Ce travail de thèse concerne le développement d'une méthode de pronostic de défaillance des systèmes de production en série. Une méthode de génération d'un indice de santé brut à partir d'un tenseur de données, appelée Méthode des Points Significatifs a été développée puis validée sur un exemple d'illustration. L'indice généré est ensuite traité par une nouvelle méthode appelée méthode des percentiles, qui permet de générer des profils monotones à partir d'un indice de santé brut. Les profils générés sont ensuite modélisés par un processus Gamma, et la fonction de densité de probabilité agrégée introduite dans ce travail a permis d'estimer le temps de vie résiduel (Remaining Useful Life (RUL)) dans un intervalle de confiance qui assure une marge de sécurité à l'utilisateur industriel. La méthode proposée est appliquée avec succès sur des données expérimentales issues des équipements de production industrielle. / This thesis develops a fault prognosis approach for Discrete Manufacturing Processes. A method of raw health index extraction from a data tensor, called Significant Points was developped and validated on an illustrative example. The generated index is later processed by a new method, called Percentile Method, which allows to generate the monotonic profiles from the raw health index. These profiles are then modelled by a Gamma process, and the aggregate probability density function introduced in this work allowed to estimate the Remaining Useful Life (RUL) in a confidence interval that ensures a safety margin for industrial users. The proposed method is applied successfully on the experimental data of industrial production machines.

This thesis is mainly focused on pricing securities of selected capital protected funds. In its theoretical part, there are summarized approaches and principals that are generally used for derivatives pricing because capital protected funds' securities contain embedded options. Emphasis is put on risk-neutral pricing using Monte Carlo simulation at that point because complicated pay-off functions of these funds are hard to be evaluated analytically. There are also presented main approaches to constructions and portfolio management of these funds from their portfolio manager's viewpoint. Finally, there is made an overview of basic types of capital protected funds issued both in The Czech republic and Europe. Analytical part is focused on evaluation of selected capital protected funds. There is applied a standard approach that is based on a simulation of Geometric Brownian Motion with constant conditional variance and correlation in contrast with an advanced approach where the conditional variance and conditional correlation matrix are simulated as well. That is accomplished with GARCH-in-mean and DCC-GARCH models. Estimated prices are compared with real market prices and there is also performance of the standard models compared with performance of advanced ones.

[pt] No Brasil, o comportamento dos preços da energia elétrica no mercado de curto prazo é especialmente incerto, pois não segue um padrão definido e é obtido a partir de um modelo computacional e não pelo equilíbrio de mercado entre oferta e demanda. Diante disto o mercado de opções e derivativos ao mesmo tempo em que promissor, tendo em vista as experiências de outros países, é insipiente, pois os agentes não conseguem utilizar metodologias tradicionais para a precificação destes produtos e acabam formatando os valores por experiências empíricas e segundo aceitação do mercado. Muitos trabalhos já foram desenvolvidos propondo novas soluções para a previsão de preços modificando profundamente a estrutura atual, por outro lado o objetivo deste trabalho em sua primeira parte não