Pour relever les défis de l'observation de la Terre et de l'astronomie, les futurs observatoires spatiaux vont requérir des télescopes de plusieurs mètres de diamètre. Les différentes contraintes liées à l'environnement spatial vont induire des déformations et des désalignements des miroirs du télescope dégradant ainsi la qualité optique des observations. L'intégration de l'optique active, utilisée depuis la fin des années 80 pour l'alignement et le maintien de la qualité optique des télescopes au sol, devient donc nécessaire. Un tel système est constitué de trois éléments : un dispositif de mesure, une fonction de correction et une boucle de contrôle qui fait le lien entre les deux éléments précédents.Les travaux de recherche présentés dans ce mémoire de doctorat s'attachent, d'une part, au développement d'un estimateur des perturbations minimisant le front d'onde résiduel dans le champ du télescope. L'analyse de cet estimateur et plus généralement des performances ultimes d'un système d'optique active spatial nous a permis de mettre en évidence l'impact des hautes fréquences spatiales sur la qualité optique. La présence de telles hautes fréquences dues à l'empreinte des supports du miroir primaire nous a poussés, d'autre part, à évaluer les possibilités de leur réduction dans le cas d'un miroir de grande dimension. A l'aide d'une modélisation éléments finis d'un tel miroir nous avons réalisé des modifications locales de la structure du miroir pour adapter ses déformations aux capacités de correction de l'optique active. / To meet the challenges of Earth observation and astronomy, future space observatories will require telescopes of several meters in diameter. The various space environment constraints will induce deformations and misalignments of the telescope mirrors, thus degrading the optical quality of observations. The integration of active optics, used since the late 80s for alignment and preservation of the optical quality of the ground telescopes, becomes mandatory. Such a system consists of three elements: a measuring device, a correction set-up and a control loop which links both previous elements.The research works presented in this PhD thesis focus, on one hand, on the development of a perturbations estimator minimizing the residual wave front in the telescope field of view. The analysis of this estimator and more generally of the ultimate performance of a space active optics system enabled us to highlight the impact of high spatial frequencies on optical quality. On the other hand, the presence of such high frequencies due to the primary mirror supports print through, urged us to evaluate the possibilities of their reduction in the case of large mirrors. Using a finite element model of such a mirror, we made local modifications of the mirror structure to adapt its deformation to the correcting capabilities of active optics.

Dans le cadre de l'élasticité linéaire 3D des microstructures complexes qui ne peuvent pas être simplement décrites en terme de constituants telles que des tissus biologiques, nous proposons, dans ce travail de recherche, une méthodologie d'identification expérimentale multi-échelle du champ stochastique d'élasticité apparent de la microstructure à l'échelle mésoscopique en utilisant des mesures de champ de déplacements aux échelles macroscopique et mésoscopique. On peut alors utiliser cette méthodologie dans le cadre de changement d'échelle pour obtenir des propriétés mécaniques à l'échelle macroscopique. Dans ce contexte, la question majeure est celle de l'identification expérimentale par résolution d'un problème statistique inverse de la modélisation stochastique introduite pour le champ d'élasticité apparent à l'échelle mésoscopique. Cette identification expérimentale permet non seulement de valider la modélisation mais encore de la rendre utile pour des matériaux existants ayant une microstructure complexe. Le présent travail de recherche est une contribution proposée dans ce cadre pour lequel l'expérimentation et validation expérimentale basée sur des mesures simultanées d'imagerie de champ aux échelles macroscopique et mésoscopique sont faites sur de l'os cortical / In the framework of linear elasticity 3D for complex microstructures that cannot be simply described in terms of components such as biological tissues, we propose, in this research work, a methodology for multiscale experimental identification of the apparent elasticity random field of the microstructure at mesoscopic scale using displacement field measurements at macroscopic scale and mesoscopic scale. We can then use this methodology in the case of changing scale to obtain the mechanical properties at macroscale. In this context, the major issue is the experimental identification by solving a statistical inverse problem of the stochastic modeling introduced for the apparent elasticity random field at mesoscale. This experimental identification allows to validate the modeling and makes it useful for existing materials with complex microstructures. This research work is proposed in this context in which experimentation and experimental validation based on simultaneous measurements of field imaging at macroscale and mesoscale are made on the cortical bonemakes it useful for existing materials with complex microstructures. This research work is proposed in this context in which experimentation and experimental validation based on simultaneous measurements of field imaging at macroscale and mesoscale are made on the cortical bone.

