Littérature scientifique sur le sujet « Estimation non-Asymptotique et robuste »

Pour étudier les distributions de fréquences des variables hydrologiques (pluies et débits) au pas de temps horaire, une méthodologie associant un générateur de chroniques de pluies horaires et un modèle conceptuel global de transformation de la pluie en débit a été développée. Sur une période de simulation donnée, la méthode génère une collection de scénarios de crues vraisemblables utilisée en prédétermination des risques hydrologiques. Les distributions de fréquences des variables hydrologiques sont construites empiriquement à partir des événements de pluies et de crues générés. L'extrapolation des distributions de fréquences des variables hydrologiques vers les fréquences rares se fait de façon empirique en augmentant la période de simulation, et non plus sur l'ajustement direct des distributions observées. Le principe de cette méthode (appelée SHYPRE : Simulation d'HYdrogrammes pour la PREdétermination) est donc d'utiliser les observations pour décrire le phénomène, afin de le reproduire statistiquement et de s'affranchir ainsi du manque d'observation. Son utilisation permet une estimation originale des quantiles de crues de fréquences courantes à rares et présente l'intérêt d'obtenir une information temporelle complète sur ces crues. De plus, on montre que l'approche fournit une estimation de quantiles de crues bien plus robuste que les ajustements statistiques des distributions observées, même pour les événements de fréquences courantes. Cette robustesse provient d'une meilleure prise en compte de l'information pluviométrique et de la stabilité de la paramétrisation du modèle pluie-débit.

Summary Objectives: The application of independence estimating equations (IEE) for controlled clinical trials (CCTs) has recently been discussed, and recommendations for its use have been derived for testing hypotheses. The robust estimator of variance has been shown to be liberal for small sample sizes. Therefore a series of modifications has been proposed. In this paper we systematically compare confidence intervals (CIs) proposed in the literature for situations that are common in CCTs. Methods: Using Monte-Carlo simulation studies, we compared the coverage probabilities of CIs and non-convergence probabilities for the parameters of the mean structure for small samples using modifications of the variance estimator proposed by Mancl and de Rouen [7], Morel et al. [8] and Pan [3]. Results: None of the proposed modifications behave well in each investigated situation. For parallel group designs with repeated measurements and binary response the method proposed by Pan maintains the nominal level. We observed non-convergence of the IEE algorithm in up to 10% of the replicates depending on response probabilities in the treatment groups. For comparing slopes with continuous responses, the approach of Morel et al. can be recommended. Conclusions: Results of non-convergence probabilities show that IEE should not be used in parallel group designs with binary endpoints and response probabilities close to 0 or 1. Modifications of the robust variance estimator should be used for sample sizes up to 100 clusters for CI estimation.

In this paper we focus on the estimation of mutual information from finite samples ( X × Y ) . The main concern with estimations of mutual information (MI) is their robustness under the class of transformations for which it remains invariant: i.e., type I (coordinate transformations), III (marginalizations) and special cases of type IV (embeddings, products). Estimators which fail to meet these standards are not robust in their general applicability. Since most machine learning tasks employ transformations which belong to the classes referenced in part I, the mutual information can tell us which transformations are most optimal. There are several classes of estimation methods in the literature, such as non-parametric estimators like the one developed by Kraskov et al., and its improved versions. These estimators are extremely useful, since they rely only on the geometry of the underlying sample, and circumvent estimating the probability distribution itself. We explore the robustness of this family of estimators in the context of our design criteria.

AbstractWe investigate the estimation methods of the multivariate non-stationary errors-in-variables models when there are non-stationary trend components and the measurement errors or noise components. We compare the maximum likelihood (ML) estimation and the separating information maximum likelihood (SIML) estimation. The latter was proposed by Kunitomo and Sato (Trend, seasonality and economic time series: the nonstationary errors-in-variables models. MIMS-RBP-SDS-3, MIMS, Meiji University. http://www.mims.meiji.ac.jp/, 2017) and Kunitomo et al. (Separating information maximum likelihood method for high-frequency financial data. Springer, Berlin, 2018). We have found that the Gaussian likelihood function can have non-concave shape in some cases and the ML method does work only when the Gaussianity of non-stationary and stationary components holds with some restrictions such as the signal–noise variance ratio in the parameter space. The SIML estimation has the asymptotic robust properties in more general situations. We explore the finite sample and asymptotic properties of the ML and SIML methods for the non-stationary errors-in variables models.

Missing data is almost inevitable in correlated-data studies. For non-Gaussian outcomes with moderate to large sequences, direct-likelihood methods can involve complex, hard-to-manipulate likelihoods. Popular alternative approaches, like generalized estimating equations, that are frequently used to circumvent the computational complexity of full likelihood, are less suitable when scientific interest, at least in part, is placed on the association structure; pseudo-likelihood (PL) methods are then a viable alternative. When the missing data are missing at random, Molenberghs et al. (2011, Statistica Sinica, 21,187–206) proposed a suite of corrections to the standard form of PL, taking the form of singly and doubly robust estimators. They provided the basis and exemplified it in insightful yet primarily illustrative examples. We here consider the important case of marginal models for hierarchical binary data, provide an effective implementation and illustrate it using data from an analgesic trial. Our doubly robust estimator is more convenient than the classical doubly robust estimators. The ideas are illustrated using a marginal model for a binary response, more specifically a Bahadur model.

The wave height and period regression curve is widely used to estimate the design wave period. In this study, the parameters of the curves are estimated, compared, and evaluated using the linear, robust linear, and nonlinear regression methods, respectively. The data used in the design wave height estimation are the annual maxima (AM) wave height and period data sets divided by typhoon and non-typhoon conditions, provided by the Ministry of Oceans and Fisheries (2019). The estimation parameters show significant differences in the local coastal waters and the estimation methods. The estimation parameters based on the Suh et al. (2008, 2010) method show the apparent bias, under-estimation in the intercept (scale) parameter, and over-estimation in the slope (exponent) parameter, respectively.

