<p>The need to carry out Uncertainty quantification (UQ) is ubiquitous in science and engineering. However, carrying out UQ for real-world problems is not straightforward and they require a lot of computational budget and resources. The objective of this thesis is to develop computationally efficient approaches based on machine learning to carry out UQ. Specifically, we addressed two problems.</p> <p><br></p> <p>The first problem is, it is difficult to carry out Uncertainty propagation (UP) in systems governed by elliptic PDEs with spatially varying uncertain fields in coefficients and boundary conditions. Here as we have functional uncertainties, the number of uncertain parameters is large. Unfortunately, in these situations to carry out UP we need to solve the PDE a large number of times to obtain convergent statistics of the quantity governed by the PDE. However, solving the PDE by a numerical solver repeatedly leads to a computational burden. To address this we proposed to learn the surrogate of the solution of the PDE in a data-free manner by utilizing the physics available in the form of the PDE. We represented the solution of the PDE as a deep neural network parameterized function in space and uncertain parameters. We introduced a physics-informed loss function derived from variational principles to learn the parameters of the network. The accuracy of the learned surrogate is validated against the corresponding ground truth estimate from the numerical solver. We demonstrated the merit of using our approach by solving UP problems and inverse problems faster than by using a standard numerical solver.</p> <p><br></p> <p>The second problem we focused on in this thesis is related to inverse problems. State of the art approach to solving inverse problems involves posing the inverse problem as a Bayesian inference task and estimating the distribution of input parameters conditioned on the observed data (posterior). Markov Chain Monte Carlo (MCMC) methods and variational inference methods provides us ways to estimate the posterior. However, these inference techniques need to be re-run whenever a new set of observed data is given leading to a computational burden. To address this, we proposed to learn a Bayesian inverse map i.e., the map from the observed data to the posterior. This map enables us to do on-the-fly inference. We demonstrated our approach by solving various examples and we validated the posteriors learned from our approach against corresponding ground truth posteriors from the MCMC method.</p>

Ces travaux portent sur la résolution successive de deux problèmes inverses en transferts thermiques : l'estimation de la densité de flux en surface d'un matériau puis de la conductivité thermique équivalente d'une couche déposée en surface de ce matériau. Le modèle direct est bidimensionnel orthotrope (géométrie réelle d'un matériau composite), instationnaire, non-linéaire et ses équations sont résolues par éléments finis. Les matériaux étudiés sont les composants face au plasma (tuiles composite carbone-carbone) dans le Tokamak JET. La densité de flux recherchée varie avec une dimension spatiale et avec le temps. La conductivité du dépôt de surface varie spatialement et peut également varier au cours du temps pendant l'expérience (toutes les autres propriétés thermophysiques dépendent de la température). Les deux problèmes inverses sont résolus à l'aide de l'algorithme des gradients conjugués associé à la méthode de l'état adjoint pour le calcul exact du gradient. La donnée expérimentale utilisée pour la résolution du premier problème inverse (estimation de flux surfacique) est le thermogramme fourni par un thermocouple enfoui. Le second problème inverse utilise, lui, les variations spatio-temporelles de la température de surface du dépôt inconnu (thermographie infrarouge) pour identifier sa conductivité. Des calculs de confiance associée aux grandeurs identifiées sont réalisés avec la démarche Monte Carlo. Les méthodes mises au point pendant ces travaux aident à comprendre la dynamique de l'interaction plasma-paroi ainsi que la cinétique de formation des dépôts de carbone sur les composants et aideront au design des composants des machines futures (WEST, ITER). / This work deals with the successive resolution of two inverse heat transfer problems: the estimation of surface heat flux on a material and equivalent thermal conductivity of a surface layer on that material. The direct formulation is bidimensional, orthotropic (real geometry of a composite material), unsteady, non-linear and solved by finite elements. The studied materials are plasma facing components (carbon-carbon composite tiles) from Tokamak JET. The searched heat flux density varies with time and one dimension in space. The surface layers conductivity varies spatially and can vary with time during the experiment (the other thermophysical properties are temperature dependent). The two inverse problems are solved by the conjugate gradient method with the adjoint state method for the exact gradient calculation. The experimental data used for the first inverse problem resolution (surface heat flux estimation) is the thermogram provided by an embedded thermocouple. The second inverse problem uses the space and time variations of the surface temperature of the unknown surface layer (infrared thermography) for the conductivity identification. The confidence calculations associated to the estimated values are done by the Monte Carlo approach. The method developed during this thesis helps to the understanding of the plasma-wall interaction dynamic, as well as the kinetic of the surface carbon layer formation on the plasma facing components, and will be helpful to the design of the components of the future machines (WEST, ITER).

