995 resultados para Continuous Optimization


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Optimization of high strength and toughness combination on the effect of weldability is very vital to be considered in offshore oil and gas industries. Having a balanced and improved high strength and toughness is very much recommended in offshore structures for an effective production and viable exploration of hydrocarbons. This thesis aims to investigate the possibilities to improve the toughness of high strength steel. High carbon contents induce hardness and needs to be reduced for increasing toughness. The rare combination of high strength with high toughness possibilities was examined by determining the following toughening mechanism of: Heat treatment and optimal microstructure, Thermomechanical processing, Effect of welding parameters on toughness and weldability of steel. The implementation of weldability of steels to attain high toughness for high strength in offshore structures is mostly in shipbuilding, offshore platforms, and pipelines for high operating pressures. As a result, the toughening mechanisms suggested have benefits to the aims of the effect of high strength to high toughness of steel for efficiency, production and cost reduction.

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The Arctic region becoming very active area of the industrial developments since it may contain approximately 15-25% of the hydrocarbon and other valuable natural resources which are in great demand nowadays. Harsh operation conditions make the Arctic region difficult to access due to low temperatures which can drop below -50 °C in winter and various additional loads. As a result, newer and modified metallic materials are implemented which can cause certain problems in welding them properly. Steel is still the most widely used material in the Arctic regions due to high mechanical properties, cheapness and manufacturability. Moreover, with recent steel manufacturing development it is possible to make up to 1100 MPa yield strength microalloyed high strength steel which can be operated at temperatures -60 °C possessing reasonable weldability, ductility and suitable impact toughness which is the most crucial property for the Arctic usability. For many years, the arc welding was the most dominant joining method of the metallic materials. Recently, other joining methods are successfully implemented into welding manufacturing due to growing industrial demands and one of them is the laser-arc hybrid welding. The laser-arc hybrid welding successfully combines the advantages and eliminates the disadvantages of the both joining methods therefore produce less distortions, reduce the need of edge preparation, generates narrower heat-affected zone, and increase welding speed or productivity significantly. Moreover, due to easy implementation of the filler wire, accordingly the mechanical properties of the joints can be manipulated in order to produce suitable quality. Moreover, with laser-arc hybrid welding it is possible to achieve matching weld metal compared to the base material even with the low alloying welding wires without excessive softening of the HAZ in the high strength steels. As a result, the laser-arc welding methods can be the most desired and dominating welding technology nowadays, and which is already operating in automotive and shipbuilding industries with a great success. However, in the future it can be extended to offshore, pipe-laying, and heavy equipment industries for arctic environment. CO2 and Nd:YAG laser sources in combination with gas metal arc source have been used widely in the past two decades. Recently, the fiber laser sources offered high power outputs with excellent beam quality, very high electrical efficiency, low maintenance expenses, and higher mobility due to fiber optics. As a result, fiber laser-arc hybrid process offers even more extended advantages and applications. However, the information about fiber or disk laser-arc hybrid welding is very limited. The objectives of the Master’s thesis are concentrated on the study of fiber laser-MAG hybrid welding parameters in order to understand resulting mechanical properties and quality of the welds. In this work only ferrous materials are reviewed. The qualitative methodological approach has been used to achieve the objectives. This study demonstrates that laser-arc hybrid welding is suitable for welding of many types, thicknesses and strength of steels with acceptable mechanical properties along very high productivity. New developments of the fiber laser-arc hybrid process offers extended capabilities over CO2 laser combined with the arc. This work can be used as guideline in hybrid welding technology with comprehensive study the effect of welding parameter on joint quality.

