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No / This paper presents a methodology for efficient shape parametrisation for automatic design optimisation using a partial differential equation (PDE) formulation. It is shown how the choice of an elliptic PDE enables one to define and parametrise geometries corresponding to complex shapes. By using the PDE formulation it is shown how the shape definition and parametrisation can be based on a boundary value approach by which complex shapes can be created and parametrised based on the shape information at the boundaries or the character lines defining the shape. Furthermore, this approach to shape definition allows complex shapes to be parametrised intuitively using a very small set of design parameters.

With the continuous growth in computing power, numerical optimisation is increasingly applied in shape optimisation using Computational Fluid Dynamics (CFD). Since CFD computations are expensive, gradient-based optimisation is preferable when the number of design variables is large. In particular the recent progress with adjoint solvers is important, as these solvers allow to compute the gradients at constant computational cost regardless of the number of design variables, and as a consequence enable the use of automatically derived and rich design spaces. One of the crucial steps in shape optimisation is the parametrisation of the geometry, which directly determines the design space and thus the nal results. This thesis focuses on CAD-based parametrisations with the CAD model continuously updated in the design loop. An existing approach that automatically derives a parametrisation from the control points of a net of B-Spline patches is extended to include NURBS. Continuity constraints for water-tightness, tangency and curvature across patch interfaces are evaluated numerically and a basis for the resulting design space is computed using Singular Value Decomposition (SVD). A CAD-based shape optimisation framework is developed, coupling a flow solver, an adjoint solver, the in-house CAD kernel and a gradient-based optimiser. The flow sensitivities provided by the adjoint solver and the geometric sensitivities computed through automatic differentiation (AD) are assembled and provided to the optimiser. An extension to maintain the design space and hence enables use of a quasi-Newton method such as the BFGS algorithm is also presented and the convergence improvements are demonstrated. The framework is applied to three shape optimisation cases to show its effectiveness. The performance is assessed and analysed. The effect of parameters that can be chosen by the user are analysed over a range of cases and best practice choices are identified.

Soit un $f(X)$ un polynôme à coefficients rationnels, $S$ un ensemble infini du nombres rationnels. Soit $f(S)$ l' ensemble image de $f(X)$ sur $S$. Si $g(X)$ est un polynôme telle que $f(S)=g(S)$ on dit que $g$ parametrise l'ensemble $f(S)$. En plus de la solution $g=f$ on peut imposer autre conditions sur le polynôme $g$; par example, si $f(S)\subset\Z$, on peut se demander si il y a un polynôme à coefficients entiers que parametrise l'ensemble $f(S)$. De plus, si l'image $f(S)$ est parametrisé par un polynôme $g$, on peut demander si il y a de relations entre les polynômes $f$ et $g$. Par example, si $h$ est un polynôme linéaire et on pose $g=f\circ h$, évidemment le polynôme $g$ parametrise l'ensemble $f(\Q)$. Réciproquement, si nous avons que $f(\Q)=g(\Q)$ (ou aussi $f(\Z)=g(\Z)$) alors par le théorème d'irréductibilité de Hilbert il y a un polynôme linéaire $h$ telle que $g=f\circ h$. Donc, si $g$ est un polynôme que parametrise l'ensemble $f(S)$, pour un ensemble infinie de nombres rationnels, nous nous demandons si il y a un polynôme $h$ telle que $f=g\circ h$. Il y a de théorèmes par Kubota que donnons de réponses positif sous certain conditions. Le but de ce thèse est l'étude de certain aspects de cet deux problèmes lié à la parametrisation de les ensembles image de polynômes.

