Baarda’s outlier test is one of the best established theories in geodetic practice. The optimal test statistic of the local model test for a single outlier is known as the normalized residual. Also other model disturbances can be detected and identified with this test. It enjoys the property of being a uniformly most powerful invariant (UMPI) test, but is not a uniformly most powerful (UMP) test. In this contribution we will prove that in the class of test statistics following a common central or non-central chi2 distribution, Baarda’s solution is also uniformly most powerful, i.e. UMPchi2 for short. It turns out that UMPchi2 is identical to UMPI, such that this proof can be seen as another proof of the UMPI property of the test. We demonstrate by an example that by means of the Monte Carlo method it is even possible to construct test statistics, which are regionally more powerful than Baarda’s solution. They follow a socalled generalized chi2 distribution. Due to high computational costs we do not yet propose this as a ”new outlier detection method”, but only as a proof that it is in principle possible to outperform the statistical power of Baarda’s test. / Der Ausreißertest nach Baarda ist eine der am besten etablierten Theorien in der geodätischen Praxis. Die optimale Teststatistik des lokalen Modelltests für einen einzelnen Ausreißer wird als normierte Verbesserung bezeichnet. Auch andere Modellabweichungen können mit diesem Test aufgedeckt und identifiziert werden. Er hat die Eigenschaft, der gleichmäßig stärkste invariante (uniformly most powerful invariant, UMPI) Test zu sein, aber er ist kein gleichmäßig stärkster (uniformly most powerful, UMP) Test. In diesem Beitrag werden wir beweisen, dass in der Klasse der Teststatistiken mit einer gewöhnlichen zentralen oder nichtzentralen chi2 Verteilung die Baardaschen Lösung auch gleichmäßig stärkster Test ist, abgekürzt UMPchi2. Es stellt sich heraus, dass UMPchi2 gleichwertig mit UMPI ist, so dass dieser Beweis als ein weiterer Beweis der UMPI-Eigenschaft des Testes angesehen werden kann. Wir zeigen an einem Beispiel, dass es mittels der Monte Carlo Methode sogar möglich ist, Teststatistiken zu konstruieren, die regional stärker ist, als die Baardasche Lösung. Diese weisen eine sogenannte verallgemeinerte chi2 Verteilung auf. Wegen der hohen Rechenkosten schlagen wir das noch nicht als neue Ausreißererkennungsmethode vor, sondern nur als Beweis, dass es im Prinzip möglich ist, die Teststärke des Ausreißertests nach Baarda zu übertreffen.

The aim of this thesis, which deals with the modernization of the Zeiss/Tesa device, which is designed to calibrate the gauge blocks, is to provide a detailed analysis of the current state of the art of this instrument and to search for gauge blocks calibration requirements. The introductory part of the thesis is devoted to the definition of basic metrological concepts and terms. One of the separate chapters contains a elaborate description of the Zeiss/Tesa device and the possibilities of its modernization. A qualified estimation of the measurement uncertainty is determined in the practical part of the thesis and a simulation of the measurement uncertainty is performed using the Monte Carlo method. The final chapter contains the technical documentation of the proposed modernization.

