The first part of the Master´s thesis describes physical principles of ultrasound and fundamental variables of ultrasound field. It also deals with mathematical description of finite element method and outlines basic principles of ultrasound computed tomography. The second part introduces finite elements generator GMSH. This part focuses on the process of ultrasound field simulation and presents software that can be used for field simulation. The last part contains examples of models.

<p dir="ltr">For additive manufacturing to be a viable method to build metal parts for industries such as nuclear, the manufactured parts must be of higher quality and have lower variation in said quality than what can be achieved today. This high variation in quality bars the techniques from being used in high safety tolerance fields, such as nuclear. If this obstacle could be overcome, the benefits of additive manufacturing would be in lower cost for complex parts, as well as the ability to design and test parts in a very short timeframe, as only the CAD model needs to be created to manufacture the part. In this study, work to achieve this lower variation of quality was approached in two ways. The first was in the development of surrogate models, utilizing machine learning, to predict the end quality of additively manufactured parts. This was done by using experimental data for the mechanical properties of built parts as outputs to be predicted, and in-situ signals captured during the manufacturing process as inputs to the model. To capture the in-situ signals, cameras were used for thermal and optical imaging, leveraging the natural layer-by-layer manufacturing method used in AM techniques. The final models were created using support vector machine and gaussian process regression machine learning algorithms, giving high correlations between the insitu signals and mechanical properties of relative density, elongation to fracture, uniform elongation, and the work hardening exponent. The second approach to this study was in the development of a reduced order model for a computer simulation of an AM build. For project, a ROM was built inside the MOOSE framework, and was developed for an AM model designed by the MOOSE team, using proper orthogonal decomposition to project the problem onto a lower dimensional subspace, using POD to design the reduced basis subspace. The ROM was able to achieve a reduction to 1% the original dimensionality of the problem, while only allowing 2-5% relative error associated with the projection.</p>