En dépit des grandes avancées dans le domaine de la recherche médicale, les maladies cardiovasculaires (MCV) représentent toujours l’une des causes principales de mortalité dans le monde, et sont globalement responsables d’un tiers des décès dus à des maladies. En raison de la diversité et de la complexité de ces MCV, les recherches dans des domaines variés tels que la biomécanique, médecine, biologie, anatomopathologie, pharmacologie et imagerie se sont accrues. Ces recherches multidisciplinaires se développent dans l’espoir de mieux comprendre ces pathologies afin de mieux les traiter, ainsi que de réduire les coûts hospitaliers liés aux traitements des patients. Mes travaux de thèse rentrent dans ce cadre-là et s’inscrivent dans le champ de la Biomécanique Cardiovasculaire lié aux maladies coronariennes. Ils visent à développer de nouveaux outils d’aide au diagnostic médical pour la cardiologie interventionnelle.Mon rapport doctoral comporte deux parties :Dans la 1ère partie, je m’intéresse à l’imagerie de la plaque coronarienne obtenue à partir de l’exploration endovasculaire par ultrason (IVUS) pratiquée en clinique et plus particulièrement en utilisant le signal radio-fréquence (RF) IVUS. Le risque de rupture d’une plaque d’athérome coronarienne vulnérable (PV) est lié à la composition composite de sa lésion athéromateuse. Les proximités de tissus biologiques très différents engendrent des gradients d’élasticité importants responsables de concentrations de contraintes de fortes amplitudes, pouvant potentiellement rompre la PV. La mécanique des milieux continus va nous aider à identifier les propriétés mécaniques de tous les constituants de la PV à partir des séquences IVUS obtenues sur patients. Plusieurs études développées au sein de notre laboratoire TIMC (telles que la Palpographie isotrope, la Modulographie isotrope) permettent une quantification préliminaire des propriétés mécaniques de tous les constituants de la lésion. Au sein de cette 1ère partie, je décris dans un premier temps ces techniques existantes, puis dans un 2ème temps je détaille et explique mes travaux de recherche développés lors de ma thèse dans ce domaine d’imagerie. J’ai essayé de répondre aux deux questions essentielles suivantes : 1) Peut-on travailler directement avec le signal IVUS b-mode disponible en routine clinique pour visualiser l’élasticité de la lésion athéromateuse? , et 2) Est-il possible d’améliorer la technique existante de palpographie isotrope afin de tenir compte des propriétés anisotropes de la lésion et de la paroi vasculaire? . Afin d’y répondre, j’ai mené des études à la fois théoriques et expérimentales pour tester les performances des nouveaux outils d’imagerie IVUS proposés.Dans la 2ème partie de ma thèse, je me suis intéressée à l’angioplastie par ballonnet et plus précisément aux propriétés viscoélasto-plastiques du ballon. En effet, il est essentiel pour le cardiologue de prendre en compte l’évolution des propriétés mécaniques du ballon lors de son utilisation répétée, et cela afin de permettre un acte chirurgical plus précis lors du gonflement du ballonnet au sein des artères coronariennes pathologiques. Cette dernière étude peut servir de base au développement d’un modèle biomécanique plus complet permettant de prédire l’évolution de la courbe pression-diamètre du ballon lors de son utilisation et plus particulièrement lors de ses gonflements consécutifs en utilisation clinique. / Cardiac catheterization has evolved from being initially received with great skepticism to becoming a standard for the diagnosis and treatment of cardiovascular disease. A myriad of derived techniques like balloon angioplasty, intravascular imaging, as well as valve and stent implantation are now routine procedures for interventional cardiologists. Despite these and other great advances in cardiovascular medicine, cardiovascular disease (CVD) still represents the main cause of mortality, accounting for as much as one out of three deaths worldwide. Due to the complexity of CVD, it has become the field of study of researchers among various disciplines in hopes to reduce the burden of the disease. One of such disciplines is mechanics, that applies its principles and approaches to create innovative tools to diagnose, prevent and treat CVD.The present thesis belongs to the field of cardiovascular biomechanics and aims to develop tools that can be of assistance to physicians in the diagnosis and treatment of coronary artery disease. This dissertation is divided into two parts:Part I: Imaging the atherosclerotic plaque in clinics, is related to the identification and assessment of coronary atherosclerotic plaque with the presentation of a novel palpography algorithm based on continuum mechanics theory.First, it was investigated whether gray-scale IVUS images are enough for obtaining an accurate elasticity map to assess plaque composition and evolution. Indeed, it was concluded that radiofrequency (RF) data provides more detailed data than b-mode IVUS images. Then a novel anisotropic elasticity-palpography algorithm is described. It computes an apparent elasticity of the plaque from radiofrequency signals obtained through IVUS images. The derivation of an anisotropic index (AI) that can be related to the mechanical properties of the arterial wall, along with a first validation using simulated IVUS images based on real patient geometries of atherosclerotic and healthy plaques is presented. Using this new palpography algorithm, a study was that aimed to validate this technique in vitro was performed. Polyvinyl-alcohol (PVA) cryogel vascular phantoms were fabricated, two of them with increased anisotropy. The phantoms were imaged with IVUS and their mechanical properties were obtained using different characterization techniques. Then, the anisotropy indices modeld with the experimental results and the ones computed with the algorithm were compared.Part II: Balloon angioplasty is focused on the treatment of coronary plaque and analyzes the mechanical properties of the balloons used for coronary angioplasty.First, the visco-elasto-plastic mechanical characterization of a specific balloon catheter model, the Maverick2 from Boston Scientific, is presented. Geometrical measurements using different microscopy techniques, balloon inflation tests, tensile tests and high-speed images are used to describe the mechanical behavior of the balloon components. The previous results are used in to define a model that can accurately predict the viscoelasto-plastic behavior of the angioplasty balloon film. These results could be used as the basis for a model to predict the inflation behavior of the angioplasty balloon during consecutive inflations in clinics.