On s’intéresse dans ce travail à l’aspect tridimensionnel (3D) de la propagation sonore en milieux océaniques petits fonds dans le cadre des problèmes inverses. Les problèmes inverses en acoustique sous-marine se basent sur la modélisation bidimensionnelle (2D) de la propagation, ignorant ainsi les effets de réfraction horizontale, qualifiés d’effets 3D. Toutefois, la propagation acoustique en environnements petits fonds, tels le plateau continental, peut être affectée par des effets 3D, leur prise en compte nécessitant l’utilisation de modèles pleinement 3D. Une inversion basée sur un modèle 3D devient inabordable pour plus de deux paramètres à la fois en raison de temps CPU particulièrement élevés. L’objectif de ce travail est d’examiner l’importance des effets 3D sur la performance et la fiabilité des procédures d’inversion habituellement utilisées dans les problèmes de l’acoustique sous-marine. Pour cela, on se place dans un guide d’onde océanique à géométrie inclinée. Des expérimentations à échelle réduite sont menées afin d’identifier et d’interpréter les effets 3D. Une procédure d’inversion par champs d’onde adaptés, formulée dans un cadre Bayesien et basée sur la recherche exhaustive dans l’espace des paramètres, est élaborée. L’inversion s’effectue en comparant des données basse fréquence du champ acoustique, recueillies le long d’antennes linéaires verticales ou horizontales, aux répliques générées par des modèles d’équation parabolique 2D et 3D. Les paramètres importants sont identifiés au moyen d’une étude de sensibilité de la fonction de coût. Dans une étape préliminaire, la performance de l’inversion est étudiée, sur données synthétiques bruitées, dans un cas simple permettant l’utilisation de modèles 2D. Une stratégied’inversion en sous-espaces résultant en une réduction importante des temps CPU pour l’inversion, est examinée. L’inversion est ensuite abordée en présence d’un fond incliné. La possibilité et les limites d’une inversion basée sur un modèle 2D sont explorées. Cette approche, mise en œuvre sur données synthétiques, met en évidence la pertinence de l’utilisation de modèles 2D en champ relativement proche. Une inversion basée sur un modèle 3D n’étant alors nécessaire que pour la pente, des temps CPU raisonnables sont ainsi réalisés. En revanche, en champ lointain, nous sommes confrontés à un risque potentiel d’estimation erronée et le recours à une modélisation 3D devient nécessaire. / This work deals with the three-dimensional (3D) aspect of sound propagation in shallow-water oceanic environments with respect to inverse problems. Inverse problems in underwater acoustics are based on twodimensional (2D) modeling of sound propagation, hence ignoring the effects of horizontal refraction, referred to as 3D propagation effects. However, the acoustic propagation in shallow-water environments, like the continental shelf, may be affected by 3D effects requiring 3D modeling to be accounted for. An inversion based on a 3D model for more than two parameters at a time becomes prohibitive due to dramatically increased CPU times. The aim of this work is to investigate the importance of the 3D effects with respect to the performance and reliability of the inversion procedures typically applied in problems of underwater acoustics. To this aim, we focus on a wedge-shaped oceanic wave guide. Laboratory scale experiments of long-range acoustic propagation are performed to identify and interpret the 3D effects due to a sloping bottom, as predicted by numerical simulations. A matched-field inversion procedure implemented within a Bayesian framework and based on the exhaustive search over the parameter space is elaborated. The inversion is performed by comparing low frequency acoustic field data, collected along vertical or horizontal line arrays, to replica generated from 2D and 3D parabolic equation codes. The recoverable parameters are identified by means of a sensitivity study of the cost function. In a preliminary step, the inversion performance is investigated on noisy synthetic data in a simple waveguide where 2D codes apply. A ubspace inversion strategy providing significant reduction in CPU times is examined. The inversion in the presence of a sloping bottom is then considered. The feasibility and the limits of an inversion matching replica from a 2D code are explored. This approach, applied on synthetic data, highlights the relevance of using 2D codes at relatively short ranges. An inversion based on a 3D code is thus only needed for the slope, and reasonable CPU times are achieved. On the other hand, important mismatch might occur at farther ranges and 3D modeling is required.