Acemoglu et al. (2008) document that the correlation between income per capita and democracy disappears when including time and country fixed effects. While their results are robust for the full sample, we find evidence for significant but heterogeneous effects of income on democracy: negative for former colonies, but positive for non-colonies. Within the sample of colonies we detect heterogeneous effects related to colonial history and early institutions. The zero mean effect estimated by Acemoglu et al. (2008) is consistent with effects of opposite signs in the different subsamples. Our findings are robust to the use of alternative data and estimation techniques. (JEL D72, O17, O47)

Given a Bell inequality, if its maximal quantum violation can be achieved only by a single set of measurements for each party or a single quantum state, up to local unitaries, one refers to such a phenomenon as self-testing. For instance, the maximal quantum violation of the Clauser-Horne-Shimony-Holt inequality certifies that the underlying state contains the two-qubit maximally entangled state and the measurements of one party contains a pair of anti-commuting qubit observables. As a consequence, the other party automatically verifies the set of states remotely steered, namely the "assemblage", is in the eigenstates of a pair of anti-commuting observables. It is natural to ask if the quantum violation of the Bell inequality is not maximally achieved, or if one does not care about self-testing the state or measurements, are we capable of estimating how close the underlying assemblage is to the reference one? In this work, we provide a systematic device-independent estimation by proposing a framework called "robust self-testing of steerable quantum assemblages". In particular, we consider assemblages violating several paradigmatic Bell inequalities and obtain the robust self-testing statement for each scenario. Our result is device-independent (DI), i.e., no assumption is made on the shared state and the measurement devices involved. Our work thus not only paves a way for exploring the connection between the boundary of quantum set of correlations and steerable assemblages, but also provides a useful tool in the areas of DI quantum certification. As two explicit applications, we show 1) that it can be used for an alternative proof of the protocol of DI certification of all entangled two-qubit states proposed by Bowles et al., and 2) that it can be used to verify all non-entanglement-breaking qubit channels with fewer assumptions compared with the work of Rosset et al.

In terrestrial ecosystems, leaves are aggregated into different spatial structures and their spatial distribution is non-random. Clumping index (CI) is a key canopy structural parameter, characterizing the extent to which leaf deviates from the random distribution. To assess leaf clumping effects on global terrestrial ET, we used a global leaf area index (LAI) map and the latest version of global CI product derived from MODIS BRDF data as well as the Boreal Ecosystem Productivity Simulator (BEPS) to estimate global terrestrial ET. The results show that global terrestrial ET in 2015 was 511.9 ± 70.1 mm yr−1 for Case I, where the true LAI and CI are used. Compared to this baseline case, (1) global terrestrial ET is overestimated by 4.7% for Case II where true LAI is used ignoring clumping; (2) global terrestrial ET is underestimated by 13.0% for Case III where effective LAI is used ignoring clumping. Among all plant functional types (PFTs), evergreen needleleaf forests were most affected by foliage clumping for ET estimation in Case II, because they are most clumped with the lowest CI. Deciduous broadleaf forests are affected by leaf clumping most in Case III because they have both high LAI and low CI compared to other PFTs. The leaf clumping effects on ET estimation in both Case II and Case III is robust to the errors in major input parameters. Thus, it is necessary to consider clumping effects in the simulation of global terrestrial ET, which has considerable implications for global water cycle research.

L'objectif de cet article est d'étudier l'impact de la vulnérabilité au changement climatique sur la croissance économique. Nous répondons à nos préoccupations en utilisant le modèle de variables instrumentales à long terme de Kripfganz et Sarafidis (2021). Nous testons ensuite l'hypothèse de Kuznets (EKC) en utilisant le modèle à seuil de Hansen (1999). Notre étude porte sur 10 pays pour la période 1995-2020. Les estimations de Kripfganz et Sarafidis (2021) utilisant ce modèle montrent que la vulnérabilité au changement climatique augmente considérablement la croissance économique à un seuil de 1 % d'environ 43,84 %. De plus, les résultats non linéaires utilisant le modèle de Hansen (1999) montrent que : (i) dans les régimes inférieurs, une augmentation de 1 % de la vulnérabilité augmente significativement la croissance économique de 5,242 % au seuil de 5 %. (ii) Sous le régime supérieur, une augmentation de 1 % de la vulnérabilité augmente significativement l'augmentation du seuil de 1 % de 5,856 %. Par conséquent, les résultats du modèle de Hansen (1999) sont cohérents avec ceux du modèle de Kripfganz et Sarafidis (2021). Ces résultats sont robustes aux évaluations de sensibilité et aux estimations des effets fixes.