busca modificar o modelo atual de previsão de preços que serve de alicerce para os contratos atuais, e por isso não pode ser desprezada. Este trabalho em sua primeira parte visa desenvolver um modelo para representar o comportamento dos preços no mercado de energia brasileiro e melhorar a previsão de preços que atualmente é fornecido pelo Newave, mas sem deslocar-se dos resultados gerados por ele. Em um segundo momento busca uma metodologia computacionalmente viável para determinar o valor de opções que podem ser oferecidas em contratos de opção de longo prazo. Para desenvolver a solução, foi proposto um processo estocástico que pudesse modelar a previsão dos preços no mercado de curto prazo reduzindo a volatilidade, mas sem se distanciar do atual modelo de previsão. Num segundo momento para permitir a precificação destes contratos este estudo aprofundou-se na teoria das opções que permite considerar as flexibilidades gerenciais, tendo por objetivo maximizar o retorno de uma determinada opção contratual. Assim, com o emprego de ferramentas como o Algoritmo Genético e Simulação Monte Carlo para aproximar a curva de exercício ótimo e o novo processo estocástico de formação de preço, foi possível determinar o valor das opções estudadas. A principal contribuição deste trabalho é criar uma metodologia coerente de precificação de opções contratuais, atualmente inexistente no mercado e que possa ser testada e avaliada pelos operadores, contribuindo para o aumento e desenvolvimento do mercado de derivativos no setor elétrico brasileiro. / [en] In Brazil, the behavior of electricity prices in the short term market is especially uncertain, because it follows a pattern set and is obtained from a computer model rather than the market equilibrium between supply and demand. In view of this the market for options and derivatives at the same time as promising, given the experiences of other countries, know not, because the agents can not use traditional methods for the pricing of these products end up formatting the values and experiences and the second empirical market acceptance. Many works have been developed proposing new solutions for forecasting prices profoundly modifying the current structure, otherwise the objective of this work in the first part does not seek to modify the current model of forecasting prices that serves as the foundation for current contracts, and so it can not be neglected. This work in its first part aims to develop a model to represent the behavior of prices in the Brazilian energy market and improve the forecasting of prices that is currently provided by Newave, but without moving the results generated by it. In a second step a search computationally feasible method to determine the value of options that can be offered on contracts for the long term. To develop the solution, we proposed a stochastic model that could forecast the market price of reducing short-term volatility, but not away from the current forecasting model. In a second time to allow the pricing of these contracts this study deepened the theory of options that allows to consider the managerial flexibility, aiming to maximize the return on a particular option contract. Thus, with the use of tools such as Genetic Algorithms and Monte Carlo simulation to approximate the optimal exercise curve and the new stochastic process of price formation, it was possible to determine the value of the options studied. The main contribution of this work is to create a consistent methodology for pricing options contract, currently non-existent in the market and that can be tested and evaluated by the operators, contributing to the growth and development of the derivatives market in the Brazilian electric sector.