Actualmente, los riesgos de diferente comportamiento (variabilidad y vinculados a eventos) pueden afectar a las edificaciones multifamiliares, generando importantes sobrecostos y desviaciones presupuestales. Esta tesis se enfoca en la elaboración de una metodología pauteada que sirva como herramienta aplicativa para cualquier proyecto de edificio multifamiliar, independientemente de su ubicación. Se ha diferenciado el análisis de los riesgos bajo las dos tipologías mencionadas por el PMBOK en su sexta edición (variabilidad y vinculados a eventos), como una tendencia novedosa. En la investigación primeramente se desarrolla una encuesta de juicio experto para identificar los riesgos más frecuentes en la muestra de estudio (distrito de Miraflores, ciudad de Lima). Seguidamente, se realiza una entrevista a los profesionales responsables de los tres proyectos que se toman como caso de estudio. En las mismas se recaban todos los datos necesarios para realizar a continuación el análisis cualitativo y el análisis cuantitativo de los diferentes riesgos investigados. Para el análisis cuantitativo se utiliza el método de Monte Carlo, a través del software @RISK. En cada proyecto se obtienen los valores de los riesgos en forma de contingencia, relacionados con el Costo Directo del presupuesto. Finalmente, a través de las convoluciones, se determinan los valores de la contingencia de los riesgos generales, o combinación simultánea de los riesgos de variabilidad y vinculados a eventos. Se puede concluir que esta metodología es muy beneficiosa al implementarse en etapas tempranas o de planificación, pues permite cuantificar los riesgos, en aras de mitigarlos y controlarlos durante la ejecución del proyecto. / Currently, the risks of different behavior (variability and linked to events) can affect multifamily buildings, generating significant cost overruns and budget deviations. This thesis focuses on the elaboration of a methodology that serves as an application tool for any multi-family building project, regardless of its location. The risk analysis has been differentiated under the two typologies mentioned by the PMBOK in its sixth edition (variability and linked to events), as a novel trend. The investigation first develops an expert judgment survey to identify the most frequent risks in the study sample (Miraflores district, Lima city). Next, an interview is conducted with the professionals responsible for the three projects that are taken as a case study. They collect all the necessary data to carry out the qualitative analysis and the quantitative analysis of the different risks investigated. The Monte Carlo method is used for quantitative analysis, through the @RISK software. In each project the values of the risks are obtained in the form of contingency, related to the Direct Cost of the budget. Finally, through the convolutions, the values of the contingency of the general risks, or simultaneous combination of the risks of variability and linked to events are determined. It can be concluded that this methodology is very beneficial when implemented in early stages or planning, since it allows quantifying the risks, in order to mitigate and control them during the execution of the project. / Tesis

The aim of the thesis is to introduce the concept of Monte Carlo method for incorporating the uncertainties into the all hydrological and operational data inputs, which are needed to design and operation of large open water reservoir. Incorporating uncertainties into data inputs during calculation of reservoir storage capacity, then the consequent active conservation storage capacity is loaded by uncertainties. In the same way the values of outflow water from reservoir and hydrological reliability are affected by these uncertainties as well. For these kind of calculations the reservoir simulation model has been used, which simulate behavior operation of reservoir and is able to evaluate the results of simulations and help to reduction risk of storage capacity failure, respectively reduction of water shortages during reservoirs operation during low water and dry periods.

Main goals of this master thesis are following: to perform the state of the art research of overpressure constructions (especially space habitats, plane fuselages); to create an own concept of the functional inside ending (hole) in the sandwich panel for a door; to perform stress-strain analysis of this concept; to perform the design optimalization of this concept in order to minimise the weight. To solve the problems above software Ansys 17.2 is chosen, because it allows to: model the material of the honeycomb core of sandwich panel as homogenous linear orthotropic material; evaluate reserve factors of all critical limit states; perform the design optimalization; perform Monte Carlo simulation. First and second design optimalizations discover, that with defined parameters: 0,635 mm width of aluminium sandwich face sheets and inner overpressure 0,1 MPa, a creation of the model, that would be safe by changing the values of design variables is not possible. Specifically, the maximum value of shear stress on the glued areas between aluminium face sheets and honeycomb core is higher than the shear strength of the glue. Therefore, two new concepts are created. First for inner pressure 0,03 MPa and bigger width of aluminium face sheets 3,175 mm, second for inner pressure 0,02 MPa and same width of aluminium face sheets 0,635 mm. For both these concepts, an overall reserve factor is calculated. First, the value of an overall reserve factor is calculated deterministically. Secondly, the value of an overall reserve factor is calculated stochastically considering the variance of material properties of the honeycomb core ± 10 % by Monte Carlo simulation. An overall reserve factor of the concept with inner pressure 0,02 MPa is determined as 1,21. An overall reserve factor of the concept with inner pressure 0,03 MPa is determined as 1,20. The weight of the concept for inner pressure 0,03 MPa is though 4 times bigger than the weight of the concept for inner pressure 0,02 MPa. In the concept for inner pressure 0,02 MPa the maximum value of HMH stress in aluminium components is critical, stochastically considered material properties of the honeycomb core don’t have a significant influence on this value. In the concept for inner pressure 0,03 MPa the value of maximum shear stress on the glued areas between aluminium face sheets and the honeycomb core is critical, stochastically considered material properties of the honeycomb core have a significant influence on this value. In the concept for inner pressure 0,03 MPa an absolute error of overall reserve factor is 8 % (overall reserve factor calculated deterministically was 1,28) which is significant. Monte Carlo simulation is also used to find that the value of Poisson ratio XY of the honeycomb core doesn’t have statistically significant influence on all limit states. Value of the reserve factor of the honeycomb core is higher than 2 in both concepts. Monte Carlo simulation discovers that this value can be significantly lower. Using Tsai-Wu failure criteria the reserve factor in the concept for inner pressure 0,02 MPa is determined as 2,72 deterministically x 2,41 stochastically (absolute error 31 %), in the concept for inner pressure 0,03 MPa the reserve factor is determined as 6,85 deterministically x 6,17 stochastically (absolute error 68 %).