Ce travail est consacré au problème d'estimation non paramétrique dans des modèles de régression en temps continu. On considère le problème d'estimation d'une fonction inconnue S supposée périodique. Cette estimation est basée sur des observations générées par un processus stochastique; ces observations peuvent être en temps continu ou discret. Pour ce faire, nous construisons une série d'estimateurs par projection et nous approchons la fonction inconnue S par une série de Fourier finie. Dans cette thèse, nous considérons le problème d'estimation dans le cadre adaptatif, c'est-à-dire le cas où la régularité de la fonction S est inconnue. Pour ce problème, nous développons une nouvelle méthode d'adaptation basée sur la procédure de sélection de modèle proposée par Konev et Pergamenshchikov (2012). Tout d'abord, cette procédure nous donne une famille d'estimateurs ; après nous choisissons le meilleur estimateur possible en minimisant une fonction coût. Nous donnons également une inégalité d'Oracle pour le risque de nos estimateurs et nous donnons la vitesse de convergence minimax
This thesis is devoted to the problem of non parametric estimation for continuous-time regression models. We consider the problem of estimating an unknown periodoc function S. This estimation is based on observations generated by a stochastic process; these observations may be in continuous or discrete time. To this end, we construct a series of estimators by projection and thus we approximate the unknown function S by a finite Fourier series. In this thesis we consider the estimation problem in the adaptive setting, i.e. in situation when the regularity of the fonction S is unknown. In this way, we develop a new adaptive method based on the model selection procedure proposed by Konev and Pergamenshchikov (2012). Firstly, this procedure give us a family of estimators, then we choose the best possible one by minimizing a cost function. We give also an oracle inequality for the risk of our estimators and we give the minimax convergence rate

Dans cette thèse nous étudions la robustesse des estimateurs sous les deux modèles de contamination non symétrique: F::(epsilon ),X=(1-epsilon )F::(theta )+epsilon H::(X) et F::(epsilon )=(1-epsilon )F::(theta )+epsilon G. Nous étudions aussi la robustesse des M-estimateurs multidimensionnels et en particulier les M-estimateurs de régression non linéaire pour lesquels nous établissons la normalité asymptotique

Cette thèse développe la méthode des fonctions modulatrices pour des estimations non-asymptotiques et robustes pour des pseudo-états des systèmes nonlinéaires d'ordre fractionnaire, des systèmes linéaires d'ordre fractionnaire avec des accélérations en sortie, et des systèmes à retards d'ordre fractionnaire. Les estimateurs conçus sont fournis en termes de formules intégrales algébriques, ce qui assure une convergence non-asymptotique. Comme une caractéristique essentielle des algorithmes d'estimation conçus, les mesures de sorties bruitées ne sont impliquées que dans les termes intégraux, ce qui confère aux estimateurs une robustesse contre les bruits. Premièrement, pour les systèmes nonlinéaires d'ordre fractionnaire et partiellement inconnu, l'estimation de la dérivée fractionnaire du pseudo-état est abordée via la méthode des fonctions modulatrices. Grâce à la loi de l'indice additif des dérivées fractionnaires, l'estimation est décomposée en une estimation des dérivées fractionnaires de la sortie et une estimation des valeurs initiales fractionnaires. Pendant ce temps, la partie inconnue est estimée via une stratégie innovante de fenêtre glissante. Deuxièmement, pour les systèmes linéaires d'ordre fractionnaire avec des accélérations comme sortie, l'estimation de l'intégrale fractionnaire de l'accélération est d'abord considérée pour les systèmes mécaniques de vibration d'ordre fractionnaire, où seules des mesures d'accélération bruitées sont disponibles. Basée sur des approches numériques existantes qui traitent des intégrales fractionnaires, notre attention se limite principalement à l'estimation des valeurs initiales inconnues en utilisant la méthode des fonctions modulatrices. Sur cette base, le résultat est ensuite généralisé aux systèmes linéaires plus généraux d'ordre fractionnaire. En particulier, le comportement des dérivées fractionnaires à zéro est étudié pour des fonctions absolument continues, ce qui est assez différent de celui de l'ordre entier. Troisièment, pour les systèmes à retards d'ordre fractionnaire, l'estimation du pseudo-état est étudiée en concevant un système dynamique auxiliaire d'ordre fractionnaire, qui fournit un cadre plus général pour générer les fonctions modulatrices requises. Avec l'introduction de l'opérateur de retard et du changement de coordonnées généralisé bicausal, l'estimation du pseudo-état du système considéré peut être réduite à celle de la forme normale correspondante. Contrairement aux travaux précédents le schéma présenté permet une estimation directe du pseudo-état plutôt que d'estimer les dérivées fractionnaires de la sortie et un ensemble de valeurs initiales fractionnaires. De plus, l'efficacité et la robustesse des estimateurs proposés sont vérifiées par des simulations numériques dans cette thèse. Enfin, un résumé de ce travail et un aperçu des travaux futurs sont tirés
This thesis develops the modulating functions method for non-asymptotic and robust estimations for fractional-order nonlinear systems, fractional-order linear systems with accelerations as output, and fractional-order time-delay systems. The designed estimators are provided in terms of algebraic integral formulas, which ensure non-asymptotic convergence. As an essential feature of the designed estimation algorithms, noisy output measurements are only involved in integral terms, which endows the estimators with robustness against corrupting noises. First, for fractional-order nonlinear systems which are partially unknown, fractional derivative estimation of the pseudo-state is addressed via the modulating functions method. Thanks to the additive index law of fractional derivatives, the estimation is decomposed into the fractional derivatives estimation of the output and the fractional initial values estimation. Meanwhile, the unknown part is fitted via an innovative sliding window strategy. Second, for fractional-order linear systems with accelerations as output, fractional integral estimation of the acceleration is firstly considered for fractional-order mechanical vibration systems, where only noisy acceleration measurements are available. Based on the existing numerical approaches addressing the proper fractional integrals of accelerations, our attention is primarily restricted to estimating the unknown initial values using the modulating functions method. On this basis, the result is further generalized to more general fractional-order linear systems. In particular, the behaviour of fractional derivatives at zero is studied for absolutely continuous functions, which is quite different from that of integer order. Third, for fractional-order time-delay systems, pseudo-state estimation is studied by designing a fractional-order auxiliary modulating dynamical system, which provides a more general framework for generating the required modulating functions. With the introduction of the delay operator and the bicausal generalized change of coordinates, the pseudo-state estimation of the considered system can be reduced to that of the corresponding observer normal form. In contrast to the previous work, the presented scheme enables direct estimation for the pseudo-state rather than estimating the fractional derivatives of the output and a bunch of fractional initial values. In addition, the efficiency and robustness of the proposed estimators are verified by numerical simulations in this thesis. Finally, a summary of this work and an insight into future work were drawn

