Inverse problems arise in a wide variety of applications including biomedicine, environmental sciences, astronomy, and more. Computing reliable solutions to these problems requires the inclusion of prior knowledge in a process that is often referred to as regularization. Most regularization techniques require suitable choices of regularization parameters. In this work, we will describe new approaches that use deep neural networks (DNN) to estimate these regularization parameters. We will train multiple networks to approximate mappings from observation data to individual regularization parameters in a supervised learning approach. Once the networks are trained, we can efficiently compute regularization parameters for newly-obtained data by forward propagation through the DNNs. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. Numerical results for tomography demonstrate the potential benefits of using DNNs to learn regularization parameters. / Master of Science / Inverse problems arise in a wide variety of applications including biomedicine, environmental sciences, astronomy, and more. With these types of problems, the goal is to reconstruct an approximation of the original input when we can only observe the output. However, the output often includes some sort of noise or error, which means that computing reliable solutions to these problems is difficult. In order to combat this problem, we can include prior knowledge about the solution in a process that is often referred to as regularization. Most regularization techniques require suitable choices of regularization parameters. In this work, we will describe new approaches that use deep neural networks (DNN) to obtain these parameters. We will train multiple networks to approximate mappings from observation data to individual regularization parameters in a supervised learning approach. Once the networks are trained, we can efficiently compute regularization parameters for newly-obtained data by forward propagation through the DNNs. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. Numerical results for tomography demonstrate the potential of using DNNs to learn regularization parameters.

To fully optimize the value of material produced from a log requires information about the log's internal defects prior to log breakdown. Studies have shown that a 7 to 21 percent improvement in log value recovery can be achieved if the location and identity of internal defects are known. Recent developments in advanced nondestructive testing methods such as CT and MRI offer, for the first time, the possibility of finding internal defects in logs prior to breakdown. Our ability to detect and recognize defects using this data depends Critically on our understanding of wood structure and our ability to devise reliable method for automated image interpretation. While a lot of work has gone into demonstrating that certain types of defects manifest themselves in such sensor imagery, there has not been a systematic approach toward making the automatic inspection of logs a practical reality. This dissertation describes work aimed at creating a viable automated technology for locating and identifying log defects. The imaging modality used in this dissertation is CT. An important first step is to establish a data base of imagery and the ground truth information to determine how the various defects manifest themselves in this imagery. The second step is to study defect characterization and determine exactly which defects are detectable. The final step is to develop a basic method of approach to automated image analysis. A data base has been created from two hardwood species. It is representative of hardwood logs in the sense that it contains almost all the major defects. Visual inspection and analysis of these CT images have shown that most defects manifest themselves in CT imagery. These defects can be detected by features such as intensity, 3-d shape, and texture. As a means of automated image analysis, a knowledge-based vision system has been developed. It consists of three components: a data acquisition unit, an image segmentation module, and scene analysis module. A 3-d adaptive LS filter has been developed in the segmentation module that is efficient in removing annual rings while preserving other needed high frequency detail. Images are segmented using a multiple threshold scheme and regions are grouped using a 3-d connected volume growing algorithm. To represent the 3-d nature of wood defects, a set of basic features have been defined and used to design a set of hypothesis tests. These features seem to be adequate for defect recognition. To cope with imprecision and ambiguity the Dempster-Shaffer model for knowledge representation is used in the vision system. As a viable alternative to Bayesian-based theory, the Dempster's method of evidential reasoning is employed that uses previously unavailable information such as the amount of ignorance and ambiguity a hypothesis exhibits. As such, the proposed vision system seems to be able to recognize a number of hardwood defects. This dissertation also explores wood texture as an additional feature in defect recognition, and contributes the first application of robust Spatial AutoRegressive modeling to wood texture analysis. Based on a correlation measure, two simple but efficient texture discrimination schemes are proposed. Incorporating a texture test in the scene analysis should improve the vision system's recognition power. As a pilot research, this dissertation has explored a number of important issues in creating a vision system for automated log inspection. Clearly, more work is needed to make the system more robust with additional species. Nevertheless, preliminary results seem to indicate that a machine vision system for automated hardwood log inspection can be developed. / Ph. D.

