Cette étude est consacrée à la modélisation spatio-temporelle de la pollution atmosphérique urbaine en utilisant un ensemble de méthodes statistiques exploitant les mesures de concentrations de polluants (NO2, O3) fournies par un réseau de surveillance de la qualité de l'air (AIRPARIF). Le principal objectif visé est l'amélioration de la cartographie des champs de concentration de polluants (le domaine d'intérêt étant la région d'Île-de-France) en utilisant, d'une part, des méthodes d'interpolation basées sur la structure spatiale ou spatio-temporelle des observations (krigeage spatial ou spatio-temporel), et d'autre part, des algorithmes, prenant en compte les mesures, pour corriger les sorties d'un modèle déterministe (Filtre de Kalman d'Ensemble). Les résultats obtenus montrent que dans le cas du dioxyde d'azote la cartographie basée uniquement sur l'interpolation spatiale (le krigeage) conduit à des résultats satisfaisants, car la répartition spatiale des stations est bonne. En revanche, pour l'ozone, c'est l'assimilation séquentielle de données appliquée au modèle (CHIMERE) qui permet une meilleure reconstitution de la forme et de la position du panache pendant les épisodes de forte pollution analysés. En complément de la cartographie, un autre but de ce travail est d'effectuer localement la prévision des niveaux d'ozone sur un horizon de 24 heures. L'approche choisie est celle mettant en œuvre des méthodes de type réseaux neuronaux. Les résultats obtenus en appliquant deux types d'architectures neuronales indiquent une précision correcte surtout pour les 8 premières heures de l'horizon de prédiction / This study is devoted to the spatio-temporal modelling of air pollution at a regional scale using a set of statistical methods in order to treat the measurements of pollutant concentrations (NO2, O3) provided by an air quality monitoring network (AIRPARIF). The main objective is the improvement of the pollutant _elds mapping using either interpolation methods based on the spatial or spatio-temporal structure of the data (spatial or spatiotemporal kriging) or some algorithms taking into account the observations, in order to correct the concentrations simulated by a deterministic model (Ensemble Kalman Filter). The results show that nitrogen dioxide mapping based only on spatial interpolation (kriging) gives the best results, while the spatial repartition of the monitoring sites is good. For the ozone mapping it is the sequential data assimilation that leads us to a better reconstruction of the plume's form and position for the analyzed cases. Complementary to the pollutant mapping, another objective was to perform a local prediction of ozone concentrations on a 24-hour horizon; this task was performed using Artificial Neural Networks. The performance indices obtained using two types of neural architectures indicate a fair accuracy especially for the first 8 hours of prediction horizon

Dans le monde industriel comme dans le monde scientifique, le développement de capteurs a toujours répondu à la volonté d’observer l’inobservable. La caméra rapide fait partie de ceux-là puisqu’elle permet de dévoiler des dynamiques invisibles, de la formation de fissure au vol du moustique. Dans un environnement extrêmement concurrentiel, ces caméras sont principalement limitées par le nombre d’images acquises par seconde. Le but de cette thèse est d’augmenter la capacité de dévoiler la dynamique invisible en enrichissant l’acquisition initiale par des modèles dynamiques. La problématique consiste alors à élaborer des méthodes permettant de relier en temps réel un modèle et la perception d’un système réel. Les bénéfices de cette utilisation offrent ainsi la possibilité de faire de l’interpolation, de la prédiction et de l’identification. Cette thèse est composée de trois parties. La première est axée sur la philosophie du traitement vidéo et propose d’utiliser des modèles élémentaires et génériques. Un algorithme d’estimation de grands mouvements est proposé mais l’approche actuellement proposée n’est pas assez générique pour être exploitée dans un contexte industriel. La deuxième partie propose d’utiliser des méthodes