Submitted by OSCAR SCUSSEL null (oscar.scussel@gmail.com) on 2017-04-29T13:57:37Z No. of bitstreams: 1 PhDThesisScussel.pdf: 4308679 bytes, checksum: 08a1260ebbd5cc5320910fff695b1037 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-05-03T16:39:39Z (GMT) No. of bitstreams: 1 scussel_o_dr_ilha.pdf: 4308679 bytes, checksum: 08a1260ebbd5cc5320910fff695b1037 (MD5) / Made available in DSpace on 2017-05-03T16:39:39Z (GMT). No. of bitstreams: 1 scussel_o_dr_ilha.pdf: 4308679 bytes, checksum: 08a1260ebbd5cc5320910fff695b1037 (MD5) Previous issue date: 2017-03-27 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Muitas aplicações da engenharia envolvem estruturas essencialmente não-lineares onde várias técnicas têm sido recentemente estudadas e investigadas por muitos pesquisadores. Dentre as várias abordagems, as que usam séries de Volterra têm apresentado propriedades úteis para fornecer um melhor entendimento para identificação e análise. Neste contexto, a presente tese propõem novas contribuições em como usar as séries de Volterra para caracterização, identificação e análise dinâmica de sistemas não-lineares usando sinais de entrada e saída e sinais somente de saída. Inicialmente, apresenta-se uma metodologia para análise de sistemas mecânicos não-lineares através das funções de resposta em frequência de alta-ordem (HOFRFs) e o conceito de HOFRFs estendidas com dados apenas de saída é introduzido e descrito em detalhes. Após isso, uma abordagem para identificação de sistemas não-lineares com base nas séries de Volterra através da expansão na base ortonormal de Kautz é proposta. Essa técnica permite identificar os seus núcleos mais facilmente e permite separar as contribuições dos termos lineares e não-lineares usando somente sinais de saída. Além disso, uma metodologia para análise modal de sistemas fracamente não-lineares sujeito a excitações com vários níveis de amplitude é também apresentada. A contribuição desse novo método reside no fato de que as HOFRFs são simplesmente estimadas como função das FRFs lineares. Basicamente, essa metodologia estende o conceito de métodos convencionais de analise modal experimental para caracterizar e tratar efeitos não-lineares. Os resultados via exemplos numéricos e experimentais apresentados ao longo da tese mostram as contribuições, benefícios e eficácia da proposta. / Most recent engineering applications involve structures essentially nonlinear where several techniques have been recently studied and investigated by many researchers. Among them, the methods based on Volterra series expansion have presented powerful properties to provide a better understanding for identification and analysis. In this context, the present thesis proposes new contributions in how to use Volterra series for characterization, identification and dynamical analysis of nonlinear systems based on input and output signals and output-only signals. Initially, a methodology for analysis of nonlinear mechanical systems through higher-order frequency response functions (HOFRFs) is presented and the concept of extended HOFRFs based on output-only is introduced and described in detail. Afterwards, an approach for identification of nonlinear systems based on Volterra series through the expansion onto orthonormal Kautz basis is proposed. This technique allows to identify the Volterra kernels easily and enable to split the contribution of the linear and nonlinear terms using input-output as well as output-only signals. Furthermore, a methodology for modal analysis of weakly nonlinear systems under multilevel excitation is also proposed. The contribution of this new approach lies in the fact that HOFRFs are simply computed as functions of the linear FRFs. Basically, it extends the conventional experimental modal analysis methods in order to characterize and treat nonlinear effects. The results based on numerical and experimental examples presented along the thesis show the contributions, benefits and effectiveness of the proposal. / FAPESP: 2012/09135-3 / CNPq: 47058/2012-0 / CNPq: 203610/2014-8