Cette thèse a pour objectif, d’une part, de concevoir des estimateurs pour les systèmessinguliers linéaires en utilisant la méthode des fonctions de modulation. D’autrepart, elle vise à développer des observateurs pour une classe de systèmes dynamiquesnon linéaires en utilisant la méthode des formes normales d’observateurs. Pour lessystèmes singuliers, les estimateurs conçus sont présentés sous forme de formulesintégrales algébriques, garantissant une convergence non asymptotique. Une caractéristique essentielle des algorithmes d’estimation conçus est que les mesures bruitées des sorties ne sont impliquées que dans des termes intégraux, conférant ainsi aux estimateurs une robustesse face aux bruits perturbateurs. Pour les systèmes non linéaires, l’idée principale de conception consiste à transformer les systèmes proposés en une forme simplifiée qui supporte les observateurs existants tels que l’observateur à grandgain et l’observateur en mode glissant. Cette forme simple est appelée forme canoniqueobservable dépendant de la sortie auxiliaire.Pour les systèmes singuliers linéaires, nous transformons le système considéré enune forme similaire à la forme canonique observable de Brunovsky en injectant lesdérivées des entrées et des sorties. Tout d’abord, pour les systèmes singuliers linéairesmono-entrée mono-sortie, la condition d’observabilité est proposée. Des formules algébriques avec une fenêtre d’intégration glissante sont obtenues pour les variables dans différentes situations sans connaître la condition initiale du système. Ensuite, pour les systèmes singuliers linéaires à multiples entrées et sorties, une méthode innovante d’estimation non asymptotique et robuste basée sur la forme canonique observable à l’aide d’un ensemble de systèmes dynamiques de modulation auxiliaires est introduite. Ces derniers systèmes auxiliaires sont donnés par la forme canonique observable contrôlable avec des conditions initiales nulles. En introduisant un ensemble de systèmes dynamiques de modulation auxiliaires qui fournit un cadre plus général pour générer les fonctions de modulation requises, des formules intégrales algébriques sont obtenues à la fois pour les variables d’état et les dérivées de sortie. De plus, l’efficacité et la robustesse des estimateurs proposés sont vérifiées par des simulations numériques dans cette thèse.Pour les systèmes dynamiques non linéaires, nous proposons une famille de systèmesdynamiques non linéaires à multiples sorties "prêts à porter" qui peuvent êtretransformés en formes normales d’observateurs dépendant de la sortie auxiliaire, permettant ainsi le support de l’observateur en mode glissant bien connu. Pour cela, aumoyen de la méthode d’extension de dynamique et d’un ensemble des changementsde coordonnées (calculs algébriques intégraux de base), les termes non linéairessont annulés par une dynamique auxiliaire ou remplacés par des fonctions non linéairesdes multiples sorties. Il convient de mentionner que cette procédure est menée à biende manière compréhensible sans recourir aux outils de la géométrie différentielle, cequi est convivial pour ceux qui ne sont pas familiers avec les calculs des crochets deLie. De plus, l’efficacité et la robustesse des observateurs proposés sont vérifiées pardes simulations numériques dans cette thèse. Deuxièmement, une classe plus large desystèmes dynamiques non linéaires à multiples entrées et sorties "prêts à porter" estfournie pour étendre et développer davantage les systèmes proposés dans le premiercas. De manière similaire, au moyen de la dynamique auxiliaire correspondante etd’un ensemble des changements de coordonnées, les systèmes fournis sont convertisen formes normales non linéaires ciblées dépendant à la fois des multiples sorties etdes variables auxiliaires. Naturellement, cette procédure est également réalisée sansrecourir aux outils géométriques. Enfin, des conclusions sont présentées avec quelques perspectives
This thesis aims, on the one hand, to design estimators for linear singular systems usingthemethod of modulation functions. On the other hand, it aims to develop observersfor a class of nonlinear dynamical systems using the method of canonical formsof observers. For singular systems, the designed estimators are presented in the formof algebraic integral equations, ensuring non-asymptotic convergence. An essentialcharacteristic of the designed estimation algorithms is that noisy measurements of theoutputs are only involved in integral terms, thereby imparting robustness to the estimatorsagainst perturbing noises. For nonlinear systems, the main design idea is totransform the proposed systems into a simplified form that accommodates existingobservers such as the high-gain observer and the sliding-mode observer. This simpleformis called auxiliary output depending observable canonical form.For the linear singular systems, we transform the considered system into a formsimilar to the Brunovsky’s observable canonical form with the injection of the inputs’and outputs’ derivatives. First, for linear singular systems with single input and singleoutput, the observability condition is proposed. The system’s input-output differentialequation is derived based on the Brunovsky’s observable canonical form. Algebraicformulas with a sliding integration window are obtained for the variables in differentsituations without knowing the system’s initial condition. Second, for linear singular systemswith multiple input and multiple output, an innovative nonasymptotic and robust estimation method based on the observable canonical form by means of a set of auxiliary modulating dynamical systems is introduced. The latter auxiliary systems are given by the controllable observable canonical with zero initial conditions. The proposed method is applied to estimate the states and the output’s derivatives for linear singular system in noisy environment. By introducing a set of auxiliary modulating dynamical systems which provides a more general framework for generating the requiredmodulating functions, algebraic integral formulas are obtained both for the state variables and the output’s derivatives. After giving the solutions of the required auxiliary systems, error analysis in discrete noisy case is addressed, where the provided noise error bound can be used to select design parameters.For the nonlinear dynamical systems, we propose a family of "ready to wear" nonlineardynamical systemswith multiple outputs that can be transformed into the outputauxiliarydepending observer normal forms which can support the well-known slidingmode observer. For this, by means of the so-called dynamics extension method anda set of changes of coordinates (basic algebraic integral computations), the nonlinearterms are canceled by auxiliary dynamics or replaced by nonlinear functions of themultiple outputs. It is worth mentioning that this procedure is finished in a comprehensible way without resort to the tools of differential geometry, which is user-friendly for those who are not familiar with the computations of Lie brackets. In addition, the efficiency and robustness of the proposed observers are verified by numerical simulations in this thesis. Second, a larger class of "ready to wear" nonlinear dynamicalsystems with multiple inputs and multiple outputs are provided to further extend anddevelop the systems proposed in the first case. In a similar way, by means of the corresponding auxiliary dynamics and a set of changes of coordinates, the provided systems are converted into targeted nonlinear observable canonical forms depending on both the multiple outputs and auxiliary variables. Naturally, this procedure is still completed without resort to geometrical tools. Finally, conclusions are outlined with some perspectives