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The iron and steelmaking industry is among the major contributors to the anthropogenic emissions of carbon dioxide in the world. The rising levels of CO2 in the atmosphere and the global concern about the greenhouse effect and climate change have brought about considerable investigations on how to reduce the energy intensity and CO2 emissions of this industrial sector. In this thesis the problem is tackled by mathematical modeling and optimization using three different approaches. The possibility to use biomass in the integrated steel plant, particularly as an auxiliary reductant in the blast furnace, is investigated. By pre-processing the biomass its heating value and carbon content can be increased at the same time as the oxygen content is decreased. As the compression strength of the preprocessed biomass is lower than that of coke, it is not suitable for replacing a major part of the coke in the blast furnace burden. Therefore the biomass is assumed to be injected at the tuyere level of the blast furnace. Carbon capture and storage is, nowadays, mostly associated with power plants but it can also be used to reduce the CO2 emissions of an integrated steel plant. In the case of a blast furnace, the effect of CCS can be further increased by recycling the carbon dioxide stripped top gas back into the process. However, this affects the economy of the integrated steel plant, as the amount of top gases available, e.g., for power and heat production is decreased. High quality raw materials are a prerequisite for smooth blast furnace operation. High quality coal is especially needed to produce coke with sufficient properties to ensure proper gas permeability and smooth burden descent. Lower quality coals as well as natural gas, which some countries have in great volumes, can be utilized with various direct and smelting reduction processes. The DRI produced with a direct reduction process can be utilized as a feed material for blast furnace, basic oxygen furnace or electric arc furnace. The liquid hot metal from a smelting reduction process can in turn be used in basic oxygen furnace or electric arc furnace. The unit sizes and investment costs of an alternative ironmaking process are also lower than those of a blast furnace. In this study, the economy of an integrated steel plant is investigated by simulation and optimization. The studied system consists of linearly described unit processes from coke plant to steel making units, with a more detailed thermodynamical model of the blast furnace. The results from the blast furnace operation with biomass injection revealed the importance of proper pre-processing of the raw biomass as the composition of the biomass as well as the heating value and the yield are all affected by the pyrolysis temperature. As for recycling of CO2 stripped blast furnace top gas, substantial reductions in the emission rates are achieved if the stripped CO2 can be stored. However, the optimal recycling degree together with other operation conditions is heavily dependent on the cost structure of CO2 emissions and stripping/storage. The economical feasibility related to the use of DRI in the blast furnace depends on the price ratio between the DRI pellets and the BF pellets. The high amount of energy needed in the rotary hearth furnace to reduce the iron ore leads to increased CO2 emissions.

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Många kvantitativa problem från vitt skilda områden kan beskrivas som optimeringsproblem. Ett mått på lösningens kvalitet bör optimeras samtidigt som vissa villkor på lösningen uppfylls. Kvalitetsmåttet kallas vanligen objektfunktion och kan beskriva kostnader (exempelvis produktion, logistik), potentialenergi (molekylmodellering, proteinveckning), risk (finans, försäkring) eller något annat relevant mått. I min doktorsavhandling diskuteras speciellt icke-linjär programmering, NLP, i ändliga dimensioner. Problem med enkel struktur, till exempel någon form av konvexitet, kan lösas effektivt. Tyvärr kan inte alla kvantitativa samband modelleras på ett konvext vis. Icke-konvexa problem kan angripas med heuristiska metoder, algoritmer som söker lösningar med hjälp av deterministiska eller stokastiska tumregler. Ibland fungerar det här väl, men heuristikerna kan sällan garantera kvaliteten på lösningen eller ens att en lösning påträffas. För vissa tillämpningar är det här oacceptabelt. Istället kan man tillämpa så kallad global optimering. Genom att successivt dela variabeldomänen i mindre delar och beräkna starkare gränser på det optimala värdet hittas en lösning inom feltoleransen. Den här metoden kallas branch-and-bound, ungefär dela-och-begränsa. För att ge undre gränser (vid minimering) approximeras problemet med enklare problem, till exempel konvexa, som kan lösas effektivt. I avhandlingen studeras tillvägagångssätt för att approximera differentierbara funktioner med konvexa underskattningar, speciellt den så kallade alphaBB-metoden. Denna metod adderar störningar av en viss form och garanterar konvexitet genom att sätta villkor på den perturberade Hessematrisen. Min forskning har lyft fram en naturlig utvidgning av de perturbationer som används i alphaBB. Nya metoder för att bestämma underskattningsparametrar har beskrivits och jämförts. I sammanfattningsdelen diskuteras global optimering ur bredare perspektiv på optimering och beräkningsalgoritmer.