When an autonomous vehicle has a mission to perform, it is of high importance that the robot has good knowledge about its position. Without good knowledge of the position, it will not be able to navigate properly and the data that it gathers, which could be of importance for the mission, might not be usable. A helicopter could for example be used to collect laser data from the terrain beneath it, which could be used to produce a 3D map of the terrain. If the knowledge about the position and orientation of the helicopter is poor then the collected laser data will be useless since it is unknown what the laser actually measures. A successful solution to position and orientation (pose) estimation of an autonomous helicopter, using an inertial measurement unit (IMU), a camera and a GPS, is proposed in this thesis. The problem is to estimate the unknown pose using sensors that measure different physical attributes and give readings containing noise. An extended Kalman filter solution to the simultaneous localisation and mapping (SLAM) is used to fuse data from the different sensors and estimate the pose of the robot. The scale invariant feature transform (SIFT) is used for feature extraction and the unified inverse depth parametrisation (UIDP) model is used to parametrise the landmarks. The orientation of the robot is described by quaternions. To be able to evaluate the performance of the filter an ABB industrial robot has been used as reference. The pose of the end tool of the robot is known with high accuracy and gives a good ground truth so that the estimations can be evaluated. The results shows that the algorithm performs well and that the pose is estimated with good accuracy. / När en autonom farkost skall utföra ett uppdrag är det av högsta vikt att den har god kännedom av sin position. Utan detta kommer den inte att kunna navigera och den data som den samlar in, relevant för uppdraget, kan vara oanvändbar. Till exempel skulle en helikopter kunna användas för att samla in laser data av terrängen under den, för att skapa en 3D karta av terrängen. Om kännedomen av helikopterns position och orientering är dålig kommer de insamlade lasermätningarna att vara oanvändbara eftersom det inte är känt vad lasern faktiskt mäter. I detta examensarbete presenteras en väl fungerande lösning för position och orienterings estimering av autonom helikopter med hjälp av en inertial measurement unit (IMU), en kamera och GPS. Problemet är att skatta positionen och orienteringen med hjälp av sensorer som mäter olika fysiska storheter och vars mätningar innehåller brus. En extended Kalman filter (EKF) lösning för simultaneous localisation and mapping (SLAM) problemet används för att fusionera data från de olika sensorerna och estimera positionen och orienteringen. För feature extrahering används scale invariant feature transform (SIFT) och för att parametrisera landmärken används unified inverse depth parametrisation (UIDP). Orienteringen av roboten beskrivs med hjälp av qvartinjoner. För att evaluera skattningarna har en ABB robot används som referens vid datainsamling. Då roboten har god kännedom om position och orientering av sitt främre verktyg gör detta att prestandan i filtret kan undersökas. Resultaten visar att algorithmen fungerar bra och att skattningar har hög noggrannhet.

Disertacijoje nagrinėjamos baltymų pėdsakų parametrizavimo dvimatės elektroforezės (2ME) gelių vaizduose problemos. Proteomikoje, analizuojant baltymus, tiriami gyvame organizme vykstantys pokyčiai. 2ME metu baltymai išskiriami pagal jų molekulines savybes. Deja 2ME gelių vaizdų automatinei analizei skirtose programose pritaikytos technologijos netinka iškraipytiems baltymų pėdsakams (dėl baltymų įsisotinimo, persisotinimo ar susiliejimo) aptikti ir parametrizuoti. Pagrindinis disertacijos tikslas – ištirti galimybę taikyti vaizdo rekonstravimo technologijas trimačiams objektams parametrizuoti, sukuriant ir ištiriant baltymų pėdsakų 2ME gelių vaizduose parametrizavimo metodus. Disertacijoje sprendžiami trys pagrindiniai uždaviniai: naujų baltymų pėdsakų matematinių modelių, tinkamų įsisotinusiems baltymų pėdsakams parametrizuoti, kūrimas; baltymų persisotinimų paieškos ir rekonstravimo metodo kūrimas ir susiliejusių baltymų pėdsakų parametrizavimo metodo kūrimas. Disertaciją sudaro įvadas, keturi skyriai ir rezultatų apibendrinimas. Įvadiniame skyriuje nagrinėjamas problemos aktualumas, iškeliamos hipotezės, formuluojamas darbo tikslas bei uždaviniai, mokslinis darbo naujumas, darbo praktinė reikšmė ir disertacijos struktūra. Pirmajame skyriuje apžvelgtos parametrizavimui taikomos vaizdo rekonstravimo technologijos. Skyriuje apžvelgtos vaizdo rekonstravimo technologijos, taikomos objektui parametrizuoti, kai naudojami keli, skirtingu kampu, gauti objekto vaizdai... [toliau žr. visą tekstą] / The problems of protein parametrisation in two-dimensional electrophoresis (2DE) gel image is analysed in this work. Analysis of the proteins gives possibility to observe the health state of living organisms. In proteomics two-dimensional electrophoresis is used for protein separation in the gel according to their isoelectric point and molecular mass. The resulting gel is scanned and analysed by automatic gel image analysis systems. Those systems are not able to deal with specific protein spot distortions found in the gel image. The over-saturated protein spots prevent proper segmentation of the 2DE gel images. The aim of the work is to investigate the possibility of image reconstruction applications for object parametrisation by creating new methods for protein spot parametrisation in 2DE gel images. Three main tasks are resolved in this work: new mathematical models for parametrisation of saturated protein spots in 2DE gel images are proposed; new method for over-saturated protein spot search and reconstruction in 2DE gel images is proposed; new method for parametrisation of overlapped protein spots in 2DE gel images is proposed. The thesis is divided into introduction, four chapters and generalisation. The review of image reconstruction techniques and current 2DE gel image analysis problems are presented in first chapter. In the second chapter – the new mathematical models for parametrisation of saturates protein spots are proposed and experimental investigation results... [to full text]

