Modeling of burden distribution in the blast furnace

The blast furnace is the main ironmaking production unit in the world which converts iron ore with coke and hot blast into liquid iron, hot metal, which is used for steelmaking. The furnace acts as a counter-current reactor charged with layers of raw material of very different gas permeability. The arrangement of these layers, or burden distribution, is the most important factor influencing the gas flow conditions inside the furnace, which dictate the efficiency of the heat transfer and reduction processes. For proper control the furnace operators should know the overall conditions in the furnace and be able to predict how control actions affect the state of the furnace. However, due to high temperatures and pressure, hostile atmosphere and mechanical wear it is very difficult to measure internal variables. Instead, the operators have to rely extensively on measurements obtained at the boundaries of the furnace and make their decisions on the basis of heuristic rules and results from mathematical models. It is particularly difficult to understand the distribution of the burden materials because of the complex behavior of the particulate materials during charging. The aim of this doctoral thesis is to clarify some aspects of burden distribution and to develop tools that can aid the decision-making process in the control of the burden and gas distribution in the blast furnace. A relatively simple mathematical model was created for simulation of the distribution of the burden material with a bell-less top charging system. The model developed is fast and it can therefore be used by the operators to gain understanding of the formation of layers for different charging programs. The results were verified by findings from charging experiments using a small-scale charging rig at the laboratory. A basic gas flow model was developed which utilized the results of the burden distribution model to estimate the gas permeability of the upper part of the blast furnace. This combined formulation for gas and burden distribution made it possible to implement a search for the best combination of charging parameters to achieve a target gas temperature distribution. As this mathematical task is discontinuous and non-differentiable, a genetic algorithm was applied to solve the optimization problem. It was demonstrated that the method was able to evolve optimal charging programs that fulfilled the target conditions. Even though the burden distribution model provides information about the layer structure, it neglects some effects which influence the results, such as mixed layer formation and coke collapse. A more accurate numerical method for studying particle mechanics, the Discrete Element Method (DEM), was used to study some aspects of the charging process more closely. Model charging programs were simulated using DEM and compared with the results from small-scale experiments. The mixed layer was defined and the voidage of mixed layers was estimated. The mixed layer was found to have about 12% less voidage than layers of the individual burden components. Finally, a model for predicting the extent of coke collapse when heavier pellets are charged over a layer of lighter coke particles was formulated based on slope stability theory, and was used to update the coke layer distribution after charging in the mathematical model. In designing this revision, results from DEM simulations and charging experiments for some charging programs were used. The findings from the coke collapse analysis can be used to design charging programs with more stable coke layers.

Utilisation of Statistics in Intelligent Web Applications

Web-portaalien aiheenmukaista luokittelua voidaan hyödyntää tunnistamaan käyttäjän kiinnostuksen kohteet keräämällä tilastotietoa hänen selaustottumuksistaan eri kategorioissa. Tämä diplomityö käsittelee web-sovelluksien osa-alueita, joissa kerättyä tilastotietoa voidaan hyödyntää personalisoinnissa. Yleisperiaatteet sisällön personalisoinnista, Internet-mainostamisesta ja tiedonhausta selitetään matemaattisia malleja käyttäen. Lisäksi työssä kuvaillaan yleisluontoiset ominaisuudet web-portaaleista sekä tilastotiedon keräämiseen liittyvät seikat.

