The aim of this study is to solve Fault Detection and Diagnosis (FDD) problems occurring in nonlinear dynamical systems by using model and knowledge-based FDD methods and to give a priority and a degree about faults. For this purpose, three model-based FDD approaches, called FDD by utilizing principal component analysis (PCA), system identification based FDD and inverse model based FDD are introduced. Performances of these approaches are tested on different nonlinear dynamical systems starting from simple to more complex. New fuzzy discrete event system (FDES) and fuzzy discrete event dynamical system (FDEDS) concepts are introduced and their applicability to an FDD problem is investigated. Two knowledge-based FDD methods based on FDES and FDEDS structures using a fuzzy rule-base are introduced and they are tested on nonlinear dynamical systems. New properties related to FDES and FDEDS such as fuzzy observability and diagnosibility concepts and a relation between them are illustrated. A dynamical rule-base extraction method with classification techniques and a dynamical and a static diagnoser design methods are also introduced. A nonlinear and event based extension of the Luenberger observer and its application as a diagnoser to isolate faults are illustrated. Finally, comparisons between the proposed model and knowledge-based FDD methods are made.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-07-14Bitstream added on 2014-06-13T19:47:29Z : No. of bitstreams: 1 carvalho_mp_me_sjrp.pdf: 275726 bytes, checksum: 321f242993a9cb5700217a8d44c3003b (MD5) / Neste trabalho estudamos problemas clássicos de controle para sistemas de equações diferenciais ordinárias lineares. O ponto de partida é a equivalência entre uma equação diferencial ordinária linear de ordem n e um sistema de n equações de primeira ordem. Problemas de controlabilidade completa, observabilidade e estabi- lização de equilíbrio são considerados. / We consider here classic problems on control for a system of ordinary diferential equations. The starting point is the equivalence between a linear equation of nth order of ordinary diferential equation and a system of n equations of first order. Problems on complete controllability, observability and stabilization of equilibrium are considered.

Dans cette thèse, nous étudions les propriétés de contrôlabilité uniforme des semidiscrets approximations de systèmes paraboliques. Dans une première partie, nous nous intéressons à la minimisation de Lq-norme (q > 2) des contrôles semidiscrete pour l'équation parabolique. Notre objectif est de dépasser la limitation de [LT06] à propos de l'ordre ½ de l'absence de limites d'opérateur de contrôle. Plus précisément, nous montrons que la propriété d'observabilité uniforme est également titulaire dans Lq (q > 2), même dans le cas d'un degré d'absence de limites supérieure à 1/2. En outre, une procédure de minimisation pour calculer les commandes d'approximation est fournie. L'étude de l'optimalité Lq dans lapremière partie est dans un contexte général. Cependant, les inégalités d'observabilité discrets qui sont obtenus ne sont pas aussi précises que celles dérivées puis avec des estimations de Carleman. Dans une seconde partie, dans le contexte particulier de unidimensionnels-finis différences nous démontrons une inégalité de Carleman pour une version semi-discret de l'opérateur parabole @t − @x(c@x) qui permet pour dériver les inégalités d'observabilité qui sont beaucoup plus précis. On considère ici que dans le cas où le coefficient de diffusion a un saut qui donne une formulation du problème de transmission. Conséquence de cette inégalité de Carleman, on en déduit cohérentes nul contrôlabilité des résultats pour les classes de linéaires et semi-linéaire des équations paraboliques. / In this thesis, we study uniform controllability properties of semi-discrete approximations for parabolic systems. In a first part, we address the minimization of the Lq-norm (q > 2) of semidiscrete controls for parabolic equation. Our goal is to overcome the limitation of [LT06] about the order 1/2 of unboundedness of the control operator. Namely, we show that the uniform observability property also holds in Lq (q > 2) even in the case of a degree of unboundedness greater than 1/2. Moreover, a minimization procedure to compute the approximation controls is provided. The study of Lq optimality in the first part is in a general context. However, the discrete observability inequalities that are obtained are not so precise than the ones derived then with Carleman estimates. In a second part, in the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi discrete version of the parabolic operator @t − @x(c@x) which allows one to derive observability inequalities that are far more precise. Here we consider in case that the diffusion coefficient has a jump which yields a transmission problem formulation. Consequence of this Carleman estimate, we deduce consistent null-controllability results for classes of linear and semi-linear parabolic equations.