Cette thèse propose une technique innovante de diagnostic non invasive pour les systèmes piles à combustible. Cette technique s’appuie sur la mesure de la signature magnétique générée par ces systèmes. A l'aide de ces champs magnétiques externes, il est possible d'obtenir une cartographie de la densité de courant interne par résolution d'un problème inverse. Ce problème est néanmoins mal posé : la solution est non unique et est extrêmement sensible au bruit. Des techniques de régularisation ont ainsi été mises en place pour filtrer les erreurs de mesures et obtenir une solution physiquement acceptable. Afin d'augmenter la qualité de reconstruction des courants, nous avons conçu notre outil de diagnostic de manière à ce qu'il soit uniquement sensible aux défaillances de la pile (capteur de défauts). De plus, cette reconstruction se base sur un nombre extrêmement faible de mesures. Une telle approche facilite l'instrumentation du système et augmente la précision et la rapidité de celui-ci. La sensibilité de notre outil à certaines défaillances (assèchements, appauvrissement en réactifs, dégradations) est démontrée. / This thesis proposes a new non invasive technique for fuel cell diagnosis. This technique relies on the measurements of the magnetic field signature created by these systems. By solving an inverse problem, it is possible to get an internal current density map. However, the inverse problem is ill-posed: the solution is not unique and it is extremely sensitive to noise. Regularization techniques were used in order to filter out measurement errors and to obtain physical realistic solutions. In order to improve the quality of the current density estimators, a diagnostic tool was built which is only sensitive to faults occurring inside the fuel cell (fault sensor). More over, our approach is based on a very low number of measurements. Such technique simplifies the experimental setup and improves the accuracy and the speed of the diagnostic tool. The sensitivity of our tool to some faults (drying out, oxygen starvation and ageing) is demonstrated.

La recherche et les questions abordées dans cette thèse sont de type inverse : la reconstitution d'une source ponctuelle ou la complétion d'une donnée à la limite inconnue à l'extrémité du domaine dans les modèles paraboliques de transport de contaminants. La modélisation mathématique des problèmes de pollution des eaux fait intervenir deux traceurs, l'oxygène dissous (OD) et la demande biochimique en oxygène (DBO) qui est la quantité d'oxygène nécessaire à la biodégradation de la matière organique. En effet, au cours des procédés d'autoépuration, certaines bactéries aérobies jouent un rôle principal. Ces micro-organismes décomposent les matières organiques polluantes en utilisant l'oxygène dissous dans le milieu. Afin de compenser ces données manquantes, les champs, solutions du problème, sont observés directement ou indirectement. Les problèmes inverses qui en résultent sont quasi certainement mal-posés voire même sévèrement mal-posés pour la plupart. Dans cette thèse, nous proposons justement une analyse aussi poussée que possible sur la question de l'identifiabilité pour les deux problèmes inverses décrits ci-dessus. Nous avons démontré un résultat d'unicité pour des sources fixes dans le cas d'observations décalées. La réalité pour l'observation est nuancée et l'idéal n'est pas acquis ; des mesures directes sur la DBO sont difficiles à obtenir. En revanche collecter des données sur l'OD est possible en temps réel et avec un faible coût. La DBO est donc observée de façon indirecte, grâce au couplage dans le système de Streeter et Phelps, l'information passe de l'OD à la DBO. Pour ce problème aussi, nous avons produit un résultat d'unicité pour la reconstruction de la source ou puits ponctuel qui serait présent dans l'équation de transport sur l'OD. Nous avons ensuite examiné des questions annexes à l'identifiabilité telles que le degré d'instabilité des équations à résoudre. De ce type d'informations dépendent le comportement des méthodes numériques et des algorithmes de calcul à utiliser. / The research and the questions approached on this thesis are inverse type : the reconstruction of point-wise source or the data completion problem in parabolic models of transport of contaminants. The mathematical modelling of the problems of water pollution includes two tracers, the dissolved oxygen (DO) and the biochemical demand in oxygen (BDO) which is the quantity of oxygen necessary for the biodegradation of organic matter. Indeed, during the biodegradation process, aerobic bacteria play a leading part. These micro-organisms decompose polluting organic matters by using the dissolved oxygen in the middle. To compensate these missing data, fields, solutions of the problem, are observed directly or indirectly. The resulting inverse problems are ill-posed. Their mathematical study rises big complications and their numerical treatment isn't easy. We demonstrated a uniqueness result for fixed sources in the case of moved observations. The reality for the observation is qualified and the ideal is not acquired; direct measures on the BOD are difficult to obtain. On the Other hand to collect data on the DO is possible in real time With a moderate cost. The BOD is thus observed in indirect way, thanks to the coupling in the system of Streeter and Phelps, the information passes from the DO to the BOD. For this problem, we produced a uniqueness result for the reconstruction of source. Then, we examined the degree of instability of the equation to be solved. The behaviour of numerical methods depend on this type of information.

