Geometric Fuzzy Logic Systems

There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems

Geometric algorithms for geographic information systems

A geographic information system (GIS) is a software package for storing geographic data and performing complex operations on the data. Examples are the reporting of all land parcels that will be flooded when a certain river rises above some level, or analyzing the costs, benefits, and risks involved with the development of industrial activities at some place. A substantial part of all activities performed by a GIS involves computing with the geometry of the data, such as location, shape, proximity, and spatial distribution. The amount of data stored in a GIS is usually very large, and it calls for efficient methods to store, manipulate, analyze, and display such amounts of data. This makes the field of GIS an interesting source of problems to work on for computational geometers. In chapters 2-5 of this thesis we give new geometric algorithms to solve four selected GIS problems.These chapters are preceded by an introduction that provides the necessary background, overview, and definitions to appreciate the following chapters. The four problems that we study in chapters 2-5 are the following: Subdivision traversal: we give a new method to traverse planar subdivisions without using mark bits or a stack. Contour trees and seed sets: we give a new algorithm for generating a contour tree for d-dimensional meshes, and use it to determine a seed set of minimum size that can be used for isosurface generation. This is the first algorithm that guarantees a seed set of minimum size. Its running time is quadratic in the input size, which is not fast enough for many practical situations. Therefore, we also give a faster algorithm that gives small (although not minimal) seed sets. Settlement selection: we give a number of new models for the settlement selection problem. When settlements, such as cities, have to be displayed on a map, displaying all of them may clutter the map, depending on the map scale. Choices have to be made which settlements are selected, and which ones are omitted. Compared to existing selection methods, our methods have a number of favorable properties. Facility location: we give the first algorithm for computing the furthest-site Voronoi diagram on a polyhedral terrain, and show that its running time is near-optimal. We use the furthest-site Voronoi diagram to solve the facility location problem: the determination of the point on the terrain that minimizes the maximal distance to a given set of sites on the terrain

High-Quality Simplification and Repair of Polygonal Models

Because of the rapid evolution of 3D acquisition and modelling methods, highly complex and detailed polygonal models with constantly increasing polygon count are used as three-dimensional geometric representations of objects in computer graphics and engineering applications. The fact that this particular representation is arguably the most widespread one is due to its simplicity, flexibility and rendering support by 3D graphics hardware. Polygonal models are used for rendering of objects in a broad range of disciplines like medical imaging, scientific visualization, computer aided design, film industry, etc. The handling of huge scenes composed of these high-resolution models rapidly approaches the computational capabilities of any graphics accelerator. In order to be able to cope with the complexity and to build level-of-detail representations, concentrated efforts were dedicated in the recent years to the development of new mesh simplification methods that produce high-quality approximations of complex models by reducing the number of polygons used in the surface while keeping the overall shape, volume and boundaries preserved as much as possible. Many well-established methods and applications require "well-behaved" models as input. Degenerate or incorectly oriented faces, T-joints, cracks and holes are just a few of the possible degenaracies that are often disallowed by various algorithms. Unfortunately, it is all too common to find polygonal models that contain, due to incorrect modelling or acquisition, such artefacts. Applications that may require "clean" models include finite element analysis, surface smoothing, model simplification, stereo lithography. Mesh repair is the task of removing artefacts from a polygonal model in order to produce an output model that is suitable for further processing by methods and applications that have certain quality requirements on their input. This thesis introduces a set of new algorithms that address several particular aspects of mesh repair and mesh simplification. One of the two mesh repair methods is dealing with the inconsistency of normal orientation, while another one, removes the inconsistency of vertex connectivity. Of the three mesh simplification approaches presented here, the first one attempts to simplify polygonal models with the highest possible quality, the second, applies the developed technique to out-of-core simplification, and the third, prevents self-intersections of the model surface that can occur during mesh simplification

Geometry–aware finite element framework for multi–physics simulations: an algorithmic and software-centric perspective