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The objective of this study was to optimize and validate the solid-liquid extraction (ESL) technique for determination of picloram residues in soil samples. At the optimization stage, the optimal conditions for extraction of soil samples were determined using univariate analysis. Ratio soil/solution extraction, type and time of agitation, ionic strength and pH of extraction solution were evaluated. Based on the optimized parameters, the following method of extraction and analysis of picloram was developed: weigh 2.00 g of soil dried and sieved through a sieve mesh of 2.0 mm pore, add 20.0 mL of KCl concentration of 0.5 mol L-1, shake the bottle in the vortex for 10 seconds to form suspension and adjust to pH 7.00, with alkaline KOH 0.1 mol L-1. Homogenate the system in a shaker system for 60 minutes and then let it stand for 10 minutes. The bottles are centrifuged for 10 minutes at 3,500 rpm. After the settlement of the soil particles and cleaning of the supernatant extract, an aliquot is withdrawn and analyzed by high performance liquid chromatography. The optimized method was validated by determining the selectivity, linearity, detection and quantification limits, precision and accuracy. The ESL methodology was efficient for analysis of residues of the pesticides studied, with percentages of recovery above 90%. The limits of detection and quantification were 20.0 and 66.0 mg kg-1 soil for the PVA, and 40.0 and 132.0 mg kg-1 soil for the VLA. The coefficients of variation (CV) were equal to 2.32 and 2.69 for PVA and TH soils, respectively. The methodology resulted in low organic solvent consumption and cleaner extracts, as well as no purification steps for chromatographic analysis were required. The parameters evaluated in the validation process indicated that the ESL methodology is efficient for the extraction of picloram residues in soils, with low limits of detection and quantification.

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This study examines the excess returns provided by G10 currency carry trading during the Euro era. The currency carry trade has been a popular trade throughout the past decades offering excess returns to investors. The thesis aims to contribute to existing research on the topic by utilizing a new set of data for the Euro era as well as using the Euro as a basis for the study. The focus of the thesis is specifically on different carry trade strategies’ performance, risk and diversification benefits. The study finds proof of the failure of the uncovered interest rate parity theory through multiple regression analyses. Furthermore, the research finds evidence of significant diversification benefits in terms of Sharpe ratio and improved return distributions. The results suggest that currency carry trades have offered excess returns during 1999-2014 and that volatility plays an important role in carry trade returns. The risk, however, is diversifiable and therefore our results support previous quantitative research findings on the topic.

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Today’s electrical machine technology allows increasing the wind turbine output power by an order of magnitude from the technology that existed only ten years ago. However, it is sometimes argued that high-power direct-drive wind turbine generators will prove to be of limited practical importance because of their relatively large size and weight. The limited space for the generator in a wind turbine application together with the growing use of wind energy pose a challenge for the design engineers who are trying to increase torque without making the generator larger. When it comes to high torque density, the limiting factor in every electrical machine is heat, and if the electrical machine parts exceed their maximum allowable continuous operating temperature, even for a short time, they can suffer permanent damage. Therefore, highly efficient thermal design or cooling methods is needed. One of the promising solutions to enhance heat transfer performances of high-power, low-speed electrical machines is the direct cooling of the windings. This doctoral dissertation proposes a rotor-surface-magnet synchronous generator with a fractional slot nonoverlapping stator winding made of hollow conductors, through which liquid coolant can be passed directly during the application of current in order to increase the convective heat transfer capabilities and reduce the generator mass. This doctoral dissertation focuses on the electromagnetic design of a liquid-cooled direct-drive permanent-magnet synchronous generator (LC DD-PMSG) for a directdrive wind turbine application. The analytical calculation of the magnetic field distribution is carried out with the ambition of fast and accurate predicting of the main dimensions of the machine and especially the thickness of the permanent magnets; the generator electromagnetic parameters as well as the design optimization. The focus is on the generator design with a fractional slot non-overlapping winding placed into open stator slots. This is an a priori selection to guarantee easy manufacturing of the LC winding. A thermal analysis of the LC DD-PMSG based on a lumped parameter thermal model takes place with the ambition of evaluating the generator thermal performance. The thermal model was adapted to take into account the uneven copper loss distribution resulting from the skin effect as well as the effect of temperature on the copper winding resistance and the thermophysical properties of the coolant. The developed lumpedparameter thermal model and the analytical calculation of the magnetic field distribution can both be integrated with the presented algorithm to optimize an LC DD-PMSG design. Based on an instrumented small prototype with liquid-cooled tooth-coils, the following targets have been achieved: experimental determination of the performance of the direct liquid cooling of the stator winding and validating the temperatures predicted by an analytical thermal model; proving the feasibility of manufacturing the liquid-cooled tooth-coil winding; moreover, demonstration of the objectives of the project to potential customers.

