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Matrix Representations and Extension of the Graph Model for Conflict ResolutionXu, Haiyan January 2009 (has links)
The graph model for conflict resolution (GMCR) provides a convenient
and effective means to model and analyze a strategic conflict.
Standard practice is to carry out a stability analysis of a graph
model, and then to follow up with a post-stability analysis, two
critical components of which are status quo analysis and coalition
analysis. In stability analysis, an equilibrium is a state that is
stable for all decision makers (DMs) under appropriate stability
definitions or solution concepts. Status quo analysis aims to
determine whether a particular equilibrium is reachable from a
status quo (or an initial state) and, if so, how to reach it. A
coalition is any subset of a set of DMs. The coalition stability
analysis within the graph model is focused on the status quo states
that are equilibria and assesses whether states that are stable from
individual viewpoints may be unstable for coalitions. Stability
analysis began within a simple preference structure which includes a
relative preference relationship and an indifference relation.
Subsequently, preference uncertainty and strength of preference were
introduced into GMCR but not formally integrated.
In this thesis, two new preference frameworks, hybrid preference and
multiple-level preference, and an integrated algebraic approach are
developed for GMCR. Hybrid preference extends existing preference
structures to combine preference uncertainty and strength of
preference into GMCR. A multiple-level preference framework expands
GMCR to handle a more general and flexible structure than any
existing system representing strength of preference. An integrated
algebraic approach reveals a link among traditional stability
analysis, status quo analysis, and coalition stability analysis by
using matrix representation of the graph model for conflict
resolution.
To integrate the three existing preference structures into a hybrid
system, a new preference framework is proposed for graph models
using a quadruple relation to express strong or mild preference of
one state or scenario over another, equal preference, and an
uncertain preference. In addition, a multiple-level preference
framework is introduced into the graph model methodology to handle
multiple-level preference information, which lies between relative
and cardinal preferences in information content. The existing
structure with strength of preference takes into account that if a
state is stable, it may be either strongly stable or weakly stable
in the context of three levels of strength. However, the three-level
structure is limited in its ability to depict the intensity of
relative preference. In this research, four basic solution concepts
consisting of Nash stability, general metarationality, symmetric
metarationality, and sequential stability, are defined at each level
of preference for the graph model with the extended multiple-level
preference. The development of the two new preference frameworks
expands the realm of applicability of the graph model and provides
new insights into strategic conflicts so that more practical and
complicated problems can be analyzed at greater depth.
Because a graph model of a conflict consists of several interrelated
graphs, it is natural to ask whether well-known results of Algebraic
Graph Theory can help analyze a graph model. Analysis of a graph
model involves searching paths in a graph but an important
restriction of a graph model is that no DM can move twice in
succession along any path. (If a DM can move consecutively, then
this DM's graph is effectively transitive. Prohibiting consecutive
moves thus allows for graph models with intransitive graphs, which
are sometimes useful in practice.) Therefore, a graph model must be
treated as an edge-weighted, colored multidigraph in which each arc
represents a legal unilateral move and distinct colors refer to
different DMs. The weight of an arc could represent some preference
attribute. Tracing the evolution of a conflict in status quo
analysis is converted to searching all colored paths from a status
quo to a particular outcome in an edge-weighted, colored
multidigraph. Generally, an adjacency matrix can determine a simple
digraph and all state-by-state paths between any two vertices.
However, if a graph model contains multiple arcs between the same
two states controlled by different DMs, the adjacency matrix would
be unable to track all aspects of conflict evolution from the status
quo. To bridge the gap, a conversion function using the matrix
representation is designed to transform the original problem of
searching edge-weighted, colored paths in a colored multidigraph to
a standard problem of finding paths in a simple digraph with no
color constraints. As well, several unexpected and useful links
among status quo analysis, stability analysis, and coalition
analysis are revealed using the conversion function.
The key input of stability analysis is the reachable list of a DM,
or a coalition, by a legal move (in one step) or by a legal sequence
of unilateral moves, from a status quo in 2-DM or $n$-DM ($n
> 2$) models. A weighted reachability matrix for a DM or a coalition along
weighted colored paths is designed to construct the reachable list
using the aforementioned conversion function. The weight of each
edge in a graph model is defined according to the preference
structure, for example, simple preference, preference with
uncertainty, or preference with strength. Furthermore, a graph model
and the four basic graph model solution concepts are formulated
explicitly using the weighted reachability matrix for the three
preference structures. The explicit matrix representation for
conflict resolution (MRCR) that facilitates stability calculations
in both 2-DM and $n$-DM ($n
> 2$) models for three existing preference structures. In addition,
the weighted reachability matrix by a coalition is used to produce
matrix representation of coalition stabilities in
multiple-decision-maker conflicts for the three preference
frameworks.
