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Truncation errors and computational cost are obstacles that still hinder large-scale applications of the Computational Fluid Dynamics method. The discontinuous Galerkin method is one of the high-order schemes utilized extensively in recent years, which is locally conservative, stable, and high-order accurate. Besides that, it can handle complex geometries and irregular meshes with hanging nodes. In this document, the nondimensional compressible Euler equations and Reynolds- Averaged Navier-Stokes equations are discretized by discontinuous Galerkin methods with a two-equations turbulence model on both structured and unstructured meshes. The traditional equation of state for an ideal gas model is substituted by a multispecies thermodynamics model in order to complete the governing equations. An approximate Riemann solver is used for computing the convective flux, and the diffusive flux is approximated with some internal penalty based schemes. The temporal discretization of the partial differential equations is either performed explicitly with the aid of Rung-Kutta methods or with semi-implicit methods. Inspired by the artificial viscosity diffusion based limiter for shock-capturing method, which has been extensively studied, a novel and robust technique based on the introduction of mass diffusion to the species governing equations to guarantee that the species mass fractions remain positive has been thoroughly investigated. This contact-surface-capturing method is conservative and a high order of accuracy can be maintained for the discontinuous Galerkin method. For each time step of the algorithm, any trouble cell is first caught by the contact-surface discontinuity detector. Then some amount of mass diffusions are added to the governing equations to change the gas mixtures and arrive at an equilibrium point satisfying some conditions. The species properties are reasonable without any oscillations. Computations are performed for many steady and unsteady flow problems. For general non-mixing fluid flows, the classical air-helium shock bubble interaction problem is the central test case for the high-order discontinuous Galerkin method with a mass diffusion based limiter chosen. The computed results are compared with experimental, exact, and empirical data to validate the fluid dynamic solver.

Metalearning aims to obtain knowledge of the relationship between the mechanism of learning and the concrete contexts in which that mechanisms is applicable. As new mechanisms of learning are continually added to the pool of learning algorithms, the chances of encountering behavior similarity among algorithms are increased. Understanding the relationships among algorithms and the interactions between algorithms and tasks help to narrow down the space of algorithms to search for a given learning task. In addition, this process helps to disclose factors contributing to the similar behavior of different algorithms. We first study general characteristics of learning tasks and their correlation with the performance of algorithms, isolating two metafeatures whose values are fairly distinguishable between easy and hard tasks. We then devise a new metafeature that measures the difficulty of a learning task that is independent of the performance of learning algorithms on it. Building on these preliminary results, we then investigate more formally how we might measure the behavior of algorithms at a ner grained level than a simple dichotomy between easy and hard tasks. We prove that, among all many possible candidates, the Classifi er Output Difference (COD) measure is the only one possessing the properties of a metric necessary for further use in our proposed behavior-based clustering of learning algorithms. Finally, we cluster 21 algorithms based on COD and show the value of the clustering in 1) highlighting interesting behavior similarity among algorithms, which leads us to a thorough comparison of Naive Bayes and Radial Basis Function Network learning, and 2) designing more accurate algorithm selection models, by predicting clusters rather than individual algorithms.

To accurately model or predict future operating conditions of a system in engineering or applied mechanics, it is necessary to understand its fundamental principles. These may be the material parameters, defining dimensional characteristics, or the boundary conditions. However, there are instances when there is little to no prior knowledge of the system properties or conditions, and consequently, the problem cannot be modeled accurately. It is therefore critical to define a method that can identify the desired characteristics of the current system without accumulating extensive computation time. This thesis formulates an inverse approach using proper orthogonal decomposition (POD) with an accompanying radial basis function (RBF) interpolation network. This method is capable of predicting the desired characteristics of a specimen even with little prior knowledge of the system. This thesis first develops a conductive heat transfer problem, and by using the truncated POD – RBF interpolation network, temperature values are predicted given a varying Biot number. Then, a simple bifurcation problem is modeled and solved for velocity profiles while changing the mass flow rate. This bifurcation problem provides the data and foundation for future research into the left ventricular assist device (LVAD) and implementation of POD – RBF. The trained POD – RBF inverse approach defined in this thesis can be implemented in several applications of engineering and mechanics. It provides model reduction, error filtration, regularization and an improvement over previous analysis utilizing computational fluid dynamics (CFD).