Ce rapport porte sur le sujet de recherche de l'identification boîte noire du système non linéaire. En effet, parmi toutes les techniques nombreuses et variées développées dans ce domaine de la recherche ces dernières décennies, il semble toujours intéressant d'étudier l'approche réseau de neurones dans l'estimation de modèle de système complexe. Même si des modèles précis ont été obtenus, les principaux inconvénients de ces techniques restent le grand nombre de paramètres nécessaires et, en conséquence, le coût important de calcul nécessaire pour obtenir le niveau de pratique de la précision du modèle désiré. Par conséquent, motivés pour remédier à ces inconvénients, nous avons atteint une méthodologie complète et efficace du système d'identification offrant une précision équilibrée, la complexité et les modèles de coûts en proposant, d'une part, de nouvelles structures de réseaux de neurones particulièrement adapté à une utilisation très large en matière de modélisation système pratique non linéaire, d'autre part, un simple et efficace technique de réduction de modèle, et, troisièmement, une procédure de réduction de coût de calcul. Il est important de noter que ces deux dernières techniques de réduction peut être appliquée à une très large gamme d'architectures de réseaux de neurones sous deux simples hypothèses spécifiques qui ne sont pas du tout contraignant. Enfin, la dernière contribution importante de ce travail est d'avoir montré que cette phase d'estimation peut être obtenue dans un cadre robuste si la qualité des données d'identification qu'il oblige. Afin de valider la procédure d'identification système proposé, des exemples d'applications entraînées en simulation et sur un procédé réel, de manière satisfaisante validé toutes les contributions de cette thèse, confirmant tout l'intérêt de ce travail
This report concerns the research topic of black box nonlinear system identification. In effect, among all the various and numerous techniques developed in this field of research these last decades, it seems still interesting to investigate the neural network approach in complex system model estimation. Even if accurate models have been derived, the main drawbacks of these techniques remain the large number of parameters required and, as a consequence, the important computational cost necessary to obtain the convenient level of the model accuracy desired. Hence, motivated to address these drawbacks, we achieved a complete and efficient system identification methodology providing balanced accuracy, complexity and cost models by proposing, firstly, new neural network structures particularly adapted to a very wide use in practical nonlinear system modeling, secondly, a simple and efficient model reduction technique, and, thirdly, a computational cost reduction procedure. It is important to notice that these last two reduction techniques can be applied to a very large range of neural network architectures under two simple specific assumptions which are not at all restricting. Finally, the last important contribution of this work is to have shown that this estimation phase can be achieved in a robust framework if the quality of identification data compels it. In order to validate the proposed system identification procedure, application examples driven in simulation and on a real process, satisfactorily validated all the contributions of this thesis, confirming all the interest of this work

Le développement des approches robustes et non paramétriques pour l’analyse et le traitement statistique de gros volumes de données présentant une forte variabilité,comme dans les domaines de l’environnement et de la génétique, est fondamental.Nous modélisons ici des données complexes de biologie appliquées à l’étude du comportement de bivalves et à l’analyse de liaison génétique. L’application des mathématiques à l’analyse du comportement de mollusques bivalves nous a permis d’aller vers une quantification et une traduction mathématique de comportements d’animaux in-situ, en milieu proche ou lointain. Nous avons proposé un modèle de régression non paramétrique et comparé 3 estimateurs non paramétriques, récursifs ou non,de la fonction de régression pour optimiser le meilleur estimateur. Nous avons ensuite caractérisé des rythmes biologiques, formalisé l’évolution d’états d’ouvertures,proposé des méthodes de discrimination de comportements, utilisé la méthode des shot-noises pour caractériser différents états d’ouverture-fermetures transitoires et développé une méthode originale de mesure de croissance en ligne.En génétique, nous avons abordé un cadre plus général de statistiques robustes pour l’analyse de liaison génétique. Nous avons développé des estimateurs robustes aux hypothèses de normalités et à la présence de valeurs aberrantes, nous avons aussi utilisé une approche statistique, où nous avons abordé la dépendance entre variables aléatoires via la théorie des copules. Nos principaux résultats ont montré l’intérêt pratique de ces estimateurs sur des données réelles de QTL et eQTL
The development of robust and nonparametric approaches for the analysis and statistical treatment of high-dimensional data sets exhibiting high variability, as seen in the environmental and genetic fields, is instrumental. Here, we model complex biological data with application to the analysis of bivalves’ behavior and to linkage analysis. The application of mathematics to the analysis of mollusk bivalves’behavior gave us the possibility to quantify and translate mathematically the animals’behavior in situ, in close or far field. We proposed a nonparametric regression model and compared three nonparametric estimators (recursive or not) of the regressionfunction to optimize the best estimator. We then characterized the biological rhythms, formalized the states of opening, proposed methods able to discriminate the behaviors, used shot-noise analysis to characterize various opening/closing transitory states and developed an original approach for measuring online growth.In genetics, we proposed a more general framework of robust statistics for linkage analysis. We developed estimators robust to distribution assumptions and the presence of outlier observations. We also used a statistical approach where the dependence between random variables is specified through copula theory. Our main results showed the practical interest of these estimators on real data for QTL and eQTL analysis