Previously, solution concepts in the graph model were traditionally
defined logically, in terms of the underlying graphs and preference
relations. When status quo analysis algorithms were developed, this
line of thinking was retained and pseudo-codes were developed
following a similar logical structure. However, as was noted in the
development of the decision support system (DSS) GMCR II, the nature
of logical representations makes coding difficult. The DSS GMCR II,
is available for basic stability analysis and status quo analysis
within simple preference, but is difficult to modify or adapt to
other preference structures. Compared with existing graphical or
logical representation, matrix representation for conflict
resolution (MRCR) is more effective and convenient for computer
implementation and for adapting to new analysis techniques.
Moreover, due to an inherent link between stability analysis and
post-stability analysis presented, the proposed algebraic approach
establishes an integrated paradigm of matrix representation for the
graph model for conflict resolution.
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Matrix Representations and Extension of the Graph Model for Conflict ResolutionXu, Haiyan January 2009 (has links)
The graph model for conflict resolution (GMCR) provides a convenient
and effective means to model and analyze a strategic conflict.
Standard practice is to carry out a stability analysis of a graph
model, and then to follow up with a post-stability analysis, two
critical components of which are status quo analysis and coalition
analysis. In stability analysis, an equilibrium is a state that is
stable for all decision makers (DMs) under appropriate stability
definitions or solution concepts. Status quo analysis aims to
determine whether a particular equilibrium is reachable from a
status quo (or an initial state) and, if so, how to reach it. A
coalition is any subset of a set of DMs. The coalition stability
analysis within the graph model is focused on the status quo states
that are equilibria and assesses whether states that are stable from
individual viewpoints may be unstable for coalitions. Stability
analysis began within a simple preference structure which includes a
relative preference relationship and an indifference relation.
Subsequently, preference uncertainty and strength of preference were
introduced into GMCR but not formally integrated.
In this thesis, two new preference frameworks, hybrid preference and
multiple-level preference, and an integrated algebraic approach are
developed for GMCR. Hybrid preference extends existing preference
structures to combine preference uncertainty and strength of
preference into GMCR. A multiple-level preference framework expands
GMCR to handle a more general and flexible structure than any
existing system representing strength of preference. An integrated
algebraic approach reveals a link among traditional stability
analysis, status quo analysis, and coalition stability analysis by
using matrix representation of the graph model for conflict
resolution.
To integrate the three existing preference structures into a hybrid
system, a new preference framework is proposed for graph models
using a quadruple relation to express strong or mild preference of
one state or scenario over another, equal preference, and an
uncertain preference. In addition, a multiple-level preference
framework is introduced into the graph model methodology to handle
multiple-level preference information, which lies between relative
and cardinal preferences in information content. The existing
structure with strength of preference takes into account that if a
state is stable, it may be either strongly stable or weakly stable
in the context of three levels of strength. However, the three-level
structure is limited in its ability to depict the intensity of
relative preference. In this research, four basic solution concepts
consisting of Nash stability, general metarationality, symmetric
metarationality, and sequential stability, are defined at each level
of preference for the graph model with the extended multiple-level
preference. The development of the two new preference frameworks
expands the realm of applicability of the graph model and provides
new insights into strategic conflicts so that more practical and
complicated problems can be analyzed at greater depth.
Because a graph model of a conflict consists of several interrelated
graphs, it is natural to ask whether well-known results of Algebraic
Graph Theory can help analyze a graph model. Analysis of a graph
model involves searching paths in a graph but an important
restriction of a graph model is that no DM can move twice in
succession along any path. (If a DM can move consecutively, then
this DM's graph is effectively transitive. Prohibiting consecutive
moves thus allows for graph models with intransitive graphs, which
are sometimes useful in practice.) Therefore, a graph model must be
treated as an edge-weighted, colored multidigraph in which each arc
represents a legal unilateral move and distinct colors refer to
different DMs. The weight of an arc could represent some preference
attribute. Tracing the evolution of a conflict in status quo
analysis is converted to searching all colored paths from a status
quo to a particular outcome in an edge-weighted, colored
multidigraph. Generally, an adjacency matrix can determine a simple
digraph and all state-by-state paths between any two vertices.