abstract: Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2015

Neste trabalho propõe-se um método de análise de observabilidade para estimação de estados e parâmetros em sistemas elétricos de potência, baseado nas equações normais. O método fundamenta-se na fatoração triangular da matriz ganho aumentada e nos conceitos de caminhos de fatoração. O mesmo utiliza rotinas já existentes no processo de estimação, sendo simples, de fácil implementação, rápida execução e não exige a solução de equações algébricas. Para comprovar a sua eficiência vários testes foram realizados, utilizando os sistemas de 6, 14 e 30 barras do IEEE, tendo sido satisfatórios os resultados obtidos. / In this work we propose a method of observability analysis for states and parameters estimation in electric power systems, based on the Normal Equations. The method is based on triangular factoration of the augmented gain matrix and on the concepts of factoration paths. It uses routines that there exist in the estimation process. These routines are simple, of easy implementation, fast execution and it doesn\'t demand the solution of algebraic equations. To prove your efficiency several tests were accomplished, using the 6, 14 and 30-bus IEEE test systems. The obtained results were satisfactory.

Desenvolveu-se neste trabalho um método para projeto e fortalecimento de planos de medição, para efeito de estimação de estados. O método proposto permite a obtenção de planos de medição que além de isentos de medidas críticas e de conjuntos críticos de medidas, garantem a observabilidade do sistema, mesmo com a perda simultânea de 1 ou 2 medidas quaisquer, ou, até mesmo, com a perda de 1 UTR. É um método numérico simples, de fácil implantação, que se baseia na análise da estrutura da matriz resultante da decomposição LDU, que é obtida através da fatoração triangular da matriz Jacobiana. Para comprovar a sua eficiência, vários testes foram realizados, utilizando os sistemas de 14 e 30 barras do IEEE, o sistema de 121 barras da ELETROSUL e o sistema de 383 barras da CHESF. / In this work a method to design and to upgrade Measurements Placement Plan for state estimation is proposed. The proposed method allows the obtention of measurements placement plans that, besides free of both critical measurements and critical sets, maintain the system observability when 1 or 2 measurements are lost, at same time, or even when a Remote Terminal Unit (RTU) is lost. It is a simple numerical method, easy to implement and based on the analysis of the structure of the resultant matrix of the decomposition LDU, that it is obtained through a triangular factorization of the Jacobian matrix. To prove the efficiency of the proposed method, several tests were made using the IEEE 14 and 30-bus systems, a 121-bus system from ELETROSUL and a 383-bus system from CHESF.

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On considère dans cette thèse l'équation des ondes posée sur un domaine $\Omega$ supposé régulier. Si $\Gamma$ désigne une surface supposée observable, on peut définir la constante d'observabilité associée à $\Gamma$. L'intérêt de cette constante est de rendre compte de la qualité de la reconstruction dans le problème inverse qui consiste à reconstruire les données initiales à partir de la mesure de la solution sur $\Gamma$. Ainsi l'étude de cette constante s'applique entre autres à la détermination de la forme et du placement optimaux de capteurs, pour la mesure de toute sorte de phénomènes ondulatoires. Le but du premier chapire est de caractériser de manière théorique les domaines $\Gamma$ de surface prescrite qui maximisent cette constante d'observabilité, ou plus exactement une version "randomizée" de ce critère. Dans le second chapitre il s'agit d'appliquer les résulats obtenus au placement optimal de capteurs pour la tomographie photoacoustique. La tomographie photoacoustique est un procédé d'imagerie médicale ultra-sonore, non invasif encore peu développé qui est une alternative précise et plus économique à l'imagerie X. C'est dans ce cadre que l'on propose une modélisation de l'influence de la forme et de la disposition des capteurs dans le problème de reconstruction de la densité des tissus. Plus particulièrement, il s'agira de construire une fonctionnelle de la forme des capteurs, rendant compte de la qualité de l'image obtenue. / In the first part of this thesis, we consider the wave equation on a regular bounded domain $\Omega$. We investigate the problem of optimizing, in some appropriate sense, the shape and location of sensors spread on an arbitrary measurable subdomain $\Gamma$ of the boundary of $\Omega$. We introduce a spectral quantity called randomized observability constant, corresponding to the best constant in an average of the classical observability inequality, over random initial data. The pupose of the first chapter is to investigate optimal domains, maximizing the new objective function. The second part consists in applying the previous results to medical imaging, and more precisely to photoacoustic tomography. This imaging technique, constitutes a cutting-edge technology that has drawn considerable attention in the medical imaging area. Firstly because it is non-ionizing and non-invasive, and also because it constitutes a precise and cheap alternative to X imaging. In this framework, we propose here to model the influence of the shape and position of sensors in the inverse problem consisting in the reconstruction of the imaged body. In a nutshell, we build a functional of the shape of the sensors, providing an account for the reconstructed image quality.