The problems of protein parametrisation in two-dimensional electrophoresis (2DE) gel image is analysed in this work. Analysis of the proteins gives possibility to observe the health state of living organisms. In proteomics two-dimensional electrophoresis is used for protein separation in the gel according to their isoelectric point and molecular mass. The resulting gel is scanned and analysed by automatic gel image analysis systems. Those systems are not able to deal with specific protein spot distortions found in the gel image. The over-saturated protein spots prevent proper segmentation of the 2DE gel images. The aim of the work is to investigate the possibility of image reconstruction applications for object parametrisation by creating new methods for protein spot parametrisation in 2DE gel images. Three main tasks are resolved in this work: new mathematical models for parametrisation of saturated protein spots in 2DE gel images are proposed; new method for over-saturated protein spot search and reconstruction in 2DE gel images is proposed; new method for parametrisation of overlapped protein spots in 2DE gel images is proposed. The thesis is divided into introduction, four chapters and generalisation. The review of image reconstruction techniques and current 2DE gel image analysis problems are presented in first chapter. In the second chapter – the new mathematical models for parametrisation of saturates protein spots are proposed and experimental investigation results... [to full text] / Disertacijoje nagrinėjamos baltymų pėdsakų parametrizavimo dvimatės elektroforezės (2ME) gelių vaizduose problemos. Proteomikoje, analizuojant baltymus, tiriami gyvame organizme vykstantys pokyčiai. 2ME metu baltymai išskiriami pagal jų molekulines savybes. Deja 2ME gelių vaizdų automatinei analizei skirtose programose pritaikytos technologijos netinka iškraipytiems baltymų pėdsakams (dėl baltymų įsisotinimo, persisotinimo ar susiliejimo) aptikti ir parametrizuoti. Pagrindinis disertacijos tikslas – ištirti galimybę taikyti vaizdo rekonstravimo technologijas trimačiams objektams parametrizuoti, sukuriant ir ištiriant baltymų pėdsakų 2ME gelių vaizduose parametrizavimo metodus. Disertacijoje sprendžiami trys pagrindiniai uždaviniai: naujų baltymų pėdsakų matematinių modelių, tinkamų įsisotinusiems baltymų pėdsakams parametrizuoti, kūrimas; baltymų persisotinimų paieškos ir rekonstravimo metodo kūrimas ir susiliejusių baltymų pėdsakų parametrizavimo metodo kūrimas. Disertaciją sudaro įvadas, keturi skyriai ir rezultatų apibendrinimas. Įvadiniame skyriuje nagrinėjamas problemos aktualumas, iškeliamos hipotezės, formuluojamas darbo tikslas bei uždaviniai, mokslinis darbo naujumas, darbo praktinė reikšmė ir disertacijos struktūra. Pirmajame skyriuje apžvelgtos parametrizavimui taikomos vaizdo rekonstravimo technologijos. Skyriuje apžvelgtos vaizdo rekonstravimo technologijos, taikomos objektui parametrizuoti, kai naudojami keli, skirtingu kampu, gauti objekto vaizdai, taikomos... [toliau žr. visą tekstą]

This thesis addresses the problem of representing few group, homogenised neutron cross sections as a function of state parameters (e.g. burn-up, fuel and moderator temperature, etc.) that describe the conditions in the reactor. The problem is multi-dimensional and the cross section samples, required for building the representation, are the result of expensive transport calculations. At the same time, practical applications require high accuracy. The representation method must therefore be efficient in terms of the number of samples needed for constructing the representation, storage requirements and cross section reconstruction time. Sparse grid methods are proposed for constructing such an efficient representation. Approximation through quasi-regression as well as polynomial interpolation, both based on sparse grids, were investigated. These methods have built-in error estimation capabilities and methods for optimising the representation, and scale well with the number of state parameters. An anisotropic sparse grid integrator based on Clenshaw-Curtis quadrature was implemented, verified and coupled to a pre-existing cross section representation system. Some ways to improve the integrator’s performance were also explored. The sparse grid methods were used to construct cross section representations for various Light Water Reactor fuel assemblies. These reactors have different operating conditions, enrichments and state parameters and therefore pose different challenges to a representation method. Additionally, an example where the cross sections have a different group structure, and were calculated using a different transport code, was used to test the representation method. The built-in error measures were tested on independent, uniformly distributed, quasi-random sample points. In all the cases studied, interpolation proved to be more accurate than approximation for the same number of samples. The primary source of error was found to be the Xenon transient at the beginning of an element’s life (BOL). To address this, the domain was split along the burn-up dimension into “start-up” and “operating” representations. As an alternative, the Xenon concentration was set to its equilibrium value for the whole burn-up range. The representations were also improved by applying anisotropic sampling. It was concluded that interpolation on a sparse grid shows promise as a method for building a cross section representation of sufficient accuracy to be used for practical reactor calculations with a reasonable number of samples. / Thesis (MSc Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