d’assimilation de données séquentielle basées sur la famille des filtres de Kalman afin d’associer un modèle avec des observations par caméras rapides pour des systèmes mécaniques. La troisième partie est une application à l’analyse modale expérimentale non linéaire. Deux schémas d’assimilation temps réel multicapteurs sont présentés et leur mise en œuvre est illustrée pour de la reconstruction 3D et de la magnification. / The development of sensors has always followed the ambition of industrial and scientific people to observe the unobservable. High speed cameras are part of this adventure, revealing invisible dynamics such as cracks formation or subtle mosquito flight. Industrial high speed vision is a very competitive domain in which cameras stand out through their acquisition speed. This thesis aims to broaden their capacity by augmenting the initial acquisition with dynamic models. This work proposes to develop methods linking in real time a model with a real system. Aimed benefits are interpolation, prediction and identification. Three parts are developed. The first one is based on video processing and submits to use kinematic elementary and generic models. An algorithm of motion estimation for large movements is proposed but the generic nature does not allow a sufficient knowledge to be conclusive. The second part proposes using sequential data assimilation methods known as Kalman filters. A scheme to assimilate video data with a mechanical model is successfully implemented. An application of data assimilation in modal analysis is developed. Two multi sensors real time assimilation schemes for nonlinear modal identification are proposed. These schemes are integrated in two applications on 3D reconstruction and motion magnification.

Depuis la révolution industrielle, les croissances économique et démographique ont augmenté de manière exponentielle induisant l’augmentation de la combustion d’énergies fossiles, telles que le charbon, le pétrole, et le gaz naturel. La combustion de ces sources d’énergie conduit à l’émission de gaz à effet de serre, principalement le dioxyde de carbone (CO2) et le méthane (CH4), qui par leur accumulation dans l’atmosphère entraînent une augmentation de l’effet de serre. Selon le GIEC (Groupe d'experts Intergouvernemental sur l'Évolution du Climat), l’implication des émissions anthropiques dans l’augmentation de l’effet de serre est extrêmement probable avec un pourcentage de certitude qui dépasse 95%. Toutefois, l’estimation des bilans régionaux d'émissions de GES reste très incertaine. L’objectif de cette thèse est de contribuer à l’amélioration de l’estimation des bilans régionaux de GES en France, en utilisant pour la première fois les concentrations atmosphériques du CO2 et de CH4 mesurées par le réseau ICOS (Integrated Carbon Observation System) et la modélisation inverse à l’échelle régionale.Dans un premier temps, on s’est focalisé sur l’étude des concentrations mesurées de CO2, CH4 et CO (monoxyde de carbone) fournis par des stations de surface. Cette étude a pour objectif l'identification des mesures atmosphériques contaminées par les émissions locales (quelques kilomètres au tour de la station) et qui provoque ce qu’on appelle « les pics de concentrations ». Trois méthodes ont été appliquées sur des séries temporelles fournies par quatre stations du réseau ICOS, afin de déterminer leur degré de contamination. Les résultats des différentes méthodes ont été comparés entre eux, puis comparés à un inventaire de données contaminées préparé manuellement par les gestionnaires des stations. Cette comparaison a permis l’évaluation de la performance des trois méthodes pour la détection réussie des pics. À l’issue de ce travail, la méthode la plus performante a été proposée pour effectuer un nettoyage automatique des séries de mesure du réseau ICOS.Dans un deuxième temps, le modèle régional de chimie-transport CHIMERE est utilisé pour simuler les concentrations atmosphériques du CO2 et du CH4 de l’année 2014 sur un domaine centré sur la France. L’objectif de cette étude est d’étudier la sensibilité des concentrations simulées en utilisant différentes données d’entrées. Premièrement, on