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.

Diskreettiaikainen liukuvan moodin säätö kiinteäoksidipolttokennon DC-tasonnostossa

Huoli ympäristön tilasta ja fossiilisten polttoaineiden hinnan nousu ovat vauhdittaneet tutkimusta uusien energialähteiden löytämiseksi. Polttokennot ovat yksi lupaavimmista tekniikoista etenkin hajautetun energiantuotannon, varavoimalaitosten sekä liikennevälineiden alueella. Polttokenno on tehonlähteenä kuitenkin hyvin epäideaalinen, ja se asettaa tehoelektroniikalle lukuisia erityisvaatimuksia. Polttokennon kytkeminen sähköverkkoon on tavallisesti toteutettu käyttämällä galvaanisesti erottavaa DC/DC hakkuria sekä vaihtosuuntaajaa sarjassa. Polttokennon kulumisen estämiseksi tehoelektroniikalta vaaditaan tarkkaa polttokennon lähtövirran hallintaa. Perinteisesti virran hallinta on toteutettu säätämällä hakkurin tulovirtaa PI (Proportional and Integral) tai PID (Proportional, Integral and Derivative) -säätimellä. Hakkurin epälineaarisuudesta johtuen tällainen ratkaisu ei välttämättä toimi kaukana linearisointipisteestä. Lisäksi perinteiset säätimet ovat herkkiä mallinnusvirheille. Tässä diplomityössä on esitetty polttokennon jännitettä nostavan hakkurin tilayhtälökeskiarvoistusmenetelmään perustuva malli, sekä malliin perustuva diskreettiaikainen integroiva liukuvan moodin säätö. Esitetty säätö on luonteeltaan epälineaarinen ja se soveltuu epälineaaristen ja heikosti tunnettujen järjestelmien säätämiseen.

Aktiivisten magneettilaakereiden tilasäädön mallinnus ja simulointi

Aktiivisten magneettilaakereiden avulla on mahdollista kannatella ferromagneettisia kappaleita, kuten sähkökoneiden roottoreita, ilman fyysistä kontaktia. Magneettilaakerit tarjoavat monia etuja, kuten esimerkiksi kitkattomuuden, verrattuina perinteisiin mekaanisiin laakereihin. Nämä edut vielä korostuvat suurnopeuskäytöissä, jotka ovat magneettilaakereiden pääasiallisia käyttökohteita. Tässä työssä esitellään magneettilaakereihin liittyvät erusteoriat ja niiden sovellustavat. Tämän jälkeen tarkastellaanmagneettilaakereiden kanssa käytettäviä säätöratkaisuja ja esitetään niille soveltuvat viritysmenetelmät. Teorioiden pohjalta rakennetaan täydellinen magneettilaakerijärjestelmän simulointimalli säätöratkaisuineen ja suoritetaan järjestelmän toimintaa kuvaavia simulointeja. Simuloinneissa saadut tulokset pyritään vielä varmentamaan suorittamalla mittauksia koelaitteistolla ja vertaamalla saatuja tuloksia keskenään.

Laitosmittaukset turbiinilaitoksen suorituskyvyn seurantaan ydinvoimalaitoksen vuosihuoltojen yhteydessä

Työssä kehitettiin höyryvoimalaitosprosessin tilan seurantaan laitosmittausrutiini, jolla tarkastellaan erityisesti turbiinilaitoksen suorituskykyä ennen ja jälkeen vuosihuoltojen. Laitosmittaukset on kehitetty Teollisuuden Voima Oyj:n Olkiluodon ydinvoimalaitosyksikköjen OL1 ja OL2 tarpeisiin. Mittauksilla saadaan tietoa vuosihuollon kokonaisvaikutuksista prosessiin eli muuttuiko mikään vuosihuollon aikana ja mitkä syyt johtivat muutokseen. Lisäksi säännöllisillä mittauksilla tavoitellaan pitkän aikavälin referenssitietoa prosessin tilasta. Esimerkkimittaukset tehtiin kevään 2008 vuosihuolloissa, R108 ja R208. Työssä on esitetty mittausten suorittaminen, tulosten laskenta ja tarkastelu sekä raportointi. Luotu mittausrutiini pohjautuu höyryturbiinien ja lämmönsiirtimien vastaanottokokeita käsitteleviin standardeihin sekä laitosten viimeisimpiin prosessimuutosten yhteydessä toteutettuihin suorituskykymittauksiin. Laitosmittauksista tehtiin vastaanottokokeita kevyemmät ja yksinkertaisemmat mittaustapahtumat, joilla saadaan kuitenkin riittävän luotettavaa tietoa. Tunnuslukuja, joita ei käytettävissä olevien mittatietojen avulla saatu suoraan selville tai laskettua massa- ja energiataseilla, määritettiin stationaarisen tilan mallinnusohjelmalla TEMPO:lla. Esimerkkimittaukset sujuivat hyvin ja saadut tulokset antoivat kaivattua lisätietoa vuosihuollon vaikutuksesta prosessiin. Generaattorin bruttoteho aleni OL1:llä ja pysyi ennallaan OL2:lla. OL1:n tehon aleneminen selittyi syöttöveden virtausmäärän vähenemisellä, johon vaikutti virtausmittalaitteen lähettimen vaihto. OL2:lla ei havaittu turbiiniprosessissa muutoksia, mutta lauhduttimien suorituskyky parani. Lauhduttimien suorituskyvyn paraneminen ilmeni asteisuuksien pienentymisenä, johon vaikuttivat puhdistaminen ja ilmavuotojen väheneminen.

