Search

International audience; A framework to perform quantification and reduction of uncertainties in a wind turbine numerical model using a global sensitivity analysis and a recursive Bayesian inference method is developed in this article. We explain how a prior probability distribution on the model parameters is transformed into a posterior probability distribution, by incorporating a physical model and real field noisy observations. Nevertheless, these approaches suffer from the so-called curse of dimensionality. In order to reduce the dimension, Sobol' indices approach for global sensitivity analysis, in the context of wind turbine modeling, is presented. A major issue arising for such inverse problems is identifiability, that is, whether the observations are sufficient to unambiguously determine the input parameters that generated the observations. Global sensitivity analysis is also used in the context of identifiability.

International audience; In the field of sensitivity analysis, Sobol’ indices are widely used to assess the importance of the inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the Sobol’ estimates. The present paper tackles this issue by rendering the replication procedure iterative. The idea is to enable the addition of new model evaluations to progressively increase the accuracy of the estimates. These evaluations are done at points located in under-explored regions of the experimental designs, but preserving their characteristics. The key feature of this approach is the construction of nested space-filling designs. For the estimation of first-order indices, a nested Latin hypercube design is used. For the estimation of closed second-order indices, two constructions of a nested orthogonal array design are proposed. Regularity and uniformity properties of the nested designs are studied.

In the perspective of estimating main effects of model inputs, two approaches are studied to iteratively construct replicated designs based on Sobol' sequences. Space-filling properties of the resulting designs are studied based on two criteria.

International audience; Among practitioners, the importance of inputs to a model output is commonly measured via the computation of Sobol' sensitivity indices. Various estimation strategies exist in the literature, most of them requiring a very high number of model evaluations. Designing methods that compete favorably both in terms of computational cost and accuracy is therefore an issue of crucial importance. In this paper, an efficient replication-based strategy is proposed to estimate the full set of first- and second-order Sobol' indices. It relies on a Sobol' pick-freeze estimation scheme and requires only two replicated designs based on randomized orthogonal arrays of strength two. The precision of this procedure is assessed with bootstrap confidence intervals, presented for the first time in the replication framework. Our developments are compared to known approaches and validated on numerical test cases. A way to estimate the full set of first-, second-order but also total-effect Sobol' indices at a very competitive cost is also described, as a combination of our procedure and the one introduced by Saltelli.

International audience; Land Use and Transport Integrated models (LUTIs) are promising approaches for urban planning. There is large literature describing their technical architectures or using them in various scientific contexts. Yet little attention has been paid to expectations of practitioners (planners) and to the operational use of such models. The gap between lab application and operational use for planning practice is still to be filled. We shed light on what would make them definitely accepted and more used by planners to evaluate a range of urban and transport policies. In addition to literature review and our own experience dealing with urban planning agencies, we have interviewed different types of end users in France to identify their motivations and barriers to use LUTI models. The results show demand for a far more bottom-up oriented approach: the models should consider objectives and general needs of end users to live up to their expectations. Only a closer collaboration between modelers and end users, and more efforts to integrate modeling into urban planning, will make LUTIs considered as relevant approaches.

International audience; In this work, we report on electrical and fluid-dynamics studies concerning the flow induced by a sliding discharge (SD). This kind of discharge was created with a three electrode system configuration: one excited with ac and the others with a dc negative voltage. The SD was activated on a quiescent fluid at atmospheric pressure. The flow field induced by the SD was analysed by measurements undertaken with Pitot probes and Schlieren Image Velocimetry. Under the conditions of our experiments two "jet flows", that blown towards the interelectrode space, were induced from the air exposed electrodes. As a consequence of the mutual interaction of these two flows and of the magnitude of each flow, a resulting plume like planar jet of adjustable direction (0- 180º) could be formed. A robust control of the axis direction of the plume could be achieved by modifying the ac voltage value.

International audience; Pushbroom cameras are widely used for earth observation applications. This sensor acquires 1-D images over time and uses the straight motion of the satellite to sweep out a region of space and build a 2-D image. The stability of the satellite is critical during the pushbroom acquisition process. Therefore its attitude is assumed to be constant over time. However, the recent manufacture of smaller and lighter satellites to reduce launching cost has weakened this assumption. Small oscillations of the satellite’s attitude can result in noticeable warps in images, and geolocation information is lost as the satellite does not capture what it ought to. Current solutions use inertial sensors to control the attitude and correct the images, but they are costly and of limited precision. As the warped images do contain information about attitude variations, we suggest using image registration to estimate them.We exploit the geometry of the focal plane and the stationary nature of the disturbances to recover undistorted images. We embed the estimation in a Bayesian framework where image registration, a prior on attitude variations and a radiometric correction model are fused to retrieve the motion of the satellite. We illustrate the performance of our algorithm on 4 satellite datasets.