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ABSTRACT Maria Peltola Electrical status epilepticus during sleep – Continuous spikes and waves during sleep Department of Clinical Neurophysiology, University of Turku Department of Clinical Neurophysiology and Department of Pediatric Neurology, Children’s Hospital, Helsinki University Central Hospital Annales Universitatis Turkuensis, Medica-Odontologica, Turku, Finland, 2014 Background: Electrical status epilepticus during sleep (ESES) is an EEG phenomenon of frequent spikes and waves occurring in slow sleep. ESES relates to cognitive deterioration in heterogeneous childhood epilepsies. Validated methods to quantitate ESES are missing. The clinical syndrome, called epileptic encephalopathy with continuous spikes and waves during sleep (CSWS) is pharmacoresistant in half of the patients. Limited data exists on surgical treatment of CSWS. Aims and methods: The effects of surgical treatment were studied by investigating electroclinical outcomes in 13 operated patients (nine callosotomies, four resections) with pharmacoresistant CSWS and cognitive decline. Secondly, an objective paradigm was searched for assessing ESES by the semiautomatic quantification of spike index (SI) and measuring spike strength from EEG. Results: Postoperatively, cognitive deterioration was stopped in 12 (92%) patients. Three out of four patients became seizure-free after resective surgery. Callosotomy resulted in greater than 90% reduction of atypical absences in six out of eight patients. The preoperative propagation of ESES from one hemisphere to the other was associated with a good response. Semiautomatic quantification of SI was a robust method when the maximal interspike interval of three seconds was used to determine the “continuous” discharge in ten EEGs. SI of the first hour of sleep appeared representative of the whole night SI. Furthermore, the spikes’ root mean square was found to be a stable measure of spike strength when spatially integrated over multiple electrodes during steady NREM sleep. Conclusions: Patients with pharmacoresistant CSWS, based on structural etiology, may benefit from resective surgery or corpus callosotomy regarding both seizure outcome and cognitive prognosis. The semiautomated SI quantification, with proper userdefined settings and the new spatially integrated measure of spike strength, are robust and promising tools for quantifying ESES. Keywords: Electrical status epilepticus during sleep, ESES, continuous spikes and waves during sleep, CSWS, epilepsy surgery, spike index, spike strength, RMS TIIVISTELMÄ Maria Peltola Unenaikainen sähköinen status epilepticus Kliininen neurofysiologia, Turun yliopisto Kliininen neurofysiologia ja lastenneurologia, Lasten ja nuorten sairaala, Helsingin yliopistollinen keskussairaala Annales Universitatis Turkuensis, Medica-Odontologica, Turku, Suomi, 2014 Tausta: Sähköinen status epilepticus unessa (ESES) on aivosähkökäyrä (EEG)-ilmiö, jossa hidasaaltounen aikana esiintyy tiheä piikkihidasaaltopurkaus. ESES:n kvantifioimiseen ei ole olemassa validoituja menetelmiä. ESES on liitetty kognitiivisen tason laskuun ja tällöin puhutaan CSWS (continuous spikes and waves during sleep) - oireyhtymästä. CSWS ei vastaa lääkehoitoon puolella potilaista ja sen epilepsiakirurgisesta hoidosta on olemassa vain vähän tietoa. Tavoitteet ja menetelmät: Selvitimme retrospektiivisesti epilepsiakirurgian vaikusta elektrokliinisiin löydöksiin 13:lla lääkeresistenttiä CSWS-oireyhtymää sairastavalla lapsella, joilla oli rakenteellinen aivojen poikkeavuus. Toinen tavoite oli löytää objektiivinen puoliautomaattinen tapa mitata purkauksen määrää ja piikkien voimakkuutta EEG:stä. Tulokset: Kognitiivisen tason jatkuva heikentyminen loppui 12 (92 %) potilaalla leikkauksen jälkeen. Kolme neljästä resektiopotilaasta tuli kohtauksettomaksi. Kallosotomian jälkeen kuudella kahdeksasta potilaasta päivittäiset kohtaukset vähenivät yli 90 %:lla. Purkauksen leviäminen leikkausta edeltävästi vain yhdestä hemisfääristä toiseen liittyi hyvään leikkaushoitovasteeseen. Piikki-indeksi, jossa käytetään jatkuvan purkauksen määritelmänä maksimissaan kolmea sekuntia piikkien välillä, osoittautui luotettavaksi menetelmäksi ESES:n kvantifioimiseen. Useammasta elektrodista integroitu piikkien neliöllinen keskiarvo oli piikin voimakkuuden vakaa mitta häiriintymättömässä NREM-unessa. Päätelmät: Lääkehoidolle vastaamatonta CSWS:ää sairastavat potilaat, joilla on rakenteellinen aivopoikkeavuus ja yhdensuuntainen purkauksen leviämismalli, näyttävät kohtausten vähenemisen lisäksi hyötyvän epilepsiakirurgiasta kognitiivisesti. Puoliautomaattinen piikki-indeksin kvantifiointi sopivilla käyttäjäasetuksilla ja uusi spatiaalisesti integroitu piikin voimakkuuden mittari ovat stabiileja ja lupaavia ESES:n kvantitatiivisia mittareita. Avainsanat: Unenaikainen sähköinen status epilepticus, ESES, CSWS, epilepsiakirurgia, piikki-indeksi, piikin voimakkuus, neliöllinen keskiarvo