The fatigue damage is one of the most common distresses observed on the asphalt concrete pavement. The initiation and propagation of the fatigue damage is a complicated phenomenon and very difficult to detect. In order to thoroughly understand the fatigue of asphalt concrete, the behaviors of the key components of asphalt concrete under cyclic loading are investigated respectively. A new experiment method is developed to test the performances of asphalt binder, mastic and mixture under cyclic loading, which provides a tool to unify the fatigue test method for both binding medium and asphalt mixture. Using the new fatigue test method, the effects of loading magnitude, temperature and loading rate to the performance of the asphalt binder under cyclic loading are estimated. Mastic and mixture specimens are prepared by adding fillers and controlled-size aggregates into the asphalt binder. The effects of filler content to the performance of mastic specimen are discussed. The differences between the test results of mastic and mixture are compared and analyzed. Incorporated with the new fatigue test, x-ray tomography system is used in this study to: 1. Analyze the structure change of the mastic specimen before and after the fatigue test. 2. Compare the void content differences between the mastic and mixture specimens. 3. Reconstruct the 3-D internal structures of mastic and mixture specimens to build up the digital specimens. The digital specimens are used in the fatigue simulation of the asphalt binder, mastic and mixture specimens based on the finite element method. The asphalt binder, filler and aggregate are treated as different materials. Damage parameter is introduced to model the degradation of elastic modulus of the asphalt binder caused by fatigue damage. Direct cyclic analysis available in ABAQUS is used to obtain the response of the material after large number of loading cycles. The basalt fibers are dispersed into the asphalt binder and mastic specimens, the effects of the basalt fiber to the performances of the binder and mastic at low temperature are analyzed using both experimental and FEM modeling methods. / Ph. D.

A new high-resolution 3-dimensional P-wave velocity model for Mt. Pinatubo volcano was developed by tomographic inversion of P-wave arrivals from 3,007 earthquakes recorded during a four month period from May to August, 1991. The arrivals were recorded by a network of seismic stations, consisting of seven pre-eruption stations and seven post-eruption stations. Two stations survived the June eruptions. First-arrival travel times were calculated using a finite-difference solution to the eikonal equation. An iterative, linearized approximation of the nonlinear tomography problem was used to solve separately for both velocity structure and hypocenter locations. Several inversions performed with different initial parameters and convergence schemes, and synthetic checkerboard reconstructions indicate a horizontal spatial resolution of velocity perturbations near 4 km. However, the network sparseness allows for a substantial trade-off between focal depth, origin time, and the vertical velocity profile. Many hypocenter clusters collapse from diffuse clouds into tighter features after 3-D relocation. These bands of earthquakes appear to represent fault-related structures. Three low-velocity (relative to the horizontal average) anomalies exist within the well-resolved portion of the velocity model. These anomalies are spatially associated with pre- and post-eruption earthquakes oriented along mapped surface fault zones. Similar anomalies observed at different volcanoes have been previously interpreted as magma related. The low-velocity anomalies at Pinatubo are interpreted as highly fractured, hot volumes of mostly competent rock, which may contain partial melt. / Master of Science

Analysis of synthetic data was performed to determine the most cost-effective tomographic monitoring system for a geologic carbon sequestration injection site. Artificial velocity models were created that accounted for the expected velocity decrease due to the existence of a CO₂ plume after underground injection into a depleted petroleum reservoir. Seismic events were created to represent induced seismicity from injection, and five different geophone arrays were created to monitor this artificial seismicity. Double-difference tomographic inversion was performed on 125 synthetic data sets: five stages of CO₂ plume growth, five seismic event regions, and five geophone arrays. Each resulting velocity model from tomoDD—the double-difference tomography program used for inversion—was compared quantitatively to its respective synthetic velocity model to determine an accuracy value. The quantitative results were examined in an attempt to determine a relationship between cost and accuracy in monitoring, verification, and accounting applications using double-difference tomography. While all scenarios resulted in little error, no such relationship could be found. The lack of a relationship between cost and error is most likely due to error inherent to the travel time calculation algorithm used. / Master of Science