In finite element simulations, the handling of geometrical objects and their discrete representation is a critical aspect in both serial and parallel scientific software environments. The development of codes targeting such envinronments is subject to great development effort and man-hours invested. In this thesis we approach these issues from three fronts. First, stable and efficient techniques for the transfer of discrete fields between non matching volume or surface meshes are an essential ingredient for the discretization and numerical solution of coupled multi-physics and multi-scale problems. In particular L2-projections allows for the transfer of discrete fields between unstructured meshes, both in the volume and on the surface. We present an algorithm for parallelizing the assembly of the L2-transfer operator for unstructured meshes which are arbitrarily distributed among different processes. The algorithm requires no a priori information on the geometrical relationship between the different meshes. Second, the geometric representation is often a limiting factor which imposes a trade-off between how accurately the shape is described, and what methods can be employed for solving a system of differential equations. Parametric finite-elements and bijective mappings between polygons or polyhedra allow us to flexibly construct finite element discretizations with arbitrary resolutions without sacrificing the accuracy of the shape description. Such flexibility allows employing state-of-the-art techniques, such as geometric multigrid methods, on meshes with almost any shape.t, the way numerical techniques are represented in software libraries and approached from a development perspective, affect both usability and maintainability of such libraries. Completely separating the intent of high-level routines from the actual implementation and technologies allows for portable and maintainable performance. We provide an overview on current trends in the development of scientific software and showcase our open-source library utopia

Hamiltonian Paths and Strands for Unified Grid Approach for Computing Aerodynamic Flows

A solution algorithm using Hamiltonian paths and strand grids is presented for compressible Reynolds-Averaged Navier–Stokes (RANS) formulation as a unified grid approach. The hidden line-structure is robustly identified on the general unstructured grid with mixed elements which provides a framework for line-solvers similar to that with a structured grid solver. A pure quadrilateral/hexahedral mesh is a prerequisite for the line identification and enables approximate factorization along the lines on the unstructured grid. Among various methods, subdivision is the easiest way to obtain a pure quadrilateral/hexahedral mesh from the general unstructured grid. Strand based grids have been employed to extend to three-dimension by extruding the surface mesh. As a result, Hamiltonian paths on the surface mesh represents two distinct surface coordinate directions and the strand grids represent the wall normal direction. These structures are analogous to the grid coordinate directions in a structured grid solver, therefore the current method is directly applicable on the typical structured grid. The numerical accuracy and convergence rate are investigated under various flow conditions. The numerical efficiency was improved with a line-implicit method compared to a point-implicit method on the unstructured grid. Both stencil- and gradient-based reconstructions are available on the unstructured grid and the numerical accuracy for each method was evaluated on both structured and unstructured grids. The combined reconstruction method was also proposed for the current mesh system which uses both stencil- and gradient-based reconstructions simultaneously but for different grid directions. The solution convergence rate has been improved further using Generalized Minimum Residual (GMRES) method. GMRES requires a preconditioning step which is performed using the line-implicit method. GMRES provides better convergence rate than the pure line-implicit method at various flow conditions. Both parts of mesh generation and flow solver are parallelized to be executed in parallel using METIS and MPI. During the mesh generation, two different domain partitioning methods are suggested for the strand grid and the unstructured volume mesh, respectively. The capability of the flow solver has been extended for rotary wing simulations: time-accurate method, turbulence model, moving grids, and overset meshes. The flow solver is also integrated into a multi-mesh/multi-solver paradigm through a Python framework which enables a more efficient solution algorithm than a single-solver. The integrated framework has been applied to various practical problems, such as wind turbine, rotor hub, and elastic rotor blades

Anisotropic output-based adaptation with tetrahedral cut cells for compressible flows

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections."September 2008."Includes bibliographical references (leaves 153-164).Anisotropic, adaptive meshing for flows around complex, three-dimensional bodies remains a barrier to increased automation in computational fluid dynamics. Two specific advances are introduced in this thesis. First, a finite-volume discretization for tetrahedral cut-cells is developed that makes possible robust, anisotropic adaptation on complex bodies. Through grid refinement studies on inviscid flows, this cut-cell discretization is shown to produce similar accuracy as boundary-conforming meshes with a small increase in the degrees of freedom. The cut-cell discretization is then combined with output-based error estimation and anisotropic adaptation such that the mesh size and shape are controlled by the output error estimate and the Hessian (i.e. second derivatives) of the Mach number, respectively. Using a parallel implementation, this output-based adaptive method is applied to a series of sonic boom test cases and the automated ability to correctly estimate pressure signatures at several body lengths is demonstrated starting with initial meshes of a few thousand control volumes. Second, a new framework for adaptation is introduced in which error estimates are directly controlled by removing the common intermediate step of specifying a desired mesh size and shape. As a result, output error control can be achieved without the adhoc selection of a specific field (such as Mach number) to control anisotropy, rather anisotropy in the mesh naturally results from both the primal and dual solutions. Furthermore, the direct error control extends naturally to higher-order discretizations for which the use of a Hessian is no longer appropriate to determine mesh shape. The direct error control adaptive method is demonstrated on a series of simple test cases to control interpolation error and discontinuous Galerkin finite element output error. This new direct method produces grids with less elements but the same accuracy as existing metric-based approaches.by Michael Andrew Park.Ph.D

