Experimental and Numerical Analysis of Different Volutes in a Centrifugal Compressor

In a centrifugal compressor the flow around the diffuser is collected and led to the pipe system by a spiral-shaped volute. In this study a single-stage centrifugal compressor with three different volutes is investigated. The compressorwas first equipped with the original volute, the cross-section of which was a combination of a rectangle and semi-circle. Next a new volute with a fully circular cross-section was designed and manufactured. Finally, the circular volute wasmodified by rounding the tongue and smoothing the tongue area. The overall performance of the compressor as well as the static pressure distribution after the impeller and on the volute surface were measured. The flow entering the volute was measured using a three-hole Cobra-probe, and flow visualisations were carriedout in the exit cone of the volute. In addition, the radial force acting on theimpeller was measured using magnetic bearings. The complete compressor with thecircular volute (inlet pipe, full impeller, diffuser, volute and outlet pipe) was also modelled using computational fluid dynamics (CFD). A fully 3-D viscous flow was solved using a Navier-Stokes solver, Finflo, developed at Helsinki University of Technology. Chien's k-e model was used to take account of the turbulence. The differences observed in the performance of the different volutes were quite small. The biggest differences were at low speeds and high volume flows,i.e. when the flow entered the volute most radially. In this operating regime the efficiency of the compressor with the modified circular volute was about two percentage points higher than with the other volutes. Also, according to the Cobra-probe measurements and flow visualisations, the modified circular volute performed better than the other volutes in this operating area. The circumferential static pressure distribution in the volute showed increases at low flow, constant distribution at the design flow and decrease at high flow. The non-uniform static pressure distribution of the volute was transmitted backwards across the vaneless diffuser and observed at the impeller exit. At low volume flow a strong two-wave pattern developed into the static pressure distribution at the impeller exit due to the response of the impeller to the non-uniformity of pressure. The radial force of the impeller was the greatest at the choke limit, the smallest atthe design flow, and moderate at low flow. At low flow the force increase was quite mild, whereas the increase at high flow was rapid. Thus, the non-uniformityof pressure and the force related to it are strong especially at high flow. Theforce caused by the modified circular volute was weaker at choke and more symmetric as a function of the volume flow than the force caused by the other volutes.

Structural and optical properties of InAs/GaAs quantum structures

The goal of the thesis was to study fundamental structural and optical properties of InAs islands and In(Ga)As quantum rings. The research was carried out at the Department of Micro and Nanosciences of Helsinki University of Technology. A good surface quality can be essential for the potential applications in optoelectronic devices. For such device applications it is usually necessary to control size, density and arrangement of the islands. In order to study the dependence of the structural properties of the islands and the quantum rings on growth conditions, atomic force microscope was used. Obtained results reveal that the size and the density of the In(Ga)As quantum rings strongly depend on the growth temperature, the annealing time and the thickness of the partial capping layer. From obtained results it is possible to conclude that to get round shape islands and high density one has to use growth temperature of 500 ̊C. In the case of formation of In(Ga)As quantum rings the effect of mobility anisotropy is observed that so the shape of the rings is not symmetric. To exclude this effect it is preferable to use a higher annealing temperature of 570 ̊C. Optical properties were characterized by PL spectroscopy. PL emission was observed from buried InAs quantum dots and In(Ga)As quantum rings grown with different annealing time and temperature and covered with a various thickness of the partial capping layer.

Time-varying Risk Premiums and Conditional Market Risk: Empirical Evidence from European Stock Markets

This study investigates the relationship between the time-varying risk premiums and conditional market risk in the stock markets of the ten member countries of Economy and Monetary Union. Second, it examines whether the conditional second moments change over time and are there asymmetric effects in the conditional covariance matrix. Third, it analyzes the possible effects of the chosen testing framework. Empirical analysis is conducted using asymmetric univariate and multivariate GARCH-in-mean models and assuming three different degrees of market integration. For a daily sample period from 1999 to 2007, the study shows that the time-varying market risk alone is not enough to explain the dynamics of risk premiums and indications are found that the market risk is detected only when its price is allowed to change over time. Also asymmetric effects in the conditional covariance matrix, which is found to be time-varying, are clearly present and should be recognized in empirical asset pricing analyses.

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.