Cette thèse traite le problème de l'estimation d'état, du diagnostic et de commande tolérante aux défauts des systèmes non linéaires représentés par un modèle de Takagi-Sugeno (T-S) à variables de prémisse non mesurables. De nombreux algorithmes pour la synthèse d'observateurs robustes vis-à-vis des perturbations, des imperfections de modélisation et des entrées inconnues sont présentés en se basant sur quatre types d'observateurs : les observateursproportionnels, les observateurs à entrées inconnues, les observateurs proportionnel intégral (PI) et multi-intégral (PMI). Par la suite, ces derniers sont utilisés pour le diagnostic de fautes affectant des systèmes non linéaires. Ceci est réalisé au moyen de trois stratégies. La première utilise l'observateur à entrée inconnue par découplage afin de rendre l'observateur insensible à certains défauts et permettre de détecter et d'isoler les défauts en construisant des bancs d'observateurs. En raison des conditions structurelles souvent insatisfaites, le découplage total des défauts de l'erreur d'estimation d'état n'est pas réalisable. Afin de s'affranchir de ces contraintes, la seconde stratégie utilise les observateurs PI et PMI pour estimer simultanément l'état et les défauts du système. La troisième stratégie qui utilise le formalisme H8 vise à concevoir un générateur de résidus minimisant l'influence des perturbations et maximisant l'influence des défauts. Un choix adéquat des paramètres du générateur de résidus permet la détection, la localisation et l'estimation des défauts. Enfin, une loi de commande tolérante aux défauts par poursuite de trajectoire d'un modèle de référence estproposée en exploitant les observateurs PI et PMI
This thesis deals with state estimation, fault diagnosis and fault tolerant control of nonlinear systems represented by a Takagi-Sugeno model with unmeasurable premise variables. The problem of state estimation of nonlinear systems with T-S model with unmeasurable premise variable is explored. Algorithms for robust observers synthesis with respect to perturbations, modeling uncertainties and unknown inputs are afterward presented. These algorithms are based on four kinds of observers called proportional, unknown input observers (UIOs), proportional-integral (PI) and multiple-integral (PMI) . The application on model-based diagnosis is studied based on three strategies. The first one uses unknown input observer to decouple some faults and makes the observers insensitive to certain faults. This allows to detect and isolate faults by constructing observers banks. Due to strong structural conditions on designing UIOs decoupling the faults on the state estimation error is not possible. To avoid this problem, the second strategy uses PI and PMI observers in order to estimate simultaneously the state and the faults of the system. The third strategy uses the H8 formalism. This aims to minimize the influence of perturbations and to maximize the effects of faults on the residual signal. An adequate choice of the residual generator parameters allows to detect, to isolate and to estimate the faults affecting the system. Lastly, a fault tolerant control law is proposed by reference trajectory tracking based on the use of PI and PMI observers

Cette thèse traite le problème de l'estimation d'état, du diagnostic et de commande tolérante aux défauts des systèmes non linéaires représentés par un modèle de Takagi-Sugeno (T-S) à variables de prémisse non mesurables. De nombreux algorithmes pour la synthèse d'observateurs robustes vis-à-vis des perturbations, des imperfections de modélisation et des entrées inconnues sont présentés en se basant sur quatre types d'observateurs : les observateurs proportionnels, les observateurs à entrées inconnues, les observateurs proportionnel intégral (PI) et multi-intégral (PMI). Par la suite, ces derniers sont utilisés pour le diagnostic de fautes des systèmes non linéaires. Ceci est réalisé au moyen de trois stratégies. La première utilise l'observateur à entrée inconnue par découplage afin de rendre l'observateur insensible à certains défauts et permettre de détecter et d'isoler les défauts en construisant des bancs d'observateurs. En raison des conditions structurelles souvent insatisfaites, le découplage total des défauts de l'erreur d'estimation d'état n'est pas réalisable. Afin de s'affranchir de ces contraintes, la seconde stratégie utilise les observateurs PI et PMI pour estimer simultanément l'état et les défauts du système. La troisième stratégie qui utilise le formalisme H_inf vise à concevoir un générateur de résidus minimisant l'influence des perturbations et maximisant l'influence des défauts. Un choix adéquat des paramètres du générateur de résidus permet la détection, la localisation et l'estimation des défauts. Enfin, une loi de commande tolérante aux défauts par poursuite de trajectoire d'un modèle de référence est proposée en exploitant les observateurs PI et PMI.