International audience; This paper deals with the estimation of grouped Sobol' indices in the case where the dependence inside each group is given by sets of linear ordered constraints. In the framework of independent inputs, the replication method allows to estimate first-order indices with only two designs. Through the use of orthogonal arrays of strength two the replication method can be applied to estimate closed second-order indices. We extend this methodology to estimate first-order and closed second-order grouped Sobol' indices under sets of linear constraints. The construction of the two designs required by the replication method is now based on the simplex geometric structure to handle the constraints within each set. We propose a space filling strategy to construct these designs.

International audience; A fundamental goal of Land Use – Transport Interaction (LUTI) models is to capture the strong interplay between land use and transportation in metropolitan areas. Inherently, sector-specific models, transport and urban alike, cannot take this interaction into account and thus miss one side of the story. LUTI models aim to fill this gap, and ultimately to provide better decision helping tools for urban and regional long term planning. LUTI models first appeared in the 1960s. The complexity of LUTI models, combined with computational limitations at the time, caused a pause in their development. However, interest in LUTI models has risen again in the 1990s and their number and complexity have been growing steadily ever since. This goes hand in hand with increasing expectations from end users as well as with new theoretical developments and a drastic increase in computational capacities, the latter enabling for instance the development of micro-simulation models.While spatial economics models may be mathematically more complex to handle, due to the requirement of reaching an equilibrium for a complex set of parameters and equations, activity-based models usually have more parameters and larger data requirements for their instantiation. Besides these differences, all LUTI models share several needs, among which – like for most models in general – a need for calibration (parameter estimation) methods in order to instantiate them and for validation approaches in order to justify their operational capacity. Both of these, parameter estimation and model validation, are complex issues; in this document we focus on numerical/computational aspects. The survey reported here is motivated by our conviction that the high complexity of current LUTI models requires the best possible numerical tools for calibration and validation. Developing and applying these tools is the primary objective set by the CITiES project funded by the French ANR (Agence Nationale de la Recherche). A starting point of this endeavor is a survey of existing state of the art reported in the LUTI literature. This document describes the scope of this ongoing study and some intermediate conclusions.

The focus of this work is calibration of the land-use module of an integrated land-use and transportation model (ILUTM). The calibration task involves estimating key parameters that dictate the output of the land-use module. Hence, an algorithm based on maximum-likelihood estimation (MLE) is developed for calibration. Furthermore, the observed values of the outputs from the land-use module are assumed to admit a Gaussian error. The ILUTM methodology used here is TRANUS which is used to model the city of Grenoble in France. The aforementioned algorithm is then applied to calibrate the land-use module of the Grenoble model. The covariance of the Gaussian error term is assumed to be unknown. It is represented as a function of the land-use module inputs and "hyperparameters.a' The resulting MLE optimization problem has 111 parameters to be estimated, 90 of which are land use parameters and 21 are hyperparameters of the Gaussian covariance kernel. The performance of the proposed calibration methodology is then compared to the traditional calibration techniques used for land use and transportation models, when applied to the Grenoble land-use model. It is observed that the proposed method outperforms the traditional technique when compared based upon a given quantity of interest.

International audience; Observation satellites use pushbroom sensors to capture images of the earth. These linear cameras acquire 1-D images over time and use the straight motion of the satellite to sweep out a region of space and build 2-D images. The stability of the imaging platform is crucial during the acquisition process to guaranty distortion free images. Positioning sensors are used to control and rectify the attitude variations of the satellite, but their sampling rate is too low to provide an accurate estimate of the motion. In this paper, we describe a way to fuse star tracker measurements with image registration in order to retrieve the attitude variations of the satellite. We introduce first a simplified motion model where the pushbroom camera is rotating during the acquisition of an image. Then we present the fusion model which combines low and high frequency informations of respectively the star tracker and the images; this is embedded in a Bayesian setting. Lastly, we illustrate the performance of our algorithm on three satellite datasets.

International audience; In this paper, we propose an algorithm that recovers binocular disparities in accordance with the surface properties of the scene under consideration. To do so, we estimate the disparity as well as the normals in the disparity space, by setting the two tasks in a unified framework. A novel joint probabilistic model is defined through two random fields to favor both intra field (within neighboring disparities and neighboring normals) and inter field (between disparities and normals) consistency. Geometric contextual information is introduced in the models for both normals and disparities, which is optimized using an appropriate alternating maximization procedure. We illustrate the performance of our approach on synthetic and real data.

