12 resultados para nonlinear system characterisation

em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland


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One of the targets of the climate and energy package of the European Union is to increase the energy efficiency in order to achieve a 20 percent reduction in primary energy use compared with the projected level by 2020. The energy efficiency can be improved for example by increasing the rotational speed of large electrical drives, because this enables the elimination of gearboxes leading to a compact design with lower losses. The rotational speeds of traditional bearings, such as roller bearings, are limited by mechanical friction. Active magnetic bearings (AMBs), on the other hand, allow very high rotational speeds. Consequently, their use in large medium- and high-speed machines has rapidly increased. An active magnetic bearing rotor system is an inherently unstable, nonlinear multiple-input, multiple-output system. Model-based controller design of AMBs requires an accurate system model. Finite element modeling (FEM) together with the experimental modal analysis provides a very accurate model for the rotor, and a linearized model of the magneticactuators has proven to work well in normal conditions. However, the overall system may suffer from unmodeled dynamics, such as dynamics of foundation or shrink fits. This dynamics can be modeled by system identification. System identification can also be used for on-line diagnostics. In this study, broadband excitation signals are adopted to the identification of an active magnetic bearing rotor system. The broadband excitation enables faster frequency response function measurements when compared with the widely used stepped sine and swept sine excitations. Different broadband excitations are reviewed, and the random phase multisine excitation is chosen for further study. The measurement times using the multisine excitation and the stepped sine excitation are compared. An excitation signal design with an analysis of the harmonics produced by the nonlinear system is presented. The suitability of different frequency response function estimators for an AMB rotor system are also compared. Additionally, analytical modeling of an AMB rotor system, obtaining a parametric model from the nonparametric frequency response functions, and model updating are discussed in brief, as they are key elements in the modeling for a control design. Theoretical methods are tested with a laboratory test rig. The results conclude that an appropriately designed random phase multisine excitation is suitable for the identification of AMB rotor systems.

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Pulsed electroacoustic (PEA) method is a commonly used non-destructive technique for investigating space charges. It has been developed since early 1980s. These days there is continuing interest for better understanding of the influence of space charge on the reliability of solid electrical insulation under high electric field. The PEA method is widely used for space charge profiling for its robust and relatively inexpensive features. The PEA technique relies on a voltage impulse used to temporarily disturb the space charge equilibrium in a dielectric. The acoustic wave is generated by charge movement in the sample and detected by means of a piezoelectric film. The spatial distribution of the space charge is contained within the detected signal. The principle of such a system is already well established, and several kinds of setups have been constructed for different measurement needs. This thesis presents the design of a PEA measurement system as a systems engineering project. The operating principle and some recent developments are summarised. The steps of electrical and mechanical design of the instrument are discussed. A common procedure for measuring space charges is explained and applied to verify the functionality of the system. The measurement system is provided as an additional basic research tool for the Corporate Research Centre of ABB (China) Ltd. It can be used to characterise flat samples with thickness of 0.2–0.5 mm under DC stress. The spatial resolution of the measurement is 20 μm.

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The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

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Streaming potential measurements for the surface charge characterisation of different filter media types and materials were used. The equipment was developed further so that measurements could be taken along the surfaces, and so that tubular membranes could also be measured. The streaming potential proved to be a very useful tool in the charge analysis of both clean and fouled filter media. Adsorption and fouling could be studied, as could flux, as functions of time. A module to determine the membrane potential was also constructed. The results collected from the experiments conducted with these devices were used in the study of the theory of streaming potential as an electrokinetic phenomenon. Several correction factors, which are derived to take into account the surface conductance and the electrokinetic flow in very narrow capillaries, were tested in practice. The surface materials were studied using FTIR and the results compared with those from the streaming potentials. FTIR analysis was also found to be a useful tool in the characterisation of filters, as well as in the fouling studies. Upon examination of the recorded spectra from different depths in a sample it was possible to determine the adsorption sites. The influence of an external electric field on the cross flow microflltration of a binary protein system was investigated using a membrane electroflltration apparatus. The results showed that a significant improvement could be achieved in membrane filtration by using the measured electrochemical properties to help adjust the process conditions.