However, if a graph model contains multiple arcs between the same
two states controlled by different DMs, the adjacency matrix would
be unable to track all aspects of conflict evolution from the status
quo. To bridge the gap, a conversion function using the matrix
representation is designed to transform the original problem of
searching edge-weighted, colored paths in a colored multidigraph to
a standard problem of finding paths in a simple digraph with no
color constraints. As well, several unexpected and useful links
among status quo analysis, stability analysis, and coalition
analysis are revealed using the conversion function.
The key input of stability analysis is the reachable list of a DM,
or a coalition, by a legal move (in one step) or by a legal sequence
of unilateral moves, from a status quo in 2-DM or $n$-DM ($n
> 2$) models. A weighted reachability matrix for a DM or a coalition along
weighted colored paths is designed to construct the reachable list
using the aforementioned conversion function. The weight of each
edge in a graph model is defined according to the preference
structure, for example, simple preference, preference with
uncertainty, or preference with strength. Furthermore, a graph model
and the four basic graph model solution concepts are formulated
explicitly using the weighted reachability matrix for the three
preference structures. The explicit matrix representation for
conflict resolution (MRCR) that facilitates stability calculations
in both 2-DM and $n$-DM ($n
> 2$) models for three existing preference structures. In addition,
the weighted reachability matrix by a coalition is used to produce
matrix representation of coalition stabilities in
multiple-decision-maker conflicts for the three preference
frameworks.
Previously, solution concepts in the graph model were traditionally
defined logically, in terms of the underlying graphs and preference
relations. When status quo analysis algorithms were developed, this
line of thinking was retained and pseudo-codes were developed
following a similar logical structure. However, as was noted in the
development of the decision support system (DSS) GMCR II, the nature
of logical representations makes coding difficult. The DSS GMCR II,
is available for basic stability analysis and status quo analysis
within simple preference, but is difficult to modify or adapt to
other preference structures. Compared with existing graphical or
logical representation, matrix representation for conflict
resolution (MRCR) is more effective and convenient for computer
implementation and for adapting to new analysis techniques.
Moreover, due to an inherent link between stability analysis and
post-stability analysis presented, the proposed algebraic approach
establishes an integrated paradigm of matrix representation for the
graph model for conflict resolution.
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Matrix representation for partitions and Mock Theta functionsBagatini, Alessandro January 2016 (has links)
Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem. / In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.
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Matrix representation for partitions and Mock Theta functionsBagatini, Alessandro January 2016 (has links)
Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem. / In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.
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Matrix representation for partitions and Mock Theta functionsBagatini, Alessandro January 2016 (has links)
Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem. / In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.
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A New Method of Knot CountingMcCartney, Kelsie Lynn 14 July 2009 (has links)
No description available.
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Automatic Transmission Power Flow Matrix Representation / Matrisrepresentation av effektflöde i automatväxellådorÖun, Martin January 2014 (has links)
The project has worked with the function and structure of epicyclical automatic transmissions. The goal of the project has been to find a mathematical way of representing the transmissions setup and possible power flows. Furthermore the project has included the generation of all theoretically possible matrix representations of two simple planetary gear sets in MATLAB as the base for a future optimization model. The result of the project is a large quantity of matrix representations of the two planetary gear sets and their connections and shafts. The result from the MATLAB program has been verified by comparing the structure and the number of solutions to all manually derived setups. The result from the program can be considered to be complete for two planetary gears but to extend the analysis to more complex planetary gears and gearboxes with more than two sets, another method is suggested. The generation process in this project has been rather complex and time consuming. The conclusions drawn from this project is that it is possible to represent many epicyclical