International audience; Satellite image registration has been investigated for several years. Nevertheless, little attention has been paid to the linear geometry of the satellite's imaging sensor, often consisting of several pushbroom cameras. Each pushbroom camera cap- tures 1-D image and uses straight motion of the satellite to build a 2-D image. Yet, attitude variations of the satellite dur- ing the aquisition process can lead to significant distortions in the 2-D image. In this paper, we expose the problem and present a constrained image registration method to estimate the satellite's attitude variations, and thus correct the distorted images. We use a Lucas Kanade framework and a piecewise polynomial model under constraints to deduce the registra- tion equation. The performances of our algorithm are shown on two satellite datasets.

International audience; Pushbroom sensors are widely used for earth observation from space; this camera captures 1-D image and uses straight motion of the satellite to build a 2-D image. Yet, attitude variations of the satellite during the aquisition process can lead to significant distortions in the 2-D image. Current solutions use inertial sensors to record attitude variations and correct images, but they are expensive and not accurate enough for high frequency variations. In this paper, we expose the problem and present an image registration method to estimate the satellite's attitude variations, and thus correct the distorted images. We use a Lucas Kanade framework to deduce the registration equation; the performances of our algorithm are shown on two satellite datasets.

International audience; Linear pushbroom cameras are widely used in passive remote sensing from space as they provide high resolution images. In earth observation applications, where several pushbroom sensors are mounted in a single focal plane, small dynamic disturbances of the satellite's orientation lead to noticeable geometrical distortions in the images. In this paper, we present a global method to estimate those disturbances, which are effectively vibrations. We exploit the geometry of the focal plane and the stationary nature of the disturbances to recover undistorted images. To do so, we embed the estimation process in a Bayesian framework. An autoregressive model is used as a prior on the vibrations. The problem can be seen as a global image registration task where multiple pushbroom images are registered to the same coordinate system, the registration parameters being the vibration coefficients. An alternating maximisation procedure is designed to obtain Maximum a Posteriori estimates (MAP) of the vibrations as well as of the autoregressive model coefficients. We illustrate the performance of our algorithm on various datasets of satellite imagery.

A longstanding problem in sequential Monte Carlo (SMC) is to mathematically prove the popular belief that resampling does improve the performance of the estimation (this of course is not always true, and the real question is to clarify classes of problems where resampling helps). A more pragmatic answer to the problem is to use adaptive procedures that have been proposed on the basis of heuristic considerations, where resampling is performed only when it is felt necessary, i.e. when some criterion (effective number of particles, entropy of the sample, etc.) reaches some prescribed threshold. It still remains to mathematically prove the efficiency of such adaptive procedures. The contribution of this paper is to propose an approach, based on a representation in terms of multiplicative functionals (in which importance weights are treated as particles, roughly speaking) to obtain the asymptotic variance of adaptive resampling procedures, when the sample size goes to infinity. It is then possible to see the impact of the threshold on the asymptotic variance, at least in the Gaussian case, where the resampling criterion has an explicit expressions in the large sample asymptotics.

International audience; This paper addresses the issues of detecting and localizing objects in a scene that are both seen and heard. We explain the benefits of a human-like configuration of sensors (binaural and binocular) for gathering auditory and visual observations. It is shown that the detection and localization problem can be recast as the task of clustering the audio-visual observations into coherent groups. We propose a probabilistic generative model that captures the relations between audio and visual observations. This model maps the data into a common audio-visual 3D representation via a pair of mixture models. Inference is performed by a version of the expectationmaximization algorithm, which is formally derived, and which provides cooperative estimates of both the auditory activity and the 3D position of each object. We describe several experiments with single- and multiple-speaker detection and localization, in the presence of other audio sources.

International audience; This paper describes the acquisition and content of a new multi-modal database. Some tools for making use of the data streams are also presented. The Computational Audio- Visual Analysis (CAVA) database is a unique collection of three synchronised data streams obtained from a binaural microphone pair, a stereoscopic camera pair and a head tracking device. All recordings are made from the perspective of a person; i.e. what would a human with natural head movements see and hear in a given environment. The database is intended to facilitate research into humans' ability to optimise their multi-modal sensory input and fills a gap by providing data that enables human centred audiovisual scene analysis. It also enables 3D localisation using either audio, visual, or audio-visual cues. A total of 50 sessions, with varying degrees of visual and auditory complexity, were recorded. These range from seeing and hearing a single speaker moving in and out of field of view, to moving around a 'cocktail party' style situation, mingling and joining different small groups of people chatting.

International audience; In this paper we carry out cooperatively both disparity and object boundary estimation by setting the two tasks in a unified Markovian framework. We introduce a new joint probabilistic model that allows to estimate disparities through a Markov random field model. Boundary estimation then cooperates with disparity estimation to gradually and jointly improve accuracy. The feedback from boundary estimation to disparity estimation is made through the use of an auxiliary field referred to as a displacement field. This field suggests the corrections that need to be applied at disparity discontinuities in order that they align with object boundaries. The joint model reduces to a Markov random field model when considering disparities while it reduces to a Markov chain when focusing on the displacement field. The performance of our approach is illustrated on real stereo images sets, demonstrating the power of this cooperative framework.

