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Heart is a vital organ that pumps blood to whole body. Synchronous contraction of the heart muscles assures that the required blood flow is supplied to organs. But sometimes the synchrony between those muscles is distorted, which results in reduced cardiac output that might lead to severe diseases, and even death. The most common of heart diseases are myocardial infarction and arrhythmias. The contraction of heart muscles is controlled by the electrical activity of the heart, therefore determination of that electrical activity could give us the information regarding the severeness and type of the disease. In order to diagnose heart diseases, classical 12 lead electrocardiogram (ECG) is the standard clinical tool. Although many cardiac diseases could be diagnosed with the 12 lead ECG, measurements from sparse electrode locations limit the interpretations. The main objective of this thesis is to determine the cardiac electrical activity from dense body surface measurements. This problem is called the inverse problem of electrocardiography. The high resolution maps of epicardial potentials could supply the physician the information that could not be obtained with any other method. But the calculation of those epicardial potentials are not easy / the problem is severely ill-posed due to the discretization and attenuation within the thorax. To overcome this ill-posedness, the solution should be constrained using prior information on the epicardial potential distributions. In this thesis, spatial and spatio-temporal Bayesian maximum a posteriori estimation (MAP), Tikhonov regularization and Kalman filter and Kalman smoother approaches are used to overcome the ill-posedness that is associated with the inverse problem of ECG. As part of the Kalman filter approach, the state transition matrix (STM) that determines the evolution of epicardial potentials over time is also estimated, both from the true epicardial potentials and previous estimates of the epicardial potentials. An activation time based approach was developed to overcome the computational complexity of the STM estimation problem. Another objective of this thesis is to study the effects of geometric errors to the solutions, and modify the inverse solution algorithms to minimize these effects. Geometric errors are simulated by changing the size and the location of the heart in the mathematical torso model. These errors are modeled as additive Gaussian noise in the inverse problem formulation. Residual-based and expectation maximization methods are implemented to estimate the measurement and process noise variances, as well as the geometric noise.

The Master’s thesis deals with the precision of machine tools, especially with the three-axis vertical milling machine. It is structurally divided into a theoretical and practical part. While the theoretical part focuses on problems of geometric errors and measuring devices, the practical one is devoted to the machine tool being tested. In this case, the data processing and the proposed statistical analysis are essential, and at the end of the thesis another possible way of developing the data processing is outlined.

Le principe de la métrologie en cours d’usinage est d'obtenir des données de mesure directement dans le flot de production. Ce principe fait suite au besoin croissant des industriels de réaliser des mesures en ligne durant une opération ou entre deux opérations d'usinage en employant le moyen de production pour mesurer la pièce usinée. La maîtrise des sources d’erreur de mesure telles que les erreurs géométriques est une condition sine qua non pour garantir la métrologie dimensionnelle traçable directement sur les machines-outils. Ces travaux portent sur la modélisation géométrique de machine-outil 5 axes, basée sur une paramétrisation normalisée des erreurs géométriques. Ce modèle est simulé et simplifié par l’utilisation d’une machine virtuelle développée comme un outil d’aide à la compréhension et à la visualisation des effets des erreurs géométriques sur l’erreur volumétrique. Un nouvel étalon matériel thermo-invariant a été développé : la Multi-Feature Bar. Raccordé à la définition internationale du mètre par un étalonnage et une intercomparaison européenne, il permet d’envisager des mesures traçables sur machine-outil dans un environnement hostile. L’identification de trois paramètres intrinsèques à cet étalon, couplée à une procédure de mesure, assure une identification complète et traçable des erreurs de mouvement d’axes linéaires. Suite à cela, l’identification des erreurs entre axes est quant à elle basée sur une analyse de combinaisons de paramètres suffisants pour caractériser au mieux l’erreur volumétrique. Une procédure d’identification des paramètres du modèle est proposée en minimisant la dérive temporelle de la structure ainsi que les effets des erreurs de mouvement précédemment identifiées. Une analyse de sensibilité des paramètres de réglages de la procédure de mesure ainsi que des effets de bruits permet de garantir la qualité de l’identification proposée. / In-process metrology consists in obtaining measurement data directly into the manufacturing process. This method results from an increasing need of manufacturers to carry out on-line measurements during one manufacturing task or between two manufacturing tasks by using the mean of production to measure the machined part. Monitoring the sources of errors like geometric errors is one of the prerequisites to ensure the traceable dimensional metrology directly on the machine tool.This thesis deals with the geometric modeling of 5-axis machine tool based on a standardized parameterization of geometric errors. This model is simulated and simplified by the use of a virtual machine developed in order to help understand and visualize the effects of geometric errors on the volumetric error.A new standard thermo-invariant material namely Multi-Feature Bar has been developed.After its calibration and after a European intercomparison, it provides a direct metrological traceability to the SI meter for dimensional measurement on machine tool in a hostile environment. The identification of three intrinsic parameters of this standard, coupled with a measurement procedure ensures complete and traceable identification of motion errors of linear axes. The identification of position and orientation errors of axis is based on an analysis of combinations of necessary parameters to characterize volumetric error and at best. A model parameter identification procedure is proposed by minimizing the time drift of the structural loop and the effects of previously identified motion errors. Asensitivity analysis of the measurement procedure settings and of the noise effects ensures the quality of this proposed identification.