Made available in DSpace on 2014-06-12T17:35:03Z (GMT). No. of bitstreams: 2 arquivo3630_1.pdf: 2374215 bytes, checksum: 64f9cdc75ffa8167dff3140c0b1e48a2 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Petróleo Brasileiro S/A / Processos semi-Markovianos (SMP) contínuos no tempo são importantes ferramentas estocásticas para modelagem de métricas de confiabilidade ao longo do tempo para sistemas para os quais o comportamento futuro depende dos estados presente e seguinte assim como do tempo de residência. O método clássico para resolver as probabilidades intervalares de transição de SMP consiste em aplicar diretamente um método geral de quadratura às equações integrais. Entretanto, esta técnica possui um esforço computacional considerável, isto é, N2 equações integrais conjugadas devem ser resolvidas, onde N é o número de estados. Portanto, esta tese propõe tratamentos matemáticos e numéricos mais eficientes para SMP. O primeiro método, o qual é denominado 2N-, é baseado em densidades de frequência de transição e métodos gerais de quadratura. Basicamente, o método 2N consiste em resolver N equações integrais conjugadas e N integrais diretas. Outro método proposto, chamado Lap-, é baseado na aplicação de transformadas de Laplace as quais são invertidas por um método de quadratura Gaussiana, chamado Gauss Legendre, para obter as probabilidades de estado no domínio do tempo. Formulação matemática destes métodos assim como descrições de seus tratamentos numéricos, incluindo questões de exatidão e tempo para convergência, são desenvolvidas e fornecidas com detalhes. A efetividade dos novos desenvolvimentos 2N- e Lap- serão comparados contra os resultados fornecidos pelo método clássico por meio de exemplos no contexto de engenharia de confiabilidade. A partir destes exemplos, é mostrado que os métodos 2N- e Lap- são significantemente menos custosos e têm acurácia comparável ao método clássico

Mathematical and statistical modeling have been at the forefront of many significant advances in many disciplines in both the academic and industry sectors. From behavioral sciences to hard core quantum mechanics in physics, mathematical modeling has made a compelling argument for its usefulness and its necessity in advancing the current state of knowledge in the 21rst century. In Finance and Insurance in particular, stochastic modeling has proven to be an effective approach in accomplishing a vast array of tasks: risk management, leveraging of investments, prediction, hedging, pricing, insurance, and so on. However, the magnitude of the damage incurred in recent market crisis of 1929 (the great depression), 1937 (recession triggered by lingering fears emanating from the great depression), 1990 (one year recession following a decade of steady expansion) and 2007 (the great recession triggered by the sub-prime mortgage crisis) has suggested that there are certain aspects of financial markets not accounted for in existing modeling. Explanations have abounded as to why the market underwent such deep crisis and how to account for regime change risk. One such explanation brought forth was the existence of regimes in the financial markets. The basic idea of market regimes underscored the principle that the market was intrinsically subjected to many different states and can switch from one state to another under unknown and uncertain internal and external perturbations. Implementation of such a theory has been done in the simplifying case of Markov regimes. The mathematical simplicity of the Markovian regime model allows for semi-closed or closed form solutions in most financial applications while it also allows for economically interpretable parameters. However, there is a hefty price to be paid for such practical conveniences as many assumptions made on the market behavior are quite unreasonable and restrictive. One assumes for instance that each market regime has a constant propensity of switching to any other state irrespective of the age of the current state. One also assumes that there are no intermediate states as regime changes occur in a discrete manner from one of the finite states to another. There is therefore no telling how meaningful or reliable interpretation of parameters in Markov regime models are. In this thesis, we introduced a sound theoretical and analytic framework for Levy driven linear stochastic models under a semi Markov market regime switching process and derived It\'o formula for a general linear semi Markov switching model generated by a class of Levy It'o processes (1). It'o formula results in two important byproducts, namely semi closed form formulas for the characteristic function of log prices and a linear combination of duration times (2). Unlike Markov markets, the introduction of semi Markov markets allows a time varying propensity of regime change through the conditional intensity matrix. This is more in line with the notion that the market's chances of recovery (respectively, of crisis) are affected by the recession's age (respectively, recovery's age). Such a change is consistent with the notion that for instance, the longer the market is mired into a recession, the more improbable a fast recovery as the the market is more likely to either worsens or undergo a slow recovery. Another interesting consequence of the time dependence of the conditional intensity matrix is the interpretation of semi Markov regimes as a pseudo-infinite market regimes models. Although semi Markov regime assume a finite number of