Inspection of parts with complex geometry and welds with structural health monitoring techniques

Structural Health Monitoring (SHM) systems were developed to evaluate the integrity of a system during operation, and to quickly identify the maintenance problems. They will be used in future aerospace vehicles to improve safety, reduce cost and minimize the maintenance time of a system. Many SHM systems were already developed to evaluate the integrity of plates and used in marine structures. Their implementation in manufacturing processes is still expected. The application of SHM methods for complex geometries and welds are two important challenges in this area of research. This research work started by studying the characteristics of piezoelectric actuators, and a small energy harvester was designed. The output voltages at different frequencies of vibration were acquired to determine the nonlinear characteristics of the piezoelectric stripe actuators. The frequency response was evaluated experimentally. AA battery size energy harvesting devices were developed by using these actuators. When the round and square cross section devices were excited at 50 Hz frequency, they generated 16 V and 25 V respectively. The Surface Response to Excitation (SuRE) and Lamb wave methods were used to estimate the condition of parts with complex geometries. Cutting tools and welded plates were considered. Both approaches used piezoelectric elements that were attached to the surfaces of considered parts. The variation of the magnitude of the frequency response was evaluated when the SuRE method was used. The sum of the square of the differences was calculated. The envelope of the received signal was used for the analysis of wave propagation. Bi-orthogonal wavelet (Binlet) analysis was also used for the evaluation of the data obtained during Lamb wave technique. Both the Lamb wave and SuRE approaches along with the three methods for data analysis worked effectively to detect increasing tool wear. Similarly, they detected defects on the plate, on the weld, and on a separate plate without any sensor as long as it was welded to the test plate.

Learning and Exploiting Camera Geometry for Computer Vision

This work explores the use of statistical methods in describing and estimating camera poses, as well as the information feedback loop between camera pose and object detection. Surging development in robotics and computer vision has pushed the need for algorithms that infer, understand, and utilize information about the position and orientation of the sensor platforms when observing and/or interacting with their environment.

The first contribution of this thesis is the development of a set of statistical tools for representing and estimating the uncertainty in object poses. A distribution for representing the joint uncertainty over multiple object positions and orientations is described, called the mirrored normal-Bingham distribution. This distribution generalizes both the normal distribution in Euclidean space, and the Bingham distribution on the unit hypersphere. It is shown to inherit many of the convenient properties of these special cases: it is the maximum-entropy distribution with fixed second moment, and there is a generalized Laplace approximation whose result is the mirrored normal-Bingham distribution. This distribution and approximation method are demonstrated by deriving the analytical approximation to the wrapped-normal distribution. Further, it is shown how these tools can be used to represent the uncertainty in the result of a bundle adjustment problem.

Another application of these methods is illustrated as part of a novel camera pose estimation algorithm based on object detections. The autocalibration task is formulated as a bundle adjustment problem using prior distributions over the 3D points to enforce the objects' structure and their relationship with the scene geometry. This framework is very flexible and enables the use of off-the-shelf computational tools to solve specialized autocalibration problems. Its performance is evaluated using a pedestrian detector to provide head and foot location observations, and it proves much faster and potentially more accurate than existing methods.

Finally, the information feedback loop between object detection and camera pose estimation is closed by utilizing camera pose information to improve object detection in scenarios with significant perspective warping. Methods are presented that allow the inverse perspective mapping traditionally applied to images to be applied instead to features computed from those images. For the special case of HOG-like features, which are used by many modern object detection systems, these methods are shown to provide substantial performance benefits over unadapted detectors while achieving real-time frame rates, orders of magnitude faster than comparable image warping methods.

The statistical tools and algorithms presented here are especially promising for mobile cameras, providing the ability to autocalibrate and adapt to the camera pose in real time. In addition, these methods have wide-ranging potential applications in diverse areas of computer vision, robotics, and imaging.

