An improved quadratic program for unweighted Euclidean 1-center location problem

AbstractIn this paper, an improved quadratic programing formulation for the solution of unweighted Euclidean 1-center location problem is presented. The original quadratic program is proposed by Nair and Chandrasekaran in 1971. Besides, they proposed a geometric approach for problem solving. Then, they concluded that the geometric approach is more efficient than the quadratic program. This conclusion is true only when all decision variables are treated as nonnegative variables. To improve the quadratic program, one of those variables should be an unrestricted variable as it is presented here. Numerically we proved that the improved quadratic program leads to the optimal solution of the problem in parts of second regardless of the size of the problem. Moreover, constrained version of the problem is solved optimally via the improved quadratic program in parts of second

A Green's function approach to the natural vibration of thin spherical shell segments - A numerical method Final report

Green function approach to natural vibration of thin spherical shell segment

The use of primitives in the calculation of radiative view factors

Compilations of radiative view factors (often in closed analytical form) are readily available in the open literature for commonly encountered geometries. For more complex three-dimensional (3D) scenarios, however, the effort required to solve the requisite multi-dimensional integrations needed to estimate a required view factor can be daunting to say the least. In such cases, a combination of finite element methods (where the geometry in question is sub-divided into a large number of uniform, often triangular, elements) and Monte Carlo Ray Tracing (MC-RT) has been developed, although frequently the software implementation is suitable only for a limited set of geometrical scenarios. Driven initially by a need to calculate the radiative heat transfer occurring within an operational fibre-drawing furnace, this research set out to examine options whereby MC-RT could be used to cost-effectively calculate any generic 3D radiative view factor using current vectorisation technologies

Volumetric Data Analysis for Reverse Engineering and Solid Additive Manufacturing: A Framework for Geometric Metrological Analysis

Poor geometric quality is one of the main constraints that hinders the wide adoption of reverse engineering (RE) and additive manufacturing (AM). RE models from a single scan will most likely generate inaccurate representations of the original design due to the uncertainties existing in individual parts and scanning procedures. On the other hand, metrological methodologies for AM significantly differ from those for the traditional manufacturing processes. Conventional statistical methodologies overlook these three-dimensional (3D) feature-independent processing techniques. In this dissertation, we develop a novel statistical data analysis framework---volumetric data analysis (VDA)---to deal with the uniqueness of both technologies. In general, this framework also addresses the rising analytical needs of 3D geometric data. Through VDA, we can simultaneously analyze the measured points on the outer surfaces and their relationships to acquire manufacturing knowledge. The main goal of this dissertation is to apply the proposed framework in multiple RE and AM applications related to their geometric quality characteristics. First, we demonstrate a novel estimator to increase the precision of RE-generated models. We built a Bayesian model with prior domain knowledge to model the landmarks’ uncertainty. We also proposed a bi-objective optimization model to answer the RE process-planning questions, e.g., how many scans and parts are required to achieve the precision requirements. The second major contribution is a study of tolerance estimation procedure for the re-manufacturing of legacy parts. We propose a systematic geometric inspection methodology for the RE and AM systems. Moreover, based on the domain knowledge in production-process design and planning, we developed methods to estimate empirical tolerances from a small batch of legacy parts. The third major contribution of this dissertation is to design an automated variance modeling algorithm for 3D scanners. The algorithm utilizes a physical object’s local geometric descriptors and Bayesian extreme learning machines to predict the landmarks’ variances. Lastly, we introduce the VDA framework to AM-oriented experimental analysis. Specifically, we propose a high-dimensional hypothesis testing procedure to statistically compare the geometric production accuracy under two AM process settings. We present new visualization tools for deviation diagnostics to aid in interpreting and comparing the process outputs

