This thesis aims to investigate if the hourly heat load consumptiondata can be used to approximate the daily consumptions patterns forbuildings connected to Göteborg Energi’s district heating network. Theapproximated data shall act as foundation for dimensioning of thedistrict heating network. In this work, it is studied how theconsumption approximation are due to changes in the outdoortemperature between different years.The aim is to develop an approximation model for hourly heat loadpatterns, heat output, water flow and return temperature from thedistrict heating substations of individual buildings regardless ofbuilding types. The approximation methods used in the hourlyapproximation model is multiple ridge regression. Regression trees areused to define breaking points such as the building balance pointtemperature from the consumer heat load pattern. Two separateregression intervals were defined based on breaking points from theregression tree. Outdoor temperature data, solar radiation data,weekday and weekends data used as predictors.The approximation model is evaluated against a reference model usingthe daily mean heat load consumption data. Evaluation between themodel and reference is made on six different building and buildingtypes during the outdoor temperature of -16, which is the designoutdoor temperature of the district heating system of Göteborg Energi.The approximated maximum heat output and water flow during the daywhere 18 % and 10 % above the approximated daily mean. Theapproximated return temperature where 43-51 °C compared to the dailymean of 42 °C for a warm year and 47-52,5 °C compared to 50 °C dailymean for a cold year.The hourly approximation model where able to capture the heat loadpatterns of different building types. However, higher demands on dataquality needs to be addressed to ensure the use of the hourlyapproximation model. / I detta examensarbete har en undersökning angående värmelastapproximationer baserade påtimupplöst kundlastdata gjorts. Värmelasterna som approximerades var värmeeffekt,vattenflöde och returtemperatur. Data för utomhustemperatur, helg och vardag samtsolinstrålningsdata har använts för att kunna approximera värmelasterna. Resultat avapproximationer har visualiserats i relation till utomhustemperaturen och har utvärderats fördimensionerande utomhustemperatur. Utvärdering gjordes på olika byggnader ochbyggnadstyper. Resultat av approximationsmodell med timupplöst kundlastdata utvärderadesmot modell baserad på dygnsmedeldata. Modellerna testades för två olika år med skildautomhustemperaturer, ett kall-år och ett varm-år.Resultat visar att det är möjligt att fånga den timvisa värmelasten hos enskilda kunder och skulleinnebära ett bättre underlag vid dimensionering. Detta då högsta värmelasten under ett dygnskiljer sig från dygnsmedellasten. Att implementera modell med timdatat ökar känsligheten imodellen och ställer högre krav på den inhämtade kundlastdatat. Mätare i fjärrvärmecentralerbör ses över för säkerställning av god mätupplösning och mätprecision.

À l'ère de la numérisation, les données devient pas cher et facile à obtenir. Cela se traduit par de nombreux nouveaux problèmes d'optimisation avec de très grandes tailles. En particulier, pour le même genre de problèmes, le nombre de variables et de contraintes sont énormes. En outre, dans de nombreux paramètres d'application tels que ceux dans l'apprentissage de la machine, une solution précise est moins préférée que celles approximatives mais robustes. Il est un véritable défi pour les algorithmes traditionnels, qui sont utilisés pour bien travailler avec des problèmes de taille moyenne, pour faire face à ces nouvelles circonstances.Au lieu de développer des algorithmes qui évoluent bien à résoudre ces problèmes directement, une idée naturelle est de les transformer en problèmes de petite taille qui se rapporte fortement aux originaux. Étant donné que les nouvelles sont de tailles gérables, ils peuvent encore être résolus efficacement par des méthodes classiques. Les solutions obtenues par ces nouveaux problèmes, cependant, nous donner un aperçu des problèmes originaux. Dans cette thèse, nous allons exploiter l'idée ci-dessus pour résoudre certains problèmes de grande dimension optimisation. En particulier, nous appliquons une technique spéciale appelée projection aléatoire pour intégrer les données du problème dans les espaces de faible dimension, et de reformuler environ le problème de telle manière qu'il devient très facile à résoudre, mais capte toujours l'information la plus importante.Dans le chapitre 3, nous étudions les problèmes d'optimisation dans leurs formes de faisabilité. En particulier, nous étudions le problème que l'on appelle l'adhésion linéaire restreint. Cette classe contient de nombreux problèmes importants tels que la faisabilité linéaire et entier. Nous proposonsd'appliquer une projection aléatoire aux contraintes linéaires etnous