states, we note that while in any give regime, the market does not stay the same but goes through an infinite number of changes through its propensity of switching to other regimes. Each of those separate intermediate states endows the market with a structure of pseudo-infinite regimes which is an answer to the long standing problem of modeling market regime with infinitely many regimes. We developed a version of Girsanov theorem specific to semi Markov regime switching stochastic models, and this is a crucial contribution in relating the risk neutral parameters to the historical parameters (3). Given that Levy driven markets and regime switching markets are incomplete, there are more than one risk neutral measures that one can use for pricing derivative contracts. Although much work has been done about optimal choice of the pricing measure, two of them jump out of the current literature: the minimal martingale measure and the minimum entropy martingale measure. We first presented a general version of Girsanov theorem explicitly accounting for semi Markov regime. Then we presented Siu and Yang pricing kernel. In addition, we developed the conditional and unconditional minimum entropy martingale measure which minimized the dissimilarity between the historical and risk neutral probability measures through a version of Kulbach Leibler distance (4). Estimation of a European option price in a semi Markov market has been attempted before in the restricted case of the Black Scholes model. The problems encountered then were twofold: First, the author employed a Markov chain Monte Carlo methods which relied much on the tractability of the likelihood function of the normal random sequences. This tractability is unavailable for most Levy processes, hence the necessity of alternative pricing methods is essential. Second, the accuracy of the parameter estimates required tens of thousands of simulations as it is often the case with Metropolis Hasting algorithms with considerable CPU time demand. Both above outlined issues are resolved by the development of a semi-closed form expression of the characteristic function of log asset prices, and it opened the door to a Fourier transform method which is derived on the heels of Carr and Madan algorithm and the Fourier time stepping algorithm (5). A round of simulations and calibrations is performed to better capture the performance of the semi Markov model as opposed to Markov regime models. We establish through simulations that semi Markov parameters and the backward recurrence time have a substantial effect on option prices ( 6). Differences between Markov and Semi Markov market calibrations are quantified and the CPU times are reported. More importantly, interpretation of risk neutral semi Markov parameters offer more insight into the dynamic of market regimes than Markov market regime models ( 7). This has been systematically exhibited in this work as calibration results obtained from a set of European vanilla call options led to estimates of the shape and scale parameters of the Weibull distribution considered, offering a deeper view of the current market state as they determine the in-regime dynamic crucial to determining where the market is headed. After introducing semi Markov models through linear Levy driven models, we consider semi Markov markets with nonlinear multidimensional coupled asset price processes (8). We establish that the tractability of linear semi Markov market models carries over to multidimensional nonlinear asset price models. Estimating equations and pricing formula are derived for historical parameters and risk neutral parameters respectively (9). The particular case of basket of commodities is explored and we provide calibration formula of the model parameters to observed historical commodity prices through the LLGMM method. We also study the case of Heston model in a semi Markov switching market where only one parameter is subjected to semi Markov regime changes. Heston model is one the most popular model in option pricing as it reproduces many more stylized facts than Black Scholes model while retaining tractability. However, in addition to having a faster deceasing smiles than observed, one of the most damning shortcomings of most diffusion models such as Heston model, is their inability to accurately reproduce short term options prices. An avenue for solving these issues consists in generalizing Heston to account for semi Markov market regimes. Such a solution is implemented and a semi analytic formula for options is obtained.

With the advent of autonomous vehicles, the issue of safety-evaluationhas become key. ISO26262 recommends using Markov chains. However, in their most common form, Markov chains lack the flexibility required to model non- exponential probability distributions and systems displaying parallelism. In these cases, generalized semi-Markov processes arebetter suited. Though, these are significantly more taxing to analyze mathematically.  This thesis instead explores the option of simulating these systemsdirectly via MATLAB’s Simulink and Stateflow. An example system, here called CASE, currently under study by Scania was used as an example. The results showed that direct simulation is indeed possible, but the computational times are significantly greater than those from standard MATLAB-functions. The method should therefore be employed on parallel systems when results with a high level of fidelity are needed, and alternative methods are not available.