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Continuous loading and unloading can cause breakdown of cranes. In seeking solution to this problem, the use of an intelligent control system for improving the fatigue life of cranes in the control of mechatronics has been under study since 1994. This research focuses on the use of neural networks as possibilities of developing algorithm to map stresses on a crane. The intelligent algorithm was designed to be a part of the system of a crane, the design process started with solid works, ANSYS and co-simulation using MSc Adams software which was incorporated in MATLAB-Simulink and finally MATLAB neural network (NN) for the optimization process. The flexibility of the boom accounted for the accuracy of the maximum stress results in the ADAMS model. The flexibility created in ANSYS produced more accurate results compared to the flexibility model in ADAMS/View using discrete link. The compatibility between.ADAMS and ANSYS softwares was paramount in the efficiency and the accuracy of the results. Von Mises stresses analysis was more suitable for this thesis work because the hydraulic boom was made from construction steel FE-510 of steel grade S355 with yield strength of 355MPa. Von Mises theory was good for further analysis due to ductility of the material and the repeated tensile and shear loading. Neural network predictions for the maximum stresses were then compared with the co-simulation results for accuracy, and the comparison showed that the results obtained from neural network model were sufficiently accurate in predicting the maximum stresses on the boom than co-simulation.

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In today’s knowledge intense economy the human capital is a source for competitive advantage for organizations. Continuous learning and sharing the knowledge within the organization are important to enhance and utilize this human capital in order to maximize the productivity. The new generation with different views and expectations of work is coming to work life giving its own characteristics on learning and sharing. Work should offer satisfaction so that the new generation employees would commit to organizations. At the same time organizations have to be able to focus on productivity to survive in the competitive market. The objective of this thesis is to construct a theory based framework of productivity, continuous learning and job satisfaction and further examine this framework and its applications in a global organization operating in process industry. Suggestions for future actions are presented for this case organization. The research is a qualitative case study and the empiric material was gathered by personal interviews concluding 15 employee and one supervisor interview. Results showed that more face to face interaction is needed between employees for learning because much of the knowledge of the process is tacit and so difficult to share in other ways. Offering these sharing possibilities can also impact positively to job satisfaction because they will increase the sense of community among employees which was found to be lacking. New employees demand more feedback to improve their learning and confidence. According to the literature continuous learning and job satisfaction have a relative strong relationship on productivity. The employee’s job description in the case organization has moved towards knowledge work due to continuous automation and expansion of the production process. This emphasizes the importance of continuous learning and means that productivity can be seen also from quality perspective. The normal productivity output in the case organization is stable and by focusing on the quality of work by improving continuous learning and job satisfaction the upsets in production can be handled and prevented more effectively. Continuous learning increases also the free human capital input and utilization of it and this can breed output increasing innovations that can increase productivity in long term. Also job satisfaction can increase productivity output in the end because employees will work more efficiently, not doing only the minimum tasks required. Satisfied employees are also found participating more in learning activities.