Engineers have long been inspired by nature's flyers. Such animals navigate complex environments gracefully and efficiently by using a variety of evolutionary adaptations for high-performance flight. Biologists have discovered a variety of sensory adaptations that provide flow state feedback and allow flying animals to feel their way through flight. A specialized skeletal wing structure and plethora of robust, adaptable sensory systems together allow nature's flyers to adapt to myriad flight conditions and regimes. In this work, motivated by biology and the successes of bio-inspired, engineered aerial vehicles, linear quadratic control of a flexible, morphing wing design is investigated, helping to pave the way for truly autonomous, mission-adaptive craft. The proposed control algorithm is demonstrated to morph a wing into desired positions. Furthermore, motivated specifically by the sensory adaptations organisms possess, this work transitions to an investigation of aircraft wing load identification using structural response as measured by distributed sensors. A novel, recursive estimation algorithm is utilized to recursively solve the inverse problem of load identification, providing both wing structural and aerodynamic states for use in a feedback control, mission-adaptive framework. The recursive load identification algorithm is demonstrated to provide accurate load estimate in both simulation and experiment. / Graduation date: 2012

A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance in structural dynamics. Unfortunately, unlike the case of deterministic oscillators, available numerical or numeric-analytic integration schemes for stochastically driven oscillators, often modelled through stochastic differential equations (SDE-s), have significantly poorer numerical accuracy. These schemes are generally derived through stochastic Taylor expansions and the limited accuracy results from difficulties in evaluating the multiple stochastic integrals. We propose a few higher-order methods based on the stochastic version of transversal linearization and another method of linearizing the nonlinear drift field based on a Girsanov change of measures. When these schemes are implemented within a Monte Carlo framework for computing the response statistics, one typically needs repeated simulations over a large ensemble. The statistical error due to the finiteness of the ensemble (of size N, say)is of order 1/√N, which implies a rather slow convergence as N→∞. Given the prohibitively large computational cost as N increases, a variance reduction strategy that enables computing accurate response statistics for small N is considered useful. This leads us to propose a weak variance reduction strategy. Finally, we use the explicit derivative-free linearization techniques for state and parameter estimations for structural systems using the extended Kalman filter (EKF). A two-stage version of the EKF (2-EKF) is also proposed so as to account for errors due to linearization and unmodelled dynamics. In Chapter 2, we develop higher order locally transversal linearization (LTL) techniques for strong and weak solutions of stochastically driven nonlinear oscillators. For developing the higher-order methods, we expand the non-linear drift and multiplicative diffusion fields based on backward Euler and Newmark expansions while simultaneously satisfying the original vector field at the forward time instant where we intend to find the discretized solution. Since the non-linear vector fields are conditioned on the solution we wish to determine, the methods are implicit. We also report explicit versions of such linearization schemes via simple modifications. Local error estimates are provided for weak solutions. Weak linearized solutions enable faster computation vis-à-vis their strong counterparts. In Chapter 3, we propose another weak linearization method for non-linear oscillators under stochastic excitations based on Girsanov transformation of measures. Here, the non-linear drift vector is appropriately linearized such that the resulting SDE is analytically solvable. In order to account for the error in replacing of non-linear drift terms, the linearized solutions are multiplied by scalar weighting function. The weighting function is the solution of a scalar SDE(i.e.,Radon-Nikodym derivative). Apart from numerically illustrating