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Yes / In large industrial systems, alarm management is one of the most important issues to improve the safety and efficiency of systems in practice. Operators of such systems often have to deal with a numerous number of simultaneous alarms. Different kinds of thresholding or filtration are applied to decrease alarm nuisance and improve performance indices, such as Averaged Alarm Delay (ADD), Missed Alarm and False Alarm Rates (MAR and FAR). Among threshold-based approaches, variable thresholding methods are well-known for reducing the alarm nuisance and improving the performance of the alarm system. However, the literature suffers from the lack of an appropriate method to assess performance parameters of Variable Threshold Alarm Systems (VTASs). This study introduces two types of variable thresholding and proposes a novel approach for performance assessment of VTASs using Priority-AND gate and semi-Markov process. Application of semi-Markov process allows the proposed approach to consider industrial measurements with non-Gaussian distributions. In addition, the paper provides a genetic algorithm based optimized design process for optimal parameter setting to improve performance indices. The effectiveness of the proposed approach is illustrated via three numerical examples and through a comparison with previous studies. / Noavaran Electronic Adar Sameh company [Grant NO: IRAM17S1].

Le premier chapitre présente les axes principaux de recherche ainsi que les problèmes traités dans cette thèse. Plus précisément, il expose une synthèse sur le sujet, en y donnant les propriétés essentielles pour la bonne compréhension de cette étude, accompagnée des références bibliographiques les plus importantes. Il présente également les motivations de ce travail en précisant les contributions originales dans ce domaine. Le deuxième chapitre est composé d’une recherche originale sur l’estimation du risque sismique, dans la zone du nord de la mer Egée (Grèce), en faisant usage de la théorie des processus semi-markoviens à temps continue. Il propose des estimateurs des mesures importantes qui caractérisent les processus semi-markoviens, et fournit une modélisation dela prévision de l’instant de réalisation d’un séisme fort ainsi que la probabilité et la grandeur qui lui sont associées. Les chapitres 3 et 4 comprennent une première tentative de modélisation du processus de génération des séismes au moyen de l’application d’un temps discret des modèles cachés markoviens et semi-markoviens, respectivement. Une méthode d’estimation non paramétrique est appliquée, qui permet de révéler des caractéristiques fondamentales du processus de génération des séismes, difficiles à détecter autrement. Des quantités importantes concernant les niveaux des tensions sont estimées au moyen des modèles proposés. Le chapitre 5 décrit les résultats originaux du présent travail à la théorie des processus stochastiques, c’est- à-dire l’étude et l’estimation du « Intensité du temps d’entrée en temps discret (DTIHT) » pour la première fois dans des chaînes semi-markoviennes et des chaînes de renouvellement markoviennes cachées. Une relation est proposée pour le calcul du DTIHT et un nouvel estimateur est présenté dans chacun de ces cas. De plus, les propriétés asymptotiques des estimateurs proposés sont obtenues, à savoir, la convergence et la normalité asymptotique. Le chapitre 6 procède ensuite à une étude de comparaison entre le modèle markovien caché et le modèle semi-markovien caché dans un milieu markovien et semi-markovien en vue de rechercher d’éventuelles différences dans leur comportement stochastique, déterminé à partir de la matrice de transition de la chaîne de Markov (modèle markovien caché) et de la matrice de transition de la chaîne de Markov immergée (modèle semi-markovien caché). Les résultats originaux concernent le cas général où les distributions sont considérées comme distributions des temps de séjour ainsi que le cas particulier des modèles qui sont applique´s dans les chapitres précédents où les temps de séjour sont estimés de manière non-paramétrique. L’importance de ces différences est spécifiée à l’aide du calcul de la valeur moyenne et de la variance du nombre de sauts de la chaîne de Markov (modèle markovien caché) ou de la chaîne de Markov immergée (modèle semi-markovien caché) pour arriver dans un état donné, pour la première fois. Enfin, le chapitre 7 donne des conclusions générales en soulignant les points les plus marquants et des perspectives pour développements futurs. / The first chapter describes the definition of the subject under study, the current state of science in this area and the objectives. In the second chapter, continuous-time semi-Markov models are studied and applied in order to contribute to seismic hazard assessment in Northern Aegean Sea (Greece). Expressions for different important indicators of the semi- Markov process are obtained, providing forecasting results about the time, the space and the magnitude of the ensuing strong earthquake. Chapters 3 and 4 describe a first attempt to model earthquake occurrence by means of discrete-time hidden Markov models (HMMs) and hidden semi-Markov models (HSMMs), respectively. A nonparametric estimation method is followed by means of which, insights into features of the earthquake process are provided which are hard to detect otherwise. Important indicators concerning the levels of the stress field are estimated by means of the suggested HMM and HSMM. Chapter 5 includes our main contribution to the theory of stochastic processes, the investigation and the estimation of the discrete-time intensity of the hitting time (DTIHT) for the first time referring to semi-Markov chains (SMCs) and hidden Markov renewal chains (HMRCs). A simple formula is presented for the evaluation of the DTIHT along with its statistical estimator for both SMCs and HMRCs. In addition, the asymptotic properties of the estimators are proved, including strong consistency and asymptotic normality. In chapter 6, a comparison between HMMs and HSMMs in a Markov and a semi-Markov framework is given in order to highlight possible differences in their stochastic behavior partially governed by their transition probability matrices. Basic results are presented in the general case where specific distributions are assumed for sojourn times as well as in the special case concerning the models applied in the previous chapters, where the sojourn time distributions are estimated non-parametrically. The impact of the differences is observed through the calculation of the mean value and the variance of the number of steps that the Markov chain (HMM case) and the EMC (HSMM case) need to make for visiting for the first time a particular state. Finally, Chapter 7 presents concluding remarks, perspectives and future work.

