When monitoring a binary process proportion p, it is usually assumed that the binary observations are independent. However, it is very common that the observations are correlated with p being the correlation between two successive observations. The first part of this research investigates the problem of monitoring p when the binary observations follow a first-order two-state Markov chain model with p remaining unchanged. A Markov Binary GLR (MBGLR) chart with an upper bound on the estimate of p is proposed to monitor a continuous stream of autocorrelated binary observations treating each observation as a sample of size n=1. The MBGLR chart with a large upper bound has good overall performance over a wide range of shifts. The MBGLR chart is optimized using the extra number of defectives (END) over a range of upper bounds for the MLE of p. The numerical results show that the optimized MBGLR chart has a smaller END than the optimized Markov binary CUSUM. The second part of this research develops a CUSUM-pp chart and a GLR-pp chart to monitor p and p simultaneously. The CUSUM-pp with two tuning parameters is designed to detect shifts in p and p when the shifted values are known. We apply two CUSUM-pp charts as a chart combination to detect increases in p and increases or decreases in p. The GLR-pp chart with an upper bound on the estimate of p, and an upper bound and a lower bound on the estimate of p works well when the shifts are unknown. We find that the GLR-pp chart has better overall performance. The last part of this research investigates the problem of monitoring p with p remains at the target value when the correlated binary observations are aggregated into samples with n>1. We assume that samples are independent and there is correlation between the observations in a sample. We proposed some GLR and CUSUM charts to monitor p and the performance of the charts are compared. The simulation results show MBNGLR has overall better performance than the other charts. / Ph. D.

<p>Deep learning has been increasingly adopted in a multitude of settings. Yet, its strong performance relies on processing data during inference that is in-distribution with its training data. Deep learning input data during deployment, however, is not guaranteed to be in-distribution with the model's training data and can often times be distorted, either intentionally (e.g., by an adversary) or unintentionally (e.g., by a sensor defect), leading to significant performance degradations. In this dissertation, we develop algorithms for a variety of applications to improve the performance of deep learning models in the presence of distorted data. We begin by first designing feature engineering methodologies to increase classification performance in noisy environments. Here, we demonstrate the efficacy of our proposed algorithms on two target detection tasks and show that our framework outperforms a variety of state-of-the-art baselines. Next, we develop mitigation algorithms to improve the performance of deep learning in the presence of adversarial attacks and nonlinear signal distortions. In this context, we demonstrate the effectiveness of our methods on a variety of wireless communications tasks including automatic modulation classification, power allocation in massive MIMO networks, and signal detection. Finally, we develop an uncertainty quantification framework, which produces distributive estimates, as opposed to point predictions, from deep learning models in order to characterize samples with uncertain predictions as well as samples that are out-of-distribution from the model's training data. Our uncertainty quantification framework is carried out on a hyperspectral image target detection task as well as on counter unmanned aircraft systems (cUAS) model. Ultimately, our proposed algorithms improve the performance of deep learning in several environments in which the data during inference has been distorted to be out-of-distribution from the training data. </p>

Heterogeneous data with different characteristics are ubiquitous in the modern digital world. For example, the observations collected from a process may change on its mean or variance. In numerous applications, data are often of mixed types including both discrete and continuous variables. Heterogeneity also commonly arises in data when underlying models vary across different segments. Besides, the underlying pattern of data may change in different dimensions, such as in time and space. The diversity of heterogeneous data structures makes statistical modeling and analysis challenging. Detection of change-points in heterogeneous data has attracted great attention from a variety of application areas, such as quality control in manufacturing, protest event detection in social science, purchase likelihood prediction in business analytics, and organ state change in the biomedical engineering. However, due to the extraordinary diversity of the heterogeneous data structures and complexity of the underlying dynamic patterns, the change-detection and analysis of such data is quite challenging. This dissertation aims to develop novel statistical modeling methodologies to analyze four types of heterogeneous data and to find change-points efficiently. The proposed approaches have been applied to solve real-world problems and can be potentially applied to a broad range of areas. / Ph. D.