étudie la sensibilité des concentrations simulées par rapport au transport en utilisant deux modèles météorologiques AROME et ECMWF. Deuxièmes, on analyse la sensibilité des concentrations simulées face aux différentes cartes d’émissions. Dans cette dernière étape, on étudie les différences entre les cartes d’émissions anthropiques séparément des cartes d’émissions biogéniques. Ce travail nous permet de quantifier à la fois les erreurs liées aux transports et les erreurs liées aux flux d’émissions. La meilleure combinaison des données d’entrée va être sélectionnée pour l’étape d’inversion des flux.Dans un dernier plan, les mesures atmosphériques des concentrations de CO2 et du CH4 sont utilisées par le système d’inversion PYMAI (Berchet et coll., 2013 et 2015) afin d’estimer les bilans régionaux d'émissions des principaux GES en France. L’inversion s’est exécutée pour un mois d’hiver (janvier) et un mois d’été (juillet) en utilisant le modèle de transport CHIMERE forcé par ECMWF et les flux de surface (EDGAR et VPRM). Le résultat de ce travail permet une réduction des incertitudes des bilans nationaux à hauteur de 35 %, et la quantification les émissions de CO2 et de CH4 à l'échelle nationale et régionale. Par contre, cette inversion ne contraint que partiellement les flux d’émissions. Cependant, la question sur l’efficacité de la quantité d’informations disponibles ressort à nouveau. / Since the industrial revolution, the economic and the demographic growths have increased exponentially,leading to an enhancement of the fossil fuels combustion, such as coal, oil, and natural gas. Consumingthese source of energy amplifies the greenhouse gas emissions, mainly carbon dioxide (CO2) and methane(CH4), whose accumulation in the atmosphere lead to the increase of the greenhouse effect. According tothe 5th assessment report of the Intergovernmental Panel on Climate Change (IPCC), it is extremely likely(95-100% of certainty) that the observed increase in the greenhouse effect is related to the increase of theanthropogenic emissions. However, the estimations of the GHG budget at the regional and the nationalscales remains highly uncertain. The aim of this thesis is to improve the estimation of the CO2 and CH4fluxes in France, using data assimilation techniques and atmospheric measurements provided by theIntegrated Carbon Observation System (ICOS) network.The first phase focuses on analyzing the measured CO2, CH4, and CO (Carbon monoxide) atmosphericconcentrations provided by surface monitoring stations. This study is concerned with the problem ofidentifying atmospheric data influenced by local emissions that can result in spikes in the GHG time series.Three methods are implemented on continuous measurements of four contrasted atmospheric sites. The aimof this analysis is to evaluate the performance of the used methods for the correctly detect the contaminateddata. This work allows us to select the most reliable method that was proposed to perform daily spikedetection in the ICOS Atmospheric Thematic Centre Quality Control (ATC-QC) software.Secondly, we simulate the atmospheric concentrations of CO2 and CH4 using the chemistry transport modelCHIMERE in a domain centered over France for the year 2014. The objective of this study is to evaluate thesensitivity of simulated concentrations using different input data (sensitivity to the meteorological transportand sensitivity to the surface fluxes). This work led to the quantification of both the transport and surfacefluxes errors based on the combination of different simulations. Thus, the most reliable combination of thebest input data was selected for the flux inversion study.Lastly, the measured CO2 and CH4 concentrations are used by the PYMAI inversion system (Berchet et al.,2013 and 2015) in order to estimate the CO2 and CH4 fluxes in France. The Inversion is performed for onemonth in winter (January) and one month in summer (July), using the transport model CHIMERE. Theinversion results have provided very interesting results for the regional estimation of the CO2 and CH4surface fluxes in France with an uncertainty reduction that may attain 35% of the national totals.