Tislauskolonnin varopurkauksen laskeminen dynaamisen simuloinnin avulla

Työn tavoitteena oli tutkia tislauskolonnin dynamiikkaa ja dynaamista mallintamista simulointien avulla. Dynaamisen simulointimallin avulla selvitettiin pentaanin erotuskolonnin toimintaa poikkeus- ja häiriötilanteissa. Lisäksi pyrittiin arvioimaan työssä käytettyjen simulointiohjelmistojen soveltuvuutta tislauksen dynaamiseen simulointiin. Työn kirjallisuusosassa käsiteltiin tislauskolonnindynamiikan mallintamista matemaattisten mallien avulla sekä tislauskolonnimallin rakentamista simulointiohjelmistoon. Kirjallisuusosassa esiteltiin myös tislauskolonnin häiriötilanteita ja niiden aiheuttamia varopurkaustapauksia. Tämän lisäksi kirjallisuusosassa käytiin läpi tislauskolonnin varoventtiilien mitoittamisen perusteita. Työn soveltavassa osassa muodostettiin tislauskolonnille dynaaminen simulointimalli Aspen HYSYS Dynamics ja PROSimulator-simulointiohjelmistolla. Mallien avulla tarkasteltiin erilaisten häiriöiden ja poikkeustilanteiden vaikutusta kolonnin käyttäytymiseen ja varopurkaus-tapauksiin. Työssä arvioitiin myös ohjelmistojen soveltuvuutta tislauksen dynaamiseen simulointiin. Työssä saatujen tulosten perusteella voidaan todeta, että dynaamisen simuloinnin avulla saadaan hyödyllistä tietoa tislauskolonnin toiminnasta häiriö- ja poikkeustilanteissa. Dynaamisen simuloinnin onnistuminen ja luotettavien tulosten saaminen edellyttää kuitenkin tarkasteltavan prosessin tuntemista ja ohjelmiston käytön hallintaa. Työssä käytetyn Aspen HYSYS Dynamics simulointiohjelmiston käytettävyydessä havaittiin puutteita ja ohjelmisto vaatii vielä kehitystyötä. Työssä käytetty PROSimulator-simulointiohjelmisto soveltui pienistä puutteista huolimatta hyvin tislauskolonnin häiriötilanteiden tutkimiseen.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Jätevesilaitosten mallinnus

TäTässä työssä tarkastellaan jäteveden biologiseen puhdistukseen käytettävän aktiiviliete-prosessin kuvaamista matemaattisen mallintamisen avulla. Jäteveden puhdistus on jo vanha keksintö ja aktiivilieteprosessikin on otettu ensimmäisen kerran pilot- käyttöön vuonna 1914. Myös jätevesilaitosten matemaattinen mallintaminen on ollut pitkään tunnettu tekniikka ja ensimmäiset dynaamiset mallit kehitettiin 1950–luvulla. Työn alkuosassa on tarkasteltu jätevesilaitosten matemaattista mallintamista kirjallisuus-lähteiden pohjalta. Tarkastelun painopiste on suunnattu erilaisiin matemaattisiin malleihin ja mallintamisen kehitykseen. Mallintamisen ohessa on kiinnitetty huomiota aktiiviliete-prosessiin ja siihen vaikuttaviin tekijöihin. Mallintamiseen vaikuttavista tekijöistä erityistä huomiota on kiinnitetty ilmastukseen, bakteerien kasvuun ja selkeytykseen sekä niiden vaikutuksiin prosessin kannalta. Matemaattisen mallintamisen tarkastelun jälkeen työssä on pohdittu CFD–mallintamisen hyödyntämismahdollisuuksia aktiivilieteprosessien kuvaamisessa. Mallintamisosiossa on tarkasteltu Activated Sludge Model No. 3 (ASM 3) mallin rakennetta ja sisältöä sekä sen eri tekijöiden vaikutuksia malliin. Työn tässä osassa on tarkasteltu myös hapensiirtoa ilmastuksessa ilmakuplista veteen ja selkeytystä osana aktiivilieteprosessia. Tässä osiossa on käyty läpi myös kaikki prosessin kannalta oleelliset yhtälöt, esimerkiksi reaktionopeus- ja massataseyhtälöt.