Our vision is as yet unsurpassed by machines because of the sophisticated representations of objects in our brains. This representation is vastly different from a pixel-based representation used in machine storages. It is this sophisticated representation that enables us to perceive two faces as very different, i.e, they are far apart in the “perceptual space”, even though they are close to each other in their pixel-based representations. Neuroscientists have proposed distances between responses of neurons to the images (as measured in macaque monkeys) as a quantification of the “perceptual distance” between the images. Let us call these neuronal dissimilarity indices of perceptual distances. They have also proposed behavioural experiments to quantify these perceptual distances. Human subjects are asked to identify, as quickly as possible, an oddball image embedded among multiple distractor images. The reciprocal of the search times for identifying the oddball is taken as a measure of perceptual distance between the oddball and the distractor. Let us call such estimates as behavioural dissimilarity indices. In this thesis, we describe a decision-theoretic model for visual search that suggests a connection between these two notions of perceptual distances. In the first part of the thesis, we model visual search as an active sequential hypothesis testing problem. Our analysis suggests an appropriate neuronal dissimilarity index which correlates strongly with the reciprocal of search times. We also consider a number of alternative possibilities such as relative entropy (Kullback-Leibler divergence), the Chernoff entropy and the L1-distance associated with the neuronal firing rate profiles. We then come up with a means to rank the various neuronal dissimilarity indices based on how well they explain the behavioural observations. Our proposed dissimilarity index does better than the other three, followed by relative entropy, then Chernoff entropy and then L1 distance. In the second part of the thesis, we consider a scenario where the subject has to find an oddball image, but without any prior knowledge of the oddball and distractor images. Equivalently, in the neuronal space, the task for the decision maker is to find the image that elicits firing rates different from the others. Here, the decision maker has to “learn” the underlying statistics and then make a decision on the oddball. We model this scenario as one of detecting an odd Poisson point process having a rate different from the common rate of the others. The revised model suggests a new neuronal dissimilarity index. The new dissimilarity index is also strongly correlated with the behavioural data. However, the new dissimilarity index performs worse than the dissimilarity index proposed in the first part on existing behavioural data. The degradation in performance may be attributed to the experimental setup used for the current behavioural tasks, where search tasks associated with a given image pair were sequenced one after another, thereby possibly cueing the subject about the upcoming image pair, and thus violating the assumption of this part on the lack of prior knowledge of the image pairs to the decision maker. In conclusion, the thesis provides a framework for connecting the perceptual distances in the neuronal and the behavioural spaces. Our framework can possibly be used to analyze the connection between the neuronal space and the behavioural space for various other behavioural tasks.

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L’objectif de ces travaux de thèse est de développer des architectures fiables de surveillance et de détection des défauts d’une machine asynchrone basées sur des techniques paramétriques de traitement du signal. Pour analyser et détecter les défauts, un modèle paramétrique du courant statorique en environnement stationnaire est proposé. Il est supposé être constitué de plusieurs sinusoïdes avec des paramètres inconnus dans le bruit. Les paramètres de ce modèle sont estimés à l’aide des techniques paramétriques telles que les estimateurs spectraux de type sous-espaces (MUSIC et ESPRIT) et l’estimateur du maximum de vraisemblance. Un critère de sévérité des défauts, basé sur l’estimation des amplitudes des composantes fréquentielles du courant statorique, est aussi proposé pour évaluer le niveau de défaillance de la machine. Un nouveau détecteur des défauts est aussi proposé en utilisant la théorie de détection. Il est principalement basé sur le test du rapport de vraisemblance généralisé avec un signal et un bruit à paramètres inconnus. Enfin, les techniques paramétriques proposées ont été évaluées à l’aide de signaux de courant statoriques expérimentaux de machines asynchrones en considérant les défauts de roulements et les ruptures de barres rotoriques. L’analyse des résultats expérimentaux montre clairement l’efficacité et la capacité de détection des techniques paramétriques proposées. / This Ph.D. thesis aims to develop reliable and cost-effective condition monitoring and faults detection architectures for induction machines. These architectures are mainly based on advanced parametric signal processing techniques. To analyze and detect faults, a parametric stator current model under stationary conditions has been considered. It is assumed to be multiple sinusoids with unknown parameters in noise. This model has been estimated using parametric techniques such as subspace spectral estimators and maximum likelihood estimator. A fault severity criterion based on the estimation of the stator current frequency component amplitudes has also been proposed to determine the induction machine failure level. A novel faults detector based on hypothesis testing has been also proposed. This detector is mainly based on the generalized likelihood ratio test detector with unknown signal and noise parameters. The proposed parametric techniques have been evaluated using experimental stator current signals issued from induction machines under two considered faults: bearing and broken rotor bars faults.Experimental results show the effectiveness and the detection ability of the proposed parametric techniques.