Depuis plusieurs années, les évolutions considérables survenues au niveau des moyens de calcul à disposition ont entraîné de nouvelles pratiques de simulation des structures mécaniques. Parmi ces nouvelles pratiques celle qui motive ces travaux de thèse est le paradigme Dynamic Data Driven Application Systems (DDDAS). L’idée fondatrice de cette approche est de mettre en place un dialogue entre un système physique et son modèle numérique. L’objectif est alors de (i) permettre un recalage du modèle numérique à l’aide de mesures faites sur le système physique ; (ii) contrôler l’évolution du système physique à l’aide de la prédiction faite par la simulation numérique. La difficulté majeure est de réaliser ce dialogue en temps réel. Ces travaux de thèse se focalisent sur l’étape de recalage de modèle du paradigme DDDAS. La problématique est alors de développer des méthodes et outils de résolution de problèmes inverses prenant en compte diverses contraintes à savoir : (i) une robustesse vis-à-vis des données corrompues ; (ii) une généricité permettant de considérer une grande variété de problèmes et de modèles mécaniques ; (iii) un temps de calcul réduit afin de tendre vers un recalage de modèle en temps réel. Le point de départ de ces travaux est l’Erreur en Relation de Comportement modifiée, approche énergétique dédiée à la résolution des problèmes inverses en mécanique, s’étant notamment illustrée par sa grande robustesse vis-à-vis des bruits de mesure. Dans un premier temps, afin de garantir un processus d’identification rapide, nous avons couplé l’Erreur en Relation de Comportement modifiée avec la réduction de modèle PGD dans le cadre de modèle linéaire, permettant ainsi de mettre en place un processus d’identification rapide et automatique. Ensuite, dans le but d’être appliquée au paradigme DDDAS, nous avons développé une démarche d’identification reposant sur un processus d’assimilation de données (le filtre de Kalman) et utilisant l’Erreur en Relation de Comportement modifiée comme opérateur d’observation toujours dans le cadre de problèmes linéaires. Nous avons ensuite étendu cette méthode d’assimilation de données à la problématique de l’identification de champs de paramètres en introduisant une séparation des discrétisations spatiales et des outils provenant de l’adaptation de maillage. Nous avons ensuite abordé la problématique des modèles mécaniques non-linéaires, au travers de modèles d’endommagement et de visco-plasticité. Pour cela nous avons dans un premier temps reformulé et étendu le concept d’Erreur en Relation de Comportement modifiée à ce cadre non-linéaire matériau et nous avons mis en place un processus de résolution dédié, s’inspirant de la méthode LaTIn. Pour finir nous avons introduit cette reformulation de l’Erreur en Relation de Comportement modifiée au sein de la méthode d’assimilation de données développée précédemment afin de traiter le recalage dynamique de modèles non-linéaires. / For several years, the considerable changes that have occurredin computing tools have led to new practices in the simulation of mechanical structures. Among them, the motivation for this work is the Dynamic Data Driven Application Systems paradigm (DDDAS). The founding idea of this approach is to establish a dialogue between a physical system and its numericalmodel. The objective is then to (i) allow a calibration of the numerical model by means of measurements performed on the physical system; (ii) control the evolution of the physical system using theprediction given by numerical simulation. The major difficulty is to realize this dialogue in real time. This work focuses on the model updating step of the DDDAS paradigm. The problem is then to develop methods and tools to solve inverse problems taking into account various constraints, namely: (i) robustness with respect to corrupted data; (ii) genericity for considering a wide variety of problems and mechanical models; (iii) a reduced computation time in order to tend towards a real-time model updating.The starting point of this work is the modified Constitutive Relation Error, an energetic approach dedicated to the solution of inverse problems in mechanics, notably illustrated by its robustness with respect to measurement noises. First, in order to guarantee a fast identification process, we have coupled the modified Constitutive Relation Error with the PGD model reduction in the linear model framework, thus enabling a fast and automatic identification process. Then, in order to be applied to the DDDAS paradigm, we have developed an identification method based on a data assimilation process (the Kalman filter) and using the modified Constitutive Relation Error as an observer alwayswithin the framework of linear problems. We have then extended this data assimilation approach to the problem of the identification of parameter fields by introducing a separation of the spatial discretizations and by introducing tools resulting from the mesh adaptation framework. We have then addressed the problem of non-linear mechanical models, through damage and visco-plasticitymodels. To this end, we have first recast and extended the concept of the modified Constitutive Relation Error to this nonlinear material framework and we have implemented a dedicated resolution process, based on the LaTIn method. Finally, we have introduced this reformulation of the modified Constitutive Relation Error in the previously data assimilation method in order to process the model updating of nonlinear models.

