Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / The understanding and quantitative description of fluid flowthrough porousmedia, is a science which has been going on for many years and investigated in a variety of disciplines. Studies in this field have primarily been based on models, which can either be described as empirical or theoretical. Part of the current study is to understand fluid flow in porous media through studying three recent theoretical pore-scale models based on the concept of a Representative Unit Cell (RUC), to represent a porous medium. Amongst other assumptions, these models assumed plane Poiseuille flow throughout each pore section of a rectangular RUC. The main objective of this study is to numerically verify this assumption using Computational Fluid Dynamics (CFD) software, FLUENT version 6.2.16. Attention is also paid to comparison between these models with the experimental data, obtained during the model tests of airflow through a timber stack end, undertaken in a wind tunnel. The laminar and intermediate airflow through a timber stack end is simulated using the commercial software FLUENT, and the results are validated against the theoretical pore-scale models and experimental data. Two turbulence models which are, the Standard k − e and Reynolds-Stress models are used in these computations, the aimbeing to determine howwell they are able to reproduce the experimental data. The numerical results are in good agreement with one of the theoretical models presented and the experimental data.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / This work entails the improvement of an existing three dimensional pore-scale model. Stagnant zones are included, the closure of the volume averaged pressure gradient is improved and an improved calculation of pore-scale averages, using the RUC, is done for the model to be a more realistic representative of the REV and thus of the foamlike material. Both the Darcy and the Forchheimer regimes are modelled and a general momentum transport equation is derived by means of an asymptotic matching technique. The RUC model is also extended to cover non-Newtonian flow. Since metallic foams are generally of porosities greater than 90%, emphasis is put on the accurate prediction of permeability for these porosities. In order to improve permeability predictions for these high porosity cases an adaptation to the RUC model was considered, whereby rectangular prisms were replaced by cylinders. Although this adaptation appears to give more accurate permeabilities at very high porosities, its implementation in a generalised model seems impractical. The prediction of the characteristic RUC side length is discussed and results of both the cylindrical strand model and the square strand model are compared to experimental work.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008. / The medical radiation treatment facility at iThemba Labs requires a precise and robust patient positioning system. The current system makes use of an accurately calibrated multi-camera stereophotogrammetry (SPG) setup that is vulnerable to physical disruptions that invalidate system calibration. The task in this thesis is to design a vision system that can be used to verify the correct operation of the SPG system. We propose an unscented Kalman filter (UKF) based structure from motion (SFM) system for this purpose. Our SFM system does not rely on calibration information used by the SPG system and provides accurate reconstruction for verification purposes. The system is critically evaluated against a set of synthetic and real motion sequences.

Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: This thesis provides an introduction to the statistical modeling technique known as graphical models. Since graph theory and probability theory are the two legs of graphical models, these two topics are presented, and then combined to produce two examples of graphical models: Bayesian Networks and Markov Random Fields. Furthermore, the max-sum, sum-product and junction tree algorithms are discussed. The graphical modeling technique is then applied to the specific problem of finding coplanar points in stereo images, taken with an uncalibrated camera. Although it is discovered that graphical models might not be the best method, in terms of speed, to use for this appliation, it does illustrate how to apply this technique in a real-life problem. / AFRIKAANSE OPSOMMING: Hierdie tesis stel die leser voor aan die statistiese modelerings-tegniek genoemd grafiese