Hierarchical Variance Reduction Techniques for Monte Carlo Rendering

Ever since the first three-dimensional computer graphics appeared half a century ago, the goal has been to model and simulate how light interacts with materials and objects to form an image. The ultimate goal is photorealistic rendering, where the created images reach a level of accuracy that makes them indistinguishable from photographs of the real world. There are many applications ñ visualization of products and architectural designs yet to be built, special effects, computer-generated films, virtual reality, and video games, to name a few. However, the problem has proven tremendously complex; the illumination at any point is described by a recursive integral to which a closed-form solution seldom exists. Instead, computer simulation and Monte Carlo methods are commonly used to statistically estimate the result. This introduces undesirable noise, or variance, and a large body of research has been devoted to finding ways to reduce the variance. I continue along this line of research, and present several novel techniques for variance reduction in Monte Carlo rendering, as well as a few related tools. The research in this dissertation focuses on using importance sampling to pick a small set of well-distributed point samples. As the primary contribution, I have developed the first methods to explicitly draw samples from the product of distant high-frequency lighting and complex reflectance functions. By sampling the product, low noise results can be achieved using a very small number of samples, which is important to minimize the rendering times. Several different hierarchical representations are explored to allow efficient product sampling. In the first publication, the key idea is to work in a compressed wavelet basis, which allows fast evaluation of the product. Many of the initial restrictions of this technique were removed in follow-up work, allowing higher-resolution uncompressed lighting and avoiding precomputation of reflectance functions. My second main contribution is to present one of the first techniques to take the triple product of lighting, visibility and reflectance into account to further reduce the variance in Monte Carlo rendering. For this purpose, control variates are combined with importance sampling to solve the problem in a novel way. A large part of the technique also focuses on analysis and approximation of the visibility function. To further refine the above techniques, several useful tools are introduced. These include a fast, low-distortion map to represent (hemi)spherical functions, a method to create high-quality quasi-random points, and an optimizing compiler for analyzing shaders using interval arithmetic. The latter automatically extracts bounds for importance sampling of arbitrary shaders, as opposed to using a priori known reflectance functions. In summary, the work presented here takes the field of computer graphics one step further towards making photorealistic rendering practical for a wide range of uses. By introducing several novel Monte Carlo methods, more sophisticated lighting and materials can be used without increasing the computation times. The research is aimed at domain-specific solutions to the rendering problem, but I believe that much of the new theory is applicable in other parts of computer graphics, as well as in other fields

Design Optimization for Spatial Arrangement of Used Nuclear Fuel Containers

Canada's proposed deep geological repository is a multiple-barrier system designed to isolate used nuclear fuel containers (UFCs) indefinitely with no release of radionuclides for at least one million years. Placing UFCs together as densely as possible is ideal for mitigating repository size and cost. However, due to heat generation from radioactive decay and material limitations, a key design criterion is that the maximum temperature inside the repository must not exceed 100 °C. To satisfy that criterion, design optimization for the spatial arrangement of UFCs in a crystalline rock repository is performed. Spatial arrangement pertains to: (i) the spacing between UFCs, (ii) the separation between placement rooms underground, and (iii) the locations of variously aged UFCs that generate heat at different rates. Most studies have considered UFCs to be identical in age during placement into the repository. Parameter analyses have also been performed to evaluate repository performance under probable geological conditions. In this work, the various ages of UFCs and the uncertainties in spacing-related design variables are of focus. Techniques for the actual placement of UFCs in the deep geological repository based on their age and methods for repository risk analysis using yield optimization are developed. The thermal evolution inside the deep geological repository is simulated using a finite element model. With many components inside the massive repository planned for upwards of 95,000 UFCs, direct optimization of the model is impractical or even infeasible due to it being computationally expensive to evaluate. Surrogate optimization is used to overcome that burden by reducing the number of detailed evaluations required to reach the optimal designs. Two placement cases are studied: (i) UFCs all having been discharged from a Canadian Deuterium Uranium reactor for 30 years, which is a worst-case scenario, and (ii) UFCs having been discharged between 30 and 60 years. Design options that have UFC spacing 1–2 m and placement room separation 10–40 m are explored. The placement locations of the variously aged UFCs are specified using either sinusoidal (cosine) functions or Kumaraswamy probability density functions. Yield optimization under assumed design variable tolerances and distributions is performed to minimize the probability of a system failure, which occurs when the maximum temperature constraint of 100 °C is exceeded. This method allows variabilities from the manufacturing and construction of the repository components that affect the design variables to be taken into account, incorporating a stochastic aspect into the design optimization that surrogate optimization would not include. Several distributions for the design variables are surveyed, and these include uniform, normal, and skewed distributions—all of which are approximated by Kumaraswamy distributions

