Detection of complex point targets with distributed assets in a MIMO radar system

The report explores the problem of detecting complex point target models in a MIMO radar system. A complex point target is a mathematical and statistical model for a radar target that is not resolved in space, but exhibits varying complex reflectivity across the different bistatic view angles. The complex reflectivity can be modeled as a complex stochastic process whose index set is the set of all the bistatic view angles, and the parameters of the stochastic process follow from an analysis of a target model comprising a number of ideal point scatterers randomly located within some radius of the targets center of mass. The proposed complex point targets may be applicable to statistical inference in multistatic or MIMO radar system. Six different target models are summarized here – three 2-dimensional (Gaussian, Uniform Square, and Uniform Circle) and three 3-dimensional (Gaussian, Uniform Cube, and Uniform Sphere). They are assumed to have different distributions on the location of the point scatterers within the target. We develop data models for the received signals from such targets in the MIMO radar system with distributed assets and partially correlated signals, and consider the resulting detection problem which reduces to the familiar Gauss-Gauss detection problem. We illustrate that the target parameter and transmit signal have an influence on the detector performance through target extent and the SNR respectively. A series of the receiver operator characteristic (ROC) curves are generated to notice the impact on the detector for varying SNR. Kullback–Leibler (KL) divergence is applied to obtain the approximate mean difference between density functions the scatterers assume inside the target models to show the change in the performance of the detector with target extent of the point scatterers.

Simulating dioxane transport in a heterogeneous glacial aquifer system (Washtenaw County, Michigan) using publicly available models and data

The primary challenge in groundwater and contaminant transport modeling is obtaining the data needed for constructing, calibrating and testing the models. Large amounts of data are necessary for describing the hydrostratigraphy in areas with complex geology. Increasingly states are making spatial data available that can be used for input to groundwater flow models. The appropriateness of this data for large-scale flow systems has not been tested. This study focuses on modeling a plume of 1,4-dioxane in a heterogeneous aquifer system in Scio Township, Washtenaw County, Michigan. The analysis consisted of: (1) characterization of hydrogeology of the area and construction of a conceptual model based on publicly available spatial data, (2) development and calibration of a regional flow model for the site, (3) conversion of the regional model to a more highly resolved local model, (4) simulation of the dioxane plume, and (5) evaluation of the model's ability to simulate field data and estimation of the possible dioxane sources and subsequent migration until maximum concentrations are at or below the Michigan Department of Environmental Quality's residential cleanup standard for groundwater (85 ppb). MODFLOW-2000 and MT3D programs were utilized to simulate the groundwater flow and the development and movement of the 1, 4-dioxane plume, respectively. MODFLOW simulates transient groundwater flow in a quasi-3-dimensional sense, subject to a variety of boundary conditions that can simulate recharge, pumping, and surface-/groundwater interactions. MT3D simulates solute advection with groundwater flow (using the flow solution from MODFLOW), dispersion, source/sink mixing, and chemical reaction of contaminants. This modeling approach was successful at simulating the groundwater flows by calibrating recharge and hydraulic conductivities. The plume transport was adequately simulated using literature dispersivity and sorption coefficients, although the plume geometries were not well constrained.