Antarctic ice sheet topography, cavity geometry, and global bathymetry (RTopo 1.0.5-beta)

Sub-ice shelf circulation and freezing/melting rates in ocean general circulation models depend critically on an accurate and consistent representation of cavity geometry. Existing global or pan-Antarctic data sets have turned out to contain various inconsistencies and inaccuracies. The goal of this work is to compile independent regional fields into a global data set. We use the S-2004 global 1-minute bathymetry as the backbone and add an improved version of the BEDMAP topography for an area that roughly coincides with the Antarctic continental shelf. Locations of the merging line have been carefully adjusted in order to get the best out of each data set. High-resolution gridded data for upper and lower ice surface topography and cavity geometry of the Amery, Fimbul, Filchner-Ronne, Larsen C and George VI Ice Shelves, and for Pine Island Glacier have been carefully merged into the ambient ice and ocean topographies. Multibeam survey data for bathymetry in the former Larsen B cavity and the southeastern Bellingshausen Sea have been obtained from the data centers of Alfred Wegener Institute (AWI), British Antarctic Survey (BAS) and Lamont-Doherty Earth Observatory (LDEO), gridded, and again carefully merged into the existing bathymetry map. The global 1-minute dataset (RTopo-1 Version 1.0.5) has been split into two netCDF files. The first contains digital maps for global bedrock topography, ice bottom topography, and surface elevation. The second contains the auxiliary maps for data sources and the surface type mask. A regional subset that covers all variables for the region south of 50 deg S is also available in netCDF format. Datasets for the locations of grounding and coast lines are provided in ASCII format.

Coccosphere geometry measurements from culture experiments on the coccolithophore species Calcidiscus leptoporus, Calcidiscus quadriperforatus and Helicosphaera carteri

Coccolithophores are a key phytoplankton group that exhibit remarkable diversity in their biology, ecology, and calcitic exoskeletons (coccospheres). An understanding of the physiological processes that underpin coccosphere architecture is essential for maximizing the information that can be retrieved from their extensive fossil record. Using culturing experiments on four modern species from three long-lived families, we investigate how coccosphere architecture responds to population shifts from rapid (exponential) to slowed (stationary) growth phases as nutrients become depleted. These experiments reveal statistical differences in cell size and the number of coccoliths per cell between these two growth phases, specifically that cells in exponential-phase growth are typically smaller with fewer coccoliths, whereas cells experiencing growth-limiting nutrient depletion have larger coccosphere sizes and greater numbers of coccoliths per cell. Although the exact numbers are species-specific, these growth-phase shifts in coccosphere geometry are common to four different coccolithophore families (Calcidiscaceae, Coccolithaceae, Isochrysidaceae, Helicosphaeraceae), demonstrating that this is a core physiological response to nutrient depletion across a representative diversity of this phytoplankton group. Polarised light microscopy was used for all coccosphere geometry measurements.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

Mechanical properties and cellular response of novel electrospun nanofibers for ligament tissue engineering: Effects of orientation and geometry

Electrospun nanofibers are a promising material for ligamentous tissue engineering, however weak mechanical properties of fibers to date have limited their clinical usage. The goal of this work was to modify electrospun nanofibers to create a robust structure that mimics the complex hierarchy of native tendons and ligaments. The scaffolds that were fabricated in this study consisted of either random or aligned nanofibers in flat sheets or rolled nanofiber bundles that mimic the size scale of fascicle units in primarily tensile load bearing soft musculoskeletal tissues. Altering nanofiber orientation and geometry significantly affected mechanical properties; most notably aligned nanofiber sheets had the greatest modulus; 125% higher than that of random nanofiber sheets; and 45% higher than aligned nanofiber bundles. Modifying aligned nanofiber sheets to form aligned nanofiber bundles also resulted in approximately 107% higher yield stresses and 140% higher yield strains. The mechanical properties of aligned nanofiber bundles were in the range of the mechanical properties of the native ACL: modulus=158±32MPa, yield stress=57±23MPa and yield strain=0.38±0.08. Adipose derived stem cells cultured on all surfaces remained viable and proliferated extensively over a 7 day culture period and cells elongated on nanofiber bundles. The results of the study suggest that aligned nanofiber bundles may be useful for ligament and tendon tissue engineering based on their mechanical properties and ability to support cell adhesion, proliferation, and elongation.