Kaksisuuntaisen DC/DC-hakkurin virtasäätö polttokennosovelluksessa

Ilmastonmuutos ja fossiilisten polttoaineiden ehtyminen ovat edesauttaneet uusiutuvien energialähteiden tutkimusta huomattavasti. Lisäksi alati kasvava sähköenergian tarve lisää hajautetun sähköntuotannon ja vaihtoehtoisten energialähteiden kiinnostavuutta. Yleisimpiä hajautetun sähköntuotannon energialähteitä ovat tuulivoima, aurinkovoima ja uutena tulokkaana polttokennot. Polttokennon kytkeminen sähköverkkoon vaatii tehoelektroniikkaa, ja yleensä yksinkertaisessa polttokennosovelluksessa polttokenno kytketään galvaanisesti erottavan yksisuuntaisen DC/DC-hakkurin ja vaihtosuuntaajan kanssa sarjaan. Polttokennon rinnalla voidaan käyttää akkua tasaamaan polttokennon syöttämää jännitettä, jolloin akun ja polttokennon väliin tarvitaan kaksisuuntainen DC/DC-hakkuri, joka pystyy siirtämään energiaa molempiin suuntiin. Tässä diplomityössä on esitetty kaksisuuntaisen DC/DC-hakkurin tilayhtälökeskiarvoistusmenetelmään perustuva malli sekä mallin perusteella toteutettu virtasäätö. Tutkittava hakkuritopologia on kokosilta-tyyppinen boost-hakkuri, ja säätömenetelmä keskiarvovirtasäätö. Työn tuloksena syntyi tilayhtälömalli kaksisuuntaiselle FB boost -hakkurille sekä sen tulokelan virran säätämiseen soveltuva säädin. Säädin toimii normaalitilanteissa hyvin, mutta erikoistilanteissa, kuten hakkurin tulojännitteen äkillisessä muutostilanteessa, vaadittaisiin tehokkaampi säädin, jolla saavutettaisiin nopeampi nousuaika ilman ylitystä ja oskillointia.

Scheduling dynamic dataflow graphs with model checking

With the shift towards many-core computer architectures, dataflow programming has been proposed as one potential solution for producing software that scales to a varying number of processor cores. Programming for parallel architectures is considered difficult as the current popular programming languages are inherently sequential and introducing parallelism is typically up to the programmer. Dataflow, however, is inherently parallel, describing an application as a directed graph, where nodes represent calculations and edges represent a data dependency in form of a queue. These queues are the only allowed communication between the nodes, making the dependencies between the nodes explicit and thereby also the parallelism. Once a node have the su cient inputs available, the node can, independently of any other node, perform calculations, consume inputs, and produce outputs. Data ow models have existed for several decades and have become popular for describing signal processing applications as the graph representation is a very natural representation within this eld. Digital lters are typically described with boxes and arrows also in textbooks. Data ow is also becoming more interesting in other domains, and in principle, any application working on an information stream ts the dataflow paradigm. Such applications are, among others, network protocols, cryptography, and multimedia applications. As an example, the MPEG group standardized a dataflow language called RVC-CAL to be use within reconfigurable video coding. Describing a video coder as a data ow network instead of with conventional programming languages, makes the coder more readable as it describes how the video dataflows through the different coding tools. While dataflow provides an intuitive representation for many applications, it also introduces some new problems that need to be solved in order for data ow to be more widely used. The explicit parallelism of a dataflow program is descriptive and enables an improved utilization of available processing units, however, the independent nodes also implies that some kind of scheduling is required. The need for efficient scheduling becomes even more evident when the number of nodes is larger than the number of processing units and several nodes are running concurrently on one processor core. There exist several data ow models of computation, with different trade-offs between expressiveness and analyzability. These vary from rather restricted but statically schedulable, with minimal scheduling overhead, to dynamic where each ring requires a ring rule to evaluated. The model used in this work, namely RVC-CAL, is a very expressive language, and in the general case it requires dynamic scheduling, however, the strong encapsulation of dataflow nodes enables analysis and the scheduling overhead can be reduced by using quasi-static, or piecewise static, scheduling techniques. The scheduling problem is concerned with nding the few scheduling decisions that must be run-time, while most decisions are pre-calculated. The result is then an, as small as possible, set of static schedules that are dynamically scheduled. To identify these dynamic decisions and to find the concrete schedules, this thesis shows how quasi-static scheduling can be represented as a model checking problem. This involves identifying the relevant information to generate a minimal but complete model to be used for model checking. The model must describe everything that may affect scheduling of the application while omitting everything else in order to avoid state space explosion. This kind of simplification is necessary to make the state space analysis feasible. For the model checker to nd the actual schedules, a set of scheduling strategies are de ned which are able to produce quasi-static schedulers for a wide range of applications. The results of this work show that actor composition with quasi-static scheduling can be used to transform data ow programs to t many different computer architecture with different type and number of cores. This in turn, enables dataflow to provide a more platform independent representation as one application can be fitted to a specific processor architecture without changing the actual program representation. Instead, the program representation is in the context of design space exploration optimized by the development tools to fit the target platform. This work focuses on representing the dataflow scheduling problem as a model checking problem and is implemented as part of a compiler infrastructure. The thesis also presents experimental results as evidence of the usefulness of the approach.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