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Estimates of genetic and phenotypic parameters were obtained by using data from families of a recurrent selection program in rice. An experiment using population CNA-IRAT 4ME/1/1 was conducted at two locations (Lambari and Cambuquira) in the State of Minas Gerais, Brazil. At Lambari, families S0:2 and S0:3 were assessed during crop seasons 1992/1993 and 1993/1994, respectively. In the Cambuquira trial, only S0:3 families were tested in 1993/1994. The experimental design was a 10 x 10 lattice with three replications. The following traits were assessed: grain yield (GY), mean number of days to flowering (FL), plant height (PH), and the incidence of neck blast (NB) caused by Pyricularia grisea and grain staining (GS) caused by Drechslera oryzae. This population proved to be promising for recurrent selection, as it had high average yield and genetic variability. Heritability estimates obtained using variance components were generally greater than estimates of realized heritability, and heritability obtained by parent-offspring regression

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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.

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In the present investigation we studied some behavioral and immunological parameters of adult gastropod mollusk, Biomphalaria tenagophila, which have been reproducing for several generations under laboratory conditions. One group of gastropods was kept on a 14-h light/10-h dark cycle, corresponding to a regular circadian cycle, and another group was exposed to continuous light for 48 h. Animals were studied along (behavioral groups) or immediately after (immunological groups) 48 h of regular circadian cycle or continuous light conditions. Stopping/floating, dragging and sliding were the behavioral aspects considered (N = 20 for regular cycle; N = 20 for continuous illumination) and number of hemocytes/µl hemolymph was the immunological parameter studied (N = 15 for regular cycle, N = 14 for continuous illumination). Animals under continuous illumination were more active (sliding = 33 episodes, dragging = 48 episodes) and displayed a lower number of hemocytes (78.0 ± 24.27/µl) when compared with mollusks kept on a regular circadian cycle (sliding = 18 episodes, dragging = 27 episodes; hemocytes = 157.6 ± 53.27/µl). The data are discussed in terms of neural circuits and neuroimmunological relations with the possible stressful effect of continuous illumination.

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The objective of this project was to introduce a new software product to pulp industry, a new market for case company. An optimization based scheduling tool has been developed to allow pulp operations to better control their production processes and improve both production efficiency and stability. Both the work here and earlier research indicates that there is a potential for savings around 1-5%. All the supporting data is available today coming from distributed control systems, data historians and other existing sources. The pulp mill model together with the scheduler, allows what-if analyses of the impacts and timely feasibility of various external actions such as planned maintenance of any particular mill operation. The visibility gained from the model proves also to be a real benefit. The aim is to satisfy demand and gain extra profit, while achieving the required customer service level. Research effort has been put both in understanding the minimum features needed to satisfy the scheduling requirements in the industry and the overall existence of the market. A qualitative study was constructed to both identify competitive situation and the requirements vs. gaps on the market. It becomes clear that there is no such system on the marketplace today and also that there is room to improve target market overall process efficiency through such planning tool. This thesis also provides better overall understanding of the different processes in this particular industry for the case company.

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Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.