Lajittumisen dynamiikka epäpuhtauksien ja kuitujen painelajittelussa

Viimevuosina kuvantamistekniikat ovat kehittyneet huomattavasti. Näiden uusien tekniikoiden avulla voidaan tarkastella erilaisia prosesseja aiempaa tarkemmin. Painelajittelun teoriat perustuvat pääasiassa makrotason mittauksien pohjalta tehtyihin matemaattisiin malleihin, ja itse lajittumistapahtumaa ei ole aiemmin päästy kovinkaan tarkasti havainnoimaan. Tämän työn tavoitteena olikin selvittää lajittumistapahtumaa uuden kuvantamistekniikan avulla. Työn kirjallisuusosassa esiteltiin lyhyesti painelajitin ja sen toiminta. Myös painelajittelun perusteoriat käytiin lyhyesti läpi. Teoriaosan pääpaino oli lajittumistapahtumassa ja siihen vaikuttavissa tekijöissä. Lisäksi teoriaosassa esiteltiin teollisen painelajittelun nykytilannetta, työtä varten tehdyn esiselvityksen pohjalta. Lajitinsimulaattorikoeajoissa selvitettiin kuitujen ja roskapartikkelien käyttäyty-mistä painelajittimessa kuvantamisen avulla. Kuvauksissa keskityttiin rakosihdin raon tapahtumiin, sekä sihtipinnan tapahtumiin. Kuvamateriaalista laskettiin kuitujen ja roskien liikenopeuksia lankasihtiprofiilin raossa, sekä sihdin pinnalla. Lisäksi tutkittiin kehänopeuden, tuotannon ja sakeuden vaikutusta liike-nopeuksiin. Kuvamateriaalista pyrittiin myös havainnoimaan mahdollista kuitujen takaisinvirtausta. Kuvantamisella saatiin uutta tietoa kuitujen ja roskapartikkelien liikkeestä painelajittimessa. Tuloksista kävi muun muassa ilmi, että roottorin elementin pienimmän välyksen kohdalla akseptoituu huomattava määrä massaa. Tämä selittyy sillä, että pienimmän välyksen kohta tuottaa huomattavan positiivisen painepulssin. Kuitujen ja roskapartikkelien nopeudet raossa noudattelivat muutenkin hyvin selkeästi elementin tuottamaa painepulssia. Lisäksi kuvamateriaalista havaittiin, että sihdin raon suulle kertyy profiilin korkuinen kuituflokki. Koko sihdin peittävää kuitumattoa ei havaittu.

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.

Höyry- ja kaasuturbiinin mallintaminen prosessisimulointiohjelmaan

Tässä diplomityössä on mallinnettu höyry- ja kaasuturbiini Balas -prosessisimulointi-ohjelmaan. Balas on Valtion Teknillisen Tutkimuskeskuksen kehittämä simulointiohjelma, erityisesti paperi- ja selluteollisuuden prosessien staattiseen simulointiin. Työn tavoitteena on kehittää simulointimallit höyry- ja kaasuturbiinille, sekä tutkia niiden toimivuutta vertaamalla simulointeja mittaus- ja mitoitustietoihin. Työssä on muodostettu matemaattiset mallit höyryturbiinille, höyryturbiinin säätövyöhykkeelle sekä höyryturbiinin off-design laskennalle. Kaasuturbiinille muodostettiin toimintakäyrät, joiden avulla tarkastellaan sen toimintaa off-design tilanteessa. Komponentit mallinnettiin diplomityövaiheessa Matlab-ympäristöön, josta ne siirretään Balasiin erillisessä työvaiheessa. Malleissa on kiinnitetty huomiota erityisesti niiden helppokäyttöisyyteen ja monipuolisuuteen. Höyryturbiinimalleja testattiin simuloimalla erään paperitehtaan yhteydessä toimivan voimalaitoksen vastapaineturbiini säätövyöhykkeineen ja vertaamalla simulointituloksia tehtaan mittaustietoihin. Kaasuturbiinimallia testattiin vertaamalla GE Power MS 7001 kaasuturbiinin mitoitustietoja vastaavilla parametreilla simuloituun tapaukseen.