Discovery of relict subglacial lakes and their geometry and mechanism of drainage

Recent proxy measurements reveal that subglacial lakes beneath modern ice sheets periodically store and release large volumes of water, providing an important but poorly understood influence on contemporary ice dynamics and mass balance. This is because direct observations of how lake drainage initiates and proceeds are lacking. Here we present physical evidence of the mechanism and geometry of lake drainage from the discovery of relict subglacial lakes formed during the last glaciation in Canada. These palaeo-subglacial lakes comprised shallow (<10 m) lenses of water perched behind ridges orientated transverse to ice flow. We show that lakes periodically drained through channels incised into bed substrate (canals). Canals sometimes trend into eskers that represent the depositional imprint of the last high-magnitude lake outburst. The subglacial lakes and channels are preserved on top of glacial lineations, indicating long-term re-organization of the subglacial drainage system and coupling to ice flow.

Plane Detection Using Affine Homography

AIRES, Kelson R. T.; ARAÚJO, Hélder J.; MEDEIROS, Adelardo A. D. Plane Detection Using Affine Homography. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 2008, Juiz de Fora, MG: Anais... do CBA 2008.

Optimal control of affine connection control systems from the point of view of Lie algebroids

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

Some Inverse Problems in Analysis and Geometry

Thesis (Ph.D.)--University of Washington, 2016-08

Influence of the cutting edge micro-geometry of PCBN tools on the flank wear in orthogonal quenched and tempered turning M2 steel

Quenched and tempered high-speed steels obtained by powder metallurgy are commonly used in automotive components, such as valve seats of combustion engines. In order to machine these components, tools with high wear resistance and appropriate cutting edge geometry are required. This work aims to investigate the influence of the edge preparation of polycrystalline cubic boron nitride (PCBN) tools on the wear behavior in the orthogonal longitudinal turning of quenched and tempered M2 high-speed steels obtained by powder metallurgy. For this research, PCBN tools with high and low-CBN content have been used. Two different cutting edge geometries with a honed radius were tested: with a ground land (S shape) and without it (E shape). Also, the cutting speed was varied from 100 to 220 m/min. A rigid CNC lathe was used. The results showed that the high-CBN, E-shaped tool presented the longest life for a cutting speed of 100 m/min. High-CBN tools with a ground land and honed edge radius (S shaped) showed edge damage and lower values of the tool’s life. Low-CBN, S-shaped tools showed similar results, but with an inferior performance when compared with tools with high CBN content in both forms of edge preparation.

Plane Detection Using Affine Homography

AIRES, Kelson R. T.; ARAÚJO, Hélder J.; MEDEIROS, Adelardo A. D. Plane Detection Using Affine Homography. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 2008, Juiz de Fora, MG: Anais... do CBA 2008.

Geometry and topography in James Joyce's Ulysses and Finnegans Wake

Following the development of non-Euclidean geometries from the mid-nineteenth century onwards, Euclid’s system had come to be re-conceived as a language for describing reality rather than a set of transcendental laws. As Henri Poincaré famously put it, ‘[i]f several geometries are possible, is it certain that our geometry [...] is true?’. By examining Joyce’s linguistic play and conceptual engagement with ground-breaking geometric constructs in Ulysses and Finnegans Wake, this thesis explores how his topographical writing of place encapsulates a common crisis between geometric and linguistic modes of representation within the context of modernity. More specifically, it investigates how Joyce presents Euclidean geometry and its topographical applications as languages, rather than ideally objective systems, for describing visual reality; and how, conversely, he employs language figuratively to emulate the systems by which the world is commonly visualised. With reference to his early readings of Giordano Bruno, Henri Poincaré and other critics of the Euclidean tradition, it investigates how Joyce’s obsession with measuring and mapping space throughout his works enters into his more developed reflections on the codification of visual signs in Finnegans Wake. In particular, this thesis sheds new light on Joyce’s developing fascination with the ‘geometry of language’ practised by Bruno, whose massive influence on Joyce is often assumed to exist in Joyce studies yet is rarely explored in any great detail.