Neurophysiologic diagnosis, clinical symptoms and neuropathologic findings in polyneuropathies

Tausta: Polyneuropatia (PNP) on ääreishermoston sairaus, joka aiheuttaa laaja-alaisia, yleensä symmetrisiä vaurioita ääreishermostossa. PNP:aan johtavia syitä on satoja. Tavoitteet: Löytää parhaat neurofysiologiset menetelmät uremian, myelooman hoidossa käytettävän talidomidin sekä Fabryn taudin aiheuttaman PNP:n diagnosoimiseksi. Fabryn taudissa tutkin lisäksi ohutsäieneuropatian aiheuttamia neuropatologisia löydöksiä iholta otetusta koepalasta. Tutkimuksissa kartoitettiin lisäksi PNP:n aiheuttamien subjektiivisten oireiden korrelaatio neurofysiologisten ja neuropatologisten löydösten kanssa. Munuaisten vajaatoimintaa sairastavilla potilailla tavoitteena oli tutkia dialyysihoidon tehon vaikutusta autonomisen hermoston toimintaan sekä yhden dialyysikerran vaikutusta neurofysiologisiin löydöksiin. Aineisto ja menetelmät: I: Tutkittiin 21 uremiapotilaan sensoristen ja motoristen hermojen vasteet, värinä- sekä lämpötuntokynnykset ennen ja jälkeen hemodialyysin. Subjektiiviset PNP oireet kartoitettiin PNP oireita kysyvillä kaavakkeella. II:12 talidomidi hoitoa saavaa myeloomapotilasta, tutkimuksen menetelmät olivat samat kuin tutkimuksessa I. III: 12 Fabryn tautia sairastavaa potilasta, edellä mainittujen neurofysiologisten tutkimusten lisäksi potilailta otettiin ihobiopsia säären alueelta. Ihobiopsiasta laskettiin ohuiden hermosyiden määrä koepalan värjäyksen jälkeen. Subjektiiviset PNP oireet kartoitettiin kyselykaavakkeella. Sydämen sykevaihtelu tutkittiin levossa taajuustason analyysillä. IV: 32 uremiapotilaan autonomisen hermoston toimintaa tutkittiin sydämen sykevaihtelun aikatason analysillä, paksujen myelinoituneiden säikeiden toimintaa tutkittiin perifeeristen sensoristen hermojen mittauksilla toistetusti noin 2.9 vuoden aikana. Tulokset: Ureemisen PNP:n diagnostiikassa herkimmät tutkimukset ovat F-aaltojen parametrit alaraajojen motorisista hermoista, värinätuntokynnys alaraajoista sekä suralishermon amplitudi. Positiiviset PNP oireet uremiassa korreloivat värinätunto-kynnyksen sekä sensoristen hermojen neurografialöydösten kanssa. Neurofysiologisten tutkimusten ajankohdalla dialyysiajankohtaan nähden ei ole merkitystä. Talidomidi-PNP on pääasiassa sensorinen, mutta motoriset syyt ovat lievästi vaurioituneet. Talidomidi PNP:ssa subjektiiviset oireet korreloivat huonosti neurofysiologisten löydösten kanssa. Fabryn taudissa naisilla on oletettua enemmän ohutsäieneuropatian aiheuttamia oireita ja löydöksiä. Paksujen säikeiden löydöksiä ei tullut esiin. Ohutsäieneuropatian diagnostiikassa ihobiopsia ja kvantitatiiviset tuntokynnysmittaustestit täydentävät toisiaan. Tehokas dialyysi parantaa autonomisen hermoston toimintaa uremiapotilailla. Päätelmät: Erityyppisten polyneuropatioiden diagnostiikassa pitää etukäteen valita PNP tyypille oikeat tutkimusmenetelmät raskaiden tutkimuspatterien vähentämiseksi sekä diagnostiikan parantamiseksi. PNP:n aiheuttamat oireet ja kliiniset löydökset pitää aina tutkia, mutta yksin ne eivät ole herkkiä PNP:n diagnostiikassa.