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Dirt counting and dirt particle characterisation of pulp samples is an important part of quality control in pulp and paper production. The need for an automatic image analysis system to consider dirt particle characterisation in various pulp samples is also very critical. However, existent image analysis systems utilise a single threshold to segment the dirt particles in different pulp samples. This limits their precision. Based on evidence, designing an automatic image analysis system that could overcome this deficiency is very useful. In this study, the developed Niblack thresholding method is proposed. The method defines the threshold based on the number of segmented particles. In addition, the Kittler thresholding is utilised. Both of these thresholding methods can determine the dirt count of the different pulp samples accurately as compared to visual inspection and the Digital Optical Measuring and Analysis System (DOMAS). In addition, the minimum resolution needed for acquiring a scanner image is defined. By considering the variation in dirt particle features, the curl shows acceptable difference to discriminate the bark and the fibre bundles in different pulp samples. Three classifiers, called k-Nearest Neighbour, Linear Discriminant Analysis and Multi-layer Perceptron are utilised to categorize the dirt particles. Linear Discriminant Analysis and Multi-layer Perceptron are the most accurate in classifying the segmented dirt particles by the Kittler thresholding with morphological processing. The result shows that the dirt particles are successfully categorized for bark and for fibre bundles.

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Streptococcus suis is an important pig pathogen but it is also zoonotic, i.e. capable of causing diseases in humans. Human S. suis infections are quite uncommon but potentially life-threatening and the pathogen is an emerging public health concern. This Gram-positive bacterium possesses a galabiose-specific (Galalpha1−4Gal) adhesion activity, which has been studied for over 20 years. P-fimbriated Escherichia coli−bacteria also possess a similar adhesin activity targeting the same disaccharide. The galabiose-specific adhesin of S. suis was identified by an affinity proteomics method. No function of the protein identified was formerly known and it was designated streptococcal adhesin P (SadP). The peptide sequence of SadP contains an LPXTG-motif and the protein was proven to be cell wall−anchored. SadP may be multimeric since in SDS-PAGE gel it formed a protein ladder starting from about 200 kDa. The identification was confirmed by producing knockout strains lacking functional adhesin, which had lost their ability to bind to galabiose. The adhesin gene was cloned in a bacterial expression host and properties of the recombinant adhesin were studied. The galabiose-binding properties of the recombinant protein were found to be consistent with previous results obtained studying whole bacterial cells. A live-bacteria application of surface plasmon resonance was set up, and various carbohydrate inhibitors of the galabiose-specific adhesins were studied with this assay. The potencies of the inhibitors were highly dependent on multivalency. Compared with P-fimbriated E. coli, lower concentrations of galabiose derivatives were needed to inhibit the adhesion of S. suis. Multivalent inhibitors of S. suis adhesion were found to be effective at low nanomolar concentrations. To specifically detect galabiose adhesin−expressing S. suis bacteria, a technique utilising magnetic glycoparticles and an ATP bioluminescence bacterial detection system was also developed. The identification and characterisation of the SadP adhesin give valuable information on the adhesion mechanisms of S. suis, and the results of this study may be helpful for the development of novel inhibitors and specific detection methods of this pathogen.

