Modern computational science permits the accurate solution of nonlinear partial differential equations (PDEs) on overlapping computational domains, known as an overset approach. The complex grid interconnectivity inherent in the overset method can introduce errors in the solution through “orphan” points, i.e., grid points for which reliable solution donor points cannot be located. For this reason, a variety of data transfer strategies based on scattered data interpolation techniques have been assessed with application to both overset and hybrid methodologies. Scattered data approaches are attractive because they are decoupled from solver type and topology, and may be readily applied within existing methodologies. In addition to standard radial basis function (RBF) interpolation, a novel steered radial basis function (SRBF) interpolation technique has been developed to introduce data adaptivity into the data transfer algorithm. All techniques were assessed by interpolating both continuous and discontinuous analytical test functions. For discontinuous functions, SRBF interpolation was able to maintain solution gradients with the steering technique being the scattered-data analog of a slope limiter. In comparison with linear mappings, the higher-order approaches were able to more accurately preserve flow physics for arbitrary grid configurations. Overset validation test cases included an inviscid convecting vortex, a shock tube, and a turbulent ship airwake. These were studied within unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations to determine quantitative and qualitative improvements when applying RBF interpolation over current methods. The convecting vortex was also analyzed on a grid configuration which contained orphan points under the state-of-the-art overset paradigm. This was successfully solved by the RBF-based algorithm, which effectively eliminated orphans by enabling high-order extrapolation. Order-of-magnitude reductions in error compared to the exact vortex solution were observed. In addition, transient conservation errors that persisted in the original overset methodology were eliminated by the RBF approach. To assess the effect of advanced mapping techniques on the fidelity of a moving grid simulation, RBF interpolation was applied to a hybrid simulation of an isolated wind turbine rotor. The resulting blade pressure distributions were comparable to a rotor simulation with refined near-body grids.

In this thesis, stable and efficient hybrid methods which combine high order finite difference methods and unstructured finite volume methods for time-dependent initial boundary value problems have been developed. The hybrid methods make it possible to combine the efficiency of the finite difference method and the flexibility of the finite volume method. We carry out a detailed analysis of the stability of the hybrid methods, and in particular the stability of interface treatments between structured and unstructured blocks. Both the methods employ so called summation-by-parts operators and impose boundary and interface conditions weakly, which lead to an energy estimate and stability. We have constructed and analyzed first-, second- and fourth-order Laplacian based artificial dissipation operators for finite volume methods on unstructured grids. The first-order artificial dissipation can handle shock waves, and the fourth-order artificial dissipation eliminates non-physical numerical oscillations efficiently. A stable hybrid method for hyperbolic problems has been developed. It is shown that the stability at the interface can be obtained by modifying the dual grid of the unstructured finite volume method close to the interface. The hybrid method is applied to the Euler equation by the coupling of two stand-alone CFD codes. Since the coupling is administered by a third separate coupling code, the hybrid method allows for individual development of the stand-alone codes. It is shown that the hybrid method is an accurate, efficient and practically useful computational tool that can handle complex geometries and wave propagation phenomena. Stable and accurate interface treatments for the linear advection–diffusion equation have been studied. Accurate high-order calculation are achieved in multiple blocks with interfaces. Three stable interface procedures — the Baumann–Oden method, the “borrowing” method and the local discontinuous Galerkin method, have been investigated. The analysis shows that only minor differences separate the different interface handling procedures. A conservative stable and efficient hybrid method for a parabolic model problem has been developed. The hybrid method has been applied to the full Navier–Stokes equations. The numerical experiments support the theoretical conclusions and show that the interface coupling is stable and converges at the correct order for the Navier–Stokes equations.