Abstract In 1995, large beds of the agarophyte Gracilariopsis lemaneiformis (Bory) Dawson, Acleto et Foldvik, were located on the NW coast of the Gulf of California. Estimations indicated the existence of more than 4,500 dry tons available for commercial harvesting. As a result, the private company PHYKOS S.A., was formed in 1996. The company obtained permits from the Mexican Government for harvesting beds located in Bahia de Los Angeles and Bahia de las Animas. In 1996, 28 tons of G. lemaneiformis were exported to Japan, and in 1997, this increased to 45 tons. But in 1998, El Nifio Southern oscillation affected the exploitation area by reducing the beds and consequently, only eight tons were exported. Approximately 90 % of the beds disappeared..However, the recovery of the beds was evident early in 1999, and they recovered fully in 2000, so that PHYKOS S.A. exported 95 and 140 tons in those years, respectively. The demand for G. lemaneiformis, and its presence in other non-exploited regions, caused the creation of a second company in January 2000. This new company, POLO S.A., obtained permits to harvest the beds of San Rafael Bay. In its first year, 36 tons of G. lemaneiformis were harvested and exported to Chile. Thus, in 2000, a total of 176 tons were harvested from the Gulf of California. This amount represents only 3.6 % of the total esti mated biomass for the west coast of the Gulf of California. G. lemaneiformis has become a new fishery for the Mexican seaweed industry in addition to the commercial exploitation of Gelidium robustum (Gard.) Hollenb. & Abb. and Macrocystis pyrifera (L.) C. Ag.

ABSTRACT Laboratory rock deformation has been extensively studied using in-situ optical and X-ray imaging and acoustic emissions (AE) measurements. These measurements have revealed rich kinematics across scales during sandstone compaction, from grain-scale breakage to sample-scale shear and compaction bands. Nevertheless, much progress remains in understanding the connection between rock deformation and grain-scale stress evolution before and after yielding and during the onset and progression of sample-scale strain localization. Such an understanding may offer opportunities for new mechanism-based constitutive models and estimation of grain-scale properties such as intra- and inter-granular bond strength. In this work, we describe the first-known simultaneous application of in-situ X-ray tomography and 3D X-ray diffraction to make strain and stress measurements in miniature samples of Nugget and Berea sandstones. This data provides a first quantification of grain-scale stress heterogeneity, grain-scale and inter-granular bond strength, and larger-scale stress heterogeneity during sandstone compaction. We discuss challenges in X- ray tomography and diffraction analyses for sandstones, which are related to challenges in identification of individual grains in tomographic images featuring minimal contrast at grain boundaries and challenges in performing diffraction microscopy from non-ideal diffraction spots generated by natural quartz crystals. We propose methods for examining the strength of inter-granular bonds and relating AE activity to stress fluctuations using our experimental data. INTRODUCTION Sandstone accommodates macroscopic deformation by a combination of microscopic mechanisms including cement bridge breakage, Hertzian particle fractures, particle crushing and pore collapse, and grain rearrangements (Paterson & Wong, 2005; Wong & Baud, 2012). Heterogeneous structures emerge at all length scales during sandstone compaction – from the contact-scale through cement-bridge breakage and chipping, to the grain-scale through breakage and pulverization, to the bulk-scale through shear and compaction band development. The evolution of these structures as a function of microscopic and macroscopic stress states and evolution is a key pursuit of rock mechanics. Success in this pursuit may enable development of robust mechanism-based constitutive models and progress in evaluating long standing questions related to associativity and other aspects of plasticity laws for rocks (Menéndez et al., 1996; Tengattini et al., 2014; Wong et al., 1997).

Abstract The study area comprises an oil play with numerous opportunities, identifying sandstone sequences with proven potential. The main sequence was deposited in the Upper Miocene within a transitional environment (external neritic), resulting in the formation of bars in deltaic facies and channels, which represents an excellent quality and lateral extension of the storage rock, but also complexity due to internal variability. The trap is structural with closure against faults, formed in an extensive tectonic regime giving rise to normal faulting and increasing the degree of complexity for the characterization of the reservoirs. Seismic data have accurate information about these characteristics, however, it is insufficient to solve the variability in the vertical scale, so incorporating all the information obtained in the wells through seismic inversion is essential when characterizing highly heterogeneous reservoirs with thin thickness. Furthermore, the geostatistical inversion combines Bayesian inference with a sampling algorithm called Markov Chain Monte Carlo (MCMC) that allows incorporating all the information from well logs, geological information, geostatistical parameters, and seismic data, generating models that honor the input data (Hameed et al., 2011). Additionally, the method provides a solution to the problem of non-uniqueness of the results, based on a statistical distribution of the multiple realizations derived from the initial model. This work proposes a flow that integrates quantitative analysis, establishing a direct link between seismic measurements and well logs, which additionally, when combined with non-linear techniques such as geostatistical seismic inversion, can minimize the differences in scales, obtaining better models, more predictive and with quantification of uncertainty. The static workflow used consists of 6 main components: Pre-stacked gather conditioning, curve modeling by rock physics (Vp, Vs and Rho), geostatistical seismic inversion (impedance P, Vp/Vs ratio, density), determination of facies cubes (oil-sand, brine-sand and shale) and petrophysical properties (Vcl, Phie, permeability) using a robust algorithm combining Bayesian inference and Markov Chain Monte Carlo (MCMC), quantification of uncertainty and volumetric estimation by ranking multiple realizations (P10, P50, P90) and transfer to a geological mesh (upscaling) ready for numerical simulation without the use of typical extrapolation algorithms such as kriging or Sequential Gaussian Simulation (SGS), managing to minimize the scale differences, obtaining better models, more predictive and capable of estimating uncertainty. With the results obtained, redefined geo-bodies were extracted, already discretizing the sandstones with good rock quality from the sandstones with good rock quality and bearing hydrocarbons to have greater precision in the development of these fields. Subsequently, the dynamic information was coupled to analyze the existing Pressure Transient Analyses (PTA) that have identified pseudo-steady state and the Rate Transient Analyses (RTA) to numerically model the response, checking the volumes obtained previously. Additionally, a benchmarking was considered with more than 590 oil producing fields in siliciclastics worldwide, considering the main properties of the fluid, porosity, facies and depositional environments and drive mechanisms, thus identifying new development opportunities with less uncertainty.

