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Owing to the ever-changing developments of battery and electric powertrain, vehicle electrification is the trend in the future. Without the presence of a combustion engine, masking effect from it reduces and noises from other components become perceivable. Among all, the cooling fan is one of the major noise sources. The design of cooling fan modules is usually carried out in the early stage before building prototype vehicles. Therefore, it is essential to come up with a method for selecting optimal fan design without performing complete vehicle testing. This is a Master's degree project in collaboration with Volvo Cars, with a focus on cooling fan noise at the charging state of electric vehicles. The main objective of this thesis is to understand the effects of fan installation. Three different setups of acoustic measurement are carried out, namely free-space, wall-mounted, and in-vehicle measurement. Correlations of these measurements are investigated through comparisons of the measurement results and the installation effects are identified through spectrum difference between free-space and in-vehicle measurement. Moreover, the implementation of spectral decomposition method enables the separation of source strength and propagation effect. Analyses of sound pressure levels are studied by looking into tonal and broadband components. In addition, sound power levels are determined by following ISO standards. Finally, a subjective rating session is held to understand the human perception of cooling fan noise. / Med anledning av den pågående utvecklingen mot elektrifiering där bilarna går mot batterier och elmotorer för framdrivning så ändras ljudbilden. Utan förbränningsmotorer som tidigare maskerade mycket av ljudet från bilarna så framträder nya ljudkällor. En sådan är kylfläkten som allt mer blir en störningskälla. Vanligtvis sker designen av kylfläktsmodulen i en tidig fas innan det finns någon prototypbil att tillgå. Detta gör att det är viktigt att utveckla metoder för att i tidig fas kunna optimera designen av kylfläkten.  Detta är ett examensarbete i samarbete med Volvo Cars med fokus på det ljud som uppstår vid laddning av eldrivna bilar. Uppsatsens huvudsakliga mål är att förstå fläktinstallationens påverkan på ljud genom att korrelera olika typer av mätningar. Detta genomfördes m.h.a tre separata konfigurationer, fritt-upphängd mätning, väggmonterad och installerad i bil. Korrelation undersöktes genom att jämföra mätresultat och analys av spektrumet. Analysen av ljudtrycksnivåerna genom att titta på dels de tonala komponenterna men också på bredbandsnivåerna. Utöver detta fastställs även ljudeffekten genom att följa gängse ISO standard. Slutligen så gjordes en subjektiv utvärdering för att få en förståelse av upplevelsen av ljudet från en kylfläkt.

La simulation numérique de systèmes d’équations différentielles raides ordinaires ou algébriques est devenue partie intégrante dans le processus de conception des systèmes mécaniques à dynamiques complexes. L’objet de ce travail est de développer des méthodes numériques pour réduire les temps de calcul par le parallélisme en suivant deux axes : interne à l’intégrateur numérique, et au niveau de la décomposition de l’intervalle de temps. Nous montrons l’efficacité limitée au nombre d’étapes de la parallélisation à travers les méthodes de Runge-Kutta et DIMSIM. Nous développons alors une méthodologie pour appliquer le complément de Schur sur le système linéarisé intervenant dans les intégrateurs par l’introduction d’un masque de dépendance construit automatiquement lors de la mise en équations du modèle. Finalement, nous étendons le complément de Schur aux méthodes de type "Krylov Matrix Free". La décomposition en temps est d’abord vue par la résolution globale des pas de temps dont nous traitons la parallélisation du solveur non-linéaire (point fixe, Newton-Krylov et accélération de Steffensen). Nous introduisons les méthodes de tirs à deux niveaux, comme Parareal et Pita dont nous redéfinissons les finesses de grilles pour résoudre les problèmes raides pour lesquels