[pt] Simulação de reservatórios de óleo e gás é uma demanda comum em engenharia de petróleo e pesquisas relacionadas, que pode requerer um elevado custo computacional de tempo e processamento ao resolver um problema matemático. Além disso, alguns métodos de caracterização de reservatórios necessitam múltiplas iterações, resultando em muitas simulações para obter um resultado. Também podemos citar os métodos baseados em conjunto, tais como o ensemble Kalman filter, o EnKF, e o Ensemble Smoother With Multiple Data Assimilation,o ES-MDA, que requerem muitas simulações. Em contrapartida, o uso de aprendizado de máquina cresceu bastante na indústria de energia. Isto pode melhorar a acurácia de predição, otimizar estratégias e outros. Visando reduzir as complexidades de simulação de reservatórios, este trabalho investiga o uso de aprendizado de máquina como uma alternativa a simuladores convencionais. O modelo Random Forest Regressor é testado para reproduzir respostas de pressão em um reservatório multi-região radial composto. Uma solução analítica é utilizada para gerar o conjunto de treino e teste para o modelo. A partir de experimentação e análise, este trabalho tem o objetivo de suplementar a utilização de aprendizado de máquina na indústria de energia. / [en] Oil and gas reservoir simulation is a common demand in petroleum engineering, and research, which may have a high computational cost, solving a mathematical numeric problem, or high computational time. Moreover, several reservoir characterization methods require multiple iterations, resulting in many simulations to obtain a reasonable characterization. It is also possible to mention ensemble-based methods, such as the ensemble Kalman filter, EnKF, and the Ensemble Smoother With Multiple Data Assimilation, ES-MDA, which demand lots of simulation runs to provide the output result. As a result, reservoir simulation might be a complex subject to deal with when working with reservoir characterization. The use of machine learning has been increasing in the energy industry. It can improve the accuracy of reservoir predictions, optimize production strategies, and many other applications. The complexity and uncertainty of reservoir models pose significant challenges to traditional modeling approaches, making machine learning an attractive solution. Aiming to reduce reservoir simulation’s complexities, this work investigates using a machine-learning model as an alternative to conventional simulators. The Random Forest regressor model is experimented with to reproduce pressure response solutions for multi-region radial composite reservoirs. An analytical approach is employed to create the training dataset in the following procedure: the permeability is sorted using a specific distribution, and the output is generated using the analytical solution. Through experimentation and analysis, this work aims to advance our understanding of using machine learning in reservoir simulation for the energy industry.

The use of numerical weather prediction (NWP) has brought significant improvements to severe weather outbreak forecasting; however, determination of the primary mode of severe weather (in particular tornadic and nontornadic outbreaks) continues to be a challenge. Uncertainty in model runs contributes to forecasting difficulty; therefore it is beneficial to a forecaster to understand the sources and magnitude of uncertainty in a severe weather forecast. This research examines the impact of data assimilation, microphysics parameterizations, and planetary boundary layer (PBL) physics parameterizations on severe weather forecast accuracy and model variability, both at a mesoscale and synoptic-scale level. NWP model simulations of twenty United States tornadic and twenty nontornadic outbreaks are generated. In the first research phase, each case is modeled with three different modes of data assimilation and a control. In the second phase, each event is modeled with 15 combinations of physics parameterizations: five microphysics and three PBL, all of which were designed to perform well in convective weather situations. A learning machine technique known as a support vector machine (SVM) is used to predict outbreak mode for each run for both the data assimilated model simulations and the different parameterization simulations. Parameters determined to be significant for outbreak discrimination are extracted from the model simulations and input to the SVM, which issues a diagnosis of outbreak type (tornadic or nontornadic) for each model run. In the third phase, standard synoptic parameters are extracted from the model simulations and a k-means cluster analysis is performed on tornadic and nontornadic outbreak data sets to generate synoptically distinct clusters representing atmospheric conditions found in each type of outbreak. Variations among the synoptic features in each cluster are examined across the varied physics parameterization and data assimilation runs. Phase I found that conventional and HIRS-4 radiance assimilation performs best of all examined assimilation variations by lowering false alarm ratios relative to other runs. Phase II found that the selection of PBL physics produces greater spread in the SVM classification ability. Phase III found that data assimilation generates greater model changes in the strength of synoptic-scale features than either microphysics or PBL physics parameterization.