L’étude du transfert radiatif dans les gaz (atmosphères planétaires, chambres de combustion, etc.) se heurte à deux principales difficultés : les hétérogénéités et la dépendance spectrale des propriétés radiatives du milieu d’intérêt. Les travaux présentés dans ce manuscrit proposent, au travers d’une approche statistique du rayonnement, une solution à ces deux limites qui ne nécessite aucune approximation de modèle physique ou numérique. Cette approche conduira au développement d’algorithmes de Monte-Carlo considérés à l’heure actuelle comme méthodes de référence dans la communauté du transfert radiatif. La difficulté liée aux hétérogénéités du milieu participant sera traitée par une technique empruntée à d’autres disciplines de la physique du transport : les algorithmes à collisions nulles. Leur application au rayonnement consiste à ajouter arbitrairement aux évènements d’absorption et de diffusion, un troisième type de collision n’ayant aucun effet sur le transport de photons : les collisions nulles. Ainsi, le coefficient d’extinction résultant de ces trois types de collision pourra être assumé comme homogène. Ensuite, il sera montré comment cette même technique lève un second verrou permettant de repenser de façon statistique l’idée de coefficient d’absorption. Cela ouvrira la voie à des algorithmes de Monte-Carlo qui estiment directement une observable radiative à partir de paramètres de transitions répertoriés dans des bases de données spectroscopiques, sans avoir à précalculer rigoureusement le coefficient d’absorption. / Two major challenges are encountered when studying radiative transfer in gases (e.g. combustion chambers or planetary atmospheres): heterogeneity and spectral dependence of radiative properties. The work introduced in this manuscript, addresses this problem through a statistical approach of radiation that requires no model or numerical approximation. This approach leads to the development of Monte-Carlo methods, currently considered as reference solutions in the community of radiative transfer. The difficulty related to heterogeneity is handled by a technique borrowed from other fields of transport physics: null-collision algorithms. Their application to radiation consists in adding to the events of absorption and scattering a third arbitrary type of collision that has no effect on the photon transport. Thus, the extinction coefficient resulting from these three types of collisions can be assumed to be homogeneous. Then, it is shown how this very same technique opens the door to rethinking statistically the concept of absorption coefficient. This leads to Monte-Carlo algorithms that directly estimate radiative observables from transition parameters indexed in molecular spectroscopic databases, without the need of rigorously precomputing absorption coefficients.

An in-depth knowledge of the structure formation process and the resulting dependency of the morphology on the reaction mechanism is a key requirement in order to design application-oriented materials. For twin polymerization, the basic idea of the reaction process is established, and important structural properties of the final nanoporous hybrid materials are known. However, the effects of changing the reaction mechanism parameters on the final morphology is still an open issue. In this work, the dependence of the morphology on the reaction mechanism is investigated based on a previously introduced lattice-based Monte Carlo method, the reactive bond fluctuation model. We analyze the effects of the model parameters, such as movability, attraction, or reaction probabilities on structural properties, like the specific surface area, the radial distribution function, the local porosity distribution, or the total fraction of percolating elements. From these examinations, we can identify key factors to adapt structural properties to fulfill desired requirements for possible applications. Hereby, we point out which implications theses parameter changes have on the underlying chemical structure.