Ce travail propose une contribution originale à la compréhension du comportement spatial des pêcheurs, basée sur les paradigmes de l'écologie comportementale et de l'écologie du mouvement. En s'appuyant sur des données du 'Vessel Monitoring System', nous étudions le comportement des pêcheurs d'anchois du Pérou à des échelles différentes: (1) les modes comportementaux au sein des voyages de pêche (i.e. recherche, pêche et trajet), (2) les patrons comportementaux parmi les voyages de pêche, (3) les patrons comportementaux par saison de pêche conditionnés par des scénarios écosystémiques et (4) les patrons spatiaux des positions de modes comportementaux, que nous utilisons pour la création de cartes de probabilité de présence d'anchois. Pour la première échelle, nous comparons plusieurs modèles Markoviens (modèles de Markov et semi-Markov cachés) et discriminatifs (forêts aléatoires, machines à vecteurs de support et réseaux de neurones artificiels) pour inférer les modes comportementaux associés aux trajectoires VMS. L'utilisation d'un ensemble de données pour lesquelles les modes comportementaux sont connus (grâce aux données collectées par des observateurs embarqués), nous permet d'entraîner les modèles dans un cadre supervisé et de les valider. Les modèles de semi-Markov cachés sont les plus performants, et sont retenus pour inférer les modes comportementaux sur l'ensemble de données VMS. Pour la deuxième échelle, nous caractérisons chaque voyage de pêche par plusieurs descripteurs, y compris le temps passé dans chaque mode comportemental. En utilisant une analyse de classification hiérarchique, les patrons des voyages de pêche sont classés en groupes associés à des zones de gestion, aux segments de la flottille et aux personnalités des capitaines. Pour la troisième échelle, nous analysons comment les conditions écologiques donnent forme au comportement des pêcheurs à l'échelle d'une saison de pêche. Via des analyses de co-inertie, nous trouvons des associations significatives entre les dynamiques spatiales des pêcheurs, des anchois et de l'environnement, et nous caractérisons la réponse comportementale des pêcheurs selon des scénarios environnementaux contrastés. Pour la quatrième échelle, nous étudions si le comportement spatial des pêcheurs reflète dans une certaine mesure la répartition spatiale de l'anchois. Nous construisons un indicateur de la présence d'anchois à l'aide des modes comportementaux géo-référencés inférés à partir des données VMS. Ce travail propose enfin une vision plus large du comportement de pêcheurs: les pêcheurs ne sont pas seulement des agents économiques, ils sont aussi des fourrageurs, conditionnés par la variabilité dans l'écosystème. Pour conclure, nous discutons de la façon dont ces résultats peuvent avoir de l'importance pour la gestion de la pêche, des analyses de comportement collectif et des modèles end-to-end. / This work proposes an original contribution to the understanding of fishermen spatial behavior, based on the behavioral ecology and movement ecology paradigms. Through the analysis of Vessel Monitoring System (VMS) data, we characterized the spatial behavior of Peruvian anchovy fishermen at different scales: (1) the behavioral modes within fishing trips (i.e., searching, fishing and cruising); (2) the behavioral patterns among fishing trips; (3) the behavioral patterns by fishing season conditioned by ecosystem scenarios; and (4) the computation of maps of anchovy presence proxy from the spatial patterns of behavioral mode positions. At the first scale considered, we compared several Markovian (hidden Markov and semi-Markov models) and discriminative models (random forests, support vector machines and artificial neural networks) for inferring the behavioral modes associated with VMS tracks. The models were trained under a supervised setting and validated using tracks for which behavioral modes were known (from on-board observers records). Hidden semi-Markov models performed better, and were retained for inferring the behavioral modes on the entire VMS dataset. At the second scale considered, each fishing trip was characterized by several features, including the time spent within each behavioral mode. Using a clustering analysis, fishing trip patterns were classified into groups associated to management zones, fleet segments and skippers' personalities. At the third scale considered, we analyzed how ecological conditions shaped fishermen behavior. By means of co-inertia analyses, we found significant associations between fishermen, anchovy and environmental spatial dynamics, and fishermen behavioral responses were characterized according to contrasted environmental scenarios. At the fourth scale considered, we investigated whether the spatial behavior of fishermen reflected to some extent the spatial distribution of anchovy. Finally, this work provides a wider view of fishermen behavior: fishermen are not only economic agents, but they are also foragers, constrained by ecosystem variability. To conclude, we discuss how these findings may be of importance for fisheries management, collective behavior analyses and end-to-end models.