Made available in DSpace on 2014-12-17T14:56:17Z (GMT). No. of bitstreams: 1 GasparFDJ_DISSERT.pdf: 3388304 bytes, checksum: 086a8f61099f69978a8b9f477f351d24 (MD5) Previous issue date: 2014-01-23 / Petr?leo Brasileiro SA - PETROBRAS / Slugging is a well-known slugging phenomenon in multiphase flow, which may cause problems such as vibration in pipeline and high liquid level in the separator. It can be classified according to the place of its occurrence. The most severe, known as slugging in the riser, occurs in the vertical pipe which feeds the platform. Also known as severe slugging, it is capable of causing severe pressure fluctuations in the flow of the process, excessive vibration, flooding in separator tanks, limited production, nonscheduled stop of production, among other negative aspects that motivated the production of this work . A feasible solution to deal with this problem would be to design an effective method for the removal or reduction of the system, a controller. According to the literature, a conventional PID controller did not produce good results due to the high degree of nonlinearity of the process, fueling the development of advanced control techniques. Among these, the model predictive controller (MPC), where the control action results from the solution of an optimization problem, it is robust, can incorporate physical and /or security constraints. The objective of this work is to apply a non-conventional non-linear model predictive control technique to severe slugging, where the amount of liquid mass in the riser is controlled by the production valve and, indirectly, the oscillation of flow and pressure is suppressed, while looking for environmental and economic benefits. The proposed strategy is based on the use of the model linear approximations and repeatedly solving of a quadratic optimization problem, providing solutions that improve at each iteration. In the event where the convergence of this algorithm is satisfied, the predicted values of the process variables are the same as to those obtained by the original nonlinear model, ensuring that the constraints are satisfied for them along the prediction horizon. A mathematical model recently published in the literature, capable of representing characteristics of severe slugging in a real oil well, is used both for simulation and for the project of the proposed controller, whose performance is compared to a linear MPC / A golfada ? um regime inst?vel do fluxo multif?sico, com oscila??es de press?o e vaz?o abruptas no processo de produ??o de petr?leo, podendo ocasionar problemas tais como vibra??o na tubula??o e alto n?vel de l?quido nos separadores. Pode ser classificada de acordo com seu local de ocorr?ncia. A mais severa destas, conhecida como golfada no riser, ocorre na tubula??o vertical que alimenta a plataforma. Conhecida tamb?m como golfada severa, ela ? capaz de causar bruscas oscila??es na press?o, nas vaz?es do processo, vibra??o excessiva, inunda??o dos tanques separadores, produ??o limitada, parada n?o programada da plataforma, entre outros aspectos negativos que motivaram a produ??o deste trabalho. Uma solu??o vi?vel para lidar com tal problema seria projetar um m?todo efetivo para a remo??o ou diminui??o deste regime, como um controlador. De acordo com a literatura, o controlador convencional PID n?o apresenta bons resultados devido ao alto grau de n?o linearidade do processo, o que impulsionou o desenvolvimento de t?cnicas avan?adas de controle. Dentre estas, o controlador preditivo, cuja a??o de controle resulta da solu??o de um problema de otimiza??o, al?m de ser uma t?cnica que apresenta robustez e pode incorporar restri??es f?sicas e/ou de seguran?a. O objetivo deste trabalho ? estudar a aplica??o de uma t?cnica de controle preditivo n?o linear ao controle de golfada severa, visando controlar a quantidade de massa l?quida no riser atuando na v?lvula de produ??o e, indiretamente, suprimir as oscila??es de vaz?o e press?o. Com