An algorithm for fitting data over a circle using tensor product splines

AbstractAn algorithm is described for surface fitting over a circle by using tensor product splines which satisfy certain boundary conditions. This algorithm is an extension of an existing one for fitting data over a rectangle. The knots of the splines are chosen automatically but a single parameter must be specified to control the tradeoff between closeness of fit and smoothness of fit. The algorithm can easily be generalized for fitting data over any domain that can be described in polar coordinates. Constraints at the boundaries of this approximation domain can be imposed

Experimental and Numerical Investigation of Tire Tread Wear on Block Level

Tread wear appears as a consequence of friction, which mainly depends on surface charac-teristics, contact pressure, slip velocity, temperature and dissipative material properties of the tread material itself. The subsequent description introduces a wear model as a function of the frictional energy rate. A post-processing as well as an adaptive re-meshing algorithm are implemented into a finite element code in order to predict wear loss in terms of mass. The geometry of block models is generated by image processing tools using photographs of the rubber samples in the laboratory. In addition, the worn block shape after the wear test is compared to simulation results

Investigation of an IC Engine Intake Flow Based on Highly Resolved LES and PIV

To reduce emissions and fuel consumption, the current generation of gasoline engines uses technologies such as direct injection, downsizing and supercharging. All of them require a strong vortical in-cylinder charge motion, usually described as “tumble”, to improve fuel-air mixing and enhance flame propagation. The tumble development strongly depends on the flow field during the intake stroke. This flow field is dominated by the intake jet, which has to be captured well in the simulation. This work investigates the intake jet on a steady-state flow bench, especially in the vicinity of the intake valve. At first, the general flow dynamics of the intake jet for three different valve lifts and three different mass flows were investigated experimentally. For the smallest valve lift (3 mm), flow-field measurements using Particle Image Velocimetry (PIV) show that the orientation of the intake jet significantly depends on the air flow rate, attaching to the pent roof for low flow rates. This phenomenon is less pronounced for higher valve lifts. An intermediate valve lift and flow rate were chosen for further investigations by scale-resolving simulations. Three different meshes (coarse, medium and fine) and two turbulence models (Sigma and Detached Eddy Simulation-Shear Stress Transport (DES-SST)) are applied to consider their effect on the numerical results. An ad-hoc post-processing methodology based on the ensemble-averaged velocity field is presented capturing the jet centerline’s mean velocity and velocity fluctuations as well as its orientation, curvature and penetration depth. The simulation results are compared to each other as well as to measurements by PIV

Mechanical Effects of Cellulose, Xyloglucan, and Pectins on Stomatal Guard Cells of Arabidopsis thaliana

Stomata function as osmotically tunable pores that facilitate gas exchange at the surface of plants. Stomatal opening and closure are regulated by turgor changes in guard cells that result in mechanically regulated deformations of guard cell walls. However, how the molecular, architectural, and mechanical heterogeneities that exist in guard cell walls affect stomatal dynamics is unclear. In this work, stomata of wild type Arabidopsis thaliana plants or of mutants lacking normal cellulose, hemicellulose, or pectins were experimentally induced to close or open. Three-dimensional images of these stomatal complexes were collected using confocal microscopy, images were landmarked, and three-dimensional finite element models (FEMs) were constructed for each complex. Stomatal opening was simulated with a 5 MPa turgor increase. By comparing experimentally measured and computationally modeled changes in stomatal geometry across genotypes, anisotropic mechanical properties of guard cell walls were determined and mapped to cell wall components. Deficiencies in cellulose or hemicellulose were both predicted to stiffen guard cell walls, but differentially affected stomatal pore area and the degree of stomatal opening. Additionally, reducing pectin molecular mass altered the anisotropy of calculated shear moduli in guard cell walls and enhanced stomatal opening. Based on the unique architecture of guard cell walls and our modeled changes in their mechanical properties in cell wall mutants, we discuss how each polysaccharide class contributes to wall architecture and mechanics in guard cells. This study provides new insights into how the walls of guard cells are constructed to meet the mechanical requirements of stomatal dynamics