Surface temperature control of a thin plate is investigated. Temperature is controlled on one side of the plate using the other side temperature measurements. This is a decades-old problem, reactivated more recently by the awareness that this is a fractional-order problem that justifies the investigation of the use of fractional order calculus. The approach is based on a transfer function obtained from the one-dimensional heat conduction equation solution that results in a fractional-order s-domain representation. Both the inverse problem approach and the fractional controller approach are studied here to control the surface temperature, the first one using inverse problem plus a Proportional only controller, and the second one using only the fractional controller. The direct problem defined as the ratio of the output to the input, while the inverse problem defined as the ratio of the input to the output. Both transfer functions are obtained, and the resulting fractional-order transfer functions were approximated using Taylor expansion and Zero-Pole expansion. The finite number of terms transfer functions were used to form an open-loop control scheme and a closed-loop control scheme. Simulation studies were done for both control schemes and experiments were carried out for closed-loop control schemes. For the fractional controller approach, the fractional controller was designed and used in a closed-loop scheme. Simulations were done for fractional-order-integral, fractional-order-derivative and fractional-integral-derivative controller designs. The experimental study focussed on the fractional-order-integral-derivative controller design. The Fractional-order controller results are compared to integer-order controller’s results. The advantages of using fractional order controllers were evaluated. Both Zero-Pole and Taylor expansions are used to approximate the plant transfer functions and both expansions results are compared. The results show that the use of fractional order controller performs better, in particular concerning the overshoot.

