Anomaly Detection in Noisy Images

Finding rare events in multidimensional data is an important detection problem that has applications in many fields, such as risk estimation in insurance industry, finance, flood prediction, medical diagnosis, quality assurance, security, or safety in transportation. The occurrence of such anomalies is so infrequent that there is usually not enough training data to learn an accurate statistical model of the anomaly class. In some cases, such events may have never been observed, so the only information that is available is a set of normal samples and an assumed pairwise similarity function. Such metric may only be known up to a certain number of unspecified parameters, which would either need to be learned from training data, or fixed by a domain expert. Sometimes, the anomalous condition may be formulated algebraically, such as a measure exceeding a predefined threshold, but nuisance variables may complicate the estimation of such a measure. Change detection methods used in time series analysis are not easily extendable to the multidimensional case, where discontinuities are not localized to a single point. On the other hand, in higher dimensions, data exhibits more complex interdependencies, and there is redundancy that could be exploited to adaptively model the normal data. In the first part of this dissertation, we review the theoretical framework for anomaly detection in images and previous anomaly detection work done in the context of crack detection and detection of anomalous components in railway tracks. In the second part, we propose new anomaly detection algorithms. The fact that curvilinear discontinuities in images are sparse with respect to the frame of shearlets, allows us to pose this anomaly detection problem as basis pursuit optimization. Therefore, we pose the problem of detecting curvilinear anomalies in noisy textured images as a blind source separation problem under sparsity constraints, and propose an iterative shrinkage algorithm to solve it. Taking advantage of the parallel nature of this algorithm, we describe how this method can be accelerated using graphical processing units (GPU). Then, we propose a new method for finding defective components on railway tracks using cameras mounted on a train. We describe how to extract features and use a combination of classifiers to solve this problem. Then, we scale anomaly detection to bigger datasets with complex interdependencies. We show that the anomaly detection problem naturally fits in the multitask learning framework. The first task consists of learning a compact representation of the good samples, while the second task consists of learning the anomaly detector. Using deep convolutional neural networks, we show that it is possible to train a deep model with a limited number of anomalous examples. In sequential detection problems, the presence of time-variant nuisance parameters affect the detection performance. In the last part of this dissertation, we present a method for adaptively estimating the threshold of sequential detectors using Extreme Value Theory on a Bayesian framework. Finally, conclusions on the results obtained are provided, followed by a discussion of possible future work.

Shock Train/Boundary-Layer Interaction in Rectangular Scramjet Isolators

Numerous studies of the dual-mode scramjet isolator, a critical component in preventing inlet unstart and/or vehicle loss by containing a collection of flow disturbances called a shock train, have been performed since the dual-mode propulsion cycle was introduced in the 1960s. Low momentum corner flow and other three-dimensional effects inherent to rectangular isolators have, however, been largely ignored in experimental studies of the boundary layer separation driven isolator shock train dynamics. Furthermore, the use of two dimensional diagnostic techniques in past works, be it single-perspective line-of-sight schlieren/shadowgraphy or single axis wall pressure measurements, have been unable to resolve the three-dimensional flow features inside the rectangular isolator. These flow characteristics need to be thoroughly understood if robust dual-mode scramjet designs are to be fielded. The work presented in this thesis is focused on experimentally analyzing shock train/boundary layer interactions from multiple perspectives in aspect ratio 1.0, 3.0, and 6.0 rectangular isolators with inflow Mach numbers ranging from 2.4 to 2.7. Secondary steady-state Computational Fluid Dynamics studies are performed to compare to the experimental results and to provide additional perspectives of the flow field. Specific issues that remain unresolved after decades of isolator shock train studies that are addressed in this work include the three-dimensional formation of the isolator shock train front, the spatial and temporal low momentum corner flow separation scales, the transient behavior of shock train/boundary layer interaction at specific coordinates along the isolator's lateral axis, and effects of the rectangular geometry on semi-empirical relations for shock train length prediction. A novel multiplane shadowgraph technique is developed to resolve the structure of the shock train along both the minor and major duct axis simultaneously. It is shown that the shock train front is of a hybrid oblique/normal nature. Initial low momentum corner flow separation spawns the formation of oblique shock planes which interact and proceed toward the center flow region, becoming more normal in the process. The hybrid structure becomes more two-dimensional as aspect ratio is increased but corner flow separation precedes center flow separation on the order of 1 duct height for all aspect ratios considered. Additional instantaneous oil flow surface visualization shows the symmetry of the three-dimensional shock train front around the lower wall centerline. Quantitative synthetic schlieren visualization shows the density gradient magnitude approximately double between the corner oblique and center flow normal structures. Fast response pressure measurements acquired near the corner region of the duct show preliminary separation in the outer regions preceding centerline separation on the order of 2 seconds. Non-intrusive Focusing Schlieren Deflectometry Velocimeter measurements reveal that both shock train oscillation frequency and velocity component decrease as measurements are taken away from centerline and towards the side-wall region, along with confirming the more two dimensional shock train front approximation for higher aspect ratios. An updated modification to Waltrup \& Billig's original semi-empirical shock train length relation for circular ducts based on centerline pressure measurements is introduced to account for rectangular isolator aspect ratio, upstream corner separation length scale, and major- and minor-axis boundary layer momentum thickness asymmetry. The latter is derived both experimentally and computationally and it is shown that the major-axis (side-wall) boundary layer has lower momentum thickness compared to the minor-axis (nozzle bounded) boundary layer, making it more separable. Furthermore, it is shown that the updated correlation drastically improves shock train length prediction capabilities in higher aspect ratio isolators. This thesis suggests that performance analysis of rectangular confined supersonic flow fields can no longer be based on observations and measurements obtained along a single axis alone. Knowledge gained by the work performed in this study will allow for the development of more robust shock train leading edge detection techniques and isolator designs which can greatly mitigate the risk of inlet unstart and/or vehicle loss in flight.