Mnoho inženýrských úloh vede na optimalizační modely s~omezeními ve tvaru obyčejných (ODR) nebo parciálních (PDR) diferenciálních rovnic, přičemž jsou v praxi často některé parametry neurčité. V práci jsou uvažovány tři inženýrské problémy týkající se optimalizace vibrací a optimálního návrhu rozměrů nosníku. Neurčitost je v nich zahrnuta ve formě náhodného zatížení nebo náhodného Youngova modulu. Je zde ukázáno, že dvoustupňové stochastické programování nabízí slibný přístup k řešení úloh daného typu. Odpovídající matematické modely, zahrnující ODR nebo PDR omezení, neurčité parametry a více kritérií, vedou na (vícekriteriální) stochastické nelineární optimalizační modely. Dále je dokázáno, pro jaký typ úloh je nutné použít stochastické programování (EO reformulace), a kdy naopak stačí řešit jednodušší deterministickou úlohu (EV reformulace), což má v praxi význam z hlediska výpočetní náročnosti. Jsou navržena výpočetní schémata zahrnující diskretizační metody pro náhodné proměnné a ODR nebo PDR omezení. Matematické modely odvozené pomocí těchto aproximací jsou implementovány a řešeny v softwaru GAMS. Kvalita řešení je určena na základě intervalových odhadů "optimality gapu" spočtených pomocí metody Monte Carlo. Parametrická analýza vícekriteriálního modelu vede na výpočet "efficient frontier". Jsou studovány možnosti aproximace modelu zahrnujícího pravděpodobnostní členy související se spolehlivostí pomocí smíšeného celočíselného nelineárního programování a reformulace pomocí penalizační funkce. Dále je vzhledem k budoucím možnostem paralelních výpočtů rozsáhlých inženýrských úloh implementován a testován PHA algoritmus. Výsledky ukazují, že lze tento algoritmus použít, i když nejsou splněny matematické podmínky zaručující konvergenci. Na závěr je pro deterministickou verzi jedné z úloh porovnána metoda konečných diferencí s metodou konečných prvků za použití softwarů GAMS a ANSYS se zcela srovnatelnými výsledky.

Experiments for the development of fusion power that are based on magnetic confinement deal with plasmas that inevitably contain energetic (non-thermal) particles. These particles come e.g. from fusion reactions or from external heating of the plasma. Ensembles of energetic ions can excite plasma waves in the Alfvén frequency range to such an extent that the resulting wave fields redistribute the energetic ions, and potentially eject them from the plasma. The redistribution of ions may cause a substantial reduction heating efficiency, and it may damage the inner walls and other components of the vessel. Understanding the dynamics of such instabilities is necessary to optimise the operation of fusion experiments and of future fusion power plants. A Monte Carlo model that describes the nonlinear wave-particle dynamics in a toroidal plasma has been developed to study the excitation of the abovementioned instabilities. A decorrelation of the wave-particle phase is added in order to model stochasticity of the system (e.g. due to collisions between particles). Based on the nonlinear description with added phase decorrelation, a quasilinear version of the model has been developed, where the phase decorrelation has been replaced by a quasilinear diffusion coefficient in particle energy. When the characteristic time scale for macroscopic phase decorrelation becomes similar to or shorter than the time scales of nonlinear wave-particle dynamics, the two descriptions quantitatively agree on a macroscopic level. The quasilinear model is typically less computationally demanding than the nonlinear model, since it has a lower dimensionality of phase space. In the presented studies, several effects on the macroscopic wave-particle dynamics by the presence of phase decorrelation have been theoretically and numerically analysed, e.g. effects on the growth and saturation of the wave amplitude, and on the so called frequency chirping events with associated hole-clump pair formation in particle phase space. Several effects coming from structures of the energy distribution of particles around the wave-particle resonance has also been studied. / <p>QC 20150330</p>

Объектом данного исследования является феррожидкость. В работе определено влияние полидисперсности на термодинамические и магнитные свойства феррожидкостей. В первой главе данной работы построена теория, описывающая термодинамические свойства бидисперсной системы дипольных твердых сфер. Разработан программный комплекс, позволяющий численно определить ряд термодинамических характеристик бидисперсной феррожидкости. Проведено сравнение теории и результатов компьютерного моделирования. Во второй главе рассмотрена полидисперсная модель дипольных твердых сфер. Вычислено дополнительное слагаемое в существующем приближении начальной магнитной восприимчивости полидисперсных феррожидкостей. Проведено сравнение теории и результатов компьютерного моделирования, известных в литературе. Определены условия работоспособности нового приближения начальной магнитной восприимчивости. / The object of this study is ferrofluid. In the study the effect of polydispersity on the thermodynamic and magnetic properties of ferrofluids was investigated. In the first chapter of this paper we construct theory describing the thermodynamic properties of the bidisperse system of dipolar hard spheres. Computer program was developed that allows numerically to identify the thermodynamic characteristics of bidisperse ferrofluid. A comparison between theory and computer simulation was performed. In the second chapter the polydisperse model of dipolar hard spheres was considered. Additional new term in the existing approximation of the initial magnetic susceptibility of polydisperse ferrofluid was calculated. A comparison between theory and computer simulations was performed. The conditions for the availability of the new approach were defined.