Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the simulation, parameter estimation, and control of mechanical systems with uncertainty. This study has led to new computational approaches for parameter estimation in nonlinear mechanical systems. The first approach is a polynomial-chaos based Bayesian approach in which maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. The second approach is based on the Extended Kalman Filter (EKF). The error covariances needed for the EKF approach are computed from polynomial chaos expansions, and the EKF is used to update the polynomial chaos representation of the uncertain states and the uncertain parameters. The advantages and drawbacks of each method have been investigated. This study has demonstrated the effectiveness of the polynomial chaos approach for control systems analysis. For control system design the study has focused on the LQR problem when dealing with parametric uncertainties. The LQR problem was written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework. The solution to the Hâ problem as well as the H2 problem can be seen as extensions of the LQR problem. This method might therefore have the potential of being a first step towards the development of computationally efficient numerical methods for Hâ design with parametric uncertainties. I would like to gratefully acknowledge the support provided for this work under NASA Grant NNL05AA18A. / Ph. D.

The exploration of oil and natural gas in offshore fields has motivated advanced researches about the environmental forces in the oceans. The waves, in particular, have been measured using different techniques, as meteorological buoys, with recent works proposing motion-based estimations procedures using the vessel, or a floating facility, in analogy with the buoys, as a wave sensor. Even though this approach has a number of benefits, the vessels, as dynamic systems, have a cut-off frequency that degrades the estimation of high-frequency waves, which are important for non-linear drift effects predictions. In order to solve this problem, it is proposed the incorporation of wave-probes - gauges used to measure the wave elevation in a point - installed on the hull of the vessel, based on literature suggestions and simple analytical arguments, using the Bayesian statistics as the standing point of a more complete estimation algorithm. In order to incorporate the measurements of the wave-probes, an extended linear model is proposed, showing that only corrections for the vertical motions of the vessel are necessary. The ideal installation positions of the wave-probes are defined using as base the utility Bayesian optimal design of experiments, which is shown to guarantee an upper bound for other optimal criteria, with the \'Elbow Criterion\" defining the optimal number of sensors to be employed. Based on the previous solutions, other proposals are made: a heuristic to solve the optimal sensor placement problem and an optimal prior exploring the probabilistic nature of the algorithm. Finally, all the proposals are tested numerically and experimentally, with a vessel model in a towing tank, concluding that the addition of the wave-probes is able to improve not only the estimation of high-frequency waves, but also the estimation over a large range of frequencies. For unimodal seas with intermediate draft, the addition of just one wave-probe reaches approximately a 37%-55% improvement in the energy parameter estimations - HS and TP; the addition of two or more probes reaches approximately a 62%-65% improvement in the same parameters estimations; the addition of four probes achieved the best cost benefit for mean direction estimation; and the addition of six probes is shown to be the recommendation for the best high-order directional estimation in the entire range of the spectrum. / A prospecção de óleo e gás natural em campos offshore tem motivado pesquisas avançadas sobre as forças ambientais em oceanos. As ondas, em particular, têm sido medidas através de diferentes técnicas, como boias meteorológicas, com trabalhos recentes propondo técnicas baseadas em movimento para que os navios, em analogia com as boias, possam ser usados como sensores de onda. Apesar desse método ter uma série de vantagens, os navios, como sistemas dinâmicos, têm uma frequência de corte que dificulta a estimação de ondas de altas frequências, que são importantes para a previsão de efeitos de deriva não-lineares. Para resolver esse problema, sugere-se a adição de wave-probes instalados no costado da embarcação, usando como justificativas sugestões da literatura e simples argumentos analíticos, com estatística Bayesiana como fundamentação para um algoritmo de estimação mais completo. Para que as medidas dos wave-probes possam ser incorporadas, um modelo linear estendido é proposto, mostrando que apenas correções para os movimentos verticais do navio são necessárias. A posição ideal de instalação dos wave-probes é definida usando como base o projeto ótimo de experimentos Bayesianos por utilidade, mostrando que o mesmo garante o limite superior de outros critérios de optimalidade, com o \"critério cotovelo\" definindo o número ótimo de sensores a serem usados. Com base nas soluções anteriores, outras propostas são feitas: uma heurística para resolver o problema de posicionamento ótimo dos sensores e uma priori ótima, explorando a natureza probabilística do algoritmo. Ao final, todas as propostas são testadas numericamente e experimentalmente, utilizando um modelo em escala em um tanque de provas, concluindo que a adição de wave-probes é capaz de melhorar não só a estimação de ondas em alta-frequência, mas também a estimação em uma ampla gama de frequências. Para mares unimodais, com calado intermediário, a adição de apenas um sensor alcançou uma melhoria de aproximadamente 37-55% na estimação dos parâmetros relacionados à energia - HS e TP; a adição de dois ou mais sensores alcançou melhorias de 62-65% na estimação de tais parâmetros; a adição de quatro sensores alcançou o melhor custo benefício para estimação da direção média; e a adição de seis sensores se mostrou ideal para estimação de ordem elevada do espectro direcional de energia.