Computational Aspects of Heat Transfer in Structures

Techniques for the computation of heat transfer and associated phenomena in complex structures are examined with an emphasis on reentry flight vehicle structures. Analysis methods, computer programs, thermal analysis of large space structures and high speed vehicles, and the impact of computer systems are addressed

Rotating Stall and Passive Flow Control on Blade Profiles and in Centrifugal Compressors

PhDThe operating range and efficiency of a centrifugal compressor is limited by the development of rotating stall and surge at low mass flow rates. To extend the operating range of a compressor, flow control in the compressor can be used to suppress secondary flow structures that lead to rotating stall. The presented work seeks to use the novel idea of placing passive vortex generators (VG) upstream of the impeller to suppress rotating stall, while also developing new concepts and optimization of microvortex generators (MVG). To accomplish this goal, a new SIMPLE-type algorithm for compressible flows was written in Code_Saturne along with a 2nd-order MUSCL scheme for convective terms and an AUSM+-up scheme for mass flux computation. The new algorithm was successfully validated against several widely-used test cases. The new algorithm was used to model the flow of the NASA CC3, a high-speed centrifugal compressor, from choke to rotating stall with a vaneless and vaned diffuser. The new algorithm predicted the performance of the compressor with a vaneless diffuser very well; satisfactory results were obtained for the compressor with a vaned diffuser. The full compressor with a vaned diffuser was used to model rotating stall. A complex stall cycle between the inlet of the impeller and diffuser was observed and studied. The fundament behavior of MVG, i.e. micro (sub-boundary layer) vortex generator, in a turbulent boundary layer was investigated in a channel flow with RANS and LES. Complementary wind tunnel testing was conducted to validate the computational predictions. The configuration of the MVG was studied to determine an optimal configuration and several conclusions were reached on the design of MVG. Most importantly triangle MVG were found to be the most efficient shape followed by NACA0012 and e423-type MVG, and a MVG angle of 18˚ to 20˚ was found to be optimal. Rectangle MVG were observed to suffer flow separation on the vanes which reduced their performance. The circulation and drag of a MVG was found to have a logarithmic relationship with the device’s Reynolds number. These findings were incorporated in a LES study to control separated flow on the e387 airfoil and achieved an improvement in lift-to-drag ratio of 11.27%. Additional recommendations for MVG implementation were given. Combining the work on the NASA CC3 with the work on MVG, vortex generators were implemented near the inlet of the impeller. A detailed optimization study was conducted for the implementation vortex generators in the compressor. It was found vortex generators equal to the boundary layer thickness were the most efficient on controlling the downstream flow. The best configuration was implemented into the full compressor with a vaned diffuser to assess the ability of vortex generators to suppress rotating stall. The vortex generators were found to suppress rotating stall and extend the operating range of the compressor

Investigation of the use of meshfree methods for haptic thermal management of design and simulation of MEMS

This thesis presents a novel approach of using haptic sensing technology combined with virtual environment (VE) for the thermal management of Micro-Electro-Mechanical-Systems (MEMS) design. The goal is to reduce the development cycle by avoiding the costly iterative prototyping procedure. In this regard, we use haptic feedback with virtua lprototyping along with an immersing environment. We also aim to improve the productivity and capability of the designer to better grasp the phenomena operating at the micro-scale level, as well as to augment computational steering through haptic channels. To validate the concept of haptic thermal management, we have implemented a demonstrator with a user friendly interface which allows to intuitively "feel" the temperature field through our concept of haptic texturing. The temperature field in a simple MEMS component is modeled using finite element methods (FEM) or finite difference method (FDM) and the user is able to feel thermal expansion using a combination of different haptic feedback. In haptic application, the force rendering loop needs to be updated at a frequency of 1Khz in order to maintain continuity in the user perception. When using FEM or FDM for our three-dimensional model, the computational cost increases rapidly as the mesh size is reduced to ensure accuracy. Hence, it constrains the complexity of the physical model to approximate temperature or stress field solution. It would also be difficult to generate or refine the mesh in real time for CAD process. In order to circumvent the limitations due to the use of conventional mesh-based techniques and to avoid the bothersome task of generating and refining the mesh, we investigate the potential of meshfree methods in the context of our haptic application. We review and compare the different meshfree formulations against FEM mesh based technique. We have implemented the different methods for benchmarking thermal conduction and elastic problems. The main work of this thesis is to determine the relevance of the meshfree option in terms of flexibility of design and computational charge for haptic physical model