modelle. Aangesien grafiek teorie en waarskynlikheidsleer die twee bene van grafiese modelle is, word hierdie areas aangespreek en dan gekombineer om twee voorbeelde van grafiese modelle te vind: Bayesian Netwerke en Markov Lukrake Liggaam. Die maks-som, som-produk en aansluitboom algoritmes word ook bestudeer. Nadat die teorie van grafiese modelle en hierdie drie algoritmes afgehandel is, word grafiese modelle dan toegepas op ’n spesifieke probleem— om punte op ’n gemeenskaplike vlak in stereo beelde te vind, wat met ’n ongekalibreerde kamera geneem is. Alhoewel gevind is dat grafiese modelle nie die optimale metode is om punte op ’n gemeenskaplike vlak te vind, in terme van spoed, word die gebruik van grafiese modelle wel ten toongestel met hierdie praktiese voorbeeld. / National Research Foundation (South Africa)

Thesis (MScIngwet)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: This thesis is a case study in optimal inventory control, applied to Clickabox factory, a South African cardboard box producer from whom cardboard boxes may be ordered at short notice via the internet. The problem of developing a decision–support system for optimal stockholding at the factory, in order to minimize cardboard off–cut wastage subject to required service levels, is addressed in this thesis. Previously a simple replenishment policy, based largely on experience, was implemented at the factory. The inventory model developed for and applied to Clickabox in this thesis takes account of a raw materials substitution cascade, as well as the stochasticity of demand, and other factors such as cost, service level and spatial requirements for the storage of stock. This combination of stochastic demand and product substitution has not, to the author’s knowledge, previously been dealt with in the literature. There are two primary deliverables of this study. The first is a suggestion as to the suitable stock composition (cardboard types from which boxes may be manufactured) to be kept in inventory at the factory. The second deliverable is a computerised decision–support system, based on the inventory model developed, to aid in future inventory replenishment decisions at Clickabox. Some of the results of this thesis have, at the time of writing, already been implemented with success at the factory. These include the suggestions given to the management of Clickabox as to the suitable stock types to be held in inventory, which have been implemented in stages since March 2003. The suggested stock composition has proven to be superior to the previous stock types held, in terms of a reduction in off–cut wastage and increased availability of suitable boards. / AFRIKAANSE OPSOMMING: Hierdie tesis is ’n gevallestudie in optimale voorraadbeheer, toegepas op Clickabox fabriek, ’n Suid–Afrikaanse kartondoosprodusent by wie kartondose op kort kennisgewing via die internet bestel kan word. In hierdie tesis word ’n besluitnemingsteunstelsel ontwikkel vir optimale bestuur van voorraad by die fabriek, wat karton afknipselvermorsing onderhewig aan vereiste diensvlakke minimeer. Vantevore is ’n eenvoudige voorraad aanvullingstrategie, wat hoofsaaklik op ondervinding gebaseer was, by die fabriek toegepas. ’n Wetenskaplike gefundeerde voorraadmodel word vir Clickabox ontwikkel en toegepas, waarin ’n rou–voorraad kaskade– substitusie proses in aanmerking geneem word, asook die stogastiese vraag na kartondose en faktore soos prys, diensvlakke en benodigde stoorruimte. Hierdie kombinasie van stogastiese vraag en rou–voorraad kaskade–substitusie is, tot die skrywer se kennis, nog nie in die literatuur behandel nie. Die studie het twee hoof–uitkomste ten doel. Die eerste is ’n aanbeveling ten opsigte van ’n geskikte rou–voorraad samestelling (kartontipes waaruit kartondose geproduseer kan word) wat by die fabriek in voorraad gehou moet word. Die tweede is ’n rekenaarmatige besluitnemingsteunstelsel, wat op die ontwikkelde voorraadbeheermodel gegrond is, en wat vir toekomstige besluite in verband met voorraadaanvulling by Clickabox bedoel is. Van die resultate wat in hierdie tesis vervat is, is reeds ten tyde van die opskryf daarvan doeltreffend by die fabriek ge¨ımplementeer. Ondermeer is die aanbeveling in verband met die geskikte voorraadsamestelling, geleidelik vanaf Maart 2003 by die fabriek ingefaseer. Dit het duidelik geword dat hierdie samestelling beter as die vorige voorraadprofiel funksioneer, in terme van ’n verlaging in afknipselvermorsing en ’n verhoging in die beskikbaarheid van geskikte kartonne.

Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: Network simulations generate large volumes of data. This thesis presents an animated visualization system that utilizes the latest affordable Computer Graphics (CG) hardware to simplify the task of visualizing and analyzing these large volumes of data. The use of modern CG hardware allows us to create an interactive system which allows the user to interact with the data sets and extract the relevant data in real time. We also present an alternate approach to the network layout problem, using Self Organizing Maps to find an aesthetic layout for a network which is fundamental to a successful network visualization. We finally discuss the design and implementation of such an network visualization tool. / AFRIKAANSE OPSOMMING: Netwerk simulasies genereer groot volumes data. Hierdie tesis stel voor ’n geanimeerde visualiseringwat gebruik maak van die nuutste bekostigbare rekenaar grafika hardeware om die visualisering van groot volumes data te vergemaklik. Die gebruik van moderne rekenaar grafika hardeware stel ons in staat om sagteware te skep wat n gebruiker in staat stel om met die data te werk. Ons stel voor ’n alternatiewe benadering om die netwerk se uitleg daar te stel, met die hulp van tegnieke wat gebruik word in die studie van neurale netwerke. Ons bespreek dan die ontwerp en implementering van so ’n netwerk visualisering program.

Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: Program slicing was originally described by Mark Weiser in 1984. He proposed this as a technique to aid in debugging because he conjectured that this is what programmers did naturally when debugging. Here program slicing is applied to an experimental concurrent language called LF. Existing techniques are adapted to accommodate the unique features of the language. / AFRIKAANSE OPSOMMING: Programdeling is oorspronklik deur Mark Weiser beskryf in 1984. Hy het dit voorgestel as ’n tegniek om ontfouting te vergemaklik, want hy het geglo dat dit is wat programmeerders van nature self doen. Programdeling word hier toegepas op ’n eksperimentele gelyklopende taal genaamd LF. Bestaande tegnieke word gewysig om die taal se unieke eienskappe in ag te neem.

Thesis (MSc)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: Cellular network operators globally loose between 3% and 5% of their annual revenue to telecommunications fraud. Hence it is of great importance that fraud management systems are implemented to detect, alarm, and shut down fraud within minutes, minimising revenue loss. Modern proprietary fraud management systems employ (i) classification methods, most often artificial neural networks learning from classified call data records to classify new call data records as fraudulent or legitimate, (ii) statistical methods building subscriber behaviour profiles based on the subscriber’s usage in the cellular network and detecting sudden changes in behaviour, and (iii) rules and threshold values defined by fraud analysts, utilising their knowledge of valid fraud cases and the false alarm rate as guidance. The purpose of this thesis is to establish a context for and evaluate the performance of well-known data mining techniques that may be incorporated in the fraud detection process. Firstly, a theoretical background of various well-known data mining techniques is provided and a number of seminal articles on fraud detection, which influenced this thesis, are summarised. The cellular telecommunications industry is introduced, including a brief discussion of the types of fraud experienced by South African cellular network operators. Secondly, the data collection process and the characteristics of the collected data are discussed. Different data mining techniques are applied to the collected data, demonstrating how user behaviour profiles may be built and how fraud may be predicted. An appraisal of the performances and appropriateness of the different data mining techniques is given in the context of the fraud detection process. Finally, an indication of further work is provided in the conclusion to this thesis, in the form of a number of recommendations for possible adaptations of the fraud detection methods, and improvements thereof. A combination of data mining techniques that may be used to build a comprehensive fraud detection model is also suggested. / AFRIKAANSE OPSOMMING: Sellulêre netwerk operateurs verloor wêreldwyd tussen 3% en 5% van hul jaarlikse inkomste as gevolg van telekommunikasie bedrog. Dit is dus van die uiterse belang dat bedrog bestuurstelsels geïmplimenteer word om bedrog op te spoor, alarms te genereer, en bedrog binne minute te staak om verlies aan inkomste tot ’n minimum te beperk. Moderne gepatenteerde bedrog bestuurstelsels maak