Diagnostics and prognostics in rotating machinery is a subject of much on-going research. There are three approaches to diagnostics and prognostics. These include experience-based approaches, data-driven techniques and model-based techniques. Bayesian data-driven techniques are gaining widespread application in diagnostics and prognostics of mechanical and allied systems including slow rotating bearings, as a result of their ability to handle the stochastic nature of the measured data well. The aim of the study is to detect incipient damage of slow rotating bearings and develop diagnostics which will be robust under changing operating conditions. Further it is required to explore and develop an optimal prognostic model for the prediction of remaining useful life (RUL) of slow rotating bearings. This research develops a novel integrated nonlinear method for the effective feature extraction from acoustic emission (AE) signals and the construction of a degradation assessment index (DAI), which is subsequently used for the fault diagnostics of slow rotating bearings. A slow rotating bearing test rig was developed to measure AE data under variable operational conditions. The proposed novel DAI obtained by the integration of the PKPCA (polynomial kernel principal component analysis), a Gaussian mixture model (GMM) and an exponentially weighted moving average (EWMA) is shown to be effective and suitable for monitoring the degradation of slow rotating bearings and is robust under variable operating conditions. Furthermore, this study integrates the novel DAI into alternative Bayesian methods for the prediction of RUL. The DAI is used as input in several Bayesian regression models such as the multi-layer perceptron (MLP), radial basis function (RBF), Bayesian linear regression (BLR), Gaussian mixture regression (GMR) and the Gaussian process regression (GPR) for RUL prediction. The combination of the DAI with the GPR model, otherwise, known as the DAI-GPR gives the best prediction. The findings show that the GPR model is suitable and effective in the prediction of RUL of slow rotating bearings and robust to varying operating conditions. Further, the models are also robust when the training and tests sets are obtained from dependent and independent samples. Finally, an optimal GPR for the prediction of RUL of slow rotating bearings based on a DAI is developed. The model performance is evaluated for cases where the training and test samples from cross validation approach are dependent as well as when they are independent. The optimal GPR is obtained from the integration or combination of existing simple mean and covariance functions in order to capture the observed trend of the bearing degradation as well as the irregularities in the data. The resulting integrated GPR model provides an excellent fit to the data and improvements over the simple GPR models that are based on simple mean and covariance functions. In addition, it achieves a near zero percentage error prediction of the RUL of slow rotating bearings when the training and test sets are from dependent samples but slightly different values when the estimation is based on independent samples. These findings are robust under varying operating conditions such as loading and speed. The proposed methodology can be applied to nonlinear and non-stationary machine response signals and is useful for preventive machine maintenance purposes. Keywords: acoustic emission, Bayesian linear regression, Bayesian techniques, covariance function, data-driven, degradation assessment index, diagnostics, experience-based, exponentially weighted moving average, Gaussian mixture model, Gaussian mixture regression, Gaussian process regression, integration, mean function, model-based, multi-layer perceptron, polynomial kernel principal component analysis, prognostics, radial basis function, remaining useful life. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Mechanical and Aeronautical Engineering / PhD / unrestricted

To propose a methodology for the uncertainty estimation in water quality modeling as related to TMDL development, four Monte Carlo (MC) based techniques—single-phase MC, two-phase MC, Generalized Likelihood Uncertainty Estimation (GLUE), and Markov Chain Monte Carlo (MCMC) —were applied to a Hydrological Simulation Program–FORTRAN (HSPF) model developed for the Mossy Creek bacterial TMDL in Virginia. Predictive uncertainty in percent violations of instantaneous fecal coliform concentration criteria for the prediction period under two TMDL pollutant allocation scenarios was estimated. The average percent violations of the applicable water quality criteria were less than 2% for all the evaluated techniques. Single-phase MC reported greater uncertainty in percent violations than the two-phase MC for one of the allocation scenarios. With the two-phase MC, it is computationally expensive to sample the complete parameter space, and with increased simulations, the estimates of single and two-phase MC may be similar. Two-phase MC reported significantly greater effect of knowledge uncertainty than stochastic variability on uncertainty estimates. Single and two-phase MC require manual model calibration as opposed to GLUE and MCMC that provide a framework to obtain posterior or calibrated parameter distributions based on a comparison between observed and simulated data and prior parameter distributions. Uncertainty estimates using GLUE and MCMC were similar when GLUE was applied following the log-transformation of observed and simulated FC concentrations. GLUE provides flexibility in selecting any model goodness of fit criteria for calculating the likelihood function and does not make any assumption about the distribution of residuals, but this flexibility is also a controversial aspect of GLUE. MCMC has a robust formulation that utilizes a statistical likelihood function, and requires normal distribution of model errors. However, MCMC is computationally expensive to apply in a watershed modeling application compared to GLUE. Overall, GLUE is the preferred approach among all the evaluated uncertainty estimation techniques, for the application of watershed modeling as related to bacterial TMDL development. However, the application of GLUE in watershed-scale water quality modeling requires further research to evaluate the effect of different likelihood functions, and different parameter set acceptance/rejection criteria. / Ph. D.

