Smooth height/age curves from stem analysis with linear programming

[Abstract]

Short-term Hydropower Planning System

The Thesis gives a decision support framework that has significant impact on the economic performance and viability of a hydropower company. The studyaddresses the short-term hydropower planning problem in the Nordic deregulated electricity market. The basics of the Nordic electricity market, trading mechanisms, hydropower system characteristics and production planning are presented in the Thesis. The related modelling theory and optimization methods are covered aswell. The Thesis provides a mixed integer linear programming model applied in asuccessive linearization method for optimal bidding and scheduling decisions inthe hydropower system operation within short-term horizon. A scenario based deterministic approach is exploited for modelling uncertainty in market price and inflow. The Thesis proposes a calibration framework to examine the physical accuracy and economic optimality of the decisions suggested by the model. A calibration example is provided with data from a real hydropower system using a commercial modelling application with the mixed integer linear programming solver CPLEX.

Structural and operational optimisation : applications in energy systems

In this work mathematical programming models for structural and operational optimisation of energy systems are developed and applied to a selection of energy technology problems. The studied cases are taken from industrial processes and from large regional energy distribution systems. The models are based on Mixed Integer Linear Programming (MILP), Mixed Integer Non-Linear Programming (MINLP) and on a hybrid approach of a combination of Non-Linear Programming (NLP) and Genetic Algorithms (GA). The optimisation of the structure and operation of energy systems in urban regions is treated in the work. Firstly, distributed energy systems (DES) with different energy conversion units and annual variations of consumer heating and electricity demands are considered. Secondly, district cooling systems (DCS) with cooling demands for a large number of consumers are studied, with respect to a long term planning perspective regarding to given predictions of the consumer cooling demand development in a region. The work comprises also the development of applications for heat recovery systems (HRS), where paper machine dryer section HRS is taken as an illustrative example. The heat sources in these systems are moist air streams. Models are developed for different types of equipment price functions. The approach is based on partitioning of the overall temperature range of the system into a number of temperature intervals in order to take into account the strong nonlinearities due to condensation in the heat recovery exchangers. The influence of parameter variations on the solutions of heat recovery systems is analysed firstly by varying cost factors and secondly by varying process parameters. Point-optimal solutions by a fixed parameter approach are compared to robust solutions with given parameter variation ranges. In the work enhanced utilisation of excess heat in heat recovery systems with impingement drying, electricity generation with low grade excess heat and the use of absorption heat transformers to elevate a stream temperature above the excess heat temperature are also studied.

Jatkuvavaletun teräksen leikkaussuunnitelman optimointi

Teollisuuden tuotannon eri prosessien optimointi on hyvin ajankohtainen aihe. Monet ohjausjärjestelmät ovat ajalta, jolloin tietokoneiden laskentateho oli hyvin vaatimaton nykyisiin verrattuna. Työssä esitetään tuotantoprosessi, joka sisältää teräksen leikkaussuunnitelman muodostamisongelman. Valuprosessi on yksi teräksen valmistuksen välivaiheita. Siinä sopivaan laatuun saatettu sula teräs valetaan linjastoon, jossa se jähmettyy ja leikataan aihioiksi. Myöhemmissä vaiheissa teräsaihioista muokataan pienempiä kokonaisuuksia, tehtaan lopputuotteita. Jatkuvavaletut aihiot voidaan leikata tilauskannasta riippuen monella eri tavalla. Tätä varten tarvitaan leikkaussuunnitelma, jonka muodostamiseksi on ratkaistava sekalukuoptimointiongelma. Sekalukuoptimointiongelmat ovat optimoinnin haastavin muoto. Niitä on tutkittu yksinkertaisempiin optimointiongelmiin nähden vähän. Nykyisten tietokoneiden laskentateho on kuitenkin mahdollistanut raskaampien ja monimutkaisempien optimointialgoritmien käytön ja kehittämisen. Työssä on käytetty ja esitetty eräs stokastisen optimoinnin menetelmä, differentiaalievoluutioalgoritmi. Tässä työssä esitetään teräksen leikkausoptimointialgoritmi. Kehitetty optimointimenetelmä toimii dynaamisesti tehdasympäristössä käyttäjien määrittelemien parametrien mukaisesti. Työ on osa Syncron Tech Oy:n Ovako Bar Oy Ab:lle toimittamaa ohjausjärjestelmää.

