The purpose of this study was to compare 4 growth curve functions (Brody, Logistic, Gompertz, and Von Bertalanffy) in describing the weight change across age in Angus cow. A total of 1,705 weight-age records from birth to at least 3-year of age from 171 cows were collected. All the growth models were fitted as a nonlinear mixed model using NLMIXED procedure in SAS9.2 (REML Approach) and MCMC method through WinBUGS (Bayesian Approach). The goodness of fit of these four models was compared in terms of AIC, BIC, and DIC. The results show that the Gompertz model fitted the data best under REML Approach while the Brody model appeared to be the best model under Bayesian Approach. The Bayesian Approach provided more flexibility in setting up the mixed model and more reasonable estimates for all the growth models compared to the REML Approach. These results show some advantages of Bayesian nonlinear mixed modeling. / text

This thesis gives a functorial interpretation of the Naive Space of Maps Nd as a parametrizing space for a family of maps from certain rational curves to P¹. / text

This work reviews concepts in drilling-based learning curves and proposes modifications to the Brett and Millheim learning curve model to enable its use for multiple learners and to characterize interaction effects between learners. Enabling the model’s use for multiple learning scenarios at once improves modeling efficiency. Interaction effects are present when learners improve from their own experience and the experience of those in close proximity to them. Quantifying interaction effects leads to a more complete understanding of performance improvement and enables more effective forecasting of drilling resources and expenditure requirements. / text

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This thesis concerns stressed spline structures. A spline is defined as `an initially straight member with identical second moment of area about any axis perpendicular to its centroidal axis, bent into a spatial curve'. An analytical proof is presented to show that the spline's torsional stiffness is of no importance in its analysis (provided construction details do not introduce any torsional moment). This paramount proof allows the formulation of a spline analysis that relies solely on three translational degrees of freedom (3DOF) per node. Applying this 3DOF analysis to unstrained curves and battened or hoop supported membranes is approximate since the bending stiffness would correspond to one direction only. A series of four test cases validates the proposed 3DOF analysis. The analysis is first applied to a laterally loaded spline ring, where solution convergence and the effect of unequal length segment modelling are investigated. Most significantly, this test case demonstrates that the spline ring has a greater out-of-plane stiffness than a pre-bent ring. This feature lies at the basis of spline stressed membranes - the spline has superior out-of-plane stiffness under the action of forces applied by the membrane. The second and third test cases -- buckling of elastica and of a shallow sinusoidal arch -- clearly demonstrate that the 3DOF analysis is much faster, more accurate, and produces results closer to the analytical values compared with a 6DOF analysis. The fourth test case proves the efficiency of the 3DOF analysis through investigating buckling behaviour and loads of four circular arches under radial loading. As the torsional stiffness does not enter the 3DOF analysis, the stiffness of a spline constructed of spliced segments is identical to that of a continuous spline. In order to demonstrate their feasibility, five medium span (161n-32m) Glass Fibre Reinforced Plastic (GFRP) and one large span (57nt) steel tensegrity stressed spline membranes are designed, form-found and analysed under realistic loading conditions. These design studies show firstly that the spline and membrane stresses occurring under loading are within acceptable material limits and secondly that buckling occurs at values much higher than those encountered in reality. This thesis has demonstrated that engineered stressed spline structures, for which the development of a 3DOF was essential, have great design potential.

This thesis is concerned with the approximation of Cartesian coordinate data by parametric curves and surfaces, with an emphasis upon a technique known as parametric orthogonal distance regression (parametric ODR). The technique has become increasingly popular in the literature over the past decade and has applications in a wide range of fields, including metrology-the science of measurement, and computer aided design (CAD) modelling. Typically, the data are obtained by recording points measured in the surface of some physical artefact, such as a manufactured part. Parametric ODR involves minimizing the shortest distances from the data to the curve or surface in some norm. Under moderate assumptions, these shortest distances are orthogonal projections from the data onto the approximant, hence the nomenclature ODR. The motivation behind this type of approximation is that, by using a distance-based measure, the resulting best fit curve or surface is independent of the position or orientation of the physical artefact from which the data is obtained. The thesis predominately concerns itself with parametric ODR in a least squares setting, although it is indicated how the techniques described can be extended to other error measures in a fairly straightforward manner. The parametric ODR problem is formulated mathematically, and a detailed survey of the existing algorithms for solving it is given. These algorithms are then used as the basis for developing new techniques, with an emphasis placed upon their efficiency and reliability. The algorithms (old and new) detailed in this thesis are illustrated by problems involving well-known geometric elements such as lines, circles, ellipse and ellipsoids, as well as spline curves and surfaces. Numerical considerations specific to these individual elements, including ones not previously reported in the literature, are addressed. We also consider a sub-problem of parametric ODR known as template matching, which involves mapping in an optimal way a set of data into the same frame of reference as a fixed curve or surface.

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published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Computer Science and Information Systems / Master / Master of Philosophy