[pt] As decisões econômicas de investimento, assim como as avaliações econômicas de projetos, são afetadas por incertezas econômicas, incertezas técnicas e por flexibilidades gerenciais embutidas em projetos. Flexibilidades gerenciais dão liberdade ao gerente para tomar decisões, tais como investir, expandir, parar temporariamente ou abandonar um determinado projeto. Tais flexibilidades possuem valor e só a teoria de opções reais consegue avaliá-las. As opções reais permitem considerar, além das incertezas, a flexibilidade gerencial, tendo por objetivo maximizar o valor da oportunidade de investimento. Para se determinar o valor de uma opção real, normalmente são utilizados modelos de árvores binomiais, diferenças finitas ou técnicas de simulação Monte Carlo. Entretanto, os métodos tradicionais de árvores binomiais e diferenças finitas são impraticáveis na avaliação de opções com mais de três fatores de incerteza, enquanto que a simulação Monte Carlo tem um custo computacional muito elevado devido ao processo iterativo da simulação estocástica na amostragem de cada variável. O objetivo deste trabalho é pesquisar uma metodologia computacionalmente viável para determinar o valor de opções reais sob diversas incertezas técnicas e de mercado. Neste contexto, é feita uma investigação multidisciplinar (lógica fuzzy, computação evolucionária, processos estocásticos e opções reais) em busca de métodos alternativos que possam reduzir o tempo computacional e assim facilitar as tomadas de decisão conseqüentes da simulação. Para isto, é proposta a união de várias técnicas: Números Fuzzy para representar determinados tipos de incertezas das quais se desconhece o processo estocástico que as modela, processos estocásticos para representar as demais incertezas e a simulação Monte Carlo para obter uma boa aproximação do valor da opção real. Além disso, aplicase um algoritmo genético em conjunto com a simulação Monte Carlo para aproximar uma regra de decisão ótima e determinar o valor da opção real no caso de se ter várias opções de investimento em um projeto. A regra ajuda na decisão entre o investimento imediato em uma das opções ou a espera por melhores condições, as quais dependem do estado das incertezas consideradas. O modelo proposto foi avaliado em problemas de opção de expansão e de opção de investimento em informação, aplicados na área de exploração e produção de petróleo, obtendo os mesmos resultados que as técnicas convencionais com uma redução expressiva do custo computacional. A principal contribuição deste trabalho é a concepção de uma nova metodologia para a determinação do valor de opções reais na presença de incertezas técnicas e de mercado, que oferece vantagens em relação aos métodos convencionais. Os resultados obtidos comprovam que o uso de números fuzzy para representar incertezas das quais se desconhece o processo estocástico que as modela, reduz significativamente o tempo computacional. Além disso, a metodologia demonstra que a técnica de algoritmos genéticos é adequada para obter uma regra de decisão ótima, com uma boa aproximação do valor da opção real, quando são consideradas várias opções de investimento. / [en] The economic decision on investment and evaluation of projects are affected by economic and technical uncertainties and by management flexibilities inserted on projects. These management flexibilities give the manager freedom to take decisions, such as to invest, to expand, to temporarily stop or to abandon a Project. These flexibilities have value and only can be evaluated thhrogh real option theory. The use of real options considers uncertainties and management flexibilities with the objective of maximizing the value of the investment opportunity. To determine the value of the real option, models of binomials tree, finite differences or Monte Carlo simulation techniques are normally used. However, the traditional methods of binomials tree and finite differences are impracticable in the evaluation of options with more than three uncertainties, while the Monte Carlo simulation presents a high computational cost due to the iterative process of the stochastic simulation in sampling each variable. The objective of this work is to investigate a computational methodology that can be used to determine the value of real option under diverse uncertainties, both of technical and market types. Therefore, this work investigates methods that can reduce computational time and thus create means for taking decisions. For this purpose, the union of several techniques is proposed: fuzzy numbers to represent some types of uncertainties of which an adequate stochastic process is unknown, stochastic process to represent other uncertainties and the Monte Carlo simulation to obtain a good approximation of the value of real options. Moreover, a genetic algorithm, together with Monte Carlo simulation, is used to approximate an optimum decision rule and to determine the value the real option when several investment options are available in a project. The rule helps decide whether to make an immediate investment in an option or to wait for better conditions; this is dependent on the state of the uncertainties considerated. The proposed model was evaluated in problems of options of expansion and of investment in information, applied in the area of oil exploration and production. Results obtained were similar to those achieved by conventional techniques, with a substantial reduction in computational time. The main contribution of this work is the conception of a new methodology for the determination of the value of real options with technical and market uncertainties. This methodology has shown to be advantages in relation to conventional methods. Results show that the use of fuzzy numbers to represent uncertainties of which the stochastic process that shapes them is unknown reduces the computational time significantly. Moreover, the methodology demonstrates that the genetic algorithm is an adequate technique for approximating a decision rule when many investment options are considered.