Unsupervised tracking algorithm for precise traffic estimation in panoramic scenes

The traffic experiment conducted by physicist Sugiyama in 2007 has been a seminal work in transportation research. In the experiment, a group of vehicles are instructed to drive on a circular track starting with uniform initial spacing. The isolated experimental environment provides a safe, economic, and controlled environment to study free flow traffic and stop-and-go waves. This dissertation introduces a novel method that automates the data collection process in such an environment. Specifically, the vehicle trajectories are measured using a 360-degree camera, and the fuel rates are recorded via on-board diagnostics (OBD) scanners. The video data from the 360-degree camera is then processed by an offline unsupervised computer vision algorithm. To validate the data collection method, the technique is then evaluated on a series of eight experiments. Validation analysis shows that the collected data are highly accurate, with a mean position bias of less than 0.002 m and a small standard deviation of 0.11 m. The positional data also yields highly reliable velocity estimates: the derived velocities are biased by only 0.02 m/s with a small standard deviation of 0.09 m/s. Beyond the experimental methodology, the produced trajectory and fuel rate data can be readily used to study human driving behaviors, to calibrate microsimulation models, to develop fuel consumption models, and to investigate engine emission. To facilitate future research, the source code and the data are made publicly available online

Geometric Modeling and Recognition of Elongated Regions in Images.

The goal of this research is the recovery of elongated shapes from patterns of local features extracted from images. A generic geometric model-based approach is developed based on general concepts of 2-d form and structure. This is an intermediate-level analysis that is computed from groupings and decompositions of related low-level features. Axial representations are used to describe the shapes of image objects having the property of elongatedness. Curve-fitting is shown to compute axial sequences of the points in an elongated cluster. Script-clustering is performed about a parametric smooth curve to extract elongated partitions of the data incorporating constraints of point connectivity, curve alignment, and strip boundedness. A thresholded version of the Gabriel Graph (GG) is shown to offer most of the information needed from the Minimum Spanning Tree (MST) and Delauney Triangulation (DT), while being easily computable from finite neighborhood operations. An iterative curve-fitting method, that is placed in the general framework of Random Sample Consensus (RANSAC) model-fitting, is used to extract maximal partitions. The method is developed for general parametric curve-fitting over discrete point patterns. A complete structural analysis is presented for the recovery of elongated regions from multispectral classification. A region analysis is shown to be superior to an edge-based analysis in the early stages of recognition. First, the curve-fitting method is used to recover the linear components of complex object regions. The rough locations to start and end a region delineation are then detected by decomposing extracted linear shape clusters with a circular operator. Experimental results are shown for a variety of images, with the main result being an analysis of a high-resolution aerial image of a suburban road network. Analyses of printed circuit board patterns and a LANDSAT river image are also given. The generality of the curve-fitting approach is shown by these results and by its possible applications to other described image analysis problems

Path planning for a redundant robot manipulator using sparse demonstration data

Seidel D. Path planning for a redundant robot manipulator using sparse demonstration data. Bielefeld: Bielefeld University; 2014.The ability to plan and execute of movements to accomplish tasks is a fundamental requirement for all types of robot, whether in industrial or in research applications. This Master Thesis addresses path planning for redundant robot platforms. The research targets two major goals. The first is to bypass the need for an explicit representation of a robot's environment, which is strained with sophisticated computations as well as required expert knowledge. This bypass allows for a considerably more flexible use of a robot, being able to adapt its path planning data to an arbitrary new environment within minutes. The second goal is to provide a real-time capable path planning method, that utilizes the advantages of redundant robot platforms and handles the increased complexity of such systems. These goals are achieved by introducing kinesthetic teaching into path planning, which has already proven to be a successful improvement for single task methods dealing with redundancy resolution. The thesis proposes an approach utilizing a topological neural network algorithm to construct an internal representation of a robot's workspace based on input data obtained from physical guidance of the robot by a user. In order to create feasible and safe movements, information from both configuration space of the robot and task space are employed. The algorithm is extended by heuristics to improve its results for the intended scenario. This modified network construction algorithm constructs a navigation graph similar to classical approaches with explicit modeling. It can be processed by means of conventional search algorithms from graph theory to generate paths between two arbitrary points in the workspace

