In the present thesis, we propose and investigate a new approach to diagnose the effects of the various degradation mechanisms, including thermal degradation at hot spots, winding deformations due to the mechanical forces from short circuit currents, partial discharges due to local electric field surges, and increased moisture levels in the cellulose insulation due to decomposition, that affect electric power transformers during their normal operation in an electric power grid. Although the proposed diagnostics method can in principle be used to detect various degradation mechanisms mentioned above, we focus in the present thesis on mechanical deformations of transformer winding structures. Such mechanical deformations are most often caused by mechanical forces from short circuit currents, but they may also be caused by initial manufacturing errors and inconsistencies not detected by the power transformers’ suppliers quality assurance processes. We model a transformer winding surrounded by the transformer-tank wall and the magnetic core as a two-dimensional parallel plate waveguide or as a three-dimensional coaxial waveguide, where one metallic boundary (plate or cylinder) represents the wall of the transformer tank and the other metallic boundary (plate or cylinder) represents the iron core that conducts the magnetic flux. In between there is a set of parallel or coaxial conductors representing the winding segments. The new principle proposed in the present thesis is to insert a number of antennas into a transformer tank to radiate and measure microwave fields interacting with metallic structures and insulation. The responses from the emitted microwave radiation are expected to be sensitive to material properties that reflect the changes caused by any harmful deterioration processes mentioned above. Specifically, we investigate the mechanical deformations of transformer winding structures by determining the locations of the individual winding segments or turns, using measurements of the scattered fields at both ends of the winding structure. We solve the propagation problem using conventional waveguide theory, including mode-matching and cascading techniques. The inverse problem is solved using modified steepest-descent optimization methods. The optimization model is tested by comparing our calculated scattering data with synthetic measurement data generated by the commercial program HFSS. A good agreement is obtained between the calculated and measured positions of winding segments for a number of studied cases, which indicates that the diagnostics method proposed in the present thesis couldbe potentially useful as a basis for the design of a future commercial on-line winding monitoring device. However, further development of the theoretical analysis of a number of typical winding deformations, improvements of the optimization algorithms and a practical study with measurements on an actual power transformer structure are all needed to make an attempt to design a commercial winding monitoring device feasible. / <p>QC 20131007</p>

Cell modulus and prestress are important determinants of cell behavior. This study creates new software tools to compute the modulus and prestress distribution within a living cell. As input, we have a sequence of images of a cell plated on a substrate with fluorescently labeled fibronectin dots. The cell generates focal adhesions with the dots and thus deforms the substrate. A sequence of images of the cell and the fibronectin dots shows their deformation. We tested three different ways to track the movement of the fluorescent fibronectin dots. We demonstrated the accuracy and the adaptability of each method on a sequence of test images with a rigid movement. We found the best method for dot tracking is a combination of successive dot identification and digital image correlation. The dot deformation provides a measure of traction forces acting on the cell. From traction forces thus inferred, we use FEM to compute the stress distribution within a cell. We consider two approaches. The first is based on the assumption that the cell has homogeneous elastic properties. This is straightforward and requires only the cell being meshed and the linear elasticity problem solved on that mesh. Second, we relaxed the homogeneity assumption. We used previously published correlations between prestress and modulus to iteratively update the modulus and prestress distributions within the cell. A novel feature of this work is the implicit reconstruction of the modulus distribution without a measured displacement field, and the reconstruction of the prestress distribution accounting for intracellular inhomogeneity.

The aim of this report is to study how machine learning can be used to reconstruct 2 dimensional computed tomography images from limited angle data. This could be used in a variety of applications where either the space or timeavailable for the CT scan limits the acquired data.In this study, three different types of models are considered. The first model uses filtered back projection (FBP) with a single learned filter, while the second uses a combination of multiple FBP:s with learned filters. The last model instead uses an FNO (Fourieer Neural Operator) layer to both inpaint and filter the limited angle data followed by a backprojection layer. The quality of the reconstructions are assessed both visually and statistically, using PSNR and SSIM measures.The results of this study show that while an FBP-based model using one or more trainable filter(s) can achieve better reconstructions than ones using an analytical Ram-Lak filter, their reconstructions still fail for small angle spans. Better results in the limited angle case can be achieved using the FNO-basedmodel.