the method through applications to non-linear oscillators, we also use the Girsanov transformation of measures to correct the truncation errors in lower order discretizations. In order to achieve efficiency in the computation of response statistics via Monte Carlo simulation, we propose in Chapter 4 a weak variance reduction strategy such that the ensemble size is significantly reduced without seriously affecting the accuracy of the predicted expectations of any smooth function of the response vector. The basis of the variance reduction strategy is to appropriately augment the governing system equations and then weakly replace the associated stochastic forcing functions through variance-reduced functions. In the process, the additional computational cost due to system augmentation is generally far less besides the accrued advantages due to a drastically reduced ensemble size. The variance reduction scheme is illustrated through applications to several non-linear oscillators, including a 3-DOF system. Finally, in Chapter 5, we exploit the explicit forms of the LTL techniques for state and parameters estimations of non-linear oscillators of engineering interest using a novel derivative-free EKF and a 2-EKF. In the derivative-free EKF, we use one-term, Euler and Newmark replacements for linearizations of the non-linear drift terms. In the 2-EKF, we use bias terms to account for errors due to lower order linearization and unmodelled dynamics in the mathematical model. Numerical studies establish the relative advantages of EKF-DLL as well as 2-EKF over the conventional forms of EKF. The thesis is concluded in Chapter 6 with an overall summary of the contributions made and suggestions for future research.

CAPES / Em ensaios não destrutivos por ultrassom, o sinal obtido a partir de um sistema de aquisição de dados real podem estar contaminados por ruído e os ecos podem ter atrasos de tempo subamostrais. Em alguns casos, esses aspectos podem comprometer a informação obtida de um sinal por um sistema de aquisição. Para lidar com essas situações, podem ser utilizadas técnicas de estimativa de atraso temporal (Time Delay Estimation ou TDE) e também técnicas de reconstrução de sinais, para realizar aproximações e obter mais informações sobre o conjunto de dados. As técnicas de TDE podem ser utilizadas com diversas finalidades na defectoscopia, como por exemplo, para a localização precisa de defeitos em peças, no monitoramento da taxa de corrosão em peças, na medição da espessura de um determinado material e etc. Já os métodos de reconstrução de dados possuem uma vasta gama de aplicação, como nos NDT, no imageamento médico, em telecomunicações e etc. Em geral, a maioria das técnicas de estimativa de atraso temporal requerem um modelo de sinal com precisão elevada, caso contrário, a localização dessa estimativa pode ter sua qualidade reduzida. Neste trabalho, é proposto um esquema alternado que estima de forma conjunta, uma referência de eco e atrasos de tempo para vários ecos a partir de medições ruidosas. Além disso, reinterpretando as técnicas utilizadas a partir de uma perspectiva probabilística, estendem-se suas funcionalidades através de uma aplicação conjunta de um estimador de máxima verossimilhança (Maximum Likelihood Estimation ou MLE) e um estimador máximo a posteriori (MAP). Finalmente, através de simulações, resultados são apresentados para demonstrar a superioridade do método proposto em relação aos métodos convencionais. / Abstract (parágrafo único): In non-destructive testing (NDT) with ultrasound, the signal obtained from a real data acquisition system may be contaminated by noise and the echoes may have sub-sample time delays. In some cases, these aspects may compromise the information obtained from a signal by an acquisition system. To deal with these situations, Time Delay Estimation (TDE) techniques and signal reconstruction techniques can be used to perform approximations and also to obtain more information about the data set. TDE techniques can be used for a number of purposes in the defectoscopy, for example, for accurate location of defects in parts, monitoring the corrosion rate in pieces, measuring the thickness of a given material, and so on. Data reconstruction methods have a wide range of applications, such as NDT, medical imaging, telecommunications and so on. In general, most time delay estimation techniques require a high precision signal model, otherwise the location of this estimate may have reduced quality. In this work, an alternative scheme is proposed that jointly estimates an echo model and time delays for several echoes from noisy measurements. In addition, by reinterpreting the utilized techniques from a probabilistic perspective, its functionalities are extended through a joint application of a maximum likelihood estimator (MLE) and a maximum a posteriori (MAP) estimator. Finally, through simulations, results are presented to demonstrate the superiority of the proposed method over conventional methods.