a finalidade de obter benef?cios ambientais e econ?micos. A t?cnica de controle preditivo proposta baseia-se no uso de aproxima??es lineares do modelo e na resolu??o repetida de um problema de otimiza??o quadr?tica que proporciona solu??es que melhoram a cada itera??o. No caso em que a converg?ncia desse algoritmo ? satisfeita, os valores preditos das vari?veis do processo s?o iguais ?queles que seriam obtidos pelo modelo n?o linear original, garantindo que as restri??es nessas vari?veis sejam satisfeitas ao longo do horizonte de predi??o. Um modelo matem?tico publicado recentemente na literatura, capaz de representar caracter?sticas da golfada severa em um po?o real, ? utilizado tanto para a simula??o, quanto para projeto do controlador proposto, cujo desempenho ? comparado ao de um controlador preditivo linear

Nesta Dissertação são propostos dois esquemas de controle para sistemas não-lineares com atraso. No primeiro, o objetivo é controlar uma classe de sistemas incertos multivariáveis, de grau relativo unitário, com perturbações não-lineares descasadas dependentes do estado, e com atraso incerto e variante no tempo em relação ao estado. No segundo, deseja-se controlar uma classe de sistemas monovariáveis, com parâmetros conhecidos, grau relativo arbitrário, atraso arbitrário conhecido e constante na saída. Admitindo-se que o atraso na entrada pode ser deslocado para a saída, então, o segundo esquema de controle pode ser aplicado a sistemas com atraso na entrada. Os controladores desenvolvidos são baseados no controle por modo deslizante e realimentação de saída, com função de modulação para a amplitude do sinal de controle. Além disso, observadores estimam as variáveis de estado não-medidas. Em ambos os esquemas de controle propostos, garante-se propriedades de estabilidade globais do sistema em malha fechada. Simulações ilustram a eficácia dos controladores desenvolvidos. / Two control schemes for nonlinear time-delay systems are proposed in this thesis. The purpose of the first scheme is to control a class of uncertain multivariable systems, with relative degree one, nonlinear unmatched state dependent disturbances, and uncertain time-varying state delay. The purpose of the second scheme is to control a class of single-input-single-output systems, with known parameters, arbitrary relative degree, with constant and known arbitrary output delay. Assuming that input delays can be transferred to the output, so the second scheme can be applied to systems with input time-delay. The developed controllers are based on sliding mode control and output feedback, with modulation function to the control signal amplitude. Furthermore, observers estimate unmeasured state variables. In both schemes, global stability properties of the closed loop system are guaranteed. Simulations illustrate the effectiveness of the proposed approaches.

Existem métodos de integração de equações algébrico diferenciais não lineares (DAEs) considerados clássicos pela literatura. Porém, neste trabalho, através uma abordagem geométrica, apresenta-se um método de integração de DAEs. Tal método é inspirado na teoria de desacoplamento de sistemas não lineares explícitos, quando se considera que as saídas são restrições algébricas. Neste caso, a DAE pode ser identificada como dinâmica zero. O resultado principal desta abordagem é que, dada uma DAE, sob certas condições, é possível a construção de um sistema explícito, de tal maneira, que as soluções desse sistema explícito convergem para as soluções da DAE. / Classical methods for numerical integration of diferential algebraic equations (DAEs) can be formal in the literature. In this work, using a diferential geometric approach, a numerical method of integration of DAEs is established. This method is inspired in the decoupling theory of nonlinear explicit systems, when one considers that the outputs are algebraic constraints. The main result is the construction of an explicit system, whose solutions converge to the solutions of the DAE.

