In this paper we consider the reconstruction of rapidly varying objects in process tomography. The evolution of the physical parameters can often be approximated with stochastic convection-diffusion and fluid dynamics models. We use the state estimation approach to obtain the tomographic reconstructions and show how these flow models can be exploited with the actual observation models that by themselves induce ill-posed problems. The state estimation problem can be stated in different ways based on the available temporal information. We concentrate on such cases in which continuous monitoring is essential but a small delay for the reconstructions is allowable. The state estimation problem is solved with the fixed-lag Kalman smoother algorithm. As the boundary observations we use the voltage data of electrical impedance tomography. We also give a numerical illustration of the approach in a case in which we track a bolus that moves rapidly through a pipeline.

Cracking and deterioration of concrete are the leading causes of a premature failing of reinforced concrete structures. To assess the condition of concrete, a variety of destructive and non-destructive testing methods have been developed. From these two methods, the non-destructive testing (NDT) is a more favorable (albeit more challenging) option since the tested target is left undamaged. The NDT modalities include acoustic, electromagnetic and radiation based techniques. In this thesis, the feasibility of electrical resistance tomography (ERT) for NDT of concrete is studied. In ERT, electric currents are injected into the target through electrodes that are are attached to the boundary of the target. The resulting voltages between the electrodes are measured and this boundary voltage data is then used to reconstruct the internal conductivity distribution of the target. The reconstruction of the internal conductivity distribution of concrete is expected to provide valuable information about the condition of the structure so that appropriate repairs can be taken in time. The difficulty in ERT, as is in any other diffuse tomography modality, is that the problem has a nature of an ill-posed inverse problem. This implies that the solutions of the problem are unstable and nonunique in the classical sense. As a consequence, extra attention must be directed to the mathematical modeling of the measurements as well as to the reconstruction methods. Furthermore, concrete is strongly heterogeneous material composed of cement matrix, aggregate and different chemical compounds that create a challenging target for electrical modalities. Previous studies have shown that ERT is a potential tool for NDT of concrete, but the quality of the reconstruction was not yet sufficient for practical applications. In this thesis, especially localizing reinforcing bars and crack identification are considered. To meet those aims, novel computational methods for the image reconstruction are developed. For the crack identification and localizing reinforcing bars, a novel adaptive meshing approach was developed. In the new approach cracks and reinforcing bars are modeled as internal structures. The results show that by employing accurate mathematical models and statistical inversion techniques based on the Bayesian framework, ERT can become an applicable tool for practical NDT of concrete.

This paper outlines the development of a large-area sensing skin for damage detection in concrete structures. The developed sensing skin consists of a thin layer of electrically conductive copper paint that is applied to the surface of the concrete. Cracking of the concrete substrate results in the rupture of the sensing skin, decreasing its electrical conductivity locally. The decrease in conductivity is detected with electrical impedance tomography (EIT) imaging. In previous works, electrically based sensing skins have provided only qualitative information on the damage on the substrate surface. In this paper, we study whether quantitative imaging of the damage is possible. We utilize application-specific models and computational methods in the image reconstruction, including a total variation (TV) prior model for the damage and an approximate correction of the modeling errors caused by the inhomogeneity of the painted sensing skin. The developed damage detection method is tested experimentally by applying the sensing skin to polymeric substrates and a reinforced concrete beam under four-point bending. In all test cases, the EIT-based sensing skin provides quantitative information on cracks and/or other damages on the substrate surface: featuring a very low conductivity in the damage locations, and a reliable indication of the lengths and shapes of the cracks. The results strongly support the applicability of the painted EIT-based sensing skin for damage detection in reinforced concrete elements and other substrates.

The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the functionality of impedance tomography relies heavily on accurate modelling of the measurement geometry. In particular, almost all reconstruction algorithms require the precise shape of the imaged body as an input. In this work, the need for prior geometric information is relaxed by introducing a Newton-type output least squares algorithm that reconstructs the admittivity distribution and the object shape simultaneously. The method is built in the framework of the complete electrode model and it is based on the Fréchet derivative of the corresponding current-to-voltage map with respect to the object boundary shape. The functionality of the technique is demonstrated via numerical experiments with simulated measurement data.

In this paper, the simultaneous retrieval of the exterior boundary shape and the interior admittivity distribution of an examined body in electrical impedance tomography is considered. The reconstruction method is built for the complete electrode model and it is based on the Fréchet derivative of the corresponding currentto-voltage map with respect to the body shape. The reconstruction problem is cast into the Bayesian framework, and maximum a posteriori estimates for the admittivity and the boundary geometry are computed. The feasibility of the approach is evaluated by experimental data from water tank measurements. The results demonstrate that the proposed method has potential for handling an unknown body shape in a practical setting.

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The ability to detect cracks in structural elements is an integral component in the assessment of structural heath and integrity. Recently, Electrical Resistance Tomography (ERT)-based sensing skins have been shown to reliably image progressive surface damage on structural members. However, so far the approach has only been tested in cases of relatively simple crack patterns. Because the spatial resolution of ERT is generally low, it is an open question whether the ERT-based sensing skins are able to image complex structural cracking patterns. In this paper, we test the accuracy of ERT for reconstructing cracking patterns experimentally and computationally. In the computational study, we use a set of numerical simulations that model progressive cracking in a rectangular beam geometry. We also investigate the effect of image reconstruction methods on the crack pattern estimates: In addition to the contemporary image reconstruction method used in the recent sensing skin studies, we test the feasibility of a novel approach where model-based structural prior information on the cracking probability is accounted for in the image reconstruction. The results of this study indicate that ERT-based sensing skins are able to detect and reconstruct complex structural cracking patterns, especially when structural prior information is utilized in the image reconstruction.