automatic transmissions in matrix form. An optimization program based on this type of matrix would simplify the design of new, more complex and more efficient epicyclical transmissions leading to more efficient vehicles. Key words: automatic transmission, planetary gear, matrix representation / Projektet har behandlat epicykliska automatväxellådor och dess uppbyggnad och funktion. Idén med projektet har varit att ta fram ett sätt för att på ett matematiskt sätt representera växellådans struktur och dess möjliga effektflöden. Utöver detta har arbetet inneburit att alla teoretiskt möjliga matrisrepresentationer för två enkla sammankopplade planetväxlar har tagits fram i MATLAB som underlag för en framtida optimeringsmodell. Resultatet av arbetet är en stor mängd uppställningar av dessa två planetväxlar och dessas sammankopplingar. Resultatet från MATLAB har jämförts och verifierats genom manuell beräkning av antalet variationer och dessas utseende. Resultatet från programmet kan anses som komplett men för en utökad analys av epicykliska automatväxellådor med fler än två planetväxlar och andra typer än den enklaste formen av planetväxel, rekommenderas en annan typ av framställning av alla möjliga variationer. Den metoden för att generera sammankopplingar som har använts i detta projekt är för komplex och tidskrävande. Slutsatsen av projektet är att det finns möjlighet att generera och representera många epicykliska automatväxellådor på matrisform. Ett optimeringsprogram baserat på denna typ av matris kan förenkla utvecklingen av nya mer avancerade och mer effektiva epicykliska automatväxelådor vilket leder till mer effektiva fordon. Nyckelord: automatisk växellåda, planetväxel, matrisrepresentation
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Uma abordagem matricial para modelagem e simulação de redes de trocadores de calor com aplicações para o gerenciamento da deposição / A matrix approach to modeling and simulation of networks of heat exchangers with applications for managing depositionLuiz Omena de Oliveira Filho 30 August 2007 (has links)
Uma rede de trocadores de calor pode ser definida como um grupo de trocadores de calor interligados com o objetivo de reduzir a necessidade de energia de um sistema, sendo largamente usada nas indústrias de processos. Entretanto, uma rede está sujeita à deposição, a qual causa um decréscimo na efetividade térmica dos trocadores. Este fenômeno é provocado pelo acúmulo de materiais indesejáveis sobre a superfície de troca térmica. Para compensar a redução de efetividade térmica causada pela deposição, torna-se necessário um aumento no consumo de utilidades. Isto eleva os custos de operação, assim como os custos de manutenção. Estima-se que os custos associados à deposição atinjam bilhões de dólares anualmente. Em face a este problema, vários trabalhos de pesquisa têm investigado métodos para prevenir a deposição e/ou gerenciar as operações em uma rede. Estudos envolvem desde a otimização de trocadores de calor individuais, simulação e monitoramento de redes, até a otimização da programação das paradas para limpeza de trocadores de calor em uma rede. O presente trabalho apresenta a proposição de um modelo para simulação de redes de trocadores de calor com aplicações no gerenciamento da deposição. Como conseqüência, foi desenvolvido um conjunto de códigos computacionais integrados, envolvendo a simulação estacionária de redes, a simulação pseudo-estacionária do comportamento de redes em relação à evolução da deposição, a estimação de parâmetros para diagnóstico do problema da deposição e a otimização operacional deste tipo de sistema. Com relação ao simulador estacionário, o modelo da rede foi formulado matricialmente e os balanços de massa e energia são resolvidos como sistemas de equações lineares. Do ponto de vista da otimização, o procedimento proposto redistribui as vazões, visando um melhor aproveitamento térmico dos trocadores da rede, como, por exemplo, buscando as vazões da rede que maximizem a temperatura da corrente de entrada no forno em unidades de destilação atmosférica de óleo cru. Os algoritmos foram implementados em alguns exemplos da literatura e em um problema de uma refinaria real. Os resultados foram promissores, o que sugere que a proposta deste trabalho pode vir a ser uma abordagem interessante para operações envolvendo redes de trocadores de calor / A Heat Exchanger Network (HEN) can be defined as a group of heat exchangers interconnected aiming to reduce the energy demand of a system, being widely used in the process industries. However, a HEN is subject to fouling, which causes a decrease on the thermal effectiveness of heat exchangers. This phenomenon is provoked by the accumulation of undesirable materials on thermal surface. In order to compensate the reduction of thermal effectiveness caused by fouling, it becomes necessary to increase the utility consumption. Thus, there is an increase of the operation costs, as maintenance costs. It is estimated that the costs associated to fouling reach billions of dollars annually. Facing this problem, several researches have