abstract: Dimensionality reduction methods are examined for large-scale discrete problems, specifically for the solution of three-dimensional geophysics problems: the inversion of gravity and magnetic data. The matrices for the associated forward problems have beneficial structure for each depth layer of the volume domain, under mild assumptions, which facilitates the use of the two dimensional fast Fourier transform for evaluating forward and transpose matrix operations, providing considerable savings in both computational costs and storage requirements. Application of this approach for the magnetic problem is new in the geophysics literature. Further, the approach is extended for padded volume domains. Stabilized inversion is obtained efficiently by applying novel randomization techniques within each update of the iteratively reweighted scheme. For a general rectangular linear system, a randomization technique combined with preconditioning is introduced and investigated. This is shown to provide well-conditioned inversion, stabilized through truncation. Applying this approach, while implementing matrix operations using the two dimensional fast Fourier transform, yields computationally effective inversion, in memory and cost. Validation is provided via synthetic data sets, and the approach is contrasted with the well-known LSRN algorithm when applied to these data sets. The results demonstrate a significant reduction in computational cost with the new algorithm. Further, this new algorithm produces results for inversion of real magnetic data consistent with those provided in literature. Typically, the iteratively reweighted least squares algorithm depends on a standard Tikhonov formulation. Here, this is solved using both a randomized singular value de- composition and the iterative LSQR Krylov algorithm. The results demonstrate that the new algorithm is competitive with these approaches and offers the advantage that no regularization parameter needs to be found at each outer iteration. Given its efficiency, investigating the new algorithm for the joint inversion of these data sets may be fruitful. Initial research on joint inversion using the two dimensional fast Fourier transform has recently been submitted and provides the basis for future work. Several alternative directions for dimensionality reduction are also discussed, including iteratively applying an approximate pseudo-inverse and obtaining an approximate Kronecker product decomposition via randomization for a general matrix. These are also topics for future consideration. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

This thesis presents research focused on developing statistical methods with emphasis on techniques that can be used for the analysis of data in imaging studies and sparse estimations for applications in high-dimensional data. The first contribution addresses the pixel/voxel-labeling problem for spatial hidden Markov models in image analysis. We formulate a Gaussian spatial mixture model with Potts model used as a prior for mixture allocations for the latent states in the model. Jointly estimating the model parameters, the discrete state variables and the number of states (number of mixture components) is recognized as a difficult combinatorial optimization. To overcome drawbacks associated with local algorithms, we implement and make comparisons between iterated conditional modes (ICM), simulated annealing (SA) and hybrid ICM with ant colony system (ACS-ICM) optimization for pixel labelling, parameter estimation and mixture component estimation. In the second contribution, we develop ACS-ICM algorithm for spatiotemporal modeling of combined MEG/EEG data for computing estimates of the neural source activity. We consider a Bayesian finite spatial mixture model with a Potts model as a spatial prior and implement the ACS-ICM for simultaneous point estimation and model selection for the number of mixture components. Our approach is evaluated using simulation studies and an application examining the visual response to scrambled faces. In addition, we develop a nonparametric bootstrap for interval estimation to account for uncertainty in the point estimates. In the third contribution, we present sparse estimation strategies in linear mixed model (LMM) for longitudinal data. We address the problem of estimating the fixed effects parameters of the LMM when the model is sparse and predictors are correlated. We propose and derive the asymptotic properties of the pretest and shrinkage estimation strategies. Simulation studies is performed to compare the numerical performance of the Lasso and adaptive Lasso estimators with the pretest and shrinkage ridge estimators. The methodology is evaluated through an application of a high-dimensional data examining effective brain connectivity and genetics. In the fourth and final contribution, we conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set. We relate longitudinal effective brain connectivity estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR). / Graduate

Tato práce se zabývá vytvořením softwarového nástroje pro simulaci přenosu tepla se zaměřením na využití inverzní úlohy. Je zde popsána základní teorie inverzních úloh a přenosu tepla, na kterou navazuje odvození numerické rovnice přenosu tepla, vhodné pro počítačovou simulaci. Hlavní část práce se věnuje návrhu a samotné implementaci softwarového řešení, s ohledem jak na funkčnost, tak na uživatelskou přívětivost. Kromě výpočtového modelu, který je zodpovědný za průběh simulace, je vytvořeno také plnohodnotné uživatelské rozhraní (GUI), umožňující jednoduchou interakci s výpočtovým modelem. Závěrem práce je prezentování dosažených výsledků a jejich porovnání s reálným experimentem, stejně jako zjištění vlivu vstupních parametrů na kvalitu simulace.

Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADT). Response Reconstruction is cast as an inverse problem whereby the desired input is inferred using the measured outputs of a system. ADT typically involves large shock loadings resulting in a nonlinear response of the structure. A promising linear regression technique known as Spanning Basis Transformation Regression (SBTR) in con- junction with non-overlapping windows casts the low dimensional nonlinear problem as a high dimensional linear problem. However, it is determined that the original implementation of SBTR struggles to invert a broader class of sensor configurations. A new windowing method called AntiDiagonal Averaging (ADA) is developed to overcome the shortcomings of the SBTR im- plementation. ADA introduces overlaps within the predicted time signal windows and averages them. The newly proposed method is tested on a numerical quarter car model and is shown to successfully invert a broader range of sensor configurations as well as being capable of describing nonlinearities in the system. / Dissertation (MEng)--University of Pretoria, 2021. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

This diploma thesis deals with genetic algorithms and their properties. Particular emphasis is placed on finding the influence of mutation and population size. Genetic algorithms are applied on inverse heat conduction problems (IHCP) in the second part of the thesis. Several different approaches and coding methods were tested. Properties of genetic algorithms were improved by definition of two new genetic operators – manipulation and sorting. Reported theoretical findings were tested on the real data of inverse heat conduction problem. The library for easy implementation of GA for solving general optimization problems in C ++ was created and is described in the last chapter.

Comprendre comment différentes régions du cerveau interagissent afin d’exécuter une tâche, est un défi très complexe. La magnéto- et l’électroencéphalographie (MEEG) sont deux techniques non-invasive d’imagerie fonctionnelle utilisées pour mesurer avec une bonne résolution temporelle l’activité cérébrale. Estimer cette activité à partir des mesures MEEG est un problème mal posé. Il est donc crucial de le régulariser pour obtenir une solution unique. Il a été montré que l’homogénéité structurelle des régions corticales reflète leur homogénéité fonctionnelle. Un des buts principaux de ce travail est d’utiliser cette information structurelle pour définir des a priori permettant de contraindre de manière plus anatomique ce problème inverse de reconstruction de sources. L’imagerie par résonance magnétique de diffusion (IRMd) est, à ce jour, la seule technique non-invasive qui fournisse des informations sur l’organisation structurelle de la matière blanche. Cela justifie son utilisation pour contraindre notre problème inverse. Nous utilisons l’information fournie par l’IRMd de deux manière différentes pour reconstruire les activations du cerveau : (1) via une méthode spatiale qui utilise une parcellisation du cerveau pour contraindre l’activité des sources. Ces parcelles sont obtenues par un algorithme qui permet d’obtenir un ensemble optimal de régions structurellement homogènes pour une mesure de similarité donnée sur tout le cerveau. (2) dans une approche spatio-temporelle qui utilise les connexions anatomiques, calculées à partir des données d’IRMd, pour contraindre la dynamique des sources. Ces méthodes sont appliquée à des données synthétiques et réelles. / Understanding how brain regions interact to perform a given task is a very challenging task. Electroencephalography (EEG) and Magnetoencephalography (MEG) are two non-invasive functional imaging modalities used to record brain activity with high temporal resolution. As estimating brain activity from these measurements is an ill-posed problem. We thus must set a prior on the sources to obtain a unique solution. It has been shown in previous studies that structural homogeneity of brain regions reflect their functional homogeneity. One of the main goals of this work is to use this structural information to define priors to constrain more anatomically the MEG/EEG source reconstruction problem. This structural information is obtained using diffusion magnetic resonance imaging (dMRI), which is, as of today, the unique non-invasive structural imaging modality that provides an insight on the structural organization of white matter. This makes its use to constrain the EEG/MEG inverse problem justified. In our work, dMRI information is used to reconstruct brain activation in two ways: (1) In a spatial method which uses brain parcels to constrain the sources activity. These parcels are obtained by our whole brain parcellation algorithm which computes cortical regions with the most structural homogeneity with respect to a similarity measure. (2) In a spatio-temporal method that makes use of the anatomical connections computed from dMRI to constrain the sources’ dynamics. These different methods are validated using synthetic and real data.