Metaanin muodostumisen mallintaminen kaatopaikalla

Methane-rich landfill gas is generated when biodegradable organic wastes disposed of in landfills decompose under anaerobic conditions. Methane is a significant greenhouse gas, and landfills are its major source in Finland. Methane production in landfill depends on many factors such as the composition of waste and landfill conditions, and it can vary a lot temporally and spatially. Methane generation from waste can be estimated with various models. In this thesis three spreadsheet applications, a reaction equation and a triangular model for estimating the gas generation were introduced. The spreadsheet models introduced are IPCC Waste Model (2006), Metaanilaskentamalli by Jouko Petäjä of Finnish Environment Institute and LandGEM (3.02) of U.S. Environmental Protection Agency. All these are based on the first order decay (FOD) method. Gas recovery methods and gas emission measurements were also examined. Vertical wells and horizontal trenches are the most commonly used gas collection systems. Emission measurements chamber method, tracer method, soil core and isotope measurements, micrometeorological mass-balance and eddy covariance methods and gas measuring FID-technology were discussed. Methane production at Ämmässuo landfill of HSY Helsinki Region Environmental Services Authority was estimated with methane generation models and the results were compared with the volumes of collected gas. All spreadsheet models underestimated the methane generation at some point. LandGEM with default parameters and Metaanilaskentamalli with modified parameters corresponded best with the gas recovery numbers. Reason for the differences between evaluated and collected volumes could be e.g. that the parameter values of the degradable organic carbon (DOC) and the fraction of decomposable degradable organic carbon (DOCf) do not represent the real values well enough. Notable uncertainty is associated with the modelling results and model parameters. However, no simple explanation for the discovered differences can be given within this thesis.

Vuotasapainon hallinta kokosiltasyötetyssä muuntajassa

Keskitaajuudella toimivia muuntajia käytetään laajalti tehoelektroniikkasovelluksissa kuten DC/DC-konverttereissa ja muissa hakkuriteholähteissä. Muuntaja on induktiivinen komponentti, jonka magneettisen tasapainon säilyttäminen hakkuriteholähteissä on laitteen virheettömän toiminnan kannalta tärkeää. Muuntajaa syöttävän virtapiirin on muodostettava symmetrinen syöttöjännite, jotta muuntajan vuo ei ajaudu positiiviseen tai negatiiviseen kyllästykseen. Tässä diplomityössä esitetään muuntajan sähkömagneettinen toimintaperiaate, kyllästymisen syyt hakkuriteholähteissä sekä kehitetään aktiivinen ohjaus vuotasapainon säilyttämiseksi. Hakkuriteholähteissä käytettävissä muuntajissa on monesti useampi kuin kaksi käämiä. Tässä työssä tutkittavassa muuntajassa on useita ensiöitä ja useita toisioita ja muuntajaa syötetään keskitaajuudella. Tämä tuo uusia ongelmia verrattuna perinteiseen yksivaiheiseen DC/DC-konvertteriin. Näihin ongelmiin esitetään ratkaisut diplomityön tutkimuksessa.

Evaluating multidimensional visualization techniques in data mining tasks

Visual data mining (VDM) tools employ information visualization techniques in order to represent large amounts of high-dimensional data graphically and to involve the user in exploring data at different levels of detail. The users are looking for outliers, patterns and models – in the form of clusters, classes, trends, and relationships – in different categories of data, i.e., financial, business information, etc. The focus of this thesis is the evaluation of multidimensional visualization techniques, especially from the business user’s perspective. We address three research problems. The first problem is the evaluation of projection-based visualizations with respect to their effectiveness in preserving the original distances between data points and the clustering structure of the data. In this respect, we propose the use of existing clustering validity measures. We illustrate their usefulness in evaluating five visualization techniques: Principal Components Analysis (PCA), Sammon’s Mapping, Self-Organizing Map (SOM), Radial Coordinate Visualization and Star Coordinates. The second problem is concerned with evaluating different visualization techniques as to their effectiveness in visual data mining of business data. For this purpose, we propose an inquiry evaluation technique and conduct the evaluation of nine visualization techniques. The visualizations under evaluation are Multiple Line Graphs, Permutation Matrix, Survey Plot, Scatter Plot Matrix, Parallel Coordinates, Treemap, PCA, Sammon’s Mapping and the SOM. The third problem is the evaluation of quality of use of VDM tools. We provide a conceptual framework for evaluating the quality of use of VDM tools and apply it to the evaluation of the SOM. In the evaluation, we use an inquiry technique for which we developed a questionnaire based on the proposed framework. The contributions of the thesis consist of three new evaluation techniques and the results obtained by applying these evaluation techniques. The thesis provides a systematic approach to evaluation of various visualization techniques. In this respect, first, we performed and described the evaluations in a systematic way, highlighting the evaluation activities, and their inputs and outputs. Secondly, we integrated the evaluation studies in the broad framework of usability evaluation. The results of the evaluations are intended to help developers and researchers of visualization systems to select appropriate visualization techniques in specific situations. The results of the evaluations also contribute to the understanding of the strengths and limitations of the visualization techniques evaluated and further to the improvement of these techniques.