investigated methods to prevent fouling and/or how to manage HEN operations. Studies involve since optimization of individual heat exchangers, simulation and fouling monitoring, until cleaning schedule optimization of HENs. The present work proposes a HEN simulation model, applied to fouling management. Consequently, it was developed a set of integrated computational codes, which involve a HEN stationary simulation, a pseudo-stationary simulation of HEN behavior related to fouling, a parameter estimation procedure for diagnosing fouling problems and an operational optimization procedure of this sort of system. Related to the stationary simulator, the HEN model is formulated using a matrix approach and the mass and energy balances are solved as linear equation systems. Focusing on optimization, it redistributes the HEN flows in order to improve the heat exchangers thermal efficiency, for example, searching for the HEN flows that maximize the inlet furnace stream temperature in crude distillation units. The algorithm was implemented to some literature examples and on a problem of a real refinery. All results show to be promising, which suggests that the proposal of this work may be an interesting approach for operations involving HENs
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Uma abordagem matricial para modelagem e simulação de redes de trocadores de calor com aplicações para o gerenciamento da deposição / A matrix approach to modeling and simulation of networks of heat exchangers with applications for managing depositionLuiz Omena de Oliveira Filho 30 August 2007 (has links)
Uma rede de trocadores de calor pode ser definida como um grupo de trocadores de calor interligados com o objetivo de reduzir a necessidade de energia de um sistema, sendo largamente usada nas indústrias de processos. Entretanto, uma rede está sujeita à deposição, a qual causa um decréscimo na efetividade térmica dos trocadores. Este fenômeno é provocado pelo acúmulo de materiais indesejáveis sobre a superfície de troca térmica. Para compensar a redução de efetividade térmica causada pela deposição, torna-se necessário um aumento no consumo de utilidades. Isto eleva os custos de operação, assim como os custos de manutenção. Estima-se que os custos associados à deposição atinjam bilhões de dólares anualmente. Em face a este problema, vários trabalhos de pesquisa têm investigado métodos para prevenir a deposição e/ou gerenciar as operações em uma rede. Estudos envolvem desde a otimização de trocadores de calor individuais, simulação e monitoramento de redes, até a otimização da programação das paradas para limpeza de trocadores de calor em uma rede. O presente trabalho apresenta a proposição de um modelo para simulação de redes de trocadores de calor com aplicações no gerenciamento da deposição. Como conseqüência, foi desenvolvido um conjunto de códigos computacionais integrados, envolvendo a simulação estacionária de redes, a simulação pseudo-estacionária do comportamento de redes em relação à evolução da deposição, a estimação de parâmetros para diagnóstico do problema da deposição e a otimização operacional deste tipo de sistema. Com relação ao simulador estacionário, o modelo da rede foi formulado matricialmente e os balanços de massa e energia são resolvidos como sistemas de equações lineares. Do ponto de vista da otimização, o procedimento proposto redistribui as vazões, visando um melhor aproveitamento térmico dos trocadores da rede, como, por exemplo, buscando as vazões da rede que maximizem a temperatura da corrente de entrada no forno em unidades de destilação atmosférica de óleo cru. Os algoritmos foram implementados em alguns exemplos da literatura e em um problema de uma refinaria real. Os resultados foram promissores, o que sugere que a proposta deste trabalho pode vir a ser uma abordagem interessante para operações envolvendo redes de trocadores de calor / A Heat Exchanger Network (HEN) can be defined as a group of heat exchangers interconnected aiming to reduce the energy demand of a system, being widely used in the process industries. However, a HEN is subject to fouling, which causes a decrease on the thermal effectiveness of heat exchangers. This phenomenon is provoked by the accumulation of undesirable materials on thermal surface. In order to compensate the reduction of thermal effectiveness caused by fouling, it becomes necessary to increase the utility consumption. Thus, there is an increase of the operation costs, as maintenance costs. It is estimated that the costs associated to fouling reach billions of dollars annually. Facing this problem, several researches have investigated methods to prevent fouling and/or how to manage HEN operations. Studies involve since optimization of individual heat exchangers, simulation and fouling monitoring, until cleaning schedule optimization of HENs. The present work proposes a HEN simulation model, applied to fouling management. Consequently, it was developed a set of integrated computational codes, which involve a HEN stationary simulation, a pseudo-stationary simulation of HEN behavior related to