V předložené práci je definována stochastická diferenciální rovnice a jsou uvedeny její základní vlastnosti. Stochastické diferenciální rovnice se používají k popisu fyzikálních jevů, které jsou ovlivněny i náhodnými vlivy. Řešením stochastického modelu je náhodný proces. Cílem analýzy náhodných procesů je konstrukce vhodného modelu, který umožní porozumět mechanismům, na jejichž základech jsou generována sledovaná data. Znalost modelu také umožňuje předvídání budoucnosti a je tak možné kontrolovat a optimalizovat činnost daného systému. V práci je nejdříve definován pravděpodobnostní prostor a Wienerův proces. Na tomto základě je definována stochastická diferenciální rovnice a jsou uvedeny její základní vlastnosti. Závěrečná část práce obsahuje příklad ilustrující použití stochastických diferenciálních rovnic v praxi.

Ce travail de thèse est une contribution à l’analyse de santé structurale de la caisse de véhicules militaires terrestres à roues. Appartenant à la gamme 20 - 30 tonnes, de tels véhicules sont déployés dans des contextes opérationnels variés où les conditions de roulage sont sévères et difficilement caractérisables. De plus, faisant face à la concurrence, la fonction mobilité des véhicules est acquise auprès de fournisseurs et n’est plus développée par Nexter Systems. De ce fait, la définition complète de cette fonction n’est plus connue. S’appuyant sur ce contexte, l’objectif principal de la thèse est d’aborder l’état de santé de la structure porteuse par approche probabiliste, afin de maitriser les techniques de calcul permettant la prise en compte de l’aléa intrinsèque des chargements liés à la diversité d’emploi des véhicules militaires terrestres. En particulier, les stratégies les plus pertinentes pour propager les incertitudes de roulage au sein d’un modèle mécanique d’un véhicule terrestre sont définies. Ces travaux décrivent comment il est possible d’exploiter une grandeur d’intérêt au sein du véhicule dans un objectif d’évaluation de la fiabilité par rapport à un critère de dommage donné. Une application sur un démonstrateur entièrement conçu par Nexter Systems illustre l’approche proposée. / This thesis is a contribution to the structural health analysis of the body of ground military vehicles. Belonging to the 20 - 30 tons range, such vehicles are deployed in a variety of operational contexts where driving conditions are severe and difficult to characterize. In addition, due to a growing industrial competition, the mobility function of vehicles is acquired from suppliers and is no longer developed by Nexter Systems. As a result, the complete definition of this function is unknown. Based on this context, the main objective of this thesis is to analyze the health of the vehicle body using a probabilistic approach in order to control the calculation techniques allowing to take into account the random nature of loads related to the use of ground military vehicles. In particular, the most relevant strategies for propagating uncertainties due to the terrain within a vehicle dynamics model are defined. This work describes how it is possible to manage an observation data measured in the vehicle for the purpose of assessing the reliability with respect to a given damage criterion. An application on a demonstrator entirely designed by Nexter Systems illustrates the proposed approach.

Im Rahmen der Arbeit wurden die Daten für Minutenreserveabrufe in den Jahren 2006 und 2007 nach Regelzonen analysiert und ein stochastisches Modell erstellt. Die detaillierte Analyse der Minutenreserveabrufe ergab eine Tageszeitabhängigkeit des Auftretens von Abrufen. In den Nachtstunden erfolgten sehr wenige bis keine Abrufe. Die jeweils abgerufenen Mengen lassen ebenfalls eine Tageszeitabhängigkeit erkennen. Auffällig war, dass die Minutenreserveabrufe in der RWE-Regelzone signifikant anders als in den übrigen Regelzonen erfolgten. Für die Modellbildung wurde ein zusammengesetzter Poisson-Prozess gewählt. Die Intensität λ blieb dabei konstant. Um die Tageszeitabhängigkeit einfließen zu lassen, wurde angenommen, dass die Mengen pro Abruf einer Normalverteilung mit tageszeitabhängigen Parametern μ und σ gehorchen. Mit Hilfe des Modells erfolgten Simulationen von Minutenreser-veabrufen für jede Regelzone. Zur Verifikation des Modells wurden die simulierten Abrufe mit den real eingetretenen Abrufen im Jahr 2008 verglichen. In Intensität der Abrufhäufigkeit und im Erwartungswert der Abrufmengen decken sich die Simulationen sehr gut mit der Realität (siehe Abbildung). Unter Anwendung des Modells lassen sich vielfältige Berechnungen beispielsweise zum Einsatz dezentraler KWK-Anlagen durchführen. In naher Zukunft ist die Er-weiterung des Modells um das in der Realität häufig eintretende Ereignis mehrerer direkt aufeinander folgender Abrufe in etwa derselben Höhe oder auch die Betrachtung negativer Minutenreserve wünschenswert.:1 Einleitung 2 Ausgangssituation 3 Analyse der Minutenreserveabrufe nach Regelzonen 4 Modellierung der abgerufenen Minutenreserve 5 Qualitätsbewertung des Modells 6 Zusammenfassung und Ausblick