Orientador: Edevar Luvizotto Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-05T20:04:30Z (GMT). No. of bitstreams: 1 Palhares_JulianaBarbosa_M.pdf: 1136611 bytes, checksum: 85a62466425d6655acb5af5bcc414c66 (MD5) Previous issue date: 2005 / Resumo: Nos sistemas de transporte de fluido líquido, têm-se a preocupação em combater às fugas ou vazamentos. Dessa fonna, este trabalho tem como objetivo aperfeiçoar o método de detecção de fugas em tubulações pelo método de resposta nos domínios fteqüência e tempo, utilizando como ferramentas matemáticas o Método da Matriz Transferência / Resposta em Freqüência e o Método das Características / Transfonnada Rápida de Fourier, sendo demonstradas as vantagens e desvantagens de cada método. E, como contribuição original, propõe um método de detecção de fugas através da análise de pulso de Alta Freqüência, localizando as fugas através da detenninação do tempo que um pulso emitido pela válvula leva para percorrer toda a tubulação e retomar à esta, denominado como Pulso Refletido / Abstract: In liquid fluid transport systems, there is a concem about avoiding leaks. Thus, this work has as objective to improve the leak detection method in pipes by úequency and time domains response method, being used as mathematical tools the method ofTransfer-Matrix / by úequency response and the Method of Characteristics / the Fast Fourier Transform, being demonstrated the advantages and disadvantages of each method. And, as new contribution, propose a leak detection method through the analysis of high frequency pulse, detecting the leaks through determination of time that a pulse produced by the valve takes to go through all pipe and come back, is denominated as a reflected pulse / Mestrado / Recursos Hidricos / Mestre em Engenharia Civil

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T17:29:03Z No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:44:17Z (GMT) No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Made available in DSpace on 2018-01-23T13:44:17Z (GMT). No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) Previous issue date: 2017-09-15 / O presente trabalho propõe uma nova metodologia de Geração de Sinal Sub-Ótimo de Excitação e Estimação Ótima de Parâmetros de sistemas não lineares. É proposto que a avaliação de cada sinal deva considerar, entre outros fatores, a diferença entre os parâmetros reais da planta e os obtidos pela estimação. Entretanto esta métrica não é trivial de ser obtida uma vez que os valores reais são desconhecidos. Para tanto é adotada a hipótese de que, se um sistema real puder ser razoavelmente aproximado por uma caixa branca, é possível utilizar este modelo como referência para indicar o impacto de um sinal sobre a estimação paramétrica. Desta forma, é utilizada uma metodologia de otimização dividida em dois níveis: (i) Nível Interno; para um dado sinal de excitação um método de otimização não linear busca o conjunto ótimo de parâmetros que minimiza o erro entre os sinais de saída do modelos original e do de referência. (ii) No nível externo um método de otimização baseado em meta-heurística é responsável por encontrar o melhor sinal de excitação com base na função custo composta de uma soma ponderada de métricas que consideram o erro entre os sinais de saída do modelo otimizado e do de referência, a diferença quadrática entre seus parâmetros, e o custo em relação ao tempo e espaço necessários para executar o experimento. Portanto, a aplicação da metodologia proposta vem suprir a necessidade de estimar sistemas não lineares apropriadamente, encontrando um conjunto de parâmetros capaz de generalizar o comportamento do sistema real, através de um sinal de excitação que cumpra requisitos práticos do processo. A eficácia da metodologia proposta é analisada em detalhes através de resultados obtidos utilizando sistemas de fluídos, sistemas caóticos e de robótica móvel, tanto sobre rodas quanto subaquática. / The present work proposes a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of nonlinear systems. It is proposed that the evaluation of each signal must to take into account, among other factors, the difference between real system parameters and the obtained by estimation. However, this metric is not trivially obtained once the real parameters values are unknown. To do so it is adopted the hypothesis that, if the system can be fairly approximate by a white box model, it is possible to use this model as a benchmark to indicate the impact of a signal on a parametric estimation. In this way, the method uses an optimization methodology divided into two levels: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the output signals of the original and the benchmark models. (ii) At the outer level, an optimization method based on metaheuristics is responsible for finding the best excitation signal, based on the cost function composed of a weighted sum of metrics, that considers the error between the output signals of the optimized model and the benchmark, the quadratic difference between its parameters, and the cost in relation to the time and space required to execute the experiment. Thus, the application of the proposed methodology comes to supply the need to estimate nonlinear systems appropriately, finding a set of parameters capable of generalizing the behavior of the real system, through an excitation signal that fulfills practical requirements of the process. The proposed methodology is analyzed in detail through results obtained using fluid systems, chaotic systems and mobile robotics, both wheeled and underwater.

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.