Prélevés de manière non invasive, les gaz respiratoires sont constitués de nombreux composés organiques volatils (VOCs) dont la quantité dépend de l’état de santé du sujet. L’analyse quantitative de l’air expiré présente alors un fort intérêt médical, que ce soit pour le diagnostic ou le suivi de traitement. Dans le cadre de ma thèse, nous proposons d’étudier un dispositif d’analyse des gaz respiratoires, et notamment de ces VOCs. Cette thèse multidisciplinaire aborde différents aspects, tels que le choix des capteurs, du matériel et des modes d’acquisition, l’acquisition des données à l’aide d’un banc gaz, et ensuite le traitement des signaux obtenus de manière à quantifier un mélange de gaz. Nous étudions la réponse d’un capteur à oxyde métallique (MOX) à des mélanges de deux gaz (acétone et éthanol) dilués dans de l’air synthétique (oxygène et azote). Ensuite, nous utilisons des méthodes de séparation de sources de manière à distinguer les deux gaz, et déterminer leur concentration. Pour donner des résultats satisfaisants, ces méthodes nécessitent d’utiliser plusieurs capteurs dont on connait la forme mathématique du modèle décrivant l’interaction du mélange avec le capteur, et qui présentent une diversité suffisante dans les mesures d’étalonnage pour estimer les coefficients de ce modèle. Dans cette thèse, nous montrons que les capteurs MOX peuvent être décrits par un modèle de mélange linéaire quadratique, et qu’un mode d’acquisition fonctionnant en double température permet de générer deux capteurs virtuels à partir d’un unique capteur physique. Pour quantifier précisément les composants du mélange à partir des mesures sur ces capteurs (virtuels), nous avons conçu des méthodes de séparation de sources, supervisées et non supervisées appliquées à ce modèle non-linéaire : l’analyse en composantes indépendantes, des méthodes de moindres carrés (algorithme de Levenberg-Marquardt), et une méthode bayésienne ont été étudiées. Les résultats expérimentaux montrent que ces méthodes permettent d’estimer les concentrations de VOCs contenus dans un mélange de gaz, de façon précise, en ne nécessitant que très peu de points de calibration. / Non-invasively taken, exhaled breath contains many volatile organic compounds (VOCs) whose amount depends on the health of the subject. Quantitative analysis of exhaled air is of great medical interest, whether for diagnosis or for a treatment follow-up. As part of my thesis, we propose to study a device to analyze exhaled breath, including these VOCs. This multidisciplinary thesis addresses various aspects, such as the choice of sensors, materials and acquisition modes, the acquisition of data using a gas bench, and then the processing of the signals obtained to quantify a gas mixture. We study the response of a metal oxide sensor (MOX) to mixtures of two gases (acetone and ethanol) diluted in synthetic air (oxygen and nitrogen). Then, we use source separation methods in order to distinguish the two gases, and to determine their concentration. To give satisfactory results, these methods require first to use several sensors for which we know the mathematical model describing the interaction of the mixture with the sensor, and which present a sufficient diversity in the calibration measurements to estimate the model coefficients. In this thesis, we show that MOX sensors can be described by a linear-quadratic mixing model, and that a dual temperature acquisition mode can generate two virtual sensors from a single physical sensor. To quantify the components of the mixture from measurements on these (virtual) sensors, we have develop supervised and unsupervised source separation methods, applied to this nonlinear model: independent component analysis, least squares methods (Levenberg Marquardt algorithm), and a Bayesian method were studied. The experimental results show that these methods make it possible to estimate the VOC concentrations of a gas mixture, accurately, while requiring only a few calibration points.

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. / 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.