Im Rahmen der Arbeit wurden die minutengenauen Daten des Regelleistungsbedarfs (Summe aus Sekundärregelleistung und Minutenreserve) der Monate April bis Dezember des Jahres 2009 einer Regelzone einer Zeitreihenanalyse unterzogen und in Komponenten gemäß dem klassischen Komponentenmodell zerlegt. Diese sind die Trendkomponente, ermittelt durch einen gleitenden Durchschnitt mit der Länge einer Stunde, weiterhin zwei periodische Komponenten mit der Periodenlänge einer Stunde sowie der Periodenlänge eines Tages und die Restkomponente, welche mit einem ARIMA(2,1,5)-Prozess modelliert wurde. In der Zukunft sollte das erstellte Modell des Regelleistungsbedarfs durch Hinzunahme einer jahreszeitlichen Komponente noch verbessert werden. Dies war im Rahmen der Arbeit nicht möglich, da keine Daten über einen Zeitraum von mehreren Jahren vorhanden waren. Zusätzlich kann geprüft werden, inwiefern mit dem Komponentenmodell Prognosen durchführbar sind. Dafür sollte die Trendkomponente anders gewählt werden, da sich der hier gewählte Weg zu sehr an den Daten orientiert. Der zweite Teil der Aufgabenstellung dieser Arbeit bestand im Identifizieren inhaltlicher Komponenten, also möglicher Zusammenhänge zwischen dem Regelleistungsbedarf und verschiedenen denkbaren Ursachen. Als potentielle Ursachen wurden der Lastverlauf sowie die Windenergieeinspeisung untersucht. Zwischen der Zeitreihe des Lastverlaufs und der des Regelleistungsbedarfs bestand eine leichte positive Korrelation, zwischen der Zeitreihe der Windenergieeinspeisung und der des Regelleistungsbedarfs eine geringe negative Korrelation.:Einleitung 1 Ausgangssituation und technische Gegebenheiten 2 Mathematische Grundlagen 3 Analyse der Regelleistungsdaten 4 Zusammenfassung und Ausblick

The presented work wants to contribute a new solution based on the analysis of stochastic signals. On the basis of the Dresden Live-Camera-System which is providing real-time information about the traffic state on 31 focal points (March 2005) one is able to use a wide range of image types under different and severe conditions. The method is based on the analysis of stochastic signals derived from the live-camra images. These signals are analyzed with cross-correlation, amplitude- and frequency filters. The resulting data enable the distinction of stable and non-stable traffic flow and the automated identification of traffic congestion. Moreover fundamental diagrams are calculated. / Die vorgelegte Arbeit beinhaltet ein neuartiges Verfahren zur automatischen Ermittlung des Verkehrszustandes aus Live-Kamera-Bildern. Die Datengrundlage dafür liefert das im Rahmen des BMBF-Leitprojektes intermobil Region Dresden geschaffenen Live-Kamerasystem mit 31 Standorten (Stand März 2005). Das entwickelte Verfahren basiert auf der Analyse stochastischer Signale, die aus den Kamerabildern ermittelt werden. Die methodischen Grundlagen des Verfahrens sind Korrelationsanalyse sowie Amplituden- und Frequenzfilterung. Die Rahmenbedingungen für den praktischen Einsatz sind durch die Variabilität von Auflösung und Blickwinkel an den unterschiedlichen Kamerastandorten geprägt. Die ermittelten Messwerte ermöglichen eine Unterscheidung der Verkehrszustände "flüssiger Verkehr", "zähflüssiger Verkehr" und "Stop&Go" und werden am Fundamentaldiagramm interpretiert.

<p>This dissertation establishes limit theory for topological functionals of geometric complexes from a stochastic process viewpoint. Standard filtrations of geometric complexes, such as the Čech and Vietoris-Rips complexes, have a natural parameter <i>r </i>which governs the formation of simplices: this is the basis for persistent homology. However, the parameter <i>r</i> may also be considered the time parameter of an appropriate stochastic process which summarizes the evolution of the filtration.</p><p>Here we examine the stochastic behavior of two of the foremost classes of topological functionals of such filtrations: the Betti numbers and the Euler characteristic. There are also two distinct setups in which the points underlying the complexes are generated, where the points are distributed randomly in <i>R^d</i> according to a general density (the traditional setup) and where the points lie in the tail of a heavy-tailed or exponentially-decaying “noise” distribution (the extreme-value theory (EVT) setup).<br></p><p>These results constitute some of the first results combining topological data analysis (TDA) and stochastic process theory. The first collection of results establishes stochastic process limits for Betti numbers of Čech complexes of Poisson and binomial point processes for two specific regimes in the traditional setup: the sparse regime—when the parameter <i>r </i>governing the formation of simplices causes the Betti numbers to concentrate on components of the lowest order; and the critical regime—when the parameter <i>r</i> is of the order <i>n^-1/d</i> and the geometric complex becomes highly connected with topological holes of every dimension. The second collection of results establishes a functional strong law of large numbers and a functional central limit theorem for the Euler characteristic of a random geometric complex for the critical regime in the traditional setup. The final collection of results establishes functional strong laws of large numbers for geometric complexes in the EVT setup for the two classes of “noise” densities mentioned above.<br></p>