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Dans le domaine automobile, bien qu’assez élaborées, les approches actuellement mises en œuvre pour analyser et prédire l’état vibro-acoustique d’un véhicule ne sont pas encore représentatives de la complexité réelle des systèmes mis en jeu. Entre autres limitations, les spécifications pour la conception restent essentiellement basées sur des cas de chargement extrêmes, utiles pour la tenue des structures mais non représentatifs de l’usage client pour les prestations vibro-acoustiques. Un objectif principal est ainsi de construire des modèles probabilistes aptes à prendre en compte les usages client et les conditions de fonctionnement réelles, en même temps que les incertitudes structurelles du véhicule comme les dispersions en fabrication. Ces modèles sont destinés à maîtriser un domaine s’étendant jusqu’aux moyennes fréquences. Pour ce faire, quatre étapes sont proposées : (1) une modélisation générique du système mécanique constitué par un véhicule, cohérente avec les réponses dynamiques dont la prédiction est souhaitée par les ingénieurs automobile ; (2) l’estimation de l’ensemble des efforts qui s’appliquent sur ce système, pour une large plage de conditions de fonctionnement véhicule ; (3) l’analyse et la modélisation de ces efforts considérés comme fonctions des conditions de fonctionnement; (4) l’étude de l’application des efforts modélisés à une structure dont les fonctions de transfert ont été calculées par une méthode d’élément finis stochastique non-paramétrique. La réponse ainsi obtenue est une image bien plus fidèle des conditions de fonctionnement du véhicule et de ses incertitudes structurelles. Pour ces étapes, des algorithmes bayésiens ad hoc sont développés et mis en œuvre sur une importante base de données issue de projets automobiles. Le cadre bayésien est particulièrement utile dans ce travail pour prendre en compte toute connaissance a priori, notamment celle des experts véhicule, et pour facilement propager l’incertitude entre les différents niveaux du modèle probabilisé. Enfin, les méthodes d’analyse choisies ici se révèlent intéressantes non seulement pour la réduction effective des données, mais aussi pour aider la compréhension physique et l’identification des phénomènes dynamiquement dominants. / In the automotive domain, although already quite elaborate, the current approaches to predict and analyse the vibro-acoustic behaviour of a vehicle are still far from the complexity of the real system. Among other limitations, design specifications are still essentially based on extreme loading conditions, useful when verifying the mechanical strength, but not representative of the actual vehicle usage, which is instead important when addressing the vibro-acoustic performance. As a consequence, one main aim here is to build a prediction model able to take into account the loading scenarios representative of the actual vehicle usage, as well as the car structural uncertainty (due, for instance, to production dispersion). The proposed model shall cover the low and mid-frequency domain. To this aim, four main steps are proposed in this work: (1) the definition of a model for a general vehicle system, pertinent to the vibro-acoustic responses of interest; (2) the estimation of the whole set of loads applied to this system in a large range of operating conditions; (3) the statistical analysis and modelling of these loads as a function of the vehicle operating conditions; (4) the analysis of the application of the modelled loads to non-parametric stochastic transfer functions, representative of the vehicle structural uncertainty. To achieve the previous steps, ad hoc Bayesian algorithms have been developed and applied to a large industrial database. The Bayesian framework is considered here particularly valuable since it allows taking into account prior knowledge, namely from automotive experts, and since it easily enables uncertainty propagation between the layers of the probabilistic model. Finally, this work shows that the proposed algorithms, more than simply yielding a model of the vibro-acoustic response of a vehicle, are also useful to gain deep insights on the dominant physical mechanisms at the origin of the response of interest.

En l’espace d’une quarantaine d’année, les connaissances sur l’angiogenèse tumorale ont littéralement explosé. Dans les années 1970, Judah Folkman démontre que les tumeurs ont besoin d’être vascularisées pour continuer à proliférer. Peu de temps après, les protagonistes principaux de l’angiogenèse tumorale ont été découverts, de même que les mécanismes dans lesquels ils sont impliqués. La décennie suivante marque le début des recherches sur les molécules à visée anti-angiogénique et c’est en 2004 que le bevacizumab (Avastin, Roche), premier médicament anti-angiogénique utilisé en oncologie, voit le jour. Parallèlement à cela, l’essor de la modélisation à effets-mixtes couplée aux progrès des outils informatiques ont permis de développer des méthodes d’analyses de données de plus en plus performantes. Dès 2009 L’agence de régulation FDA (Food and Drug Administration) aux Etats-Unis a identifié le rôle central de la modélisation numérique pour mieux analyser les données d’efficacité et de toxicité, préclinique et clinique en cancérologie. Le but de ce projet est d’étudier les effets de différents inhibiteurs de l’angiogenèse sur la dynamique tumorale, en se basant sur une approche populationnelle. Les modèles développés seront des modèles à base d’équations différentielles ordinaires intègrant des données et des informations issues de la littérature. L’objectif de ces modèles est de caractériser la dynamique des tailles tumorales chez les animaux et chez les patients, afin de comprendre les effets des traitements anti-angiogéniques et apporter un soutien pour le développement de ces molécules ou pour la prise de décisions thérapeutiques par les cliniciens. / Within the last 40 years, knowledge of tumor angiogenesis has literally exploded. In the seventies, Judah Folkman demonstrated that tumors need to be vascularized to continue to proliferate. Shortly after, the main protagonists of tumor angiogenesis have been discovered, as well as the mechanisms in which they are involved. The next decade is the beginning of the research on molecules with anti-angiogenic effects and in 2004 bevacizumab (Avastin, Roche), the first antiangiogenic drug used in oncology, was available for treating solid cancer patients. Along with this, the increasing interest of mixed-effects modeling coupled with advances in computer tools allowed developing more efficient methods of data analysis. In 2009, the regulatory agency FDA (Food and Drug Administration) in the United States has identified the central role of numerical modeling to better analyze the efficacy and toxicity preclinical and clinical oncology data. The aim of this project is to study the effects of different angiogenesis inhibitors on tumor dynamics, based on a population approach. The developed models are models based on ordinary differential equations and that integrate data and information from the literature. The objective of these models is to characterize the dynamics of tumor sizes in animals and patients in order to understand the effects of anti-angiogenic treatments and provide support for the development of these molecules, or to help clinicians for therapeutic decision making.