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.

Ionsonde Measurement Trend

Time series analysis has gone through different developmental stages before the current modern approaches. These can broadly categorized as the classical time series analysis and modern time series analysis approach. In the classical one, the basic target of the analysis is to describe the major behaviour of the series without necessarily dealing with the underlying structures. On the contrary, the modern approaches strives to summarize the behaviour of the series going through its underlying structure so that the series can be represented explicitly. In other words, such approach of time series analysis tries to study the series structurally. The components of the series that make up the observation such as the trend, seasonality, regression and disturbance terms are modelled explicitly before putting everything together in to a single state space model which give the natural interpretation of the series. The target of this diploma work is to practically apply the modern approach of time series analysis known as the state space approach, more specifically, the dynamic linear model, to make trend analysis over Ionosonde measurement data. The data is time series of the peak height of F2 layer symbolized by hmF2 which is the height of high electron density. In addition, the work also targets to investigate the connection between solar activity and the peak height of F2 layer. Based on the result found, the peak height of the F2 layer has shown a decrease during the observation period and also shows a nonlinear positive correlation with solar activity.

Modeling of non-isothermalvapor membrane separation with thermodynamic models and generalized mass transfer equations

A rigorous unit operation model is developed for vapor membrane separation. The new model is able to describe temperature, pressure, and concentration dependent permeation as wellreal fluid effects in vapor and gas separation with hydrocarbon selective rubbery polymeric membranes. The permeation through the membrane is described by a separate treatment of sorption and diffusion within the membrane. The chemical engineering thermodynamics is used to describe the equilibrium sorption of vapors and gases in rubbery membranes with equation of state models for polymeric systems. Also a new modification of the UNIFAC model is proposed for this purpose. Various thermodynamic models are extensively compared in order to verify the models' ability to predict and correlate experimental vapor-liquid equilibrium data. The penetrant transport through the selective layer of the membrane is described with the generalized Maxwell-Stefan equations, which are able to account for thebulk flux contribution as well as the diffusive coupling effect. A method is described to compute and correlate binary penetrant¿membrane diffusion coefficients from the experimental permeability coefficients at different temperatures and pressures. A fluid flow model for spiral-wound modules is derived from the conservation equation of mass, momentum, and energy. The conservation equations are presented in a discretized form by using the control volume approach. A combination of the permeation model and the fluid flow model yields the desired rigorous model for vapor membrane separation. The model is implemented into an inhouse process simulator and so vapor membrane separation may be evaluated as an integralpart of a process flowsheet.

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Photoelectric Measurements and Modeling of Bacteriorhodopsin

Recent technology has provided us with new information about the internal structures and properties of biomolecules. This has lead to the design of applications based on underlying biological processes. Applications proposed for biomolecules are, for example, the future computers and different types of sensors. One potential biomolecule to be incorporated in the applications is bacteriorhodopsin. Bacteriorhodopsin is a light-sensitive biomolecule, which works in a similar way as the light sensitive cells of the human eye. Bacteriorhodopsin reacts to light by undergoing a complicated series of chemical and thermal transitions. During these transitions, a proton translocation occurs inside the molecule. It is possible to measure the photovoltage caused by the proton translocations when a vast number of molecules is immobilized in a thin film. Also the changes in the light absorption of the film can be measured. This work aimed to develop the electronics needed for the voltage measurements of the bacteriorhodopsin-based optoelectronic sensors. The development of the electronics aimed to get more accurate information about the structure and functionality of these sensors. The sensors used in this work contain a thick film of bacteriorhodopsin immobilized in polyvinylalcohol. This film is placed between two transparent electrodes. The result of this work is an instrumentation amplifier which can be placed in a small space very close to the sensor. By using this amplifier, the original photovoltage can be measured in more detail. The response measured using this amplifier revealed two different components, which could not be distinguished earlier. Another result of this work is the model for the photoelectric response in dry polymer films.