Abstract Subsurface lithofacies sequences encountered in the Kutch & Saurashtra Basin has its own set of challenges brought about due to its complex geological settings. These challenges are related to drilling, logging and completion and demand rigorous planning for the upcoming wells with detailed analysis of hazards associated with the overburden and reservoir rocks. In the study, these challenges are found to be linked with three prime geological sequences. Detailed integrated geomechanical analysis with inputs from drilling parameters, real-time formation experience, geophysical and geological are conducted for the improvement in borehole condition and improvising the effective drilling rate. A customized geomechanical workflow has been adopted to construct Mechanical Earth Model (MEM, Plumb et al., 2000) for strategic wells across the basin. Wellbore stability events related to geomechanics were reproduced and analyzed. The cause of the events was established and mitigatory methods were proposed. In addition, stress orientation along the wellbore trajectory and across the basin was estimated using breakouts identified on images and multi-arm calipers. Fast shear azimuth from Dipole Shear Sonic anisotropy analysis was also integrated to provide more robust and accurate estimates. Wells in the region are characterized by slow ROP, high torque and drag, wellbore instabilities (severe held ups, cavings, stuck pipes, string stalling etc.) and challenges while logging and running casing. The study has characterized these challenges and identified required solutions linked to the three geological sequences - weak Tertiary, Late Cretaceous Deccan Trap and Early Cretaceous to Jurassic clastic formations. The Tertiary formations are relatively weak (UCS∼300 to 1500psi) and prone to sanding and cavings due to breakouts. MEM based mud weight window estimation predicts that shear/failure hole collapse can be prevented using 10ppg to 11ppg mud weight. The formations below the Deccan Trap are locally categorized under Mesozoic sequence. The Deccan Trap and Mesozoic formations are extremely hard, tight, extremely stressed, heavily fractured and in some areas are also of HPHT nature. Rock strength shows a wide variation (UCS ∼5,000psi to 25,000psi) making bit selection a difficult task. Borehole failure is complex and cuttings analysis shows the signature of both shear and weak plane failure. Fractures on the image logs, rotation of breakouts, and fast shear azimuth support this theory. Mixing fracture sealing agents along with the use of optimal mud weights is found to be the most likely drilling solution. The understanding developed in the region and implementation of recommended steps assisted in successful drilling of two recent wells wherein gun-barrel shape borehole condition in both Tertiary and the Mesozoic sequence was achieved. The non-productive time was reduced by nearly 40 days increasing the effective ROP by 40%. In addition, smooth borehole prevented any major issues while carrying out casing and cementing operations.

Current and future GNC systems for exploration missions to small celestial bodies, planets and moons require an increasing level of on-board autonomy. Drivers for this increase include the lack of direct ground control because of communication delays, the operation in partly unknown environments, and the enhancement of the scientific exploitation through increased mission availability. To fulfill the increasing demand for more autonomous missions, key technologies for the GNC system have to be developed, which enable on-board intelligence, online monitoring for safety-critical operations, adaptable robust control, planning, and decision making. This paper focuses on the particular challenges of autonomous precise mobility on Small Solar System Bodies (SSSBs). The developed solutions from the research projects Astrone [1] and NEO-MAPP [2] are jointly presented. They consist of 1) vision-based navigation (VBN), 2) hazard detection and avoidance (HDA), 3) path planning and trajectory generators, fault detection isolation and recovery (FDIR), and 4) verification and validation (V&V) methods. VBN is necessary for SSSB missions because of their GPS-denied environment. Its two main functionalities are the spacecraft state estimation with respect to the target body and the generation of a geometrical map. The two functions are typically accomplished by including visual and ranging sensors in the GNC system, such as LiDARs, cameras (optical and/or infrared), and Laser Range Finders (LFRs). HDA accesses the generated map and the sensor inputs from the VBN module and selects possible new safer landing sites. It processes data obtained from the multiple sensors in order to evaluate various surface characteristics such as slope, roughness, and illumination. A decision making logic has to be established to pick the most suitable landing site. When the HDA selects a new landing site, the precomputed nominal trajectory has to be modified on-board based on the sensors information. This requires real-time capable guidance algorithms, which includes the various constraints of the GNC system and the mission operational requirements. In the safety-critical landing scenario, the GNC system has to be monitored on-board through the FDIR system for increased reliability. Lastly, all these novel autonomous functionalities have to be tested with adequate V&V methods and facilities. In the full paper, the solutions to the challenges 1) to 4) are discussed in more detail by presenting the novel GNC architectures of the two projects. Whereas the NEO-MAPP project focuses on the landing scenario, Astrone covers autonomous mobility functionalities for close surface operations. Taken together, they present a novel autonomous precise mobility on SSSBs to increase the scientific return for future missions. These technologies are not just applicable to SSSB missions, but can also be transferred to other planetary landings such as the Moon and Mars. Furthermore, traditional model-based solutions are compared to non-traditional AI-based solutions. For instance, HDA can either rely on maps generated from LiDARs using geometrical metrics or on images from cameras directly using convolutional neural networks. The applicability and pros and cons of AI solutions for each of the key technologies are discussed. [1] Martin, M., et al., “Astrone – GNC for Enhanced Surface Mobility on Small Solar System Bodies,” ESA GNC Conference 2021. [2] Caroselli, E., Belien, F., Falke, A., Curti, F. and Förstner, R., “NEO-MAPP µLander GN&C for Safe Autonomous Landing on Small Solar System Bodies”, AAS GNC 2022 Conference.