POSE ESTIMATION AND 3D RECONSTRUCTION USING SENSOR FUSION

A camera maps 3-dimensional (3D) world space to a 2-dimensional (2D) image space. In the process it loses the depth information, i.e., the distance from the camera focal point to the imaged objects. It is impossible to recover this information from a single image. However, by using two or more images from different viewing angles this information can be recovered, which in turn can be used to obtain the pose (position and orientation) of the camera. Using this pose, a 3D reconstruction of imaged objects in the world can be computed. Numerous algorithms have been proposed and implemented to solve the above problem; these algorithms are commonly called Structure from Motion (SfM). State-of-the-art SfM techniques have been shown to give promising results. However, unlike a Global Positioning System (GPS) or an Inertial Measurement Unit (IMU) which directly give the position and orientation respectively, the camera system estimates it after implementing SfM as mentioned above. This makes the pose obtained from a camera highly sensitive to the images captured and other effects, such as low lighting conditions, poor focus or improper viewing angles. In some applications, for example, an Unmanned Aerial Vehicle (UAV) inspecting a bridge or a robot mapping an environment using Simultaneous Localization and Mapping (SLAM), it is often difficult to capture images with ideal conditions. This report examines the use of SfM methods in such applications and the role of combining multiple sensors, viz., sensor fusion, to achieve more accurate and usable position and reconstruction information. This project investigates the role of sensor fusion in accurately estimating the pose of a camera for the application of 3D reconstruction of a scene. The first set of experiments is conducted in a motion capture room. These results are assumed as ground truth in order to evaluate the strengths and weaknesses of each sensor and to map their coordinate systems. Then a number of scenarios are targeted where SfM fails. The pose estimates obtained from SfM are replaced by those obtained from other sensors and the 3D reconstruction is completed. Quantitative and qualitative comparisons are made between the 3D reconstruction obtained by using only a camera versus that obtained by using the camera along with a LIDAR and/or an IMU. Additionally, the project also works towards the performance issue faced while handling large data sets of high-resolution images by implementing the system on the Superior high performance computing cluster at Michigan Technological University.

Intergranular Corrosion and Stress Corrosion Cracking of Extruded AA6005A

A research program focused on understanding the intergranular corrosion (IGC) and stress corrosion cracking (SCC) behavior of AA6005A aluminum extrusions is presented in this dissertation. The relationship between IGC and SCC susceptibility and the mechanisms of SCC in AA6005A extrusions were studied by examining two primary hypotheses. IGC susceptibility of the elongated grain structure in AA6005A exposed to low pH saltwater was found to depend primarily on the morphology of Cu-containing precipitates adjacent to the grain boundaries in the elongated grain structure. IGC susceptibility was observed when a continuous (or semi-continuous) film of Cu-containing phase was present along the grain boundaries. When this film coarsened to form discrete Cu-rich precipitates, no IGC was observed. The morphology of the Cu-rich phase depended on post-extrusion heat treatment. The rate of IGC penetration in the elongated grain structure of AA6005A-T4 and AA6005A-T6 extrusions was found to be anisotropic with IGC propagating most rapidly along the extrusion direction, and least rapidly along the through thickness direction. A simple 3-dimensional geometric model of the elongated grain structure was accurately described the observed IGC anisotropy, therefore it was concluded that the anisotropic IGC susceptibility in the elongated grain structure was primarily due to geometric elongation of the grains. The velocity of IGC penetration along all directions in AA6005A-T6 decreased with exposure time. Characterization of the local environment within simulated corrosion paths revealed that a pH gradient existed between the tip of the IGC path and the external environment. Knowledge of the local environment within an IGC path allowed development of a simple model based on Fick's first law that considered diffusion of Al3+ away from the tip of the IGC path. The predicted IGC velocity agreed well with the observed IGC velocity, therefore it was determined that diffusion of Al3+ was the primary factor in determining the velocity of IGC penetration. The velocity of crack growth in compact tensile (CT) specimens of AA6005A-T6 extrusion exposed to 3.5% NaCl at pH = 1.5 was nearly constant over a range of applied stress intensities, exposure times, and crack lengths. The crack growth behavior of CT specimens of AA6005A-T6 extrusion exposed to a solution of 3.5% NaCl at pH = 2.0 exhibited similar behavior, but the crack velocity was ~10.5X smaller than that those exposed to a solution at pH =1.5. Analysis of the local stress state and polarization behavior at the crack tip predicted that increasing the pH of the bulk solution from 1.5 to 2.0 would decrease the corrosion current density at the crack tip by approximately 11.8X. This predicted decrease in corrosion current density was in reasonable agreement with the observed decrease in SCC velocity associated with increasing the solution pH from 1.5 to 2.0. The agreement between the predicted and observed SCC velocities suggested that the electrochemical reactions controlling SCC in AA6005A-T6 extrusions are ultimately controlled by the pH gradient that exists between the crack tip and external environment.

Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.