[pt] O ensemble smoother with multiple data assimilation (ES-MDA) se tornou um poderoso estimador de parâmetros. A principal ideia do ES-MDA é assimilar os mesmos dados com a matriz de covariância dos erros dos dados inflada. Na implementação original do ES-MDA, os fatores de inflação e o número de assimilações são escolhidos a priori. O único requisito é que a soma dos inversos de tais fatores seja igual a um. Naturalmente, escolhendo-os iguais ao número de assimilações cumpre este requerimento. Contudo, estudos recentes mostraram uma relação entre a equação de atualização do ES-MDA com a solução para o problema inverso regularizado. Consequentemente, tais elementos agem como os parâmetros de regularização em cada assimilação. Assim, estudos propuseram técnicas para gerar tais fatores baseadas no princípio da discrepância. Embora estes estudos tenham propostos técnicas, um procedimento ótimo para gerar os fatores de inflação continua um problema em aberto. Mais ainda, tais estudos divergem em qual método de regularização é sufiente para produzir os melhores resultados para o ES-MDA. Portanto, nesta tese é abordado o problema de gerar os fatores de inflação para o ESMDA e suas influências na performance do método. Apresentamos uma análise numérica do impacto de tais fatores nos parâmetros principais do ES-MDA: o tamanho do conjunto, o número de assimilações e o vetor de atualização dos parâmetros. Com a conclusão desta análise, nós propomos uma nova técnica para gerar os fatores de inflação para o ES-MDA baseada em um método de regularização para algorítmos do tipo Levenberg-Marquardt. Investigando os resultados de um problema de inundação de um reservatório 2D, o novo método obtém melhor estimativa tanto para os parâmetros do modelo tanto quanto para os dados observados. / [en] The ensemble smoother with multiple data assimilation (ES-MDA) gained much attention as a powerful parameter estimation method. The main idea of the ES-MDA is to assimilate the same data multiple times with an inflated data error covariance matrix. In the original ES-MDA implementation, these inflation factors, such as the number of assimilations, are selected a priori. The only requirement is that the sum of the inflation factors inverses must be equal to one. Therefore, selecting them equal to the number of assimilations is a straightforward choice. Nevertheless, recent studies have shown a relationship between the ES-MDA update equation and the solution to a regularized inverse problem. Hence, the inflation factors play the role of the regularization parameter at each ES-MDA assimilation step. As a result, they have also suggested new procedures to generate these elements based on the discrepancy principle. Although several studies proposed efficient techniques to generate the ES-MDA inflation factors, an optimal procedure to generate them remains an open problem. Moreover, the studies diverge on which regularization scheme is sufficient to provide the best ES-MDA outcomes. Therefore, in this work, we address the problem of generating the ES-MDA inflation factors and their influence on the method s performance. We present a numerical analysis of the influence of such factors on the main parameters of the ES-MDA, such as the ensemble size, the number of assimilations, and the ES-MDA vector of model parameters update. With the conclusions presented in the aforementioned analysis, we propose a new procedure to generate ES-MDA inflation factors based on a regularizing scheme for Levenberg-Marquardt algorithms. It is shown through a synthetic two-dimensional waterflooding problem that the new method achieves better model parameters and data match compared to the other ES-MDA implementations available in the literature.