This thesis addresses the problem of representing few group, homogenised neutron cross sections as a function of state parameters (e.g. burn-up, fuel and moderator temperature, etc.) that describe the conditions in the reactor. The problem is multi-dimensional and the cross section samples, required for building the representation, are the result of expensive transport calculations. At the same time, practical applications require high accuracy. The representation method must therefore be efficient in terms of the number of samples needed for constructing the representation, storage requirements and cross section reconstruction time. Sparse grid methods are proposed for constructing such an efficient representation. Approximation through quasi-regression as well as polynomial interpolation, both based on sparse grids, were investigated. These methods have built-in error estimation capabilities and methods for optimising the representation, and scale well with the number of state parameters. An anisotropic sparse grid integrator based on Clenshaw-Curtis quadrature was implemented, verified and coupled to a pre-existing cross section representation system. Some ways to improve the integrator’s performance were also explored. The sparse grid methods were used to construct cross section representations for various Light Water Reactor fuel assemblies. These reactors have different operating conditions, enrichments and state parameters and therefore pose different challenges to a representation method. Additionally, an example where the cross sections have a different group structure, and were calculated using a different transport code, was used to test the representation method. The built-in error measures were tested on independent, uniformly distributed, quasi-random sample points. In all the cases studied, interpolation proved to be more accurate than approximation for the same number of samples. The primary source of error was found to be the Xenon transient at the beginning of an element’s life (BOL). To address this, the domain was split along the burn-up dimension into “start-up” and “operating” representations. As an alternative, the Xenon concentration was set to its equilibrium value for the whole burn-up range. The representations were also improved by applying anisotropic sampling. It was concluded that interpolation on a sparse grid shows promise as a method for building a cross section representation of sufficient accuracy to be used for practical reactor calculations with a reasonable number of samples. / Thesis (MSc Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

Avec la découverte en juillet 2012 par les collaborations CMS et ATLAS d'un nouveau scalaire, aux propriétés similaires à celles d'un boson prédit plus de 50 ans auparavant, la phénoménologie au-delà du modèle standard (SM) a fait un grand pas. En effet, la découverte de cette pièce manquante du puzzle électrofaible a rendu certains modèles impossibles, tout en renforçant la crédibilité du SM. Cependant, on sait que le SM n'est pas le mot de la fin, car certaines de ses prédictions ne s'accordent pas avec les expériences, et ce boson est donc vu comme une porte vers de nouveaux secteurs de la physique. Après une introduction au SM et aux statistiques de la physique des particules, nous présenterons un paramétrage des couplages mesurés au LHC, afin de contraindre, via ces couplages, des modèles de physique au-delà du SM, plus fondamentaux. Ce paramétrage, s'intéressant particulièrement aux couplages à boucles, permettrait de lever une corrélation existant entre les paramètres actuellement utilisés. Nous étudierons ensuite la possibilité d'existence d'un scalaire, plus léger que celui observé, et ayant échappé aux recherches passées, et de sa recherche au LHC à l'aide de ce paramétrage. Nous donnerons des exemples de paramètres faisant apparaître un tel scalaire, dans le 2HDM et le NMSSM. Enfin, nous verrons que le scalaire peut influencer la production d'une paire de bosons de jauge faible, et qu'à l'aide de notre paramétrage, l'analyse de ce processus peut être utilisée de manière cohérente avec les mesures au pic de masse pour contraindre ces couplages. Nous finirons avec quelques limites de cette approche, ainsi que des propositions d'améliorations / With the discovery of a new particle in July 2012 by the CMS and ATLAS experiments, with properties resembling those of a boson predicted about 50 years earlier by theorists, the search for physics outside of the standard model of particle physics (SM) has made a big step. Indeed, the existence of this piece of the electroweak symmetry breaking proved wrong many theories, while giving more credit to the SM. However, because of some observations it fails to match, we know the SM cannot be the final word, and it is hoped that the study of this new particle will be a path to new sectors of physics. After a brief description of the SM and of the statistics of particle physics, we will present a way to parametrise the couplings measured at CERN, in order to constrain, through these couplings, more fundamental models describing physics beyond the standard model. This parametrisation, focusing on loop-induced couplings, would allow to lift a correlation existing between parameters currently used by experimentalists. We will then study the feasibility of a search for another scalar, lighter than the one discovered and which would have escaped previous searches, through the use of the same parametrisation. In two models, the 2HDM and the NSSSM, values of parameters yet unconstrained are shown.Finally, we will see that this scalar can also influence the joint production of two weak gauge bosons. We will show that the analysis of this process can be used in a coherent manner with on-shell Higgs measurements to constrain its couplings through our parametrisation. We will then end with a brief look at some limitation of this approach, before suggesting ways to overcome them