fouling, a parameter estimation procedure for diagnosing fouling problems and an operational optimization procedure of this sort of system. Related to the stationary simulator, the HEN model is formulated using a matrix approach and the mass and energy balances are solved as linear equation systems. Focusing on optimization, it redistributes the HEN flows in order to improve the heat exchangers thermal efficiency, for example, searching for the HEN flows that maximize the inlet furnace stream temperature in crude distillation units. The algorithm was implemented to some literature examples and on a problem of a real refinery. All results show to be promising, which suggests that the proposal of this work may be an interesting approach for operations involving HENs
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Representation and Efficient Computation of Sparse Matrix for Neural Networks in Customized HardwareYan, Lihao January 2022 (has links)
Deep Neural Networks are widely applied to various kinds of fields nowadays. However, hundreds of thousands of neurons in each layer result in intensive memory storage requirement and a massive number of operations, making it difficult to employ deep neural networks on mobile devices where the hardware resources are limited. One common technique to address the memory limitation is to prune and quantize the neural networks. Besides, due to the frequent usage of Rectified Linear Unit (ReLU) function or network pruning, majority of the data in the weight matrices will be zeros, which will not only take up a large amount of memory space but also cause unnecessary computation operations. In this thesis, a new value-based compression method is put forward to represent sparse matrix more efficiently by eliminating these zero elements, and a customized hardware is implemented to realize the decompression and computation operations. The value-based compression method is aimed to replace the nonzero data in each column of the weight matrix with a reference value (arithmetic mean) and the relative differences between each nonzero element and the reference value. Intuitively, the data stored in each column is likely to contain similar values. Therefore, the differences will have a narrow range, and fewer bits rather than the full form will be sufficient to represent all the differences. In this way, the weight matrix can be further compressed to save memory space. The proposed value-based compression method reduces the memory storage requirement for the fully-connected layers of AlexNet to 37%, 41%, 47% and 68% of the compressed model, e.g., the Compressed Sparse Column (CSC) format, when the data size is set to 8 bits and the sparsity is 20%, 40%, 60% and 80% respectively. In the meanwhile, 41%, 53% and 63% compression rates of the fully-connected layers of the compressed AlexNet model with respect to 8-bit, 16-bit and 32-bit data are achieved when the sparsity is 40%. Similar results are obtained for VGG16 experiment. / Djupa neurala nätverk används i stor utsträckning inom olika fält nuförtiden. Emellertid ställer hundratusentals neuroner per lager krav på intensiv minneslagring och ett stort antal operationer, vilket gör det svårt att använda djupa neurala nätverk på mobila enheter där hårdvaruresurserna är begränsade. En vanlig teknik för att hantera minnesbegränsningen är att beskära och kvantifiera de neurala nätverken. På grund av den frekventa användningen av Rectified Linear Unit (ReLU) -funktionen eller nätverksbeskärning kommer majoriteten av datat i viktmatriserna att vara nollor, vilket inte bara tar upp mycket minnesutrymme utan också orsakar onödiga beräkningsoperationer. I denna avhandling presenteras en ny värdebaserad komprimeringsmetod för att representera den glesa matrisen mer effektivt genom att eliminera dessa nollelement, och en anpassad hårdvara implementeras för att realisera dekompressions- och beräkningsoperationerna. Den värdebaserade komprimeringsmetoden syftar till att ersätta icke-nolldata i varje kolumn i viktmatrisen med ett referensvärde (aritmetiskt medelvärde) och de relativa skillnaderna mellan varje icke-nollelement och referensvärdet. Intuitivt kommer data som lagras i varje kolumn sannolikt att innehålla liknande värden. Därför kommer skillnaderna att ha ett smalt intervall, och färre bitar snarare än den fullständiga formen kommer att räcka för att representera alla skillnader. På så sätt kan viktmatrisen komprimeras ytterligare för att spara minnesutrymme. Den föreslagna värdebaserade komprimeringsmetoden minskar minneslagringskravet för de helt anslutna lagren av AlexNet till 37%, 41%, 47% och 68% av den komprimerade modellen, t.ex. Compressed Sparse Column (CSC) format, när datastorleken är inställd på 8 bitar och sparsiteten är 20%, 40%, 60% respektive 80%. Under tiden uppnås 41%, 53% och 63% komprimeringshastigheter för de helt anslutna lagren i den komprimerade AlexNet-modellen med avseende på 8- bitars, 16-bitars och 32-bitars data när sparsiteten är 40%. Liknande resultat erhålls för VGG16-experiment.
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