In applied mechanics it is always necessary to understand the fundamental properties of a system in order to generate an accurate numerical model or to predict future operating conditions. These fundamental properties include, but are not limited to, the material parameters of a specimen, the boundary conditions inside of a system, or essential dimensional characteristics that define the system or body. However in certain instances there may be little to no knowledge about the systems conditions or properties; as a result the problem cannot be modeled accurately using standard numerical methods. Consequently, it is critical to define an approach that is capable of identifying such characteristics of the problem at hand. In this thesis, an inverse approach is formulated using proper orthogonal decomposition (POD) with an accompanying radial basis function (RBF) network to estimate the current material parameters of a specimen with little prior knowledge of the system. Specifically conductive heat transfer and linear elasticity problems are developed in this thesis and modeled with a corresponding finite element (FEM) or boundary element (BEM) method. In order to create the truncated POD-RBF network to be utilized in the inverse approach, a series of direct FEM or BEM solutions are used to generate a statistical data set of temperatures or deformations in the system or body, each having a set of various material parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt (LM) algorithm. For now, the LM algorithm can be simply defined as a direct relation to the minimization of the Euclidean norm of the objective Least Squares function(s). The trained POD-RBF inverse technique outlined in this thesis provides a flexible by which this inverse approach can be implemented into various fields of engineering and mechanics. More importantly this approach is designed to offer an inexpensive way to accurately estimate material characteristics or properties using nondestructive techniques. While the POD-RBF inverse approach outlined in this thesis focuses primarily in application to conduction heat transfer, elasticity, and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or industries.

To accurately model or predict future operating conditions of a system in engineering or applied mechanics, it is necessary to understand its fundamental principles. These may be the material parameters, defining dimensional characteristics, or the boundary conditions. However, there are instances when there is little to no prior knowledge of the system properties or conditions, and consequently, the problem cannot be modeled accurately. It is therefore critical to define a method that can identify the desired characteristics of the current system without accumulating extensive computation time. This thesis formulates an inverse approach using proper orthogonal decomposition (POD) with an accompanying radial basis function (RBF) interpolation network. This method is capable of predicting the desired characteristics of a specimen even with little prior knowledge of the system. This thesis first develops a conductive heat transfer problem, and by using the truncated POD – RBF interpolation network, temperature values are predicted given a varying Biot number. Then, a simple bifurcation problem is modeled and solved for velocity profiles while changing the mass flow rate. This bifurcation problem provides the data and foundation for future research into the left ventricular assist device (LVAD) and implementation of POD – RBF. The trained POD – RBF inverse approach defined in this thesis can be implemented in several applications of engineering and mechanics. It provides model reduction, error filtration, regularization and an improvement over previous analysis utilizing computational fluid dynamics (CFD).

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In this age, there are many applications of inverse problems to lots of areas ranging from astronomy, geoscience and so on. For example, image reconstruction and deblurring require the use of methods to solve inverse problems. Since the problems are subject to many factors and noise, we can't simply apply general inversion methods. Furthermore in the problems of interest, the number of unknown variables is huge, and some may depend nonlinearly on the data, such that we must solve nonlinear problems. It is quite different and significantly more challenging to solve nonlinear problems than linear inverse problems, and we need to use more sophisticated methods to solve these kinds of problems. / Master of Science / In various research areas, there are many required measurements which can't be observed due to physical and economical reasons. Instead, these unknown measurements can be recovered by known measurements. This phenomenon can be modeled and be solved by mathematics.

This thesis develops an immersed finite element (IFE) space for numerical simulations arising from beam design with multiple materials. This IFE space is based upon meshes that can be independent of interface of the materials used to form a beam. Both the forward and inverse problems associated with the beam equation are considered. The order of accuracy of this IFE space is numerically investigated from the point of view of both the interpolation and finite element solution of the interface boundary value problems. Both single and multiple interfaces are considered in our numerical simulation. The results demonstrate that this IFE space has the optimal order of approximation capability. / Master of Science