the un-modeled dynamics by using the information fed back from tiltmeter data. Indeed the proposed algorithm is able to provide reasonably faithful estimates of the fracture geometry, which are shown to converge to the actual hydraulic fracture geometry as the number of tiltmeters is increased. Since the location of tiltmeters can affect the resolution of the method, the algorithm can also

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“…The algorithms in the latter category were implemented through the calculation of the Dirichlet-to-Neumann map or Neumann-to-Dirichlet map, and the gray value at each pixel can be calculated directly and independently [11]- [14]. In recent years, 3-D ERT are used to monitor drug release three-dimensionally as a function of time [15], to serve as an adjunct modality for enhancing standard clinical ultrasound imaging of the prostate [16], to image the rapidly varying objects in the flow pipes [17], and to monitor sedimentation in the control and optimization of industrial sedimentation processes [18] and etc. Compared with the 2-D ERT, the 3-D ERT requires more spatial information; as a result, usually more electrodes are required.…”

Section: Introductionmentioning

confidence: 99%

Direct Image Reconstruction for 3-D Electrical Resistance Tomography by Using the Factorization Method and Electrodes on a Single Plane

Cao

2013

IEEE Trans. Instrum. Meas.

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A direct reconstruction method for three-dimensional (3-D) electrical resistance tomography was introduced by using the factorization method. Compared with the traditional image reconstruction algorithms based on the sensitivity/Jacobian matrix, the conductivity distribution in any part of the 3-D region of interest can be obtained directly and independently. A new way to calculate the Neumann-to-Dirichlet map was also introduced by using the adjacent current pattern. Several phantoms were constructed for image reconstruction in three dimensions. The data were collected from 16 electrodes on a single cross section, which can be only used to produce two-dimensional images in the literature. Neither matrix inversion nor iteration was used in the process of image reconstruction. The reconstructed results validated the feasibility of the method.

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State estimation in process tomography—Three‐dimensional impedance imaging of moving fluids

Cited by 23 publications

References 24 publications

Smoothened Complete Electrode Model

Smoothened Complete Electrode Model

Monitoring hydraulic fractures: state estimation using an extended Kalman filter

Direct Image Reconstruction for 3-D Electrical Resistance Tomography by Using the Factorization Method and Electrodes on a Single Plane

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