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It is known already from 1970´s that laser beam is suitable for processing paper materials. In this thesis, term paper materials mean all wood-fibre based materials, like dried pulp, copy paper, newspaper, cardboard, corrugated board, tissue paper etc. Accordingly, laser processing in this thesis means all laser treatments resulting material removal, like cutting, partial cutting, marking, creasing, perforation etc. that can be used to process paper materials. Laser technology provides many advantages for processing of paper materials: non-contact method, freedom of processing geometry, reliable technology for non-stop production etc. Especially packaging industry is very promising area for laser processing applications. However, there are only few industrial laser processing applications worldwide even in beginning of 2010´s. One reason for small-scale use of lasers in paper material manufacturing is that there is a shortage of published research and scientific articles. Another problem, restraining the use of laser for processing of paper materials, is colouration of paper material i.e. the yellowish and/or greyish colour of cut edge appearing during cutting or after cutting. These are the main reasons for selecting the topic of this thesis to concern characterization of interaction of laser beam and paper materials. This study was carried out in Laboratory of Laser Processing at Lappeenranta University of Technology (Finland). Laser equipment used in this study was TRUMPF TLF 2700 carbon dioxide laser that produces a beam with wavelength of 10.6 μm with power range of 190-2500 W (laser power on work piece). Study of laser beam and paper material interaction was carried out by treating dried kraft pulp (grammage of 67 g m-2) with different laser power levels, focal plane postion settings and interaction times. Interaction between laser beam and dried kraft pulp was detected with different monitoring devices, i.e. spectrometer, pyrometer and active illumination imaging system. This way it was possible to create an input and output parameter diagram and to study the effects of input and output parameters in this thesis. When interaction phenomena are understood also process development can be carried out and even new innovations developed. Fulfilling the lack of information on interaction phenomena can assist in the way of lasers for wider use of technology in paper making and converting industry. It was concluded in this thesis that interaction of laser beam and paper material has two mechanisms that are dependent on focal plane position range. Assumed interaction mechanism B appears in range of average focal plane position of 3.4 mm and 2.4 mm and assumed interaction mechanism A in range of average focal plane position of 0.4 mm and -0.6 mm both in used experimental set up. Focal plane position 1.4 mm represents midzone of these two mechanisms. Holes during laser beam and paper material interaction are formed gradually: first small hole is formed to interaction area in the centre of laser beam cross-section and after that, as function of interaction time, hole expands, until interaction between laser beam and dried kraft pulp is ended. By the image analysis it can be seen that in beginning of laser beam and dried kraft pulp material interaction small holes off very good quality are formed. It is obvious that black colour and heat affected zone appear as function of interaction time. This reveals that there still are different interaction phases within interaction mechanisms A and B. These interaction phases appear as function of time and also as function of peak intensity of laser beam. Limit peak intensity is the value that divides interaction mechanism A and B from one-phase interaction into dual-phase interaction. So all peak intensity values under limit peak intensity belong to MAOM (interaction mechanism A one-phase mode) or to MBOM (interaction mechanism B onephase mode) and values over that belong to MADM (interaction mechanism A dual-phase mode) or to MBDM (interaction mechanism B dual-phase mode). Decomposition process of cellulose is evolution of hydrocarbons when temperature is between 380- 500°C. This means that long cellulose molecule is split into smaller volatile hydrocarbons in this temperature range. As temperature increases, decomposition process of cellulose molecule changes. In range of 700-900°C, cellulose molecule is mainly decomposed into H2 gas; this is why this range is called evolution of hydrogen. Interaction in this range starts (as in range of MAOM and MBOM), when a small good quality hole is formed. This is due to “direct evaporation” of pulp via decomposition process of evolution of hydrogen. And this can be seen can be seen in spectrometer as high intensity peak of yellow light (in range of 588-589 nm) which refers to temperature of ~1750ºC. Pyrometer does not detect this high intensity peak since it is not able to detect physical phase change from solid kraft pulp to gaseous compounds. As interaction time between laser beam and dried kraft pulp continues, hypothesis is that three auto ignition processes occurs. Auto ignition of substance is the lowest temperature in which it will spontaneously ignite in a normal atmosphere without an external source of ignition, such as a flame or spark. Three auto ignition processes appears in range of MADM and MBDM, namely: 1. temperature of auto ignition of hydrogen atom (H2) is 500ºC, 2. temperature of auto ignition of carbon monoxide molecule (CO) is 609ºC and 3. temperature of auto ignition of carbon atom (C) is 700ºC. These three auto ignition processes leads to formation of plasma plume which has strong emission of radiation in range of visible light. Formation of this plasma plume can be seen as increase of intensity in wavelength range of ~475-652 nm. Pyrometer shows maximum temperature just after this ignition. This plasma plume is assumed to scatter laser beam so that it interacts with larger area of dried kraft pulp than what is actual area of beam cross-section. This assumed scattering reduces also peak intensity. So result shows that assumably scattered light with low peak intensity is interacting with large area of hole edges and due to low peak intensity this interaction happens in low temperature. So interaction between laser beam and dried kraft pulp turns from evolution of hydrogen to evolution of hydrocarbons. This leads to black colour of hole edges.

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Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.