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24738号 / 情博第826号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 磯 祐介, 准教授 吉川 仁, 准教授 藤原 宏志, 教授 西村 直志(京都大学 名誉教授) / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Despite the advancements in the development of autonomous vehicles (AVs), there are still numerous complex situations in which AVs may encounter challenges. In recent years, the concept of teleoperation, which entails establishing a connection between a remote operator and the AV, has garnered substantial attention from both AV companies and governmental bodies as a viable safety backup method. However, a research gap is apparent when it comes to the remote manipulation of AVs positioned at a considerable distance. This gap involves a) AV with a temporal delay through real-time direct control within the constraints of current wireless communication technology in an unpredictable road environment, and b) enhancing the AV's inherent detection capabilities to augment its autonomous control abilities, thereby reducing the operator's workload. To address this research gap, this dissertation introduces an innovative teleoperation system. Initially, we devise a control system utilizing the wave variable approach as a communication method to alleviate the impact of signal latency. And Radial Basis Function Networks (RBFN) are employed to effectively manage the uncertain nonlinear dynamics of the vehicle. Subsequently, a saliency-based object detection (OD) algorithm, named SalienDet, is proposed to identify objects not present in the training sample set. SalienDet incorporates saliency maps generated without prior information into the neural network, enhancing image features for unfamiliar objects. This augmentation significantly aids the OD algorithm in detecting previously unknown objects, thereby empowering the AV to possess an improved perception ability. This advancement is particularly valuable when the operator imparts driving advice to the AV instead of exercising direct control. In conclusion, this dissertation makes a noteworthy contribution to AV teleoperation by furnishing a comprehensive solution that spans various aspects of AV teleoperation. / Doctor of Philosophy / This dissertation revolves around the teleoperation of autonomous vehicles (AVs), with the objective of formulating a comprehensive teleoperation system that encompasses two critical aspects: direct control and indirect control. In the initial segment of the dissertation, we introduce a real-time teleoperation direct control system based on neural networks. This framework plays a pivotal role in assisting operators in navigating AVs efficiently, especially in the face of challenges such as communication delays and complex external environments. Following this, we present a novel saliency-based object detection (OD) algorithm. This algorithm empowers the AV to recognize potential objects beyond its prior knowledge, thereby enhancing its level of autonomous control, particularly when operators opt not to exercise direct control over the remote AV. Our research findings delve into the essential facets of AV teleoperation. The developed teleoperation system serves as a valuable reference for future researchers and engineers dedicated to advancing autonomous vehicle technology.

The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions. / Ph. D.