leur efficacité parallèle est limitée. Les estimateurs de l’erreur globale, nous permettent de construire une extension parallèle de l’extrapolation de Richardson pour remplacer le premier niveau de calcul. Et nous proposons une parallélisation de la méthode de correction du résidu. / This PhD Thesis deals with the development of parallel numerical methods for solving Ordinary and Algebraic Differential Equations. ODE and DAE are commonly arising when modeling complex dynamical phenomena. We first show that the parallelization across the method is limited by the number of stages of the RK method or DIMSIM. We introduce the Schur complement into the linearised linear system of time integrators. An automatic framework is given to build a mask defining the relationships between the variables. Then the Schur complement is coupled with Jacobian Free Newton-Krylov methods. As time decomposition, global time steps resolutions can be solved by parallel nonlinear solvers (such as fixed point, Newton and Steffensen acceleration). Two steps time decomposition (Parareal, Pita,...) are developed with a new definition of their grids to solved stiff problems. Global error estimates, especially the Richardson extrapolation, are used to compute a good approximation for the second grid. Finally we propose a parallel deferred correction

In this dissertation, we use the Natural transform decomposition method to obtain approximate analytical solution of fractional differential equations. This technique is a combination of decomposition methods and natural transform method. We use the Adomian decomposition, the homotopy perturbation and the Daftardar-Jafari methods as our decomposition methods. The fractional derivatives are considered in the Caputo and Caputo- Fabrizio sense. / Mathematical Sciences / M. Sc. (Applied Mathematics)

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

Πολλά είναι τα προβλήματα απόφασης τα οποία μπορούν να μοντελοποιηθούν ως προβλήματα γραμμικού προγραμματισμού. Πολλές όμως είναι και οι καταστάσεις όπου δεν είναι λογικό να υποτεθεί ότι οι παράμετροι του μοντέλου καθορίζονται προσδιοριστικά. Για παράδειγμα, μελλοντικές παραγωγικότητες σε ένα πρόβλημα παραγωγής, εισροές σε μία δεξαμενή που συνδέεται με έναν υδροσταθμό παραγωγής ηλεκτρικού ρεύματος, απαιτήσεις στους διάφορους κόμβους σε ένα δίκτυο μεταφορών κλπ, είναι καταλληλότερα μοντελοποιημένες ως αβέβαιες παράμετροι, οι οποίες χαρακτηρίζονται στην καλύτερη περίπτωση από τις κατανομές πιθανότητας. Η αβεβαιότητα γύρω από τις πραγματοποιημένες τιμές εκείνων των παραμέτρων δεν μπορεί να εξαλειφθεί πάντα εξαιτίας της εισαγωγής των μέσων τιμών τους ή μερικών άλλων (σταθερών) εκτιμήσεων κατά τη διάρκεια της διαδικασίας μοντελοποίησης. Δηλαδή ανάλογα με την υπό μελέτη κατάσταση, το γραμμικό προσδιοριστικό μοντέλο μπορεί να μην είναι το κατάλληλο μοντέλο για την περιγραφή του προβλήματος που θέλουμε να λύσουμε. Σε αυτή τη διπλωματική υπογραμμίζουμε την ανάγκη να διευρυνθεί το πεδίο της μοντελοποίησης των προβλημάτων απόφασης που παρουσιάζονται στην πραγματική ζωή με την εισαγωγή του στοχαστικού προγραμματισμού. / There are many practical decision problems than can be modeled as linear programs. However, there are also many situations that it is unreasonable to assume that the coefficients of model are deterministically fixed. For instance, future productivities in a production problem, inflows into a reservoir connected to a hydro power station, demands at various nodes in a transportation network, and so on, are often appropriately modeled as uncertain parameters, which are at best characterized by probability distributions. The uncertainty about the realized values of those parameters cannot always be wiped out just by inserting their mean values or some other (fixed) estimates during the modelling process. That is, depending on the practical situation under consideration, the linear deterministic model may not be the appropriate model for describing the problem we want to solve. In this project we emphasize the need to broaden the scope of modelling real life decision problems by inserting stochastic programming.