La traçada ideal per a un Formula Student autònom

Quan es tracta d'esports de motor, la traçada és un factor molt important en el temps per volta. L'objectiu d'aquest projecte consisteix en determinar la trajectòria a seguir al llarg d'un circuit i la velocitat a la qual recórrer-la per un Formula Student autònom. Per fer-ho, es presenten dos algoritmes amb característiques diferents en funció del temps de còmput disponible els quals milloren el temps per volta que s'obtindria al traçar pel centre de la pista. És habitual, a l'hora de dissenyar traçades, utilitzar constructes geomètrics com la curvatura o la longitud si bé la definició d'aquesta depèn només d'una altra magnitud: el temps. En el present treball es proposa optimitzar directament aquesta mètrica, i es demostra que és possible de fer-ho mitjançant algoritmes evolutius obtenint millores significatives respecte al plantejament purament geomètric. A més, s'utilitza una eina de generació aleatòria de circuits per tal de poder avaluar estadísticament els algoritmes presentats així com d'altres d'articles d'índole similar. Aquesta comparativa no només es duu a terme teòricament, sinó que s'utilitza una simulació del vehicle per comprovar la factibilitat de les trajectòries obtingudes. Als resultats es pot observar com la tècnica proposada presenta avantatges a l'hora d'obtenir el comportament desitjat així com també un millor temps per volta, és a dir, una millor traçada.When it comes to motorsports, the racing line is a crucial factor in lap time. The goal of this project is to determine the trajectory to be followed along a circuit and the velocity at which to travel it for an autonomous Formula Student vehicle. To do so, two algorithms with different characteristics based on the available computing time are presented, which improve the lap time that would be obtained by tracing the center of the track. When designing racing lines, it is common to use geometric constructs such as curvature or length, although the definition of the optimal path comes down to only one other magnitude: time. This project proposes directly optimizing this metric and demonstrates that it is indeed possible to do so using evolutionary algorithms, obtaining significant improvements over purely geometric approaches. In addition, a tool for random circuit generation is used to statistically evaluate the algorithms presented as well as other similar articles. This comparison is not only carried out theoretically but also uses a vehicle simulation to verify the feasibility of the obtained trajectories. The results show that the proposed technique has advantages in achieving the desired behavior as well as a better lap time, that is, a better racing line

Adaptive Sampling For Efficient Online Modelling

This thesis examines methods enabling autonomous systems to make active sampling and planning decisions in real time. Gaussian Process (GP) regression is chosen as a framework for its non-parametric approach allowing flexibility in unknown environments. The first part of the thesis focuses on depth constrained full coverage bathymetric surveys in unknown environments. Algorithms are developed to find and follow a depth contour, modelled with a GP, and produce a depth constrained boundary. An extension to the Boustrophedon Cellular Decomposition, Discrete Monotone Polygonal Partitioning is developed allowing efficient planning for coverage within this boundary. Efficient computational methods such as incremental Cholesky updates are implemented to allow online Hyper Parameter optimisation and fitting of the GP's. This is demonstrated in simulation and the field on a platform built for the purpose. The second part of this thesis focuses on modelling the surface salinity profiles of estuarine tidal fronts. The standard GP model assumes evenly distributed noise, which does not always hold. This can be handled with Heteroscedastic noise. An efficient new method, Parametric Heteroscedastic Gaussian Process regression, is proposed. This is applied to active sample selection on stationary fronts and adaptive planning on moving fronts where a number of information theoretic methods are compared. The use of a mean function is shown to increase the accuracy of predictions whilst reducing optimisation time. These algorithms are validated in simulation. Algorithmic development is focused on efficient methods allowing deployment on platforms with constrained computational resources. Whilst the application of this thesis is Autonomous Surface Vessels, it is hoped the issues discussed and solutions provided have relevance to other applications in robotics and wider fields such as spatial statistics and machine learning in general

Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15