Thesis (PhD) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: This work considers the efficient numerical analysis of large, aperiodic finite antenna arrays. A Method of Moments (MoM) based domain decomposition technique called the Domain Green's Function Method (DGFM) is formulated to address a wide range of array problems in a memory and runtime efficient manner. The DGFM is a perturbation approach that builds on work initially conducted by Skrivervik and Mosig for disjoint arrays on multi-layered substrates, a detailed review of which will be provided in this thesis. Novel extensions considered for the DGFM are as follows: a formulation on a higher block matrix factorisation level that allows for the treatment of a wider range of applications, and is essentially independent of the elemental basis functions used for the MoM matrix formulation of the problem. As an example of this, both conventional Rao-Wilton-Glisson elements and also hierarchical higher order basis functions were used to model large array structures. Acceleration techniques have been developed for calculating the impedance matrix for large arrays including one based on using the Adaptive Cross Approximation (ACA) algorithm. Accuracy improvements that extend the initial perturbation assumption on which the method is based have also been formulated. Finally, the DGFM is applied to array geometries in complex environments, such as that in the presence of finite ground planes, by using the Numerical Green's Function (NGF) method in the hybrid NGF-DGFM formulation. In addition to the above, the DGFM is combined with the existing domain decomposition method, viz., the Characteristic Basis Function Method (CBFM), to be used for the analysis of very large arrays consisting of sub-array tiles, such as the Low-Frequency Array (LOFAR) for radio astronomy. Finally, interesting numerical applications for the DGFM are presented, in particular their usefulness for the electromagnetic analysis of large, aperiodic sparse arrays. For this part, the accuracy improvements of the DGFM are used to calculate quantities such as embedded element patterns, which is a major extension from its original formulation. The DGFM has been integrated as part of an efficient array analysis tool in the commercial computational electromagnetics software package, FEKO. / AFRIKAANSE OPSOMMING: In hierdie werkstuk word die doeltre ende analise van eindige, aperiodiese antenna samestellings behandel. Eindige gebied benaderings wat op die Moment Metode (MoM) berus, word as vetrekpunt gebruik. `n Tegniek genaamd die Gebied Green's Funksie Metode (GGFM) word voorgestel en is geskik vir die analise van `n verskeidenheid van ontkoppelde samestellings. Die e ektiewe gebruik van rekenaargeheue en looptyd is onderliggend in die implementasie daarvan. Die GGFM is 'n perturbasie metode wat op die oorspronklike werk van Skrivervik en Mosig berus. Laasgenoemde is hoofsaaklik ontwikkel vir die analise van ontkoppelde antenna samestellings op multilaag di elektrikums. `n Deeglike oorsig van voorafgaande word in die tesis verskaf. In hierdie tesis is die bogenoemde werk op `n unieke wyse uitgebrei: `n ho er blok matriks vlak formulering is ontwikkel wat dit moontlik maak vir die analise van `n verskeidenheid strukture en wat onafhanklik is van die onderliggende basis funksies. Beide lae-vlak Rao-Wilton-Glisson (RWG) basis funksies, asook ho er orde hierargiese basis funksies word gebruik vir die modellering van groot antenna samestellings. Die oorspronklike perturbasie aanname is uitgebrei deur akkuraatheidsverbeteringe vir die tegniek voor te stel. Die Aanpasbare Kruis Benaderings (AKB) tegniek is onder andere gebruik om spoed verbeteringe vir die GGFM te bewerkstellig. Die GGFM is verder uitgebrei vir die analise van antenna samestellings in `n komplekse omgewing, bv. `n antenna samestelling bo `n eindige grondplaat. Die Numeriese Green's Funksie (NGF) metode is hiervoor ingespan en die hibriede NGF-GGFM is ontwikkel. Die GGFM is verder met die Karakteristieke Basis Funksie Metode (KBFM) gekombineer. Die analise van groot skikkings wat bestaan uit sub-skikkings, soos die wat tans by die \Low- Frequency Array (LOFAR) " vir radio astronomie in Nederland gebruik word, kan hiermee gedoen word. In die werkstuk word die GGFM ook toegepas op `n reeks interessante numeriese voorbeelde, veral die toepaslike EM analise van groot aperiodiese samestellings. Die akkuraatheidsverbeteringe vir die GGFM maak die berekening van elementpatrone vir skikkings moontlik. Die GGFM is by the sagteware pakket FEKO geintegreer.

A solar and diesel-wind hybrid power control systems is proposed in the thesis. The system consists of solar power, wind power, diesel-engine, a static synchronous compensator and an intelligent power controller. MATLAB/Simulink was used to build the dynamic model and simulate the solar and diesel-wind hybrid power system. A static synchronous compensator was used to supply reactive power and regulate the voltage of the hybrid system. To achieve a fast and stable response for the real power control, an intelligent controller was proposed, which consists of the Radial Basis Function Network (RBFN) and the Elman Neural Network (ENN) for maximum power point tracking (MPPT). The pitch angle control of wind power uses ENN controller, and the output is fed to the wind turbine to achieve the MPPT. The solar system uses RBFN, and the output signal is used to control the DC / DC boost converters to achieve the MPPT.

Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. / A popular method for interpolating multidimensional scattered data is using radial basis functions. In this thesis we present the basic theory of radial basis function interpolation and also regard the solvability and stability of the method. Solving the interpolant directly has a high computational cost for large datasets, hence using numerical methods to approximate the interpolant is necessary. We consider some recent numerical algorithms. Software to implement radial basis function interpolation and to display the 3D interpolants obtained, is developed. We present results obtained from using our implementation for radial basis functions on GIS and 3D face data as well as an image warping application.