CNPq; FUNTEF-PR / Sensores wire-mesh (WMS) são capazes de gerar imagens da seção transversal de escoamentos multifásicos e tem sido amplamente utilizados para investigar fenômenos de escoamentos em plantas piloto. Tais dispositivos são capazes de medir parâmetros de escoamento tais como distribuição da fração de fase (por exemplo fração de gás ou líquido) e visualizar escoamentos multifásicos com alta resolução temporal e espacial. Sendo portanto, uma ferramenta importante para investigações de escoamentos mais detalhadas. No entanto, seu princípio de medição é baseado em eletrodos intrusivos posicionados dentro do tubo onde o escoamento flui. A resolução da imagem gerada pelo sensor é dada pelo número de cruzamentos entre os fios transmissores e receptores. Em muitos processos, no entanto, efeitos de intrusividade de tal sensor pode ser uma limitação no seu uso. Por isso, um número reduzido de fios poderia permitir uma expansão do campo de aplicações do sensor wire-mesh. Por essa razão, o presente trabalho sugere um método de reconstrução de imagem para aumentar a resolução dos dados de um sensor wire-mesh com um número de eletrodos menor que o ótimo. Desta forma, os efeitos de intrusividade no processo investigado poderiam ser reduzidos. O método de reconstrução é baseado em uma abordagem estatística de regularização e é conhecido como Maximum a Posteriori (MAP). Dados de escoamento de um WMS 16x16 são usados para determinar um modelo gaussiano multivariável do escoamento, o qual são empregados como regularização na reconstrução. Uma matriz de sensitividade é estimada pelo método de elementos finitos (FEM) para incorporar o algoritmo MAP. Dados experimentais são usados para validar o método proposto, sendo comparado com interpolação do tipo spline. Resultados experimentais mostram que a reconstrução por MAP possui um desempenho melhor do que interpolação do tipo spline, alcançando desvios de fração de vazio dentro de uma faixa de ± 10% na grande maioria dos pontos de operação. A validação foi executada em um loop de escoamento horizontal água/gás em regime intermitente (golfada). / Wire-mesh sensors (WMS) are able to generate cross-sectional images of multiphase flow and have been widely used to investigate flow phenomena in pilot plant studies. Such devices are able to measure flow parameters such as phase fraction (e.g. gas/liquid fraction) distribution and visualize multiphase flows with high temporal and spatial resolution. Hence, being important tool for detailed flow investigation. However, its sensing principle is based on intrusive electrodes placed inside the pipe where a multiphase flow streams. The image resolution generated by the sensor is given by the number of crossing points formed by the transmitter and receptor wires. In many processes, however, the intrusive effect of such sensor might be a limitation on its use. Therefore, a reduced number of wires could possibly increase the application field of wire-mesh sensors. For this reason, the present work presents an image reconstruction method to increase resolution of WMS data with less than optimal number of electrode wires. In this way, a reduction of intrusive effects on the process under investigation may be achieved. The reconstruction method is based on statistical view of regularization and is known as Maximum a Posterior (MAP). 16x16 WMS flow data are used to determine a Multivariate Gaussian flow model, which in turn is used as regularization in the reconstruction. A sensitive matrix is estimated by finite element method (FEM) to incorporate MAP algorithm. Experimental data are used to validate the proposed method, which is compared with spline interpolation. Experimental results show that the MAP reconstruction performs better than interpolation and achieves deviation in gas void fraction estimation in the range of ±10% in the vast majority of operating points. The tests were performed in a horizontal water-gas flow loop operating at intermittent (slug) flow regime.