Emerging sensors and intelligent traffic technologies provide extensive data sets in a traffic network. However, realizing the full potential of such data sets for a unique representation of real-world states is challenging due to data accuracy, noise, and temporal-spatial resolution. Data assimilation is a known group of methodological approaches that exploit physics-informed traffic models and data observations to perform short-term predictions of the traffic state in freeway environments. At the same time, neural networks capture high non-linearities, similar to those presented in traffic networks. Despite numerous works applying different variants of Kalman filters, the possibility of traffic state estimation with deep-learning-based methodologies is only partially explored in the literature. We present a deep-learning modeling approach to perform traffic state estimation on large freeway networks. The proposed framework is trained on local observations from static and moving sensors and identifies differences between well-trusted data and model outputs. The detected patterns are then used throughout the network, even where there are no available observations to estimate fundamental traffic quantities. The preliminary results of the work highlight the potential of deep learning for traffic state estimation.

This thesis presents a method, Ensemble Kalman Filter (EnKF), applied to a highresolution, shallow water equations model (DG ADCIRC-2DDI) of the Lower St. Johns River with observation data at four gauging stations. EnKF, a sequential data assimilation method for non-linear problems, is developed for tidal flow simulation for estimation of state variables, i.e., water levels and depth-integrated currents for overland unstructured finite element meshes. The shallow water equations model is combined with observation data, which provides the basis of the EnKF applications. In this thesis, EnKF is incorporated into DG ADCIRC-2DDI code to estimate the state variables. Upon its development, DG ADCIRC-2DDI with EnKF is first validated by implementing to a low-resolution, shallow water equations model of a quarter annular harbor with synthetic observation data at six gauging stations. Second, DG ADCIRC-2DDI with EnKF is implemented to a high-resolution, shallow water equations model of the Lower St. Johns River with real observation data at four gauging stations. Third, four different experiments are performed by applying DG ADCIRC-2DDI with EnKF to the Lower St. Johns River.

[pt] O ES-MDA tem sido usado amplamente no que diz respeito a problemas inversos de reservatórios de petróleo, usando a estatística bayesiana como cerne. Propriedades importantes como a permeabilidade, raio da zona de skin e permeabilidade da zona de skin, são estimadas a partir de dados de histórico de reservatório usando esse método baseado em conjuntos. Nessa tese, a pressão medida no poço durante um teste de injetividade foi calculada usando uma abordagem analítica de um reservatório multicamadas, com zona de skin, usando a Transformada de Laplace. O algoritmo de Stehfest foi usado para inverter os dados para o campo real. Além disso, ao usarmos essa abordagem, conseguimos obter facilmente a vazão em cada camada como um novo dado a ser considerado no ES-MDA, enriquecendo a estimativa dos dados desejados. Por usarmos a vazão e a pressão como dados de entrada no ES-MDA, é de suma importância que a diferença de ordens de grandezas não influencie em nossas estimativas e por isso optou-se por usar o ES-MDA na forma adimensional. Visando uma maior precisão de nossas estimativas, usou-se um algoritmo de otimização dos fatores de inflação do ES-MDA. / [en] The ES-MDA has been extensively used concerning inverse problems of oil reservoirs, using Bayesian statistics as the core. Important properties such as permeability, skin zone radius, and skin zone permeability are estimated from historical reservoir data using this set-based method. In this thesis, the pressure measured at the well during an injectivity test was calculated using an analytical approach of a multilayer reservoir, with skin zone, using the Laplace Transform. Stehfest s algorithm was used to invert the data to the real field. Furthermore, using this approach, we were able to easily obtain the flow rate in each layer as new data to be considered in the ES-MDA, enriching the estimation of the targeted data. As we use flow rate and pressure as input data in the ES-MDA, it is important to assure that the difference in orders of magnitude does not influence our estimates. For this reason, we chose to use the ES-MDA in the dimensionless form. Aiming at a greater precision of our estimates, we used an algorithm to optimize the ES-MDA inflation factors.