A quantitative view on fuzzy numbers

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

Application of Computational Fluid Dynamics in Modeling Blood Flow in Human Thoracic Aorta

The aim of this study was to simulate blood flow in thoracic human aorta and understand the role of flow dynamics in the initialization and localization of atherosclerotic plaque in human thoracic aorta. The blood flow dynamics in idealized and realistic models of human thoracic aorta were numerically simulated in three idealized and two realistic thoracic aorta models. The idealized models of thoracic aorta were reconstructed with measurements available from literature, and the realistic models of thoracic aorta were constructed by image processing Computed Tomographic (CT) images. The CT images were made available by South Karelia Central Hospital in Lappeenranta. The reconstruction of thoracic aorta consisted of operations, such as contrast adjustment, image segmentations, and 3D surface rendering. Additional design operations were performed to make the aorta model compatible for the numerical method based computer code. The image processing and design operations were performed with specialized medical image processing software. Pulsatile pressure and velocity boundary conditions were deployed as inlet boundary conditions. The blood flow was assumed homogeneous and incompressible. The blood was assumed to be a Newtonian fluid. The simulations with idealized models of thoracic aorta were carried out with Finite Element Method based computer code, while the simulations with realistic models of thoracic aorta were carried out with Finite Volume Method based computer code. Simulations were carried out for four cardiac cycles. The distribution of flow, pressure and Wall Shear Stress (WSS) observed during the fourth cardiac cycle were extensively analyzed. The aim of carrying out the simulations with idealized model was to get an estimate of flow dynamics in a realistic aorta model. The motive behind the choice of three aorta models with distinct features was to understand the dependence of flow dynamics on aorta anatomy. Highly disturbed and nonuniform distribution of velocity and WSS was observed in aortic arch, near brachiocephalic, left common artery, and left subclavian artery. On the other hand, the WSS profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The comparison of instantaneous WSS profiles revealed that the model with straight branching arteries had relatively lower WSS compared to that in the aorta model with curved branches. In addition to this, significant differences were observed in the spatial and temporal profiles of WSS, flow, and pressure. The study with idealized model was extended to study blood flow in thoracic aorta under the effects of hypertension and hypotension. One of the idealized aorta models was modified along with the boundary conditions to mimic the thoracic aorta under the effects of hypertension and hypotension. The results of simulations with realistic models extracted from CT scans demonstrated more realistic flow dynamics than that in the idealized models. During systole, the velocity in ascending aorta was skewed towards the outer wall of aortic arch. The flow develops secondary flow patterns as it moves downstream towards aortic arch. Unlike idealized models, the distribution of flow was nonplanar and heavily guided by the artery anatomy. Flow cavitation was observed in the aorta model which was imaged giving longer branches. This could not be properly observed in the model with imaging containing a shorter length for aortic branches. The flow circulation was also observed in the inner wall of the aortic arch. However, during the diastole, the flow profiles were almost flat and regular due the acceleration of flow at the inlet. The flow profiles were weakly turbulent during the flow reversal. The complex flow patterns caused a non-uniform distribution of WSS. High WSS was distributed at the junction of branches and aortic arch. Low WSS was distributed at the proximal part of the junction, while intermedium WSS was distributed in the distal part of the junction. The pulsatile nature of the inflow caused oscillating WSS at the branch entry region and inner curvature of aortic arch. Based on the WSS distribution in the realistic model, one of the aorta models was altered to induce artificial atherosclerotic plaque at the branch entry region and inner curvature of aortic arch. Atherosclerotic plaque causing 50% blockage of lumen was introduced in brachiocephalic artery, common carotid artery, left subclavian artery, and aortic arch. The aim of this part of the study was first to study the effect of stenosis on flow and WSS distribution, understand the effect of shape of atherosclerotic plaque on flow and WSS distribution, and finally to investigate the effect of lumen blockage severity on flow and WSS distributions. The results revealed that the distribution of WSS is significantly affected by plaque with mere 50% stenosis. The asymmetric shape of stenosis causes higher WSS in branching arteries than in the cases with symmetric plaque. The flow dynamics within thoracic aorta models has been extensively studied and reported here. The effects of pressure and arterial anatomy on the flow dynamic were investigated. The distribution of complex flow and WSS is correlated with the localization of atherosclerosis. With the available results we can conclude that the thoracic aorta, with complex anatomy is the most vulnerable artery for the localization and development of atherosclerosis. The flow dynamics and arterial anatomy play a role in the localization of atherosclerosis. The patient specific image based models can be used to diagnose the locations in the aorta vulnerable to the development of arterial diseases such as atherosclerosis.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Ristikkorakenteisen hihnakuljetinsillan mitoitustyökalun kehittäminen