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, três técnicas para resolver numericamente problemas inversos de transporte de partículas neutras a uma velocidade para aplicações em engenharia nuclear são desenvolvidas. É fato conhecido que problemas diretos estacionários e monoenergéticos de transporte são caracterizados por estimar o fluxo de partículas como uma função-distribuição das variáveis independentes de espaço e de direção de movimento, quando os parâmetros materiais (seções de choque macroscópicas), a geometria, e o fluxo incidente nos contornos do domínio (condições de contorno), bem como a distribuição de fonte interior são conhecidos. Por outro lado, problemas inversos, neste trabalho, buscam estimativas para o fluxo incidente no contorno, ou a fonte interior, ou frações vazio em barras homogêneas. O modelo matemático usado tanto para os problemas diretos como para os problemas inversos é a equação de transporte independente do tempo, a uma velocidade, em geometria unidimensional e com o espalhamento linearmente anisotrópico na formulação de ordenadas discretas (SN). Nos problemas inversos de valor de contorno, dado o fluxo emergente em um extremo da barra, medido por um detector de nêutrons, por exemplo, buscamos uma estimativa precisa para o fluxo incidente no extremo oposto. Por outro lado, nos problemas inversos SN de fonte interior, buscamos uma estimativa precisa para a fonte armazenada no interior do domínio para fins de blindagem, sendo dado o fluxo emergente no contorno da barra. Além disso, nos problemas inversos SN de fração de vazio, dado o fluxo emergente em uma fronteira da barra devido ao fluxo incidente prescrito no extremo oposto, procuramos por uma estimativa precisa da fração de vazio no interior da barra, no contexto de ensaios não-destrutivos para aplicações na indústria. O código computacional desenvolvido neste trabalho apresenta o método espectronodal de malha grossa spectral Greens function (SGF) para os problemas diretos SN em geometria unidimensional para gerar soluções numéricas precisas para os três problemas inversos SN descritos acima. Para os problemas inversos SN de valor de contorno e de fonte interior, usamos a propriedade da proporcionalidade da fuga de partículas; ademais, para os problemas inversos SN de fração de vazio, oferecemos a técnica a qual nos referimos como o método físico da bissecção. Apresentamos resultados numéricos para ilustrar a precisão das três técnicas, conforme descrito nesta tese. / In this work, three techniques for numerically solving one-speed neutral particle inverse transport problems for nuclear engineering applications are developed. It is well known that direct steady-state monoenergetic transport problems are characterized by estimating the flux of particles as a distribution function of space and direction-of-motion independent variables, when the material parameters (cross sections), the geometry, and the incoming flux at the boundaries of the domain (boundary conditions), as well as the interior source distribution are known. Conversely, inverse problems, in this work, seek for estimates to the incident boundary flux, or interior source, or void fractions in homogeneous slabs. The mathematical model used for direct and inverse problems is the time-independent one-speed slab-geometry transport equation with linearly anisotropic scattering in the discrete ordinates (SN) formulation. In the boundary-value inverse problems, given the existing flux at one boundary of the slab, as measured by a neutron detector, for example, we seek for accurate estimate for the incident flux at the opposite boundary. On the other hand, in the interior source inverse SN problems, we seek for accurate estimate for the interior source stored within the slab for shielding purpose, given the exiting flux at the boundary of the slab. Furthermore, as with the void fraction inverse SN problems, given the exiting flux at one boundary of the slab due to prescribed incident flux at the opposite boundary, we seek for accurate estimate of the void fraction within the slab in the context of non-destructive testing applications in industry. The computer code developed in this work presents the coarse-mesh spectral Greens function (SGF) nodal method for direct SN problems in slab geometry to generate accurate numerical solutions to the three inverse SN problems described above. For the boundary-value and interior source inverse SN problems, we use the proportionality property of the leakage of particles; moreover, for the void fraction inverse SN problems, we offer the technique that we refer to as the physical bisection method. We present numerical results to illustrate the accuracy of the three techniques, as described in this dissertation.