International audience; In this paper we propose an original approach to solve the Inverse Kinematics problem. Our framework is based on Sequential Monte Carlo Methods and has the advantage to avoid the classical pitfalls of numerical inversion methods since only direct calculations are required. The resulting algorithm accepts arbitrary constraints and exhibits linear complexity with respect to the number of degrees of freedom. Hence, the proposed system is far more efficient for articulated figures with a high number of degrees of freedom

International audience; A Generalized Expectation Maximization (GEM) algorithm is used to retrieve the pose of a person from a monocular video sequence shot with a moving camera. After embedding the set of possible poses in a low dimensional space using Principal Component Analysis, the configuration that gives the best match to the input image is held as estimate for the current frame. This match is computed iterating GEM to assign edge pixels to the correct body part and to find the body pose that maximizes the likelihood of the assignments.

International audience; Due to the growing need for large quantities of human animation data in the entertainment industry, it has become a necessity to compress motion capture sequences in order to ease their storage and transmission. We present a novel, lossy compression method for human motion data that exploits both temporal and spatial coherence. Given one motion, we first approximate the poses manifold using Principal Geodesics Analysis (PGA) in the configuration space of the skeleton. We then search this approximate manifold for poses matching end-effectors constraints using an iterative minimization algorithm that allows for real-time, data-driven inverse kinematics. The compression is achieved by only storing the approximate manifold parametrization along with the end-effectors and root joint trajectories, also compressed, in the output data. We recover poses using the IK algorithm given the end-effectors trajectories. Our experimental results show that considerable compression rates can be obtained using our method, with few reconstruction and perceptual errors.

We address the issue of localizing individuals in a scene that contains several people engaged in a multiple-speaker conversation. We use a human-like configuration of sensors (binaural and binocular) to gather both auditory and visual observations. We show that the localization problem can be recast as the task of clustering the audio-visual observations into coherent groups. We propose a probabilistic generative model that captures the relations between audio and visual observations. This model maps the data to a representation of the common 3D scene-space, via a pair of Gaussian mixture models. Inference is performed by a version of the Expectation Maximization algorithm, which provides cooperative estimates of both the activity (speaking or not) and the 3D position of each speaker.

International audience; In this paper, we address the problem of estimating the motion of fluid flows that are visualized through a Schlieren system. Such a system is well known in fluid mechanics as it enables the visualization of unseeded flows. As the resulting images exhibit very low photometric contrasts, classical motion estimation methods based on the brightness consistency assumption (correlation-based approaches, optical flow methods) are completely inefficient. This work aims at proposing a sound energy based estimator dedicated to these particular images. The energy function to be minimized is composed of (a) a novel data term describing the fact that the observed luminance is linked to the gradient of the fluid density and (b) a specific div curl regularization term. The relevance of our estimator is demonstrated on real-world sequences.

We present a method for 3D object modeling and recognition which is robust to scale and illumination changes, and to viewpoint variations. The object model is derived from the local features extracted and tracked on an image sequence of the object. The recognition phase is based on an SVM classifier. We analyse in depth all the crucial steps of the method, and report very promising results on a dataset of 11 objects, that show how the method is also tolerant to occlusions and moderate scene clutter.

This paper presents a 3D object recognition method that exploits the spatio-temporal coherence of image sequences to capture the object most relevant features. We start from an image sequence that describes the object’s visual appearance from different view points. We extract local features (SIFT) and track them over the sequence. The tracked interest points form trains of features that are used to build a vocabulary for the object. Training images are represented with respect to that vocabulary and an SVM classifier is trained to recognize the object. We present very promising results on a dataset of 11 objects. Tests are performed under varying illumination, scale, and scene clutter.

International audience; The recent development of Sequential Monte Carlo methods (also called particle filters) has enabled the definition of efficient algorithms for tracking applications in image sequences. The efficiency of these approaches depends on the quality of the state-space exploration, which may be inefficient due to a crude choice of the function used to sample in the associated probability space. A careful study of this issue led us to consider the modeling of the tracked dynamic system with partial linear Gaussian models. Such models are characterized by a non linear dynamic equation, a linear measurement equation and additive Gaussian noises. They allow inferring an analytic expression of the optimal importance function used in the diffusion process of the particle filter, and enable building a relevant approximation of a validation gate. Despite of these potential advantages partial linear Gaussian models have not been investigated. The aim of this paper is therefore to demonstrate that such models can be of real interest facing difficult usual issues such as occlusions, ambiguities due to cluttered backgrounds and large state space. Three instances of these models are proposed. After a theoretical analysis, their significance is demonstrated by their performance for tracking points and planar objects in challenging real-world image sequences.