Quantum Tomography with Phase Space Measurements

This thesis addresses the use of covariant phase space observables in quantum tomography. Necessary and sufficient conditions for the informational completeness of covariant phase space observables are proved, and some state reconstruction formulae are derived. Different measurement schemes for measuring phase space observables are considered. Special emphasis is given to the quantum optical eight-port homodyne detection scheme and, in particular, on the effect of non-unit detector efficiencies on the measured observable. It is shown that the informational completeness of the observable does not depend on the efficiencies. As a related problem, the possibility of reconstructing the position and momentum distributions from the marginal statistics of a phase space observable is considered. It is shown that informational completeness for the phase space observable is neither necessary nor sufficient for this procedure. Two methods for determining the distributions from the marginal statistics are presented. Finally, two alternative methods for determining the state are considered. Some of their shortcomings when compared to the phase space method are discussed.

Analysis and validation of space averaged drag model for numerical simulations of gas-solid flows in fluidized beds

This thesis presents an approach for formulating and validating a space averaged drag model for coarse mesh simulations of gas-solid flows in fluidized beds using the two-fluid model. Proper modeling for fluid dynamics is central in understanding any industrial multiphase flow. The gas-solid flows in fluidized beds are heterogeneous and usually simulated with the Eulerian description of phases. Such a description requires the usage of fine meshes and small time steps for the proper prediction of its hydrodynamics. Such constraint on the mesh and time step size results in a large number of control volumes and long computational times which are unaffordable for simulations of large scale fluidized beds. If proper closure models are not included, coarse mesh simulations for fluidized beds do not give reasonable results. The coarse mesh simulation fails to resolve the mesoscale structures and results in uniform solids concentration profiles. For a circulating fluidized bed riser, such predicted profiles result in a higher drag force between the gas and solid phase and also overestimated solids mass flux at the outlet. Thus, there is a need to formulate the closure correlations which can accurately predict the hydrodynamics using coarse meshes. This thesis uses the space averaging modeling approach in the formulation of closure models for coarse mesh simulations of the gas-solid flow in fluidized beds using Geldart group B particles. In the analysis of formulating the closure correlation for space averaged drag model, the main parameters for the modeling were found to be the averaging size, solid volume fraction, and distance from the wall. The closure model for the gas-solid drag force was formulated and validated for coarse mesh simulations of the riser, which showed the verification of this modeling approach. Coarse mesh simulations using the corrected drag model resulted in lowered values of solids mass flux. Such an approach is a promising tool in the formulation of appropriate closure models which can be used in coarse mesh simulations of large scale fluidized beds.

Modeling of residual stresses and distortion due to welding in fillet welds

Welding has a growing role in modern world manufacturing. Welding joints are extensively used from pipes to aerospace industries. Prediction of welding residual stresses and distortions is necessary for accurate evaluation of fillet welds in relation to design and safety conditions. Residual stresses may be beneficial or detrimental, depending whether they are tensile or compressive and the loading. They directly affect the fatigue life of the weld by impacting crack growth rate. Beside theoretical background of residual stresses this study calculates residual stresses and deformations due to localized heating by welding process and subsequent rapid cooling in fillet welds. Validated methods are required for this purpose due to complexity of process, localized heating, temperature dependence of material properties and heat source. In this research both empirical and simulation methods were used for the analysis of welded joints. Finite element simulation has become a popular tool of prediction of welding residual stresses and distortion. Three different cases with and without preload have been modeled during this study. Thermal heat load set is used by calculating heat flux from the given heat input energy. First the linear and then nonlinear material behavior model is modeled for calculation of residual stresses. Experimental work is done to calculate the stresses empirically. The results from both the methods are compared to check their reliability. Residual stresses can have a significant effect on fatigue performance of the welded joints made of high strength steel. Both initial residual stress state and subsequent residual stress relaxation need to be considered for accurate description of fatigue behavior. Tensile residual stresses are detrimental and will reduce the fatigue life and compressive residual stresses will increase it. The residual stresses follow the yield strength of base or filler material and the components made of high strength steel are typically thin, where the role of distortion is emphasizing.