Le thème de cette thèse est l'identification de paramètres tels que la conductivité hydraulique, K, pour un problème d'intrusion marine dans un aquifère isotrope et libre. Plus précisément, il s'agit d'estimer la conductivité hydraulique en fonction d'observations ou de mesures sur le terrain faites sur les profondeurs des interfaces (h, h₁), entre l'eau douce et l'eau salée et entre le milieu saturé et la zone insaturée. Le problème d'intrusion marine consiste en un système à dérivée croisée d'edps de type paraboliques décrivant l'évolution de h et de h₁. Le problème inverse est formulé en un problème d'optimisation où la fonction coût minimise l'écart quadratique entre les mesures des profondeurs des interfaces et celles fournies par le modèle. Nous considérons le problème exact comme une contrainte pour le problème d'optimisation et nous introduisons le Lagrangien associé à la fonction coût. Nous démontrons alors que le système d'optimalité a au moins une solution, les princcipales difficultés étant de trouver le bon ensemble pour les paramètres admissibles et de prouver la différentiabilité de l'application qui associe (h(K), h₁(K₁)) à K. Ceci constitue le premier résultat de la thèse. Le second résultat concerne l'implémentation numérique du problème d'optimisation. Notons tout d'abord que, concrètement, nous ne disposons que d'observations ponctuelles (en espace et en temps) correspondant aux nombres de puits de monitoring. Nous approchons donc la fonction coût par une formule de quadrature qui est ensuite minimisée en ultilisant l'algorithme de la variable à mémoire limitée (BLMVM). Par ailleurs, le problème exact et le problème adjoint sont discrétisés en espace par une méthode éléments finis P₁-Lagrange combinée à un schéma semi-implicite en temps. Une analyse de ce schéma nous permet de prouver qu'il est d'ordre 1 en temps et en espace. Certains résultats numériques sont présentés pour illustrer la capacité de la méthode à déterminer les paramètres inconnus. Dans la troisième partie de la thèse, nous considérons la conductivité hydraulique comme un paramètre stochastique. Pour réaliser une étude numérique rigoureuse des effets stochastiques sur le problème d'intrusion marine, nous utilisons les développements de Wiener pour tenir compte des variables aléatoires. Le système initiale est alors transformé en une suite de systèmes déterministes qu'on résout pour chaque coefficient stochastique du développement de Wiener. / This thesis is concerned with the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem involving a nonhomogeneous, isotropic and free aquifer. The involved PDE model is a coupled system of nonlinear parabolic equations completed by boudary and initial conditions, as well as compatibility conditions on the data. The main unknowns are the saltwater/freshwater interface depth and the elevation of upper surface of the aquifer. The inverse problem is formulated as the optimization problem where the cost function is a least square functional measuring the discrepancy between experimental interfaces depths and those provided by the model. Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. The main difficulties are to find the set of all eligible parameters and to prove the differentiability of the operator associating to the hydraulic conductivity K, the state variables (h, h₁). This is the first result of the thesis. The second result concerns the numerical implementation of the optimization problem. We first note that concretely, we only have specific observations (in space and in time) corresponding to the number of monitoring wells, we then adapt the previous results to the case of discrete observations data. The gradient of the cost function is computed thanks to an approximate formula in order to take into account the discrete observations data. The cost functions then is minimized by using a method based on BLMVM algorithm. On the other hand, the exact problem and the adjoint problem are discretized in space by a P₁-Lagrange finite element method combined with a semi-implicit time discretization scheme. Some numerical results are presented to illustrate the ability of the method to determine the unknown parameters. In the third part of the thesis we consider the hydraulic conductivity as a stochastic parameter. To perform a rigorous numerical study of stochastic effects on the saltwater intrusion problem, we use the spectral decomposition and the stochastic variational problem is reformulated to a set of deterministic variational problems to be solved for each Wiener polynomial chaos.