Les entreprises de transport et de distribution sont confrontées à des difficultés d’exploitation liées à la taille et à la complexité de leur processus de livraison. Dans cette problématique, nous proposons une approche globale du Problème Général de Livraison (PGL).Au niveau méthodologique, c’est une approche hiérarchique (stratégique, tactique, opérationnelle) et structurée. Il s’agit de concevoir et d’exploiter un PGL en le décomposant en problèmes de livraisons élémentaires identifiés et le plus possible indépendants les uns des autres (problèmes de transport, de hubs, d’agences, de tournées...).Au niveau algorithmique, des modèles et algorithmes de résolution ont été proposés pour résoudre ces problèmes élémentaires de livraison dans la phase opérationnelle en tenant compte, en particulier, du nombre et de la capacité limités des moyens de transport.Au niveau applicatif, deux exemples réels sont traités : le système de livraison d’une entreprise de Vente à Distance et le système de livraison des casernes de pompiers du Nord de la France à partir de la pharmacie centrale de Lille / Transport and delivery companies are confronted by difficulties in their transportation process due to the scale and the complexity of their distribution process. In this context, we propose a comprehensive approach to General Delivery Problem (GDP). In terms of methodology, it is a hierarchical (strategic, tactical and operational) and structured approach. It consists of designing and decomposing the GDP into well identified basic delivery problems as independent as possible. These basic transport problems involve the problems about transportation, intermediate facility, agencies, routings, etc. At the algorithm level, models and solution algorithms have been proposed to solve these basic delivery problems in the operational phase, taking account in particular transportation restriction about the number and capacity of vehicles.At the application level, two real examples are discussed: one is the delivery system of a delivery company; the other one is the delivery system of the Regional Fire and Emergency Center in the north of France

Made available in DSpace on 2016-06-02T19:51:35Z (GMT). No. of bitstreams: 1 1770.pdf: 2888839 bytes, checksum: 18c57ba21e9192d597b74f8d1d0fc997 (MD5) Previous issue date: 2008-02-29 / Universidade Federal de Minas Gerais / This is a study of approximations based on parametric decomposition methods used in open queueing networks for modeling discrete job-shop manufacturing systems. These approximations play an important role in evaluating the performance of productive systems and have proved effective in many situations. Besides, these approximations are relatively easy to apply requiring fewer data compared to other methods because they use the average rate and SCV (square coefficient of variation) as the only parameters to characterize the network arrival and service processes. This work is aimed at analyzing and comparing several approximations since they are not yet available in the literature. Hence, several network situations were tested in order to identify the most adequate approximation for each situation. Firstly, a two-station network was analyzed followed by the analysis of a five-station network and lastly, a real example of a semiconductor plant, analyzed by Bitran e Tirupati (1988), was used. In order to reach these goals, the state of the art of approximation methods to evaluate the performance of open queueing networks was studied, and the approximations were compared using the experiment planning technique, important factors for building network configuration and data analysis The findings of this work demonstrate that approximations can be highly efficient to evaluate the performance of discrete job-shop manufacturing systems. Regardless of the configurations studied, it is worth mentioning that approximations 3 and 2, in general, showed the best results if compared to the other values obtained from simulations to evaluate the performance of open queueing networks, OQN,. The other approximations tended to overestimate E(Lj) when the number of stations is higher. This study intends to contribute to the development of computing systems in order to support project decisions and the planning and control of discrete manufacturing systems using approximations based on the parametric decomposition method / Esta dissertação estuda as aproximações baseadas nos métodos analíticos paramétricos de decomposição usados em redes de filas abertas que modelam sistemas discretos de manufatura do tipo job-shop. Estas aproximações possuem um importante papel na