Sustainable Waste-to-Energy Production: Performance Evaluation of Distributed Generation fuelled by Landfill Gas

The environmental impact of landfill is a growing concern in waste management practices. Thus, assessing the effectiveness of the solutions implemented to alter the issue is of importance. The objectives of the study were to provide an insight of landfill advantages, and to consolidate landfill gas importance among others alternative fuels. Finally, a case study examining the performances of energy production from a land disposal at Ylivieska was carried out to ascertain the viability of waste to energy project. Both qualitative and quantitative methods were applied. The study was conducted in two parts; the first was the review of literatures focused on landfill gas developments. Specific considerations were the conception of mechanism governing the variability of gas production and the investigation of mathematical models often used in landfill gas modeling. Furthermore, the analysis of two main distributed generation technologies used to generate energy from landfill was carried out. The review of literature revealed a high influence of waste segregation and high level of moisture content for waste stabilization process. It was found that the enhancement in accuracy for forecasting gas rate generation can be done with both mathematical modeling and field test measurements. The result of the case study mainly indicated the close dependence of the power output with the landfill gas quality and the fuel inlet pressure.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Stochastic variability of output levels in a pulp mill

Quite often, in the construction of a pulp mill involves establishing the size of tanks which will accommodate the material from the various processes in which case estimating the right tank size a priori would be vital. Hence, simulation of the whole production process would be worthwhile. Therefore, there is need to develop mathematical models that would mimic the behavior of the output from the various production units of the pulp mill to work as simulators. Markov chain models, Autoregressive moving average (ARMA) model, Mean reversion models with ensemble interaction together with Markov regime switching models are proposed for that purpose.

Regulation of cell fate by c-FLIP phosphorylation

Programmed cell death is an important physiological cellular process that maintains homeostasis and protects multicellular organisms from diseases. Apoptosis is the principal mode of cell death, which eliminates unwanted cells and an enormous effort has been made to understand the molecular mechanisms of the signaling pathway and its regulatory systems. Irregular apoptosis often has life-threatening consequences to humans, including cancer, autoimmune diseases and degenerative diseases. In cancer for example, cell death is an attractive target to eradicate uncontrollably proliferating cells that have disregard pro-apoptotic signaling. Targeted therapeutic approaches are not as effective as once expected, since now we know that the cell death pathways are not sole entities in cells, but are highly associated with various cellular processes. Proteins that regulate apoptosis can also control non-apoptotic signaling pathways. For example, c-FLIP is a protein that can either inhibit or promote caspase-8 activation, which is required to induce apoptosis. Not only has c-FLIP opposing effects on initiating apoptosis, but it also regulates various pro-survival signaling pathways in the cell. It is well known that protein expression level is a determinant of how c-FLIP can regulate different signaling pathways, but other regulatory mechanisms potentially affecting the role of c-FLIP are less well understood. This work addresses novel insights into the mechanisms of c-FLIP post-translational modifications and their functional consequences. We have identified that phosphorylation is an important inception for subcellular localization of c-FLIP, thereby dictating which apoptotic and non-apoptotic signaling pathways c-FLIP could regulate to promote cell survival. Furthermore, we have constructed mathematical models to unite independent studies to establish more systematic c-FLIP signaling pathways to understand the dynamics of extrinsically-induced apoptosis.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Uncertainty of Efficiency Measurements in Electric Drives

The two central goals of this master's thesis are to serve as a guidebook on the determination of uncertainty in efficiency measurements and to investigate sources of uncertainty in efficiency measurements in the field of electric drives by a literature review, mathematical modeling and experimental means. The influence of individual sources of uncertainty on the total instrumental uncertainty is investigated with the help of mathematical models derived for a balance and a direct air cooled calorimeter. The losses of a frequency converter and an induction motor are measured with the input-output method and a balance calorimeter at 50 and 100 % loads. A software linking features of Matlab and Excel is created to process measurement data, calculate uncertainties and to calculate and visualize results. The uncertainties are combined with both the worst case and the realistic perturbation method and distributions of uncertainty by source are shown based on experimental results. A comparison of the calculated uncertainties suggests that the balance calorimeter determines losses more accurately than the input-output method with a relative RPM uncertainty of 1.46 % compared to 3.78 - 12.74 % respectively with 95 % level of confidence at the 93 % induction motor efficiency or higher. As some principles in uncertainty analysis are open to interpretation the views and decisions of the analyst can have noticeable influence on the uncertainty in the measurement result.