[pt] A partir da disponibilização comercial de imagens de alta resolução, modelos 3D de superfícies geradas a partir de imagens aéreas e de satélite tornaram-se uma alternativa mais atraente para aplicações como planejamento de telecomunicações, monitoramento de desastres e planejamento urbano. A exatidão dos modelos 3D da superfície terrestre baseados em pares de imagens estereoscópicas depende da exatidão com que pontos homólogos são localizados em ambas as imagens. Os métodos automáticos de localização de pontos homólogos em imagens digitais baseados em área, combinados com técnicas de crescimento de região, são capazes de produzir uma nuvem densa e exata de pontos homólogos. Entretanto, o processo de crescimento de região pode ser interrompido em regiões da imagem cujo efeito de uma variação abrupta da paralaxe no eixo x aparece de maneira importante. Neste caso, novas sementes devem ser introduzidas, normalmente por um operador humano. A partir dessas novas sementes, o processo será reiniciado. Dependendo do tipo da imagem utilizada e da estrutura 3D da região mapeada, a intervenção humana pode ser considerável. Propõe-se então uma alternativa completamente automatizada no qual se combinam as técnicas do SIFT (Scale Invariant Feature Transform), mínimos quadrados e crescimento de região. Experimentos realizados em pares de imagens aéreas e de satélite cobrindo diversos tipos de terrenos mostraram a eficácia do método proposto, especialmente em regiões com mudanças abruptas de elevação, como fachadas de prédios altos. / [en] After the high resolution images became commercially available, 3D surface models generated from space-born stereo images turned into an attractive alternative for applications such as telecommunication planning, disaster monitoring and urban planning. The accuracy of the 3D models of the earth surface depends on the accuracy of corresponding points located in both images. Area-based automatic image matching combined with a region-growing technique are able to provide a dense and accurate grid of corresponding points. However the region-growing process may stop at image patches where the effect of a sudden change in the x-parallax is important. In such a case new seed points must be provided, usually by human operator. From the additional seed points the region-growing procedure may continue. Depending upon the type of image and the 3D-structure of the mapped area, the human intervention may be considerable. A fully automatic alternative that combines the SIFT (Scale Invariant Feature Transform), least square matching and region-growing technique is proposed in this work. Experiments conducted on stereo pairs of Ikonos and aerial images covering different terrain types have shown the effectiveness of the proposed method especially in locations with abrupt height changes, such as façades of high buildings.

[pt] O presente trabalho desenvolve um método híbrido com a finalidade de criar um índice de qualidade para distribuidoras de energia elétrica. Esse método é construído através da fusão do Método de Análise Hierárquica (AHP) e Técnicas de Amortecimento Exponencial. Com isso, é possível avaliar uma distribuidora levando em conta múltiplos critérios e seus diversos índices passados. / [en] This work develops a hybrid method in order to create a quality index for electric power distribution companies. This method is built through the merger of the Analytical Hierarchy Process (AHP) and exponential smoothing techniques. Thus, it is possible to evaluate a distribution company taking into account multiple criteria and its several indexes in the past.

Le présent travail a consisté à évaluer, améliorer et valider plus avant une méthode de couplage faible CFD/CAA, notamment relativement à son application à des problèmes réalistes de bruit avion. Entre autres choses, il a été ici montré dans quelle mesure une telle méthode hybride peut effectivement (i) s’accommoder des contraintes inhérentes aux applications réalistes, (ii) sans être menacée par certains de ses inévitables effets de bord (tels que la dégradation du signal auxquelles sont soumises les données CFD, lorsqu’elles sont traitées ou exploitées acoustiquement). / The present work consisted in improving, assessing and validating further the CFD/CAA surface weak coupling methodology, with respect to its application to realistic problems of aircraft noise. In particular, it was here shown how far such hybrid methodology could (i) cope with all stringent constraints that are dictated by real-life applications, (ii) without being jeopardized by some of the unavoidable side-effects (such as the signal degradation to which CFD data are subjected, when processed or being then acoustically exploited).

This research is situated in the field of Computational AeroAcoustics (CAA). The thesis focuses on the computation of the aerodynamic noise generated by turbulent flows around wing, fan, or propeller airfoils. The computation of the noise radiated from a device is the first step for designers to understand the acoustical characteristics and to determine the noise sources in order to modify the design toward having acoustically efficient products. As a case study, the broadband or trailing-edge noise emanating from a CD (Controlled-Diffusion) airfoil, belonging to a fan is studied. The hybrid methods of aeroacoustic are applied to simulate and predict the radiated noise. The necessary tools were researched and developed. The hybrid methods consist in two steps simulations, where the determination of the aerodynamic field is decoupled from the computation of the acoustic waves propagation to the far field, so the first part of this thesis is devoted to an aerodynamic study of the considered airfoil. In this part of the thesis, a complete aerodynamic study has been performed. Some aspects have been developed in the used in-house solver SFELES, including the implementation of a new SGS model, a new outlet boundary condition and a new transient format which is used to extract the noise sources to be exported to the acoustic solver, ACTRAN. The second part of this thesis is concerned with the aeroacoustic study where four methods have been applied, among them two are integral formulations and the two others are partial-differential equations. The first method applied is Amiet’s theory, implemented in Matlab, based on the wall-pressure spectrum extracted in a point near the trailing edge. The second method is Curle’s formulation. It is applied proposing two approaches; the first approach is the implementation of the volume and surface integrals in SFELES to be calculated simultaneously with the flow in order to avoid the storage of noise sources which requires a huge space. In the second approach, the fluctuating aerodynamic forces, already obtained during the aerodynamics simulation, are used to compute the noise considering just the surface sources. Finally, Lighthil and Möhring analogies have been applied via the acoustic solver ACTRAN using sources extracted via SFELES. Maps of the radiated noise are demonstrated for several frequencies. The refraction effects of the mean flow have been studied. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

