Sistema baseado em regras fuzzy do tipo Takagi-Sugeno aplicado a ecos de radares meteorológicos

Pós-graduação em Ciências Ambientais - Sorocaba

A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

MODULARITY BASED FUZZY COMMUNITY DETECTION IN SOCIAL NETWORKS

Fuzzy community detection is to identify fuzzy communities in a network, which are groups of vertices in the network such that the membership of a vertex in one community is in [0,1] and that the sum of memberships of vertices in all communities equals to 1. Fuzzy communities are pervasive in social networks, but only a few works have been done for fuzzy community detection. Recently, a one-step forward extension of Newman’s Modularity, the most popular quality function for disjoint community detection, results into the Generalized Modularity (GM) that demonstrates good performance in finding well-known fuzzy communities. Thus, GMis chosen as the quality function in our research. We first propose a generalized fuzzy t-norm modularity to investigate the effect of different fuzzy intersection operators on fuzzy community detection, since the introduction of a fuzzy intersection operation is made feasible by GM. The experimental results show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure. Then, we focus on how to find optimal fuzzy communities in a network by directly maximizing GM, which we call it Fuzzy Modularity Maximization (FMM) problem. The effort on FMM problem results into the major contribution of this thesis, an efficient and effective GM-based fuzzy community detection method that could automatically discover a fuzzy partition of a network when it is appropriate, which is much better than fuzzy partitions found by existing fuzzy community detection methods, and a crisp partition of a network when appropriate, which is competitive with partitions resulted from the best disjoint community detections up to now. We address FMM problem by iteratively solving a sub-problem called One-Step Modularity Maximization (OSMM). We present two approaches for solving this iterative procedure: a tree-based global optimizer called Find Best Leaf Node (FBLN) and a heuristic-based local optimizer. The OSMM problem is based on a simplified quadratic knapsack problem that can be solved in linear time; thus, a solution of OSMM can be found in linear time. Since the OSMM algorithm is called within FBLN recursively and the structure of the search tree is non-deterministic, we can see that the FMM/FBLN algorithm runs in a time complexity of at least O (n2). So, we also propose several highly efficient and very effective heuristic algorithms namely FMM/H algorithms. We compared our proposed FMM/H algorithms with two state-of-the-art community detection methods, modified MULTICUT Spectral Fuzzy c-Means (MSFCM) and Genetic Algorithm with a Local Search strategy (GALS), on 10 real-world data sets. The experimental results suggest that the H2 variant of FMM/H is the best performing version. The H2 algorithm is very competitive with GALS in producing maximum modularity partitions and performs much better than MSFCM. On all the 10 data sets, H2 is also 2-3 orders of magnitude faster than GALS. Furthermore, by adopting a simply modified version of the H2 algorithm as a mutation operator, we designed a genetic algorithm for fuzzy community detection, namely GAFCD, where elite selection and early termination are applied. The crossover operator is designed to make GAFCD converge fast and to enhance GAFCD’s ability of jumping out of local minimums. Experimental results on all the data sets show that GAFCD uncovers better community structure than GALS.

DC MICROGRID STABILIZATION THROUGH FUZZY CONTROL OF INTERLEAVED, HETEROGENEOUS STORAGE ELEMENTS

As microgrid power systems gain prevalence and renewable energy comprises greater and greater portions of distributed generation, energy storage becomes important to offset the higher variance of renewable energy sources and maximize their usefulness. One of the emerging techniques is to utilize a combination of lead-acid batteries and ultracapacitors to provide both short and long-term stabilization to microgrid systems. The different energy and power characteristics of batteries and ultracapacitors imply that they ought to be utilized in different ways. Traditional linear controls can use these energy storage systems to stabilize a power grid, but cannot effect more complex interactions. This research explores a fuzzy logic approach to microgrid stabilization. The ability of a fuzzy logic controller to regulate a dc bus in the presence of source and load fluctuations, in a manner comparable to traditional linear control systems, is explored and demonstrated. Furthermore, the expanded capabilities (such as storage balancing, self-protection, and battery optimization) of a fuzzy logic system over a traditional linear control system are shown. System simulation results are presented and validated through hardware-based experiments. These experiments confirm the capabilities of the fuzzy logic control system to regulate bus voltage, balance storage elements, optimize battery usage, and effect self-protection.

Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images.

An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster's shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Hybrid incremental modeling based on least squares and fuzzy K-NN for monitoring tool wear in turning processes

There is now an emerging need for an efficient modeling strategy to develop a new generation of monitoring systems. One method of approaching the modeling of complex processes is to obtain a global model. It should be able to capture the basic or general behavior of the system, by means of a linear or quadratic regression, and then superimpose a local model on it that can capture the localized nonlinearities of the system. In this paper, a novel method based on a hybrid incremental modeling approach is designed and applied for tool wear detection in turning processes. It involves a two-step iterative process that combines a global model with a local model to take advantage of their underlying, complementary capacities. Thus, the first step constructs a global model using a least squares regression. A local model using the fuzzy k-nearest-neighbors smoothing algorithm is obtained in the second step. A comparative study then demonstrates that the hybrid incremental model provides better error-based performance indices for detecting tool wear than a transductive neurofuzzy model and an inductive neurofuzzy model.

Extending the expressiveness of fuzzy logic languages

En el trabajo que aquí presentamos se incluye la base teórica (sintaxis y semántica) y una implementación de un framework para codificar el razonamiento de la representación difusa o borrosa del mundo (tal y como nosotros, seres humanos, entendemos éste). El interés en la realización de éste trabajo parte de dos fuentes: eliminar la complejidad existente cuando se realiza una implementación con un lenguaje de programación de los llamados de propósito general y proporcionar una herramienta lo suficientemente inteligente para dar respuestas de forma constructiva a consultas difusas o borrosas. El framework, RFuzzy, permite codificar reglas y consultas en una sintaxis muy cercana al lenguaje natural usado por los seres humanos para expresar sus pensamientos, pero es bastante más que eso. Permite representar conceptos muy interesantes, como fuzzificaciones (funciones usadas para convertir conceptos no difusos en difusos), valores por defecto (que se usan para devolver resultados un poco menos válidos que los que devolveríamos si tuviésemos la información necesaria para calcular los más válidos), similaridad entre atributos (característica que utilizamos para buscar aquellos individuos en la base de datos con una característica similar a la buscada), sinónimos o antónimos y, además, nos permite extender el numero de conectivas y modificadores (incluyendo modificadores de negación) que podemos usar en las reglas y consultas. La personalización de la definición de conceptos difusos (muy útil para lidiar con el carácter subjetivo de los conceptos borrosos, donde nos encontramos con que cualificar a alguien de “alto” depende de la altura de la persona que cualifica) es otra de las facilidades incluida. Además, RFuzzy implementa la semántica multi-adjunta. El interés en esta reside en que introduce la posibilidad de obtener la credibilidad de una regla a partir de un conjunto de datos y una regla dada y no solo el grado de satisfacción de una regla a partir de el universo modelado en nuestro programa. De esa forma podemos obtener automáticamente la credibilidad de una regla para una determinada situación. Aún cuando la contribución teórica de la tesis es interesante en si misma, especialmente la inclusión del modificador de negacion, sus multiples usos practicos lo son también. Entre los diferentes usos que se han dado al framework destacamos el reconocimiento de emociones, el