To understand and to be able to forecast natural phenomena is increasingly important nowadays, as those predictions are often the basis of many decisions, whether economical or ecological. In order todo so, mathematical models are introduced to represent the reality at a specific scale, and are then implemented numerically. However in this process of modelling, many complex phenomena occurring at a smaller scale than the one studied have to be simplified and quantified. This often leads to the introduction of additional parameters, which then need to be properly estimated. Classical methods of estimation usually involve an objective function, that measures the distance between the simulations and some observations, which is then optimised. Such an optimisation require many runs of the numerical model and possibly the computation of its gradient, thus can be expensive to evaluate computational-wise.However, some other uncertainties can also be present, which represent some uncontrollable and external factors that affect the modelling. Those variables will be qualified as environmental. By modelling them with a random variable, the objective function is then a random variable as well, that we wish to minimise in some sense. Omitting the random nature of the environmental variable can lead to localised optimisation, and thus a value of the parameters that is optimal only for the fixed nominal value. To overcome this, the minimisation of the expected value of the objective function is often considered in the field of optimisation under uncertainty for instance.In this thesis, we focus instead on the notion of regret, that measures the deviation of the objective function from its optimal value given a realisation of the environmental variable. This regret (either additive or relative) translates a notion of robustness through its probability of exceeding a specified threshold. So, by either controlling the threshold or the probability, we can define a family of estimators based on this regret.The regret can quickly become expensive to evaluate since it requires an optimisation of the objective for every realisation of the environmental variable. We then propose to use Gaussian Processes (GP) in order to reduce the computational burden of this evaluation. In addition to that, we propose a few adaptive methods in order to improve the estimation: the next points to evaluate are chosen sequentially according to a specific criterion, in a Stepwise Uncertainty Reduction (SUR) strategy. Finally, we will apply some of the methods introduced in this thesis on an academic problem of parameter estimation. We will study the calibration of the bottom friction of a model of the Atlantic ocean near the French coasts, while introducing some uncertainties in the forcing of the tide, and get a robust estimation of this friction parameter in a twin experiment setting.; De nombreux phénomènes physiques sont modélisés afin d'en mieux connaître les comportements ou de pouvoir les prévoir. Cependant pour représenter la réalité, de nombreux processus doivent être simplifiés, car ils sont souvent trop complexes, ou apparaissent à une échelle bien inférieure à celle de l'étude du phénomène. Au lieu decomplétement les omettre, les effets de ces processus sont souvent retranscrits dans les modèles à l'aide de paramétrisations, c'est-à-dire en introduisant des termes les quantifiant, et qui doivent être ensuite estimées. Les méthodes classiques d'estimation se basent sur la définition d'une fonction objectif qui mesure l'écart entre le modèle numérique et la réalité, qui est ensuite optimisée. Cependant, au delà de l'incertitude sur la valeur du paramètre à estimer, un autre type d'incertitude peut aussi être présent. Cela permet de représenter la variabilité intrinsèque de certains processus externes, qui vont avoir un effet sur la modélisation. Ces variables vont être qualifiées d'environnementales. En les modélisant à l'aide d'une variable aléatoire, la fonction objectif devient à son tour une variable aléatoire, que l'on va chercher à minimiser dans un certain sens. Si on omet ce caractère aléatoire, on peut se retrouver avec un paramètre optimal uniquement pour la valeur nominale du paramètre environnemental, et le modèle peut s'éloigner de la réalité pour d'autres réalisations. Ce problème d'optimisation sous incertitudes est souvent abordé en optimisant les premiers moments de la variable aléatoire, l'espérance en particulier. Dans cette thèse, nous nous intéressons plutôt à la notion de regret, qui mesure l'écart entre la fonction objectif et la valeur optimale qu'elle peut atteindre, pour la réalisation de la variable environnementale donnée. Cette idée de regret (additif ou bien relatif) nous permet de proposer une notion de robustesse à travers l'étude de sa probabilité de dépasser un certain seuil, ou inversement à travers le calcul de ses quantiles. À l'aide de ce seuil, ou de l'ordre du quantile choisi, on peut donc définir une famille d'estimateurs basés sur le regret.Néanmoins, le calcul du regret, et donc des quantités dérivées peut vite devenir très coûteux, car il nécessite une optimisation par rapport au paramètre de contrôle. Nous proposons donc d'utiliser des processus Gaussiens (GP) afin de construire un modèle de substitution, et donc de réduire cette contrainte en pratique. Nous proposons aussides méthodes itératives basées notamment sur la stratégie SUR (Stepwise Uncertainty Reduction, Réduction d'incertitudes séquentielle): le point à évaluer ensuite est choisi selon un critère permettant d'améliorer au mieux des quantités associées au regret-relatif.Enfin, nous appliquons les outils présentés dans cette thèse à un problème académique d'estimation de paramètre. Nous étudions ainsi la calibration sous incertitudes du paramètre de friction de fond d'un modèle océanique, représentant la façade atlantique des côtes françaises, ainsi que la Manche dans un cadre d'expériences jumelles.