avaliação do desempenho de sistemas produtivos e vem se mostrando eficiente para uma grande diversidade de situações. Além disso, são aproximações relativamente fáceis de serem aplicadas, necessitando poucos dados em relação a outros métodos, pois utilizam apenas a média e o scv (coeficiente quadrático de variação) como parâmetros para caracterizar os processos de chegadas e os processos de serviço da rede. O foco deste trabalho está em realizar análises e comparações entre diversas aproximações, pois ainda não existe nenhuma comparação mais efetiva entre elas na literatura. Para isso, diversas situações de redes foram exploradas para identificar quais aproximações são mais adequadas para quais situações. Primeiramente é analisado uma rede com 2 estações, posteriormente uma outra com 5 estações e por fim usou um exemplo real de uma fábrica de semi-condutores, analisada por Bitran e Tirupati (1988). Para que seja possível atingir esses objetivos, estudou-se o estado da arte das aproximações dos métodos de avaliação de desempenho para redes de filas abertas, e comparouse as aproximações por meio de técnicas de planejamento de experimentos, parte importante na construção das configurações das redes e análise dos resultados. Os resultados apresentados nesta dissertação mostram que essas aproximações podem ser bem eficientes ao avaliar o desempenho de sistemas discretos de manufatura do tipo job-shop. Independente das configurações analisadas, vale destacar a Aproximação 3 e a Aproximação 2, em geral, obtendo os melhores resultados, entre as aproximações, em comparação aos valores obtidos pela simulação para avaliar o desempenho de redes de filas OQN. As outras aproximações demonstraram certo comportamento em sobreestimar E(Lj), quando o número de estações aumentam. Este estudo pretende contribuir para o desenvolvimento de sistemas computacionais 13 para apoiar decisões de projeto, planejamento e controle dos sistemas discretos de manufatura, usando aproximações baseadas em métodos de decomposição paramétrico

PETROBRAS / Este trabalho apresenta uma abordagem para otimização do scheduling de uma rede dutoviária real com uma origem e múltiplos destinos, a rede OSBRA. A rede é composta por uma refinaria que abastece cinco órgãos ligados por um único poliduto. Decisões sobre bateladas (volumes operacionais) de diferentes produtos a serem enviados pela refinaria e recebidos nos órgãos de consumo ao longo de um horizonte de tempo devem ser tomadas de modo otimizado de forma a controlar os níveis de estocagem, respeitando limites operacionais da rede de dutos. Propõe-se uma abordagem de solução por decomposição que utiliza Programação Linear Inteira Mista (PLIM) em conjunto com algoritmos heurísticos. A abordagem está dividida em 2 etapas: (i) alocação e sequenciamento e (ii) programação das entregas. A etapa de alocação e sequenciamento é responsável por determinar a ordem, o volume e a vazão de cada batelada que deverá ser bombeada da refinaria para os órgãos. Esta etapa é composta por um modelo PLIM que é executado iterativamente em uma abordagem com horizonte com tempo rolante. Em seguida, a etapa de programação de entregas detalha como ocorrem as entregas das bateladas em cada órgão, considerando a operação de rebombeio no último trecho de duto. Para o rebombeio, executa-se um modelo matemático iterativamente também utilizando o conceito de horizonte rolante, definindo uma nova sequência de bateladas que deverão ser bombeadas pelo órgão de Goiânia para Brasília, ou seja, no trecho de duto mais distante da refinaria. Consideram-se características próximas da realidade de operação da rede OSBRA, como controle de inventário, limites de vazão, variação diária de demanda, manutenção de tanque, manutenção de duto (total ou parcial). Dois estudos de caso são apresentados considerando cenários baseados em dados reais com horizontes de programação de 30 dias, no qual o segundo foi submetido a diversas modificações com o intuito de evidenciar funcionalidades da abordagem proposta. A análise dos resultados permite concluir que a abordagem de solução apresenta resultados adequados para a operação dos especialistas da rede, dessa forma podendo auxiliar no processo de decisão do scheduling da rede OSBRA. / This work presents an approach to optimize the scheduling of a real pipeline network with one source and multiple destinations, the OSBRA network. The network consists of a refinery that supplies five terminals, which are connected by a single pipeline. Batches of different products are sent from refinery and received by terminals during a time horizon. Optimized scheduling decisions must be taken to