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Waste combustion has gone from being a volume reducing discarding-method to an energy recovery process for unwanted material that cannot be reused or recycled. Different fractions of waste are used as fuel today, such as; municipal solid waste, refuse derived fuel, and solid recovered fuel. Furthermore, industrial waste, normally a mixture between commercial waste and building and demolition waste, is common, either as separate fuels or mixed with, for example, municipal solid waste. Compared to fossil or biomass fuels, waste mixtures are extremely heterogeneous, making it a complicated fuel. Differences in calorific values, ash content, moisture content, and changing levels of elements, such as Cl and alkali metals, are common in waste fuel. Moreover, waste contains much higher levels of troublesome trace elements, such as Zn, which is thought to accelerate a corrosion process. Varying fuel quality can be strenuous on the boiler system and may cause fouling and corrosion of heat exchanger surfaces. This thesis examines waste fuels and waste combustion from different angles, with the objective of giving a better understanding of waste as an important fuel in today’s fuel economy. Several chemical characterisation campaigns of waste fuels over longer time periods (10-12 months) was used to determine the fossil content of Swedish waste fuels, to investigate possible seasonal variations, and to study the presence of Zn in waste. Data from the characterisation campaigns were used for thermodynamic equilibrium calculations to follow trends and determine the effect of changing concentrations of various elements. The thesis also includes a study of the thermal behaviour of Zn and a full—scale study of how the bed temperature affects the volatilisation of alkali metals and Zn from the fuel. As mixed waste fuel contains considerable amounts of fresh biomass, such as wood, food waste, paper etc. it would be wrong to classify it as a fossil fuel. When Sweden introduced waste combustion as a part of the European Union emission trading system in the beginning of 2013 there was a need for combustion plants to find a usable and reliable method to determine the fossil content. Four different methods were studied in full-scale of seven combustion plants; 14Canalysis of solid waste, 14C-analysis of flue gas, sorting analysis followed by calculations, and a patented balance method that is using a software program to calculate the fossil content based on parameters from the plant. The study showed that approximately one third of the coal in Swedish waste mixtures has fossil origins and presented the plants with information about the four different methods and their advantages and disadvantages. Characterisation campaigns also showed that industrial waste contain higher levels of trace elements, such as Zn. The content of Zn in Swedish waste fuels was determined to be approximately 800 mg kg-1 on average, based on 42 samples of solid waste from seven different plants with varying mixtures between municipal solid waste and industrial waste. A review study of the occurrence of Zn in fuels confirmed that the highest amounts of Zn are present in waste fuels rather than in fossil or biomass fuels. In tires, Zn is used as a vulcanizing agent and can reach concentration values of 9600-16800 mg kg-1. Waste Electrical and Electronic Equipment is the second Zn-richest fuel and even though on average Zn content is around 4000 mg kg-1, the values of over 19000 mg kg-1 were also reported. The increased amounts of Zn, 3000-4000 mg kg-1, are also found in municipal solid waste, sludge with over 2000 mg kg-1 on average (some exceptions up to 49000 mg kg-1), and other waste derived fuels (over 1000 mg kg-1). Zn is also found in fossil fuels. In coal, the average level of Zn is 100 mg kg-1, the higher amount of Zn was only reported for oil shale with values between 20-2680 mg kg-1. The content of Zn in biomass is basically determined by its natural occurrence and it is typically 10-100 mg kg-1. The thermal behaviour of Zn is of importance to understand the possible reactions taking place in the boiler. By using thermal analysis three common Zn-compounds were studied (ZnCl2, ZnSO4, and ZnO) and compared to phase diagrams produced with thermodynamic equilibrium calculations. The results of the study suggest that ZnCl2(s/l) cannot exist readily in the boiler due to its volatility at high temperatures and its conversion to ZnO in oxidising conditions. Also, ZnSO4 decomposes around 680°C, while ZnO is relatively stable in the temperature range prevailing in the boiler. Furthermore, by exposing ZnO to HCl in a hot environment (240-330°C) it was shown that chlorination of ZnO with HCl gas is possible. Waste fuel containing high levels of elements known to be corrosive, for example, Na and K in combination with Cl, and also significant amounts of trace elements, such as Zn, are demanding on the whole boiler system. A full-scale study of how the volatilisation of Na, K, and Zn is affected by the bed temperature in a fluidised bed boiler was performed parallel with a lab-scale study with the same conditions. The study showed that the fouling rate on deposit probes were decreased by 20 % when the bed temperature was decreased from 870°C to below 720°C. In addition, the lab-scale experiments clearly indicated that the amount of alkali metals and Zn volatilised depends on the reactor temperature.