In the context of energy transition, wind power generation is developing rapidly. Meanwhile, in the framework of digitalization of the industry, the exploitation of collected data can be optimized by combination with numerical models. Such models can be complex and costly as they involve dynamic equations coupled with different physics. Furthermore, some of their input parameters related to the model properties as well as the external conditions can be badly known. These uncertainties affect the predictions obtained from model simulations and thus can impact the components lifetime for example. This dissertation focuses consequently on quantifying and reducing the input parameter uncertainties involved in an aero-servo-elastic wind turbine model. Nevertheless, the widely used methods in uncertainty quantification are not suitable in the present industrial context because of the stochastic nature of the external solicitation and the time consuming behavior of the simulator. Our main contributions are twofold.Firstly, we want to quantify the impact of the uncertainties on the fatigue behavior of a wind turbine. We propose a global sensitivity analysis (GSA) methodology, based on the so-called Sobol' indices, for stochastic computer simulations. Such techniques, which often refer to the probabilistic framework and Monte Carlo (MC) methods, require a lot of calls to the numerical model. The uncertain input parameters are modeled by independent random variables gathered into a random vector and characterized by their probability distribution function (pdf). Variance-based GSA for time consuming deterministic computer models is usually performed by approximating the model by a surrogate regression. Among the different surrogates, we focus on Gaussian process (GP) regression characterized by its mean and covariance functions. One advantage of the GP regression metamodeling is to provide both a prediction of the numerical model and the associated uncertainty. In order to take into account the inherent randomness from stochastic simulations, we propose as a surrogate for the mean of the output of interest a GP regression with heteroscedastic noise. Then, this surrogate model is used to perform a sensitivity analysis based on classical MC estimation procedure.Secondly, we propose a Bayesian inference framework to carry out the calibration of influential input parameters from in situ measurements. It uses some measurements to update some prior pdfs on the unknown input parameters through the Bayes’ theorem. Recent decades have been marked by a simultaneous development of sensor technologies and internet of things capabilities. Thus, our research efforts have been directed toward inference techniques where the data are sequentially processed when new observations become available. In this context, model parameter inference can be carried out using data assimilation methods. We carry out the calibration using an ensemble Kalman filter (EnKF). Nevertheless, unlike the model properties having a static or slow time-variant behavior, the parameters related to the external conditions have a dynamic aspect. Thus, we propose to carry out the inference problem using an EnKF coupled with an analog forecasting strategy based on nearest neighbors to model the underlying dynamic model. However, such problems can be solved assuming that several conditions of well-posedness and identifiability are achieved. We exploit the relationship between non-identifiability of input parameters and total Sobol' indices. Indeed, for each measure output, we compute total Sobol indices associated to input parameters. If all the total Sobol' indices associated to a prescribed input parameter are "small", it means that this parameter is non-identifiable. Due to the functional nature of the measurements, we rely on a dimension reduction preliminary step through principal component analysis and then we compute an aggregated Sobol' index for each model parameter., Dans un contexte énergétique en pleine transition, l'énergie d'origine éolienne se développe rapidement. Parallèlement, dans le cadre de la digitalisation de l'industrie, l'exploitation des données collectées peut être optimisée par combinaison avec des modèles numériques d'éoliennes. Ces modèles peuvent être complexes et coûteux car ils impliquent des équations dynamiques non linéaires couplées à différentes physiques. De plus, certains de leurs paramètres d'entrée peuvent être mal ou peu connus. Ces incertitudes affectent les prédictions obtenues à partir de ces simulations et peuvent avoir un impact important sur la surveillance de l'état de la structure. Cette thèse se concentre sur la quantification et la réduction des incertitudes des paramètres d'entrée d’un modèle aéro-servo-élastique d'une éolienne. Néanmoins, les méthodes largement utilisées de quantification des incertitudes ne conviennent pas à notre contexte industriel du fait de la nature stochastique et du coût de chaque évaluation du simulateur. Nos principales contributions sont les suivantes.Premièrement, nous quantifions l'impact des incertitudes sur le comportement en fatigue d'une éolienne. Nous proposons une méthodologie d'analyse de sensibilité globale (ASG) basée sur les indices de Sobol' dans le cadre de simulations numériques stochastiques. De telles techniques, qui font souvent référence au cadre probabiliste et aux méthodes de Monte Carlo (MC), nécessitent de nombreux appels au modèle. Les paramètres d'entrée incertains sont modélisés par des variables aléatoires indépendantes regroupées dans un vecteur aléatoire et caractérisées par leur loi de probabilité. De telles analyses pour des simulations déterministes coûteuses en temps de calcul sont en général réalisées en approchant le modèle par un métamodèle. Nous nous concentrons sur un métamodèle de type processus gaussien (PG) caractérisé par sa moyenne et sa fonction de covariance. Il présente l’avantage de fournir à la fois une prédiction du modèle numérique et l'incertitude associée. Cependant, l’ASG basée sur ce type de modèle de substitution ne tient pas compte du caractère aléatoire inhérent à la simulation stochastique. Ainsi, nous proposons de modéliser la moyenne de la sortie d’intérêt avec un modèle par un PG avec bruit hétéroscédastique. Ensuite, ce métamodèle est utilisé pour effectuer une ASG avec une procédure classique d'estimation MC.Deuxièmement, nous proposons une procédure d'inférence bayésienne à partir de mesures in situ permettant de réduire les incertitudes qui entachent les paramètres d'entrée influents sur le comportement en fatigue de l'éolienne. Les dernières décennies ont été marquées par un développement simultané des technologies de capteurs et de l'internet des objets. Ainsi, nos efforts de recherche ont été orientés vers des techniques d'inférence où les données sont traitées séquentiellement lorsque de nouvelles observations deviennent disponibles. Dans ce contexte, l'inférence des paramètres du modèle peut être effectuée à l'aide de méthodes d'assimilation de données. Nous nous focalisons tout particulièrement sur le filtre de Kalman d'ensemble (EnKF). Lorsque le modèle dynamique sous-jacent des paramètres d'entrée est inconnu, nous proposons d'utiliser une procédure d'inférence combinant un EnKF à une stratégie de prévision par analogues basée sur une méthode des plus proches voisins. Cependant, seule l'inférence des paramètres identifiables a du sens. Un paramètre n'ayant aucune influence sur les sorties mesurées n'est pas identifiable. Cette influence est mesurée en estimant les indices de Sobol' totaux des sorties mesurées aux paramètres d'entrée. En raison de la nature fonctionnelle des sorties mesurées, nous nous appuyons sur une réduction de dimension par analyse en composantes principales préalable à l’estimation d’un indice de Sobol' agrégé pour chaque sortie mesurée aux paramètres du modèle.