Many real-world systems experience deterioration with usage and age, which often leads to low product quality, high production cost, and low system availability. Most previous maintenance and reliability models in the literature do not incorporate condition monitoring information for decision making, which often results in poor failure prediction for partially observable deteriorating systems. For that reason, the development of fault prediction and control scheme using condition-based maintenance techniques has received considerable attention in recent years. This research presents a new framework for predicting failures of a partially observable deteriorating system using Bayesian control techniques. A time series model is fitted to a vector observation process representing partial information about the system state. Residuals are then calculated using the fitted model, which are indicative of system deterioration. The deterioration process is modeled as a 3-state continuous-time homogeneous Markov process. States 0 and 1 are not observable, representing healthy (good) and unhealthy (warning) system operational conditions, respectively. Only the failure state 2 is assumed to be observable. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The form of the optimal control policy that maximizes the long-run expected average availability per unit time has been investigated. It has been proved that a control limit policy is optimal for decision making. The model parameters have been estimated using the Expectation Maximization (EM) algorithm. The optimal Bayesian fault prediction and control scheme, considering long-run average availability maximization along with a practical statistical constraint, has been proposed and compared with the age-based replacement policy. The optimal control limit and sampling interval are calculated in the semi-Markov decision process (SMDP) framework. Another Bayesian fault prediction and control scheme has been developed based on the average run length (ARL) criterion. Comparisons with traditional control charts are provided. Formulae for the mean residual life and the distribution function of system residual life have been derived in explicit forms as functions of a posterior probability statistic. The advantage of the Bayesian model over the well-known 2-parameter Weibull model in system residual life prediction is shown. The methodologies are illustrated using simulated data, real data obtained from the spectrometric analysis of oil samples collected from transmission units of heavy hauler trucks in the mining industry, and vibration data from a planetary gearbox machinery application.

Many real-world systems experience deterioration with usage and age, which often leads to low product quality, high production cost, and low system availability. Most previous maintenance and reliability models in the literature do not incorporate condition monitoring information for decision making, which often results in poor failure prediction for partially observable deteriorating systems. For that reason, the development of fault prediction and control scheme using condition-based maintenance techniques has received considerable attention in recent years. This research presents a new framework for predicting failures of a partially observable deteriorating system using Bayesian control techniques. A time series model is fitted to a vector observation process representing partial information about the system state. Residuals are then calculated using the fitted model, which are indicative of system deterioration. The deterioration process is modeled as a 3-state continuous-time homogeneous Markov process. States 0 and 1 are not observable, representing healthy (good) and unhealthy (warning) system operational conditions, respectively. Only the failure state 2 is assumed to be observable. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The form of the optimal control policy that maximizes the long-run expected average availability per unit time has been investigated. It has been proved that a control limit policy is optimal for decision making. The model parameters have been estimated using the Expectation Maximization (EM) algorithm. The optimal Bayesian fault prediction and control scheme, considering long-run average availability maximization along with a practical statistical constraint, has been proposed and compared with the age-based replacement policy. The optimal control limit and sampling interval are calculated in the semi-Markov decision process (SMDP) framework. Another Bayesian fault prediction and control scheme has been developed based on the average run length (ARL) criterion. Comparisons with traditional control charts are provided. Formulae for the mean residual life and the distribution function of system residual life have been derived in explicit forms as functions of a posterior probability statistic. The advantage of the Bayesian model over the well-known 2-parameter Weibull model in system residual life prediction is shown. The methodologies are illustrated using simulated data, real data obtained from the spectrometric analysis of oil samples collected from transmission units of heavy hauler trucks in the mining industry, and vibration data from a planetary gearbox machinery application.