attend inventory issues at the same time that operational constraints are respected. This work proposes a decomposition approach solution using Mixed Integer Linear Programming (MILP) combined with heuristic algorithms. The solution approach is divided into two phases: (i) allocation and sequencing and (ii) scheduling of deliveries. The allocation and sequencing phase is responsible for determining the order, volume, and flow rate of each batch to be pumped from the refinery to the terminals. This phase is composed of an MILP model that runs iteratively in a rolling horizon approach. In a following step, the scheduling of deliveries phase details how the batches' deliver will occur in each terminal, considering the repumping operation in the last pipeline segment. For the repumping, a mathematical model is executed iteratively, also using the concept of rolling horizon, setting a new sequence of batches to be pumped from Goiânia to Brasília, the farthest pipeline segment from the refinery. Similar characteristics of the real OSBRA network are considered, such as inventory control, flow limits, daily demand, tank maintenance, total or partial pipeline maintenance. Two study cases considering scenarios based on real data with a 30-day programming horizon are presented, in which the second case was subjected to a series of modifications in order to evidence the proposed approach functionalities. The result's analysis supports the conclusion that the solution approach provides adequate results for the operation of the network experts. Thus, the obtained results can aid the operational scheduling decision of OSBRA network.

Muitos problemas de otimização reais apresentam mais de uma função-objetivo. Quando os objetivos são conflitantes, estratégias especializadas são necessárias, como é o caso dos algoritmos evolutivos multiobjetivo (MOEAs, do inglês Multi-objective Optimization Evolutionary Algorithms). Entretanto, se a avaliação das funções-objetivo é custosa (alto custo computacional ou econômico) muitos MOEAs propostos são impraticáveis. Uma alternativa pode ser a utilização de um modelo de aprendizado de máquina que aproxima o cálculo do fitness (surrogate) no algoritmo de otimização. Este trabalho propõe e investiga uma plataforma chamada ELMOEA/D que agrega MOEAs do estado da arte baseados em decomposição de objetivos (MOEA/D) e máquinas de aprendizado extremo (ELMs, do inglês Extreme Learning Machines) como modelos surrogate. A plataforma proposta é testada com diferentes variantes do algoritmo MOEA/D e apresenta bons resultados em problemas benchmark, comparada a um algoritmo da literatura que também utiliza MOEA/D mas modelos surrogates baseados em redes com função de base radial. A plataforma ELMOEA/D também é testada no Problema de Predição de Estrutura de Proteínas (PPEP). Apesar dos resultados alcançados pela proposta não serem tão animadores quanto aqueles obtidos nos benchmarks (quando comparados os algoritmos com e sem surrogates), diversos aspectos da proposta e do problema são explorados. Por fim, a plataforma ELMOEA/D é aplicada a uma formulação alternativa do PPEP com sete objetivos e, com estes resultados, várias direções para trabalhos futuros são apontadas. / Many real optimization problems have more than one objective function. When the objectives are in conflict, there is a need for specialized strategies, as is the case of the Multi-objective Optimization Evolutionary Algorithms (MOEAs). However, if the functions evaluation is expensive (high computational or economical costs) many proposed MOEAs are impractical. An alternative might be the use of a machine learning model to approximate the fitness function (surrogates) in the optimization algorithm. This work proposes and investigates a framework called ELMOEA/D that aggregates state-of-the-art MOEAs based on decomposition of objectives (MOEA/D) and extreme learning machines as surrogate models. The proposed framework is tested with different MOEA/D variants and show good results in benchmark problems, compared to a literature algorithm that also encompasses MOEA/D but uses surrogate models based on radial basis function networks. The ELMOEA/D framework is also applied to the protein structure prediction problem (PSPP). Despite the fact that the results achieved by the proposed approach were not as encouraging as the ones achieved in the benchmarks (when the algorithms with and without surrogates are compared), many aspects of both algorithm and problem are explored. Finally, the ELMOEA/D framework is applied to an alternative formulation of the PSPP and the results lead to various directions for future works.