Land Use and Transportation Integrated (LUTI) models have become a norm for representing the interactions between land use and the transportation of goods and people in a territory. These models are mainly used to evaluate alternative planning scenarios, simulating their impact on land cover and travel demand.LUTI models and other mathematical models used in various fields are most of the time based on complex computer codes. These codes often involve poorly-known inputs whose uncertainty can have significant effects on the model outputs.Global sensitivity analysis methods are useful tools to study the influence of the model inputs on its outputs. Among the large number of available approaches, the variance based method introduced by Sobol' allows to calculate sensitivity indices called Sobol' indices. These indices quantify the influence of each model input on the outputs and can detect existing interactions between inputs.In this framework, we favor a particular method based on replicated designs of experiments called replication method. This method appears to be the most suitable for our application and is advantageous as it requires a relatively small number of model evaluations to estimate first-order or second-order Sobol' indices.This thesis focuses on extensions of the replication method to face constraints arising in our application on the LUTI model Tranus, such as the presence of dependency among the model inputs, as far as multivariate outputs.Aside from that, we propose a recursive approach to sequentially estimate Sobol' indices. The recursive approach is based on the iterative construction of stratified designs, latin hypercubes and orthogonal arrays, and on the definition of a new stopping criterion. With this approach, more accurate Sobol' estimates are obtained while recycling previous sets of model evaluations. We also propose to combine such an approach with quasi-Monte Carlo sampling.An application of our contributions on the LUTI model Tranus is presented., Le développement et l'utilisation de modèles intégrés transport-urbanisme sont devenus une norme pour représenter les interactions entre l'usage des sols et le transport de biens et d'individus sur un territoire. Ces modèles sont souvent utilisés comme outils d'aide à la décision pour des politiques de planification urbaine.Les modèles transport-urbanisme, et plus généralement les modèles mathématiques, sont pour la majorité conçus à partir de codes numériques complexes. Ces codes impliquent très souvent des paramètres dont l'incertitude est peu connue et peut potentiellement avoir un impact important sur les variables de sortie du modèle.Les méthodes d'analyse de sensibilité globales sont des outils performants permettant d'étudier l'influence des paramètres d'un modèle sur ses sorties. En particulier, les méthodes basées sur le calcul des indices de sensibilité de Sobol' fournissent la possibilité de quantifier l'influence de chaque paramètre mais également d'identifier l'existence d'interactions entre ces paramètres.Dans cette thèse, nous privilégions la méthode dite à base de plans d'expériences répliqués encore appelée méthode répliquée. Cette méthode a l'avantage de ne requérir qu'un nombre relativement faible d'évaluations du modèle pour calculer les indices de Sobol' d'ordre un et deux.Cette thèse se focalise sur des extensions de la méthode répliquée pour faire face à des contraintes issues de notre application sur le modèle transport-urbanisme Tranus, comme la présence de corrélation entre paramètres et la prise en compte de sorties multivariées.Nos travaux proposent également une approche récursive pour l'estimation séquentielle des indices de Sobol'. L'approche récursive repose à la fois sur la construction itérative d'hypercubes latins et de tableaux orthogonaux stratifiés et sur la définition d'un nouveau critère d'arrêt. Cette approche offre une meilleure précision sur l'estimation des indices tout en permettant de recycler des premiers jeux d'évaluations du modèle. Nous proposons aussi de combiner une telle approche avec un échantillonnage quasi-Monte Carlo.Nous présentons également une application de nos contributions pour le calage du modèle de transport-urbanisme Tranus.