Cette thèse traite du problème d'observation et d'estimation des variables caractéristiques des systèmes dynamiques. Il s’agit d’une problématique fondamentale qui est au cœur de nombreux domaines relavant des sciences de l'ingénieur. Les travaux sont conduits dans un contexte ensembliste. Les techniques développées pour l’estimation de l’état et des variables d’entrées ont pour objectif final le contrôle de cohérence des systèmes non linéaires à temps continu. Une première approche conjugue les relations de parité et les différentiateurs à modes glissants pour l’estimation des entrées d’un système non linéaire. Les domaines des entrées compatibles avec les mesures sont alors reconstruits grâce à l’analyse par intervalles et aux techniques de satisfaction de contraintes. Il est montré que la relaxation des contraintes de stabilité/coopérativité pour la construction d’un observateur intervalle peut se faire grâce à des changements de base déterminés de différentes manières et pouvant être variants ou invariants dans le temps. Des simulations numériques illustrent les techniques proposées. Une application à un système aéronautique est également présentée à l’aide d’un jeu de données réelles. / This thesis deals with the problem of a dynamical system observation and the estimation of its characteristic variables; the latter point constitutes the core element in many engineering science fields. The final aim is to build a general framework for integrity control and fault detection of such systems within a bounded error context. The developments offered herein make use of parity relations, sliding mode differentiators, interval observers and constraint satisfaction problems. Input reconstruction techniques are developed for a general class of nonlinear continuous-time systems. Domains are reconstructed for the input values which are consistent with the measurements using interval analysis and constraint satisfaction techniques. It is shown that time-varying or invariant coordinate changes may relax the applicability conditions (stability/cooperativity) of the interval observer design methods. Sliding mode differentiators were also used to enhance interval observer accuracy. The proposed approaches are illustrated through computer simulations and they have been applied to aircraft servo loop control surface for robust and early detection of abnormal positions.

Dans cette étude on s'intéresse à la dynamique d'une classe de systèmes non-linéaires décrits par des équations aux dérivées partielles (EDP) du type hyperbolique. L'objectif de l'étude est de construire des lois de contrôle par feedback dynamique de la sortie afin de stabiliser le système autour d'un point d'équilibre d'une part, et, d'autre part, de réguler la sortie vers le point de consigne. Nous considérons la classe des systèmes gouvernés par des EDP quasi-linéaires du type hyperbolique à deux variables indépendantes (une variable temporelle et une variable spatiale). Pour le bien-posé du système dynamique non seulement l'état initial mais aussi certaines conditions frontières doivent être prescrites en cohérence avec les EDP. Nous supposons que l'observation et le contrôle sont ponctuels. Autrement dit l'action du contrôle intervient dans le système via les conditions frontières et l'observation est effectuée aux points de la frontière. Notre étude est motivée par l'observation que de nombreux processus physiques sont modélisés par ce type d'équations EDP. Nous citons, par exemple, des processus tels que flux trafique en transport, flux de gaz dans un réseau de pipeline, échangeurs thermiques en génie des procédés, équations de télégraphe dans des lignes de transmission, canaux d'irrigation en génie civil etc. Nous commençons l'étude par une EDP non-linéaire scalaire. Dans ce cas-là nous proposons un correcteur intégral stabilisant qui assure la régulation de la sortie avec l'erreur statique nulle. Nous prouvons la stabilisation locale du système non-linéaire par le correcteur intégral en construisant une fonctionnelle de Lyapunov appropriée. La conception des correcteurs proportionnels et intégraux (PI) que nous proposons est étendue dans un cadre de systèmes de deux EDP. Nous prouvons la stabilisation du système en boucle fermée à l'aide d'une nouvelle fonctionnelle de Lyapunov. La synthèse des correcteurs PI stabilisants se poursuit dans un cadre de réseaux formés d'un nombre fini de systèmes à deux EDP : réseau étoilé et réseau série en cascade. Les contrôles et les observations se trouvent localisés aux différents nœuds de connexion. Pour ces configurations nous présentons un ensemble de correcteurs PI stabilisants qui assurent la régulation vers le point de consigne. Les correcteurs PI que nous concevons sont validés par des simulations numériques à partir des