<div> Space operations from the dawn of the Space Age have resulted in a large, and growing, resident space object population. However, the availability of sensor resources is limited, which presents a challenge to Space Situational Awareness applications. When direct communication with an object is not possible, whether that is due to a lack of access for active satellites or due to the object being characterized as debris, the only independent information source for learning about the resident space object population comes from measurements. Optical measurements are often a cost-effective method for obtaining information about resident space objects.<br></div><div> This work uses observability analysis to investigate the relationship between desired resident space object characteristics and the information resulting from ground-based optical measurements. Observability is a concept developed in modern control theory for evaluating whether the information contained within measurements is sufficient to describe the dynamical progression of a system over time. In this work, observability is applied to Space Situational Awareness applications to determine what object characteristic information can be recovered from ground-based optical measurements and under which conditions these determinations are possible. In addition, the constraints and limitations of applying observability to Space Situational Awareness applications are assessed and quantified.<br></div>

In recent years, microservice architecture has surpassed monolithic architecture in popularity among developers by providing a flexible way of developing complex distributed applications. Whereas a monolithic application functions as a single indivisible unit, a microservices-based application comprises a collection of loosely coupled services that communicate with each other to fulfill the requirements of the application. Consequently, different services in a microservices-based application can be developed and deployed independently. However, this flexibility is achieved at the expense of reduced observability of microservices-based applications complicating the debugging of such applications. The reduction of observability can be compensated by performing distributed tracing in microservices-based applications. Distributed tracing refers to observing requests propagating through a distributed system to collect observability data that can aid in understanding the interactions among the services and pinpoint failures and performance issues in the system. Open- Telemetry, an open-source observability framework supported by Cloud Native Computing Foundation (CNCF), defines a standardized specification for generating observability data. Nevertheless, instrumenting an application with an observability framework incurs performance overhead. To tackle this deterioration of performance and to reduce the cost of persisting observability data, only a subset of the requests are typically traced by performing head-based or tail-based sampling. In this work, we present a tail-based sampling framework using stream processing techniques. The developed framework demonstrated promising performance in our experiments by saving approximately a third of memory-based storage compared to an OpenTelemetry tail-based sampling module. Moreover, being compliant with the OpenTelemetry specifications, our framework aligns well with the OpenTelemetry ecosystem. / Under de senaste åren har mikrotjänstarkitektur överträffat monolitisk arkitektur i popularitet bland utvecklare genom att erbjuda ett flexibelt sätt att utveckla komplexa distribuerade tillämpningar. Medan en monolitisk tillämpning fungerar som en enda odelbar enhet, består en mikrotjänstbaserad tillämpning av en samling löst kopplade tjänster som kommunicerar med varandra för att uppfylla tillämpningens krav. Därför kan olika tjänster i en mikrotjänstbaserad tillämpning utvecklas och driftsättas oberoende av varandra. Denna flexibilitet uppnås dock på bekostnad av minskad observerbarhet för mikrotjänstbaserade tillämpningar, vilket försvårar felsökningen av sådana tillämpningar. Den minskade observerbarheten kan kompenseras genom att utföra distribuerad spårning i mikrotjänstbaserade tillämpningar. Distribuerad spårning innebär att man observerar förfrågningar som sprids genom ett distribuerat system för att samla in data om observerbarhet som kan hjälpa till att förstå interaktionerna mellan tjänsterna och lokalisera fel och prestandaproblem i systemet. OpenTelemetry, ett ramverk för observerbarhet med öppen källkod som stöds av Cloud Native Computing Foundation (CNCF), definierar en standardiserad specifikation för att generera observerbarhetsdata. Att instrumentera en tillämpning med ett ramverk för observerbarhet medför dock en överbelastning av prestanda. För att hantera denna försämring av prestanda och för att minska kostnaden för att bevara observerbarhetsdata spåras vanligtvis endast en delmängd av förfrågningarna genom att utföra s.k. “head-based sampling” eller “tail-based sampling”. I det här arbetet presenterar vi ett ramverk för tail-based sampling med hjälp av strömbehandlingsteknik. Den utvecklade ramen visade lovande prestanda i våra experiment genom att spara ungefär en tredjedel av den minnesbaserade lagringen jämfört med en OpenTelemetry-modul för tail-based sampling. Eftersom vårt ramverk är förenligt med OpenTelemetry-specifikationerna är det dessutom väl anpassat till OpenTelemetry-ekosystemet.