O problema de dimensionamento de lotes determina um plano de produção que apoia às tomadas de decisões, a médio prazo, em meios industriais. Este plano de produção indica as quantidades de cada item que devem ser produzidas em cada período do horizonte de planejamento, de acordo com um objetivo dado e satisfazendo a demanda dos clientes. Diversos métodos de solução foram propostas na literatura, considerando a dificuldade de solução de algumas classes de problemas e a necessidade de métodos que gerem soluções de alta qualidade em um tempo computacional adequado. Neste trabalho, abordamos heurísticas baseadas na formulação matemática (LP-and-fix, relax-and-fix e fix-and-optimize), uma metaheurística (algoritmo de abelhas) e dois métodos híbridos, utilizados na solução de dois problemas distintos de dimensionamento de lotes multiestá- gio com limitação de capacidade. Consideramos também, a utilização de três formulações da literatura, para verificar a influência de cada uma sobre as abordagens de solução verificadas. Os resultados computacionais demonstraram que os métodos baseados na formulação matemática do problema se mostraram eficientes, mas limitados normalmente a ótimos locais, enquanto os métodos híbridos puderam superar estes ótimos locais, utilizando conceitos da metaheurística algoritmo de abelhas para isto. Além disso, pudemos verificar a influência de uma formulação \"forte\" sobre as soluções geradas pelas abordagens de solução, demonstrando que métodos baseados em relaxação linear conseguem obter maiores vantagens deste tipo de formulação, mas outras abordagens podem ou não obter estas vantagens, dependendo do problema abordado / The lot-sizing problem determines a production plan, which supports the decision making, in the medium term, at the industrial environment. This production plan indicates the amounts of each item to be produced in each period of the planning horizon, according to a given objective and satisfying customer\'s demand. Diverse solution methods have been proposed in the literature, considering the difficulty of solving some problem classes and the need of methods to generate solutions quickly. In this work, we develop matheuristics (LP-and-fix, relax-and-fix and fix-and-optimize), one metaheuristic (bees algorithm) and two hybrid methods, used to solve two different multilevel capacitated lot-sizing problems. We also consider the use of three different formulations of the literature to verify the influence of each one on the solutions approaches. The computational results show that the matheuristics proved to be efficient, but usually limited to local optima, while the hybrid methods could escape from these local optima, using concepts of bees algorithm to do this. Additionally, we test the effect of a tight formulation on the solutions approaches, demonstrating that LP-based heuristics can obtain further advantages from this type of formulation, but other approaches can take these advantages, depending on the problem addressed

[pt] Apresenta-se uma formulação particular do método híbrido dos elementos de contorno para a análise de problemas planos de potencial e de elasticidade que, apesar de completamente geral, é apropriada a aplicações de mecânica da fratura. Funções do tipo de Westergaard são usadas como soluções fundamentais, Em uma generalização de uma proposta inicialmente feita por Tada et al. A formulação leva a conceitos de elementos de contorno de deslocamentos semelhante à apresentada por Crouch e Starfield, mas em um contexto variacional que permite interpretações mecânicas bem simples das equações matriciais resultantes. Problemas de topologia geral podem ser modelados, como no caso de domínios infinitos ou multiplamente conexos. A formulação, que é diretamente aplicável a placas com entalhes ou trincas curvas externas ou internas, permite a descrição adequada de altos gradientes de tensão e é uma ferramenta simples de avaliação de fatores de intensidade de tensão, com o que se podem verificar numericamente conceitos estabelecidos por Rice em 1968. Esta dissertação tem foco na fundamentação matemática da formulação para problemas de potencial e de elasticidade. Apresenta-se a implementação da formulação e são discutidos vários exemplos numéricos de validação. / [en] A particular implementation of the hybrid boundary element method is presented for the two dimensional analysis of potential and elasticity problems, which although general in concept, is suited for fracture mechanics applications. Generalized Westergaard stress functions, as proposed by Tada et al in 1993, are used as the problem‘s fundamental solutions. The proposed formulation leads to displacement-based concepts that resemble those presented by Crouch and Starfield, although in a variational framework that leads to matrix equations with sound mechanical meanings. Problems of general topology, such as in the case of unbounded and multiply-connected domains, may be modeled. The formulation, which is directly applicable to notches and generally curved, internal or external cracks, is specially suited for the description of the stress field in the vicinity of crack tips and is an easy means of evaluating stress intensity factors and of checking some basic concepts laid down by Rice in 1968. This dissertation focuses on the mathematical fundamentals of the formulation. Several validating numerical examples are presented.