The knapsack problem approach in solving partial hedging problems of options

En option är ett finansiellt kontrakt som ger dess innehavare en rättighet (men medför ingen skyldighet) att sälja eller köpa någonting (till exempel en aktie) till eller från säljaren av optionen till ett visst pris vid en bestämd tidpunkt i framtiden. Den som säljer optionen binder sig till att gå med på denna framtida transaktion ifall optionsinnehavaren längre fram bestämmer sig för att inlösa optionen. Säljaren av optionen åtar sig alltså en risk av att den framtida transaktion som optionsinnehavaren kan tvinga honom att göra visar sig vara ofördelaktig för honom. Frågan om hur säljaren kan skydda sig mot denna risk leder till intressanta optimeringsproblem, där målet är att hitta en optimal skyddsstrategi under vissa givna villkor. Sådana optimeringsproblem har studerats mycket inom finansiell matematik. Avhandlingen "The knapsack problem approach in solving partial hedging problems of options" inför en ytterligare synpunkt till denna diskussion: I en relativt enkel (ändlig och komplett) marknadsmodell kan nämligen vissa partiella skyddsproblem beskrivas som så kallade kappsäcksproblem. De sistnämnda är välkända inom en gren av matematik som heter operationsanalys. I avhandlingen visas hur skyddsproblem som tidigare lösts på andra sätt kan alternativt lösas med hjälp av metoder som utvecklats för kappsäcksproblem. Förfarandet tillämpas även på helt nya skyddsproblem i samband med så kallade amerikanska optioner.

Susteinable steelmaking by process integration

Environmental issues, including global warming, have been serious challenges realized worldwide, and they have become particularly important for the iron and steel manufacturers during the last decades. Many sites has been shut down in developed countries due to environmental regulation and pollution prevention while a large number of production plants have been established in developing countries which has changed the economy of this business. Sustainable development is a concept, which today affects economic growth, environmental protection, and social progress in setting up the basis for future ecosystem. A sustainable headway may attempt to preserve natural resources, recycle and reuse materials, prevent pollution, enhance yield and increase profitability. To achieve these objectives numerous alternatives should be examined in the sustainable process design. Conventional engineering work cannot address all of these substitutes effectively and efficiently to find an optimal route of processing. A systematic framework is needed as a tool to guide designers to make decisions based on overall concepts of the system, identifying the key bottlenecks and opportunities, which lead to an optimal design and operation of the systems. Since the 1980s, researchers have made big efforts to develop tools for what today is referred to as Process Integration. Advanced mathematics has been used in simulation models to evaluate various available alternatives considering physical, economic and environmental constraints. Improvements on feed material and operation, competitive energy market, environmental restrictions and the role of Nordic steelworks as energy supplier (electricity and district heat) make a great motivation behind integration among industries toward more sustainable operation, which could increase the overall energy efficiency and decrease environmental impacts. In this study, through different steps a model is developed for primary steelmaking, with the Finnish steel sector as a reference, to evaluate future operation concepts of a steelmaking site regarding sustainability. The research started by potential study on increasing energy efficiency and carbon dioxide reduction due to integration of steelworks with chemical plants for possible utilization of available off-gases in the system as chemical products. These off-gases from blast furnace, basic oxygen furnace and coke oven furnace are mainly contained of carbon monoxide, carbon dioxide, hydrogen, nitrogen and partially methane (in coke oven gas) and have proportionally low heating value but are currently used as fuel within these industries. Nonlinear optimization technique is used to assess integration with methanol plant under novel blast furnace technologies and (partially) substitution of coal with other reducing agents and fuels such as heavy oil, natural gas and biomass in the system. Technical aspect of integration and its effect on blast furnace operation regardless of capital expenditure of new operational units are studied to evaluate feasibility of the idea behind the research. Later on the concept of polygeneration system added and a superstructure generated with alternative routes for off-gases pretreatment and further utilization on a polygeneration system producing electricity, district heat and methanol. (Vacuum) pressure swing adsorption, membrane technology and chemical absorption for gas separation; partial oxidation, carbon dioxide and steam methane reforming for methane gasification; gas and liquid phase methanol synthesis are the main alternative process units considered in the superstructure. Due to high degree of integration in process synthesis, and optimization techniques, equation oriented modeling is chosen as an alternative and effective strategy to previous sequential modelling for process analysis to investigate suggested superstructure. A mixed integer nonlinear programming is developed to study behavior of the integrated system under different economic and environmental scenarios. Net present value and specific carbon dioxide emission is taken to compare economic and environmental aspects of integrated system respectively for different fuel systems, alternative blast furnace reductants, implementation of new blast furnace technologies, and carbon dioxide emission penalties. Sensitivity analysis, carbon distribution and the effect of external seasonal energy demand is investigated with different optimization techniques. This tool can provide useful information concerning techno-environmental and economic aspects for decision-making and estimate optimal operational condition of current and future primary steelmaking under alternative scenarios. The results of the work have demonstrated that it is possible in the future to develop steelmaking towards more sustainable operation.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.