Design, Development, and Testing of Near-Optimal Satellite Attitude Control Strategies

Advances in space technology and interest toward remote sensing mission have grown in the recent years, requiring the attitude control subsystems of observation satellites to increase their performances in terms of pointing accuracy and on-board implementability. Moreover, an increased interest in small satellite missions and the recent technological developments related to the CubeSats standard have drastically reduced the cost of producing and flying a satellite mission. In this context, the proposed research aims to improve the state of the art for satellite attitude control methodologies by proposing a near-optimal attitude control strategy, simulated in a high-fidelity environment. Two strategies are presented, both are based on the implementation of a direct method, the Inverse Dynamics in the Virtual Domain (IDVD), and a nonlinear programming solver, the Sequential Gradient-Restoration Algorithm (SGRA). The IDVD allows the transcription of the original optimal control problem into an equivalent nonlinear programming problem. SGRA is adopted for the quick determination of near-optimal attitude trajectories. The two optimization criteria considered are the target acquisition time and the maneuver energy associated to the actuation torques. In addition, the development and initial testing of a satellite attitude simulator testbed for on-ground experimentation of attitude, determination, and control methodologies is proposed. The Suspended Satellite Three-Axis Rotation Testbed (START) is a novel low-cost satellite three-axis attitude simulator testbed, it is located at the Aerospace Robotics Testbed Laboratory (ARTLAB). START is mainly composed by a 3D printed base, a single-board computer, a set of actuators, and an electric battery. The suspension system is based on three thin high tensile strength wires allowing a three degrees-of freedom rotation range comparable to the one of air bearing-based floating testbeds, and minimal resistive torque in all the rotations axis. This set up will enable the hardware in-the-loop experimentation of attitude guidance navigation and control strategies. Finally, a set of guidelines to select a solver for the solution of nonlinear programming problems is proposed. With this in mind, a comparison of the convergence performances of commonly used solvers for both unconstrained and constrained nonlinear programming problems is presented. The terms of comparison involve accuracy, convergence rate, and convergence speed. Because of its popularity among research teams in academia and industry, MATLAB is used as common implementation platform for the solvers

Information extraction techniques for multispectral scanner data

The applicability of recognition-processing procedures for multispectral scanner data from areas and conditions used for programming the recognition computers to other data from different areas viewed under different measurement conditions was studied. The reflective spectral region approximately 0.3 to 3.0 micrometers is considered. A potential application of such techniques is in conducting area surveys. Work in three general areas is reported: (1) Nature of sources of systematic variation in multispectral scanner radiation signals, (2) An investigation of various techniques for overcoming systematic variations in scanner data; (3) The use of decision rules based upon empirical distributions of scanner signals rather than upon the usually assumed multivariate normal (Gaussian) signal distributions

Aeronautical engineering: A continuing bibliography with indexes

This bibliography lists 425 reports, articles and other documents introduced into the NASA scientific and technical information system in January 1985

CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics 1999

These proceedings represent a collection of the latest advances in aeroelasticity and structural dynamics from the world community. Research in the areas of unsteady aerodynamics and aeroelasticity, structural modeling and optimization, active control and adaptive structures, landing dynamics, certification and qualification, and validation testing are highlighted in the collection of papers. The wide range of results will lead to advances in the prediction and control of the structural response of aircraft and spacecraft