voulons trouver des conditions sur T, de sorte que les deux problèmes de faisabilité sont équivalentes avec une forte probabilité.Dans le chapitre 4, nous continuons à étudier le problème ci-dessus dans le cas où l'ensemble restreint est un ensemble convexe. Nous établissons les relations entre les problèmes originaux et projetés sur la base du concept de la largeur gaussienne, qui est populaire dans la détection comprimé. En particulier, nous montrons que les deux problèmes sont équivalents avec une forte probabilité aussi longtemps que pour une projection aléatoire échantillonné à partir ensemble sous-gaussienne avec grande dimension suffisante (dépend de la largeur gaussienne).Dans le chapitre 5, nous étudions le problème de l'adhésion euclidienne:.. `` Étant donné un vecteur b et un euclidienne ensemble fermé X, décider si b est en Xor pas "Ceci est une généralisation du problème de l'appartenance linéaire restreinte précédemment considéré. Nous employons une gaussienne projection aléatoire T pour l'intégrer à la fois b et X dans un espace de dimension inférieure et étudier la version projetée correspondant. Lorsque X est fini ou dénombrable, en utilisant un argument simple, nous montrons que les deux problèmes sont équivalents presque sûrement quelle que soit la dimension projetée. Dans le cas où X peut être indénombrable, nous prouvons que les problèmes initiaux et prévus sont également équivalentes si la dimension d projetée est proportionnelle à une dimension intrinsèque de l'ensemble X. En particulier, nous employons la définition de doubler la dimension estimer la relation entre les deux problèmes.Dans le chapitre 6, nous proposons d'appliquer des projections aléatoires pour la zone de confiance sous-problème. Nous réduisons le nombre de variables en utilisant une projection aléatoire et prouver que des solutions optimales pour le nouveau problème sont en fait des solutions approchées de l'original. Ce résultat peut être utilisé dans le cadre de confiance-région pour étudier l'optimisation de boîte noire et l'optimisation des produits dérivés libre. / In the digitization age, data becomes cheap and easy to obtain. That results in many new optimization problems with extremely large sizes. In particular, for the same kind of problems, the numbers of variables and constraints are huge. Moreover, in many application settings such as those in Machine learning, an accurate solution is less preferred as approximate but robust ones. It is a real challenge for traditional algorithms, which are used to work well with average-size problems, to deal with these new circumstances.Instead of developing algorithms that scale up well to solve these problems directly, one natural idea is to transform them into small-size problems that strongly relates to the originals. Since the new ones are of manageable sizes, they can still be solved efficiently by classical methods. The solutions obtained by these new problems, however, will provide us insight into the original problems. In this thesis, we will exploit the above idea to solve some high-dimensional optimization problems. In particular, we apply a special technique called random projection to embed the problem data into low dimensional spaces, and approximately reformulate the problem in such a way that it becomes very easy to solve but still captures the most important information. Therefore, by solving the projected problem, we either obtain an approximate solution or an approximate objective value for the original problem.We will apply random projection to study a number of important optimization problems, including linear and integer programming (Chapter 3), convex optimization with linear constraints (Chapter 4), membership and approximate nearest neighbor (Chapter 5) and trust-region subproblems (Chapter 6).In Chapter 3, we study optimization problems in their feasibility forms. In particular, we study the so-called restricted linear membership problem. This class contains many important problems such as linear and integer feasibility. We proposeto apply a random projection to the linear constraints, andwe want to find conditions on T, so that the two feasibility problems are equivalent with high probability.In Chapter 4, we continue to study the above problem in the case the restricted set is a convex set. Under that assumption, we can define a tangent cone at some point with minimal squared error. We establish the relations between the original and projected problems based on the concept of Gaussian width, which is popular in compressed sensing. In particular, we prove thatthe two problems are equivalent with high probability as long as for some random projection sampled from sub-gaussian ensemble with large enough dimension (depends on the gaussian width).In Chapter 5, we study the Euclidean membership problem: ``Given a vector b and a Euclidean closed set X, decide whether b is in Xor not". This is a