La tomographie par rayons X multi-énergétiques (MECT) permet d'obtenir plus d'information concernant la structure interne de l'objet par rapport au scanner CT classique. Un de ses intérêts dans l’imagerie médicale est d'obtenir les images de fractions d’eau et d’os. Dans l'état de l'art, les intérêts de MECT n'est pas encore découvert largement. Les approches de reconstruction existantes sont très limitées dans leurs performances. L'objectif principal de ce travail est de proposer des approches de reconstruction de haute qualité qui pourront être utilisés dans la MECT afin d’améliorer la qualité d’imagerie.Ce travail propose deux approches de reconstruction bayésiennes. La première est adaptée au système avec un détecteur discriminant en énergie. Dans cette approche, nous considérons que les polychromaticités de faisceaux sont négligeables. En utilisant le modèle linéaire de la variance et la méthode d'estimation maximum à postériori (MAP), l'approche que nous avons proposé permets de prendre en compte les différents niveaux de bruit présentés sur les mesures multi-énergétiques. Les résultats des simulations montrent que, dans l'imagerie médicale, les mesures biénergies sont suffisantes pour obtenir les fractions de l'eau et de l'os en utilisant l'approche proposée. Des mesures à la troisième énergie est nécessaire uniquement lorsque l'objet contient des matériaux lourdes. Par exemple, l’acier et l'iode. La deuxième approche est proposée pour les systèmes où les mesures multi-énergétiques sont obtenues avec des faisceaux polychromatiques. C'est effectivement la plupart des cas dans l'état actuel du practice. Cette approche est basée sur un modèle direct non-linéaire et un modèle bruit gaussien où la variance est inconnue. En utilisant l’inférence bayésienne, les fractions de matériaux de base et de la variance d'observation pourraient être estimées à l'aide de l'estimateur conjoint de MAP. Sous réserve à un modèle a priori Dirac attribué à la variance, le problème d'estimation conjointe est transformé en un problème d'optimisation avec une fonction du coût non-quadratique. Pour le résoudre, l'utilisation d'un algorithme de gradient conjugué non-linéaire avec le pas de descente quasi-optimale est proposée.La performance de l'approche proposée est analysée avec des données simulées et expérimentales. Les résultats montrent que l'approche proposée est robuste au bruit et aux matériaux. Par rapport aux approches existantes, l'approche proposée présente des avantages sur la qualité de reconstruction. / Multi-Energy Computed Tomography (MECT) makes it possible to get multiple fractions of basis materials without segmentation. In medical application, one is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical MECT measurements are usually obtained with polychromatic X-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in Beam-Hardening Artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log pre-processing and the water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on non-linear forward models counting the beam polychromaticity show great potential for giving accurate fraction images.This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint Maximum A Posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a non-quadratic cost function. To solve it, the use of a monotone Conjugate Gradient (CG) algorithm with suboptimal descent steps is proposed.The performances of the proposed approach are analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For a variety of materials, less than 5% estimation errors are observed on their average decomposition fractions.The proposed approach is a statistical reconstruction approach based on a non-linear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

[Truncated abstract] The multi-object filtering problem is a logical and fundamental generalization of the ubiquitous single-object vector filtering problem. Multi-object filtering essentially concerns the joint detection and estimation of the unknown and time-varying number of objects present, and the dynamic state of each of these objects, given a sequence of observation sets. This problem is intrinsically challenging because, given an observation set, there is no knowledge of which object generated which measurement, if any, and the detected measurements are indistinguishable from false alarms. Multi-object filtering poses significant technical challenges, and is indeed an established area of research, with many applications in both military and commercial realms. The new and emerging approach to multi-object filtering is based on the formal theory of random finite sets, and is a natural, elegant and rigorous framework for the theory of multiobject filtering, originally proposed by Mahler. In contrast to traditional approaches, the random finite set framework is completely free of explicit data associations. The random finite set framework is adopted in this dissertation as the basis for a principled and comprehensive study of multi-object filtering. The premise of this framework is that the collection of object states and measurements at any time are treated namely as random finite sets. A random finite set is simply a finite-set-valued random variable, i.e. a random variable which is random in both the number of elements and the values of the elements themselves. Consequently, formulating the multiobject filtering problem using random finite set models precisely encapsulates the essence of the multi-object filtering problem, and enables the development of principled solutions therein. '...' The performance of the proposed algorithm is demonstrated in simulated scenarios, and shown at least in simulation to dramatically outperform traditional single-object filtering in clutter approaches. The second key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on moment approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is also demonstrated in practical scenarios, and shown to considerably outperform traditional multi-object filtering approaches. The third key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on functional approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is compared with the previous, and shown to appreciably outperform the previous in certain classes of situations. The final key contribution is the definition of a consistent and efficiently computable metric for multi-object performance evaluation. It is shown that the finite set theoretic state space formulation permits a mathematically rigorous and physically intuitive construct for measuring the estimation error of a multi-object filter, in the form of a metric. This metric is used to evaluate and compare the multi-object filtering algorithms developed in this dissertation.