Linear pushbroom cameras are widely used for earth observation applications. This sensor acquires 1-D images over time and uses the straight motion of the satellite to sweep out a region of space and build 2-D image ; it operates in the same way as a usual flatbed scanner. Main advantages of such technology are : robustness in the space context, higher resolution than classical 2-D CCD sensors and low production cost. To build color images, several pushbroom cameras of different modalities are set in parallel onto the satellite’s focal plane. This acquisition process is dependent of the time and assumes that the satellite’s attitude remains constant during the image recording. However, the recent manufacture of smal- ler satellites with higher sampling resolution has weakened this assumption. The satellite may oscillates around its rotations axis, and an angular variation of a few microradians can result in noticeable warps in images. Current solutions use inertial sensors on board the satellite to control the attitude and correct the images, but they are costly and of limited precision. As warped images do contain the information of attitude variations, we suggest to use image registration to es- timate them. We exploit the geometry of the focal plane and the stationary nature of the disturbances to recover undistorted images. To do so, we embed the estimation process in a Bayesian framework where image registration, prior on attitude variations and mea- surements of a star tracker are fused to retrieve the motion of the satellite. We illustrate the performance of our algorithm on four satellite datasets provided by EADS Astrium.; Les caméras pushbroom sont omniprésentes en imagerie satellitaire. Ce capteur linéaire enregistre des images 1-D et utilise le défilement du satellite autour de la terre pour construire des bandeaux d’image ; son principe de fonctionnement est identique aux scanners et photocopieurs que l’on peut utiliser tous les jours. Les avantages liés à cette technologie sont principalement une résolution d’image étendue qui va bien au delà des caméras perspectives, un coût d’exploitation faible et une robustesse au contexte spatial. Pour reconstruire des images couleur, le plan focal d’un satellite embarque plusieurs caméras pushbroom sensibles à différentes bandes spectrales de la lumière. Ce mode d’acquisition dépendant du temps suppose que l’orientation du satellite, également appelée attitude dans cette étude, ne varie pas au cours du survol d’une scène. Les satellites ont jusqu’à maintenant été considérés comme stables du fait de leur inertie. Cependant les technologies récentes développées dans la recherche spatiale tendent à réduire leur taille et alléger leur poids pour les rendre plus agiles et moins coûteux en énergie lors de leur mise en orbite. La résolution des capteurs a également été améliorée, ce qui rend nettement plus critique la moindre oscillation de l’imageur. Ces facteurs cumulés font qu’un changement d’attitude de quelques microradians peut provoquer des déformations géométriques notables dans les images. Les solutions actuelles utilisent les capteurs de positionnement du satellite pour asservir son attitude et rectifier les images, mais elles sont coûteuses et limitées en précision. Les images contiennent pourtant une information cohérente sur les mouvements du satellite de par leurs éventuelles déformations. Nous proposons dans cette étude de retrouver les variations d’attitude par recalage des images enregistrées par le satellite. Nous exploitons la disposition des caméras pushbroom dans le plan focal ainsi que la nature stationnaire des oscillations pour conduire l’estimation. Le tout est présenté dans un cadre bayesien, où les données images peuvent se mêler avec une information a priori sur le mouvement ainsi que des mesures exogènes fournies par un capteur stellaire couramment appelé star tracker. Différentes solutions sont décrites et comparées sur des jeux de données satellitaires fournis par le constructeur de satellite EADS Astrium.