Radio Tomographic imaging (RTI) is an exciting new field that utilizes a sensor network of a large number of relatively simple radio nodes for inverse imaging, utilizing similar mathematical algorithms to those used in medical imaging. Previous work in this field has almost exclusively focused on device-free object location and tracking. In this thesis, the application of RTI to propagation problems will be studied-- specifically using RTI to measure the strength and location of attenuating objects in an area of interest, then using this knowledge of the shadowing present in an area for radio coverage prediction. In addition to radio coverage prediction, RTI can be used to improve the quality of RSS-based position location estimates. Because the traditional failing of RSS-based multilateration is ranging error due to attenuating objects, RTI has great potential for improving the accuracy of these estimates if shadowing objects are accounted for. In this thesis, these two problems will primarily be studied. A comparison with other inverse imaging, remote sensing, and propagation modeling techniques of interest will be given, as well as a description of the mathematical theory used for tomographic image reconstruction. Proof-of-concept of the efficacy of applying RTI to position location will be given by computer simulation, and then physical experiments with an RTI network consisting of 28 Zigbee radio sensors will be used to verify the validity of these assertions. It will be shown in this thesis that RTI does provide noticeable improvement in RSS-based position location accuracy in cluttered environments, and it produces much more accurate RSS estimates than a standard exponential path-loss model is able to provide. / Master of Science

State-of-Health (SoH), a specified measure of stability, is a critical parameter for determining the safe operating area of a battery cell and battery packs to avoid abuse and prevent failure and accidents. A series of experiments were performed to evaluate the performance of a 4P1S battery array using electrochemical impedance spectroscopy to identify key frequencies that may describe battery state of health at any state of charge. Using a large sample number of cells, the state of health frequency, fSoH, for these LiFePO4 26650 cells is found to be 158 Hz. Four experiments were performed to evaluate the lifetime in different configurations: single-cell at 1C (2.6A), single-cell at 10C (26A), four cells in parallel at 10C (ideal match), and four cells in parallel (manufacturer match). The lifetime for each experiment set degraded substantially, with the final parallel series reaching end of life at 400 cycles, a 75.32% reduction in life compared to operating solo. Analysis of the fSoH data for these cells revealed a change in imaginary impedance at the critical frequency that corresponded to changes in the capacity and current data, supporting the development of a single-frequency diagnostic tool. An electrochemical model of the battery was generated, and it indicated the anode material was aging faster than the SEI layer, the opposite of normal cell degradation. A post-mortem analysis of cells from three configurations (baseline, single-cell, and parallel-cell) supported the modeling, as physical damage to the copper current collector in the anode was visible in the parallel-connected cell. / Ph. D. / Lithium-ion batteries are used in a large number of applications, from cellular phones to laptops and electric vehicles. In low power devices, such as a laptop, these batteries can be relatively stable if the associated circuitry is designed properly. However, as the amount of power required from the battery increases, the possibility of an internal battery fault will also increase. The ability to determine the stability of the battery for military applications such as laser weapon systems, electromagnetic railguns or commercial systems such as electric vehicles or industrial-scale micro-grids becomes critical to prevent catastrophic events such as fires. Additionally, the ability to determine the battery State-of-Health (SoH), a specified measure of stability, will enable advance warning of a failing battery to optimize the logistics chain in an operational system. A battery marked as “bad” can be scheduled for replacement before a failure actually occurs. This dissertation has designed a series of experiments that establishes the technology to detect these internals faults, and applies them to a scaled battery system that represents a much larger system. When batteries are placed in parallel and discharged at very high currents, typical of the military applications, the lifetime for the cells was reduced by 75% when compared to batteries discharged under the same conditions by themselves. A post-mortem analysis of cells from three different conditions (uncycled, single-cell, parallel-cell) reveals physical damage to the internal electrodes that indicates a high level of internal destruction occurs at high currents when in parallel arrays.

The National Science Foundation has announced a plan to establish a Deep Underground Science and Engineering Laboratory (DUSEL) for interdisciplinary research in physics, geosciences, biosciences and engineering. The proposed laboratory will extend to a depth of about 2200 meters and will consist of research facilities for long term study. To date, eight sites in North America have been proposed to host DUSEL. One of these sites, known as Kimballton, is located near Butt Mountain in Giles County in southwestern Virginia. Two seismic lines were acquired along the top of Butt Mountain in June of 2004 to support the ongoing integrated site characterization effort by the Kimballton Science Team. Both lines, approximately 3 km in length, are standard multifold seismic reflection data aimed at imaging faults, thrust sheets, and repeated sections of Paleozoic rocks in the vicinity of the proposed Kimballton site. Crooked line geometry, irregular geophone spacing, ground roll, and poor impedance contrasts between juxtapositioned rock units were challenges in processing the data. Non-standard processing techniques included the use of travel time tomography to accurately constrain near surface velocities, the use of 2D median filters to remove ground roll, and stacking only offsets exceeding 500 m. Interpretation of seismic data supports a triplicated stratigraphic section caused by the stacking of the the St. Clair and Narrows thrust sheets. The St. Clair and Narrows faults are interpreted as shear zones within ductile units of the Martinsburg Formation. 3D travel time tomography was used to build a near surface velocity model of Lines 1 and 2 for the purposes of imaging near surface structure and constraining the extent of topographic lineaments, which are interpreted as bedrock joint systems. Interpretation of the velocity models suggests that the broadly folded strata of the Butt Mountain synclinorium dip gently to the east along the hinge surface. The surface extrapolation of the Lookout Rock fault and the intersection of topographic lineaments with the seismic lines are expressed as low velocity zones that extend to depths of 150 m. This may be related to accelerated weathering along jointed rock surfaces. Results of this study have already been incorporated into the NSF proposal submitted by the Kimballton Science Team (http://www.phys.vt.edu/~kimballton/s2p/b2.pdf). / Master of Science