A solution to the vehicle state estimation problem is given using the Kalman filtering and the Particle filtering theories. Vehicle states are necessary for an active or a semi-active suspension control system, which is intended to enhance ride comfort, road handling and stability of the vehicle. Due to a lack of information on road disturbances, conventional estimation techniques fail to provide accurate estimates of all the required states. The proposed estimation algorithm, named Supervisory Kalman Filter (SKF), consists of a Kalman filter with an extra update step which is inspired by the particle filtering technique. The extra step, called a supervisory layer, operates on the portion of the state vector that cannot be estimated by the Kalman filter. First, it produces N randomly generated state vectors, the particles, which are distributed based on the Kalman filter’s last updated estimate. Then, a resampling stage is implemented to collect the particles with higher probability. The effectiveness of the SKF is demonstrated by comparing its estimation results with that of the Kalman filter and the particle filter when a test vehicle is passing over a bump. The estimation results confirm that the SKF precisely estimates those states of the vehicle that cannot be estimated by either the Kalman filter or the particle filter, without any direct measurement of the road disturbance inputs. Once the vehicle states are provided, a suspension control law, the Skyhook strategy, processes the current states and adjusts the damping forces accordingly to provide a better and safer ride for the vehicle passengers. This thesis presents a novel systematic and practical methodology for the design and implementation of the Skyhook control strategy for vehicle’s semi-active suspension systems. Typically, the semi-active control strategies (including the Skyhook strategy) have switching natures. This makes the design process difficult and highly dependent on extensive trial and error. The proposed methodology maps the discontinuous control system model to a continuous linear region, where all the time/frequency design techniques, established in the conventional control system theory, can be applied. If the semiactive control law is designed to satisfy ride and stability requirements, an inverse mapping offers the ultimate control law. The effectiveness of the proposed methodology in the design of a semi-active suspension control system for a Cadillac SRX 2005 is demonstrated by real-time road tests. The road tests results verify that the use of the newly developed systematic design methodology reduces the required time and effort in real industrial problems.

With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages. Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.

A solution to the vehicle state estimation problem is given using the Kalman filtering and the Particle filtering theories. Vehicle states are necessary for an active or a semi-active suspension control system, which is intended to enhance ride comfort, road handling and stability of the vehicle. Due to a lack of information on road disturbances, conventional estimation techniques fail to provide accurate estimates of all the required states. The proposed estimation algorithm, named Supervisory Kalman Filter (SKF), consists of a Kalman filter with an extra update step which is inspired by the particle filtering technique. The extra step, called a supervisory layer, operates on the portion of the state vector that cannot be estimated by the Kalman filter. First, it produces N randomly generated state vectors, the particles, which are distributed based on the Kalman filter’s last updated estimate. Then, a resampling stage is implemented to collect the particles with higher probability. The effectiveness of the SKF is demonstrated by comparing its estimation results with that of the Kalman filter and the particle filter when a test vehicle is passing over a bump. The estimation results confirm that the SKF precisely estimates those states of the vehicle that cannot be estimated by either the Kalman filter or the particle filter, without any direct measurement of the road disturbance inputs. Once the vehicle states are provided, a suspension control law, the Skyhook strategy, processes the current states and adjusts the damping forces accordingly to provide a better and safer ride for the vehicle passengers. This thesis presents a novel systematic and practical methodology for the design and implementation of the Skyhook control strategy for vehicle’s semi-active suspension systems. Typically, the semi-active control strategies (including the Skyhook strategy) have switching natures. This makes the design process difficult and highly dependent on extensive trial and error. The proposed methodology maps the discontinuous control system model to a continuous linear region, where all the time/frequency design techniques, established in the conventional control system theory, can be applied. If the semiactive control law is designed to satisfy ride and stability requirements, an inverse mapping offers the ultimate control law. The effectiveness of the proposed methodology in the design of a semi-active suspension control system for a Cadillac SRX 2005 is demonstrated by real-time road tests. The road tests results verify that the use of the newly developed systematic design methodology reduces the required time and effort in real industrial problems.

<p>With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages.</p><p>Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.</p>