The reliable operation of planetary gearboxes is critical for the sustained operation of many machines such as wind turbines and helicopter transmissions. Hybrid methods that make use of the respective advantages of physics-based and data-driven models can be valuable in addressing the unique challenges associated with the condition monitoring of planetary gearboxes. In this dissertation, a hybrid framework for diagnostics and prognostics of planetary gearboxes is proposed. The proposed framework aims to diagnose and predict the root crack length in a planet gear tooth from accelerometer measurements. Physics-based and data-driven models are combined to exploit their respective advantages, and it is assumed that no failure data is available for training these models. Components required for the implementation of the proposed framework are studied separately and challenges associated with each component are discussed. The proposed hybrid framework comprises a health state estimation and health state prediction part. In the health state estimation part of the proposed framework, the crack length is diagnosed from the measured vibration response. To do this, the following model components are implemented: A first finite element model is used to simulate the crack growth path in the planet gear tooth. Thereafter, a second finite element model is used to establish a relationship between the gearbox time varying mesh stiffness, and the crack length in the planet gear tooth. A lumped mass model is then used to model the vibration response of the gearbox housing subject to the gearbox time varying mesh stiffness excitation. The measurements from an accelerometer mounted on the gearbox housing are processed by computing the synchronous average. Finally, these model components are combined with an additional data-driven model for diagnosing the crack length from the measured vibration response through the solution of an inverse problem. After the crack length is diagnosed through the health state estimation model, the Paris crack propagation law and Bayesian state estimation techniques are used to predict the remaining useful life of the gearbox. To validate the proposed hybrid framework, an experimental setup is developed. The experimental setup allows for the measurement of the vibration response of a planetary gearbox with different tooth root crack lengths in the planet gear. However, challenges in reliably detecting the damage in the experimental setup lead to the use of simulated data for studying the respective components of the hybrid method. Studies conducted using simulated data highlighted interesting challenges that need to be overcome before a hybrid diagnostics and prognostics framework for planetary gearboxes can be applied in practice. / Dissertation (MSc)--University of Pretoria, 2021. / Eskom EPPEI / Mechanical and Aeronautical Engineering / Msc / Unrestricted

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Radar Cross Section (RCS) is an important parameter in radar engineering. Often, electrically large structures are of interest in RCS analysis due to the high operating frequencies of radar systems. Simulation of these problems can be more e cient than measurement due to the cost associated with measurement. The Method of Moments/Physical Optics (MoM/PO) hybrid method combines the advantages of the MoM and PO, making it suited to solving electrically large problems that may contain some small complex detail. The requirement for high meshing resolution when analysing some electromagnetic problems, however, signi cantly increases memory requirements. As a result, the hybrid MoM/PO becomes computationally expensive for electrically large problems. In this work, a linear phase term is introduced into the RWG basis function formulation of the MoM/PO hybrid. The addition of the linear phase term allows the use of large triangular mesh elements in the PO region, resulting in the analysis of electrically large problems. The bene t of this formulation is that it allows a reduction in computational cost whilst maintaining the accuracy of the hybrid MoM/PO. This improved hybrid is tested on various planar test cases and results show that it attains the same level of accuracy as the original MoM/PO hybrid. / AFRIKAANSE OPSOMMING: Radardeursnit is 'n belangrike parameter in radaringenieurswese. As gevolg van die hoë frekwensies wat deur baie radarstelsels gebruik word, is elektriesgroot probleme dikwels van belang in die berekening van die radardeursnit van teikens. Die modellering en berekening van die radardeursnit van teikens kan meer kostedoeltre end as metings wees, as gevolg van die beduidende koste van radardeursnitmetings. Die hibriede Moment-Metode/Fisiese-Optika tegniek kombineer die voordele van die twee tegnieke, wat dit geskik maak vir elektries-groot probleme met klein, komplekse detail. Indien die gewone benadering egter gevolg word om 'n hoë resolusie faset-model te gebruik, bly dit berekeningsintensief met groot rekenaar geheuevereistes vir elektries-groot probleme. In hierdie studie word 'n lineêre fase term ingesluit in die formulering van die Rao-Wilton-Glisson (RWG) basisfunksies vorm van die hibriede Moment-Metode/Fisiese-Optika tegniek. Die toevoeging van die lineêre fase term maak dit moontlik om groot driehoekfasette in die Fisiese-Optika gebied te gebruik, wat beteken dat elektries-groot probleme makliker opgelos kan word. Die voordeel van hierdie nuwe formulering is dat die berekeningslas en -tyd verminder word terwyl die akkuraatheid van die oorspronklike hibriede Moment-Metode/Fisiese-Optika tegniek behou word. Hierdie verbeterde hibriede tegniek word getoets aan die hand van verskeie platvlak toetsgevalle en die resultate dui daarop dat die akkuraatheid vergelykbaar is met die van die oorspronklike hibriede Moment-Metode/Fisiese-Optika tegniek.