modèles non-linéaires EDP. La contribution de la thèse, par rapport à la littérature existante, consiste en l'élaboration de nouvelles fonctionnelles de Lyapunov pour une classe de systèmes stabilisés par correcteur PI. En effet une grande quantité de résultats ont été obtenus sur la stabilisation des systèmes hyperboliques par feedback statique de la sortie. Toutefois il existe encore peu de résultats sur la stabilisation de ces systèmes par feedback dynamique de la sortie. L'étude de la thèse est consacrée sur l'élaboration des fonctionnelles de Lyapunov permettant d'obtenir des correcteurs PI stabilisants. L'approche de Lyapunov direct que nous avons proposée a pour l'avantage de permettre d'étudier la robustesse des lois de feedback de la sortie PI vis-à-vis de la non-linéarité. Une autre contribution de la thèse consiste en la construction des programmes de Malab permettant d'effectuer des simulations numériques pour la validation des correcteurs conçus. Pour la résolution numérique des EDP hyperboliques nous avons discrétisé nos systèmes par le schéma numérique de Preissmann. Nous avons chaque fois un système d'équations algébriques non-linéaires à résoudre de façon récurrente. L'apport des simulations numériques nous permet de mieux comprendre la méthodologie applicative de la théorie du contrôle en dimension infinie / In this study we are interested in the dynamics of a class of nonlinear systems described by partial differential equations (PDE) of the hyperbolic type. The aim of the study is to construct control laws by dynamic feedback of the output in order to stabilize the system around an equilibrium point on the one hand and to regulate the output to the set-point. We consider the class of systems governed by hyperbolic PDEs with two independent variables (one time variable and one spatial variable). For the well-posed dynamic system not only the initial state but also certain boundary conditions must be prescribed in coherence with the PDEs. We assume that observation and control are punctual. In other words, the action of the control intervenes in the system via the boundary conditions and the observation is carried out at the points of the border. Our study is motivated by the observation that many physical processes are modeled by this type of PDE equations. Examples include processes such as traffic flow in transportation, gas flows in a pipeline network, heat exchangers in process engineering, telegraph equations in transmission lines, civil engineering irrigation channels, to cite but a few.We begin the study with a scalar nonlinear PDE. In this case we propose a stabilizing integral controller which ensures the regulation of the output with zero static error. We prove the local stabilization of the nonlinear system by the integral controller by constructing an appropriate Lyapunov functional. The design of the proportional and integral (PI) controllers that we propose is extended in a framework of two PDE systems. We prove the stabilization of the closed-loop system with a new Lyapunov functional. The synthesis of stabilizing PI controllers is carried out in a framework of networks formed by a finite number of two PDE systems: star network and serial network in cascade. Controls and observations are located at the different connection nodes. For these configurations we present a set of stabilizing PI controllers that regulate the output to the set-point. The PI controllers that we design are validated by numerical simulations from the nonlinear PDE models. The contribution of the thesis compared to the existing literature consists in the development of new Lyapunov functionals for the class of systems looped by a PI controller. Indeed, a large number of results have been obtained from the stabilization of hyperbolic systems by static feedback of the output. However, there are still few results with the stabilization of these systems by the output dynamic feedback. The study of the thesis is devoted to the development of the Lyapunov functional to obtain stabilizing PI controllers. The direct Lyapunov approach that we have proposed has the advantage of allowing to study the robustness of the output dynamic feedback laws in the form of PI controllers with respect to the nonlinearity. Another contribution of the thesis consists of the Malab program construction allowing to carry out numerical simulations for the validation of the conceived controllers. For the numerical resolution of hyperbolic PDEs, we have discretized our systems using the Preissmann numerical scheme. Each time moment we have a system of non-linear algebraic equations to be solved in a recurring way. The contribution of numerical simulations allows us to better understand the application methodology of the infinite dimension control theory