Hihnakuljettimia käytetään muun muassa voimalaitos- ja sellutehdasympäristöissä kuljettamaan kiinteää polttoainetta tai haketta pitkiä matkoja. Pitkät hihnakuljettimet asennetaan yleensä teräsristikoista rakennettujen kuljetinsiltojen sisään. Kuljetinsilta toimii siis hihnakuljettimen ja hoitokäytävän runkona sekä suojaa kuljetinta ja kuljetettavaa materiaalia säältä. Tässä diplomityössä on laadittu mitoitustyökalu, jolla voidaan nopeasti mitoittaa ristikkorakenteisen hihnakuljetinsillan sauvat sekä määrittää rakenteen massa. Laskentaohjelma on toteutettu Microsoft Excel -taulukkolaskentana. Sillan poikkileikkaus voi olla suljettu symmetrinen umpirakenne tai avorakenne, jossa on ulokkeellinen hoitotaso. Ristikon sauvat ovat RHS-putkia. Rakenteeseen voi vaikuttaa jatkuvia kuormia, pistekuormia sekä näistä johdetut, ekvivalenttiin staattiseen voimaan perustuvat maanjäristyskuormat. Diplomityössä on perehdytty mitoitustyökalussa sovellettuihin teorioihin. Voimasuureiden laskenta perustuu 2-tukisina palkkeina käsiteltävien siltalohkojen ratkaisuun ja palkkianalogiaan, jossa ristikon sauvavoimat ratkaistaan käsittelemällä ristikkoa palkkina. Sauvojen kestävyyden laskenta perustuu SFS-EN 1993-1-1 -normiin, joka on osa Eurocode -rakennesuunnittelunormistoa. Lisäksi työssä on käsitelty ristikkoliitosten mitoitusta SFS-EN 1993-1-8 mukaan. Mitoitusohjelman toimivuutta on testattu tarkastelemalla esimerkkisiltaa laaditulla mitoituspohjalla ja Autodesk Robot Professional 2013 -FE-analyysiohjelmisuolla. Tulosten perusteella mitoitustyökalua voidaan käyttää ainakin tarjousvaiheen nopeisiin tarkasteluihin ja omamassan määritykseen, mutta myös lopulliseen mitoitukseen, mikäli hyväksytään konservatiivinen mitoitus.

Context-specific independence in graphical models

The theme of this thesis is context-speci c independence in graphical models. Considering a system of stochastic variables it is often the case that the variables are dependent of each other. This can, for instance, be seen by measuring the covariance between a pair of variables. Using graphical models, it is possible to visualize the dependence structure found in a set of stochastic variables. Using ordinary graphical models, such as Markov networks, Bayesian networks, and Gaussian graphical models, the type of dependencies that can be modeled is limited to marginal and conditional (in)dependencies. The models introduced in this thesis enable the graphical representation of context-speci c independencies, i.e. conditional independencies that hold only in a subset of the outcome space of the conditioning variables. In the articles included in this thesis, we introduce several types of graphical models that can represent context-speci c independencies. Models for both discrete variables and continuous variables are considered. A wide range of properties are examined for the introduced models, including identi ability, robustness, scoring, and optimization. In one article, a predictive classi er which utilizes context-speci c independence models is introduced. This classi er clearly demonstrates the potential bene ts of the introduced models. The purpose of the material included in the thesis prior to the articles is to provide the basic theory needed to understand the articles.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

On Distributed Storage Codes

Distributed storage systems are studied. The interest in such system has become relatively wide due to the increasing amount of information needed to be stored in data centers or different kinds of cloud systems. There are many kinds of solutions for storing the information into distributed devices regarding the needs of the system designer. This thesis studies the questions of designing such storage systems and also fundamental limits of such systems. Namely, the subjects of interest of this thesis include heterogeneous distributed storage systems, distributed storage systems with the exact repair property, and locally repairable codes. For distributed storage systems with either functional or exact repair, capacity results are proved. In the case of locally repairable codes, the minimum distance is studied. Constructions for exact-repairing codes between minimum bandwidth regeneration (MBR) and minimum storage regeneration (MSR) points are given. These codes exceed the time-sharing line of the extremal points in many cases. Other properties of exact-regenerating codes are also studied. For the heterogeneous setup, the main result is that the capacity of such systems is always smaller than or equal to the capacity of a homogeneous system with symmetric repair with average node size and average repair bandwidth. A randomized construction for a locally repairable code with good minimum distance is given. It is shown that a random linear code of certain natural type has a good minimum distance with high probability. Other properties of locally repairable codes are also studied.