This study presents a study on the binder film thickness effect on aggregate contact behavior. As a three-phase material composed of aggregates, asphalt binder and air voids, asphalt mixture could be considered as a visco-elastic material in the low stress level. Since the behavior of the mixture depends largely on the relationship of different components, a well developed contact model for micro-structural modeling is very important for understanding the deformation mechanism of the mixture. In this study, the contact modeling of asphalt mixture was reviewed and the numerical tools used to investigate the micromechanical behavior of asphalt mixture will also be introduced. By using the cabinet x-ray tomography system, the displacement and resistant force of a system of particles bonded by a thin layer binder are measured and recorded. Then, the results are compared with the theoretical solutions of a normal compliance model for a system comprised of two elastic particles bonded by a thin layer of visco-elastic binder. A closed-form time-dependent relationship between the contact forces and the relative particle/binder movements was developed. A reasonable agreement between experiments results and model predicted results is obtained combined with parametric analysis. / Master of Science

Regenerative medicine involves formation of tissue or organ for replacement of a wounded or dysfunctional tissue. Healthy cells extracted from the patient are expanded and are seeded on a three-dimensional biodegradable scaffold. The structure is then placed in a bioreactor and is provided with nutrients for the cells, which proliferate and migrate throughout the scaffold to eventually form a desired to tissue that can be transplanted into the patient's body.  Inability to monitor this complex process of regeneration in real-time makes control and optimization of this process extremely difficult. Histology, the gold standard used for tissue structural assessment, is a static technique that only provides "snapshots" of the progress and requires the specimen to be sacrificed. This inefficiency severely limits our understanding of the biological processes associated with tissue growth during the in vitro pre-conditioning phase. Optical Coherence Tomography (OCT) enables imaging of cross sectional structure in biological tissues by measuring the echo time delay of backreflected light. OCT has recently emerged as an important method to assess the structures of physiological, pathological as well as tissue engineered blood vessels. The goal of the present study is to develop an imaging system for non-destructive monitoring of blood vessels maturing within a bioreactor. Non-destructive structural imaging of tissue-engineered blood vessels cultured in a novel bioreactor was performed using free-space and catheter-based OCT imaging, while monitoring of the endothelium development was performed using a fluorescence imaging system that utilizes a commercial OCT catheter. The project included execution of three specific aims. Firstly, we developed OCT instrumentation to determine geometrical and optical properties of porcine and human skin in real-time. The purpose of the second aim was to assess structural development of tissue-engineered blood vessels maturing in a bioreactor. We constructed a novel quartz-based bioreactor that will permit free space and catheter-based OCT imaging of vascular grafts. The grafts were made of biodegradable PCL-collagen and seeded with multipotent mesenchymal cells. We imaged the maturing grafts over 30 days to assess changes in graft wall thickness. We also monitored change in optical properties of the grafts based on free-space OCT scanning.   Finally, in order to visualize the proliferation of endothelial cells and development of the endothelium, we developed an imaging system that utilizes a commercial OCT catheter for single-cell-level imaging of the growing endothelium of a tissue-engineered blood vessel. We have developed two modules of an imaging system for non-destructive monitoring of maturing bioengineered vascular grafts. The first module provides the ability to non-destructively examine the structure of the grafts while the second module can track the progress of endothelialization. As both modules use the same endoscope for imaging, when operated in sequence, they will produce high-resolution, three-dimensional, structural details of the graft and two-dimensional spatial distribution of ECs on the lumen. This non-destructive, multi-modality imaging can be potentially used to monitor and assess the development of luminal bioengineered constructs such as colon or trachea. / Ph. D.