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Biofilms are surface-attached multispecies microbial communities that are embedded by their self-produced extracellular polymeric substances. This lifestyle enhances the survival of the bacteria and plays a major role in many chronic bacterial infections. For instance, periodontitis is initiated by multispecies biofilms. The phases of active periodontal tissue destruction and notably increased levels of proinflammatory mediators, such as the key inflammatory mediator interleukin (IL)-1beta, are typical of the disease. The opportunistic periodontal pathogen Aggregatibacter actinomycetemcomitans is usually abundant at sites of aggressive periodontitis. Despite potent host immune system responses to subgingival invaders, A. actinomycetemcomitans is able to resist clearance attempts. Moreover, some strains of A. actinomycetemcomitans can generate genetic diversity through natural transformation, which may improve the species’ adjustment tothe subgingival environment in the long term. Some biofilm forming species are known to bind and sense human cytokines. As a response to cytokines, bacteria may increase biofilm formation and alter their expression of virulence genes. Specific outer membrane receptors for interferon-γ or IL-1β have been characterised in two Gram-negative pathogens. Because little is known about periodontal pathogens’ ability to sense cytokines, we used A. actinomycetemcomitans as a model organism to investigate how the species responds to IL-1beta. The main aims of this thesis were to explore cytokine binding on single-species A. actinomycetemcomitans biofilms and to determine the effects of cytokines on the biofilm formation and metabolic activity of the species. Additionally, the cytokine’s putative internalisation and interaction with A. actinomycetemcomitans proteins were studied. The possible impact of biofilm IL-1beta sequestering on the proliferation and apoptosis of gingival keratinocyte cells was evaluated in an organotypic mucosa co-culture model. Finally, the role of the extramembranous domain of the outer membrane protein HofQ (emHofQ) in DNA binding linked to DNA uptake in A. actinomycetemcomitans was examined. Our main finding revealed that viable A. actinomycetemcomitans biofilms can bind and take up the IL-1β produced by gingival cells. At the sites of pathogen-host interaction, the proliferation and apoptosis of gingival keratinocytes decreased slightly. Notably, the exposure of biofilms to IL-1beta caused their metabolic activity to drop, which may be linked to the observed interaction of IL-1beta with the conserved intracellular proteins DNA binding protein HU and the trimeric form of ATP synthase subunit beta. A Pasteurellaceaespecific lipoprotein, which had no previously determined function, was characterized as an IL-1beta interacting membrane protein that was expressed in the biofilm cultures of all tested A. actinomycetemcomitans strains. The use of a subcellular localisation tool combined with experimental analyses suggested that the identified lipoprotein, bacterial interleukin receptor I (BilRI), may be associated with the outer membrane with a portion of the protein oriented towards the external milieu. The results of the emHofQ study indicated that emHofQ has both the structural and functional capability to bind DNA. This result implies that emHofQ plays a role in DNA assimilation. The results from the current study also demonstrate that the Gram-negative oral species appears to sense the central proinflammatory mediator IL-1beta.

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The white adipose tissue mainly serves the purpose of energy storage, while brown adipose tissue (BAT) has the capacity to generate heat under cold conditions in mammals and in human infants. BAT is controlled by the central nervous system, and BAT function is accompanied by increased energy expenditure. However, it was not previously certain whether adult humans also have functional BAT. The aim of this doctoral work was to identify functional BAT in adult humans and to characterise its glucose uptake and blood flow under cold and insulin stimulation conditions in lean and in obese humans, by using positron emission tomography. Further, the impact of weight loss on BAT glucose uptake was assessed. Cerebral glucose uptake was also studied in relation to BAT function and cold exposure. The results showed that healthy adult humans have functional BAT, as assessed by the intense cold-induced glucose uptake and by biopsies. BAT was also found to be a highly insulinsensitive tissue in lean humans, but the effects of insulin and cold exposure were attenuated in obese humans, although the glucose uptake capacity of cold-activated BAT might be increased by weight loss. Blood flow in the BAT of lean humans was associated with whole-body energy expenditure. The presence of cold-activated BAT was related to lower body mass index and higher insulin sensitivity. Finally, BAT activation was linked to the activity of the cerebellum, the thalamus and certain neocortical regions. The cold-induced cerebral glucose uptake was also lower in obese than in lean adult humans.

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The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.