generalization of the restricted linear membership problem considered previously. We employ a Gaussian random projection T to embed both b and X into a lower dimension space and study the corresponding projected version: ``Decide whether Tb is in T(X) or not". When X is finite or countable, using a straightforward argument, we prove that the two problems are equivalent almost surely regardless the projected dimension. In the case when X may be uncountable, we prove that the original and projected problems are also equivalent if the projected dimension d is proportional to some intrinsic dimension of the set X. In particular, we employ the definition of doubling dimension estimate the relation between the two problems.In Chapter 6, we propose to apply random projections for the trust-region subproblem. We reduce the number of variables by using a random projection and prove that optimal solutions for the new problem are actually approximate solutions of the original. This result can be used in the trust-region framework to study black-box optimization and derivative-free optimization.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18621号 / 情博第545号 / 新制||情||96(附属図書館) / 31521 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 永持 仁, 教授 太田 快人, 教授 髙橋 豊 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Computing the most specific concept (msc) is an inference task that can be used to support the 'bottom-up' construction of knowledge bases for KR systems based on description logics. For description logics that allow for number restrictions or existential restrictions, the msc need not exist, though. Previous work on this problem has concentrated on description logics that allow for universal value restrictions and number restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. More precisely, we show that, for the description logic ALE (which allows for conjunction, universal value restrictions, existential restrictions, negation of atomic concepts) the msc of an ABox-individual only exists in case of acyclic ABoxes. For cyclic ABoxes, we show how to compute an approximation of the msc. Our approach for computing the (approximation of the) msc is based on representing concept descriptions by certain trees and ABoxes by certain graphs, and then characterizing instance relationships by homomorphisms from trees into graphs. The msc/approximation operation then mainly corresponds to unraveling the graphs into trees and translating them back into concept descriptions.

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One of the questions arising as regards to structured materials is how one can compute their cluster concentrations. Specifically, we are interested in deriving the concentrations of the micro-structures in the NMC (Nickel-Manganese-Cobalt) layer of the cathodes of Li-ion batteries. A simulated annealing approach has been used lately for detecting the structure of the whole lattice which is computationally heavy. Here we propose a mathematical model, called cluster approximation model, in the form of a dynamical system for describing the concentrations of different clusters inside the lattice. However, the dynamical system is hierarchical which requires to be truncated. Truncation of the hierarchical system is performed by the nearest-neighbor closure scheme. Also, a novel framework is proposed for an optimal closure of the dynamical system in order to enhance the accuracy of the model. The parameters of the model are reconstructed by the least square approach as a constrained optimization problem by minimizing the mismatch between the experimental data and the model outputs. The model is validated based on the experimental data on a known Li-ion battery cathode and different approximation schemes are compared. The results clearly show that the proposed approach significantly outperforms the conventional method. / Thesis / Master of Science (MSc)

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FL₀ that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches. / Accepted to LATA 2017

Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty years ago, a controversy has boiled over the regions of validity and relative merits of the methods. Although the methods fail for strong fluctuations and distant path lengths, these two perturbation methods are the only approaches available for weak fluctuations in a random in homogeneous media. The approximations have also been applied to the inverse problem for optical and acoustical tomography. The intent of this thesis is to investigate the work of previous authors and attempt to clarify the distinctions of each method. The conclusion will be reached that neither approximation is necessarily better than the other in general for all applications. A careful consideration of the problem following the points given should point towards the use of one approximation over the other. / Master of Science