gebruik van (i) klassifikasie metodes, mees dikwels kunsmatige neurale netwerke wat leer vanaf geklassifiseerde oproep rekords en gebruik word om nuwe oproep rekords as bedrog-draend of nie bedrog-draend te klassifiseer, (ii) statistiese metodes wat gedragsprofiele van ’n intekenaar bou, gebaseer op die intekenaar se gedrag in die sellulêre netwerk, en skielike verandering in gedrag opspoor, en (iii) reëls en drempelwaardes wat deur bedrog analiste daar gestel word, deur gebruik te maak van hulle ondervinding met geldige gevalle van bedrog en die koers waarteen vals alarms gegenereer word. Die doel van hierdie tesis is om ’n konteks te bepaal vir en die werksverrigting te evalueer van bekende data ontginningstegnieke wat in bedrog opsporingstelsels gebruik kan word. Eerstens word ’n teoretiese agtergrond vir ’n aantal bekende data ontginningstegnieke voorsien en ’n aantal gedagteryke artikels wat oor bedrog opsporing handel en wat hierdie tesis beïnvloed het, opgesom. Die sellulêre telekommunikasie industrie word bekend gestel, insluitend ’n kort bespreking oor die tipes bedrog wat deur Suid-Afrikaanse sellulˆere telekommunikasie netwerk operateurs ondervind word. Tweedens word die data versamelingsproses en die eienskappe van die versamelde data bespreek. Verskillende data ontginningstegnieke word vervolgens toegepas op die versamelde data om te demonstreer hoe gedragsprofiele van gebruikers gebou kan word en hoe bedrog voorspel kan word. Die werksverrigting en gepastheid van die verskillende data ontginningstegnieke word bespreek in die konteks van die bedrog opsporingsproses. Laastens word ’n aanduiding van verdere werk in die gevolgtrekking tot hierdie tesis verskaf, en wel in die vorm van ’n aantal aanbevelings oor moontlike aanpassings en verbeterings van die bedrog opsporingsmetodes wat beskou en toegepas is. ’n Omvattende bedrog opsporingsmodel wat gebruik maak van ’n kombinasie van data ontginningstegnieke word ook voorgestel.

Thesis (MscEng)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: Outliers may be defined as observations that are sufficiently aberrant to arouse the suspicion of the analyst as to their origin. They could be the result of human error, in which case they should be corrected, but they may also be an interesting exception, and this would deserve further investigation. Identification of outliers typically consists of an informal inspection of a plot of the data, but this is unreliable for dimensions greater than two. A formal procedure for detecting outliers allows for consistency when classifying observations. It also enables one to automate the detection of outliers by using computers. The special case of univariate data is treated separately to introduce essential concepts, and also because it may well be of interest in its own right. We then consider techniques used for detecting multiple outliers in a multivariate normal sample, and go on to explain how these may be generalized to include cluster analysis. Multivariate outlier detection is based on the Minimum Covariance Determinant (MCD) subset, and is therefore treated in detail. Exact bivariate algorithms were refined and implemented, and the solutions were used to establish the performance of the commonly used heuristic, Fast–MCD. / AFRIKAANSE OPSOMMING: Uitskieters word gedefinieer as waarnemings wat tot s´o ’n mate afwyk van die verwagte gedrag dat die analis wantrouig is oor die oorsprong daarvan. Hierdie waarnemings mag die resultaat wees van menslike foute, in welke geval dit reggestel moet word. Dit mag egter ook ’n interressante verskynsel wees wat verdere ondersoek benodig. Die identifikasie van uitskieters word tipies informeel deur inspeksie vanaf ’n grafiese voorstelling van die data uitgevoer, maar hierdie benadering is onbetroubaar vir dimensies groter as twee. ’n Formele prosedure vir die bepaling van uitskieters sal meer konsekwente klassifisering van steekproefdata tot gevolg hˆe. Dit gee ook geleentheid vir effektiewe rekenaar implementering van die tegnieke. Aanvanklik word die spesiale geval van eenveranderlike data behandel om noodsaaklike begrippe bekend te stel, maar ook aangesien dit in eie reg ’n area van groot belang is. Verder word tegnieke vir die identifikasie van verskeie uitskieters in meerveranderlike, normaal verspreide data beskou. Daar word ook ondersoek hoe hierdie idees veralgemeen kan word om tros analise in te sluit. Die sogenaamde Minimum Covariance Determinant (MCD) subversameling is fundamenteel vir die identifikasie van meerveranderlike uitskieters, en word daarom in detail ondersoek. Deterministiese tweeveranderlike algoritmes is verfyn en ge¨ımplementeer, en gebruik om die effektiwiteit van die algemeen gebruikte heuristiese algoritme, Fast–MCD, te ondersoek.

Thesis (PhD)--University of Stellenbosch, 2001. / ENGLISH ABSTRACT: In this thesis we examine some aspects of automatic face recognition, with specific reference to the eigenface technique. We provide a thorough theoretical analysis of this technique which allows us to explain many of the results reported in the literature. It also suggests that clustering can improve the performance of the system and we provide experimental evidence of this. From the analysis, we also derive an efficient algorithm for updating the eigenfaces. We demonstrate the ability of an eigenface-based system to represent faces efficiently (using at most forty values in our experiments) and also demonstrate our updating algorithm. Since we are concerned with aspects of face recognition, one of the important practical problems is locating the face in a image, subject to distortions such as rotation. We review two well-known methods for locating faces based on the eigenface technique.e These algorithms are computationally expensive, so we illustrate how the Synthetic Discriminant Function can be used to reduce the cost. For our purposes, we propose the concept of a linearly interpolating SDF and we show how this can be used not only to locate the face, but also to estimate the extent of the distortion. We derive conditions which will ensure a SDF is linearly interpolating. We show how many of the more popular SDF-type filters are related to the classic SDF and thus extend our analysis to a wide range of SDF-type filters. Our analysis suggests that by carefully choosing the training set to satisfy our condition, we can significantly reduce the size of the training set required. This is demonstrated by using the equidistributing principle to design a suitable training set for the SDF. All this is illustrated with several examples. Our results with the SDF allow us to construct a two-stage algorithm for locating faces. We use the SDF-type filters to obtain initial estimates of the location and extent of the distortion. This information is then used by one of the more accurate eigenface-based techniques to obtain the final location from a reduced search space. This significantly reduces the computational cost of the process. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons sommige aspekte van automatiese gesigs- herkenning met spesifieke verwysing na die sogenaamde eigengesig ("eigen- face") tegniek. ‘n Deeglike teoretiese analise van hierdie tegniek stel ons in staat om heelparty van die resultate wat in die literatuur verskyn te verduidelik. Dit bied ook die moontlikheid dat die gedrag van die stelsel sal verbeter as die gesigte in verskillende klasse gegroepeer word. Uit die analise, herlei ons ook ‘n doeltreffende algoritme om die eigegesigte op te dateer. Ons demonstreer die vermoë van die stelsel om gesigte op ‘n doeltreffende manier te beskryf (ons gebruik hoogstens veertig eigegesigte) asook ons opdateringsalgoritme met praktiese voorbeelde. Verder ondersoek ons die belangrike probleem om gesigte in ‘n beeld te vind, veral as rotasie- en skaalveranderinge plaasvind. Ons bespreek twee welbekende algoritmes om gesigte te vind wat op eigengesigte gebaseer is. Hierdie algoritme is baie duur in terme van numerise berekeninge en ons ontwikkel n koste-effektiewe metode wat op die sogenaamde "Synthetic Discriminant Functions" (SDF) gebaseer is. Vir hierdie doel word die begrip van lineêr interpolerende SDF’s ingevoer. Dit stel ons in staat om nie net die gesig te vind nie, maar ook ‘n skatting van sy versteuring te bereken. Voorts kon ons voorwaardes aflei wat verseker dat ‘n SDF lineêr interpolerend is. Aangesien ons aantoon dat baie van die gewilde SDF-tipe filters aan die klassieke SDF verwant is, geld ons resultate vir ‘n hele verskeidenheid SDF- tipe filters. Ons analise toon ook dat ‘n versigtige keuse van die afrigdata mens in staat stel om die grootte van die afrigstel aansienlik te verminder. Dit word duidelik met behulp van die sogenaamde gelykverspreidings beginsel ("equidistributing principle") gedemonstreer. Al hierdie aspekte van die SDF’s word met voorbeelde geïllustreer. Ons resultate met die SDF laat ons toe om ‘n tweestap algoritme vir die vind van ‘n gesig in ‘n beeld te ontwikkel. Ons gebruik eers die SDF-tipe filters om skattings vir die posisie en versteuring van die gesig te kry en dan verfyn ons hierdie skattings deur een van die teknieke wat op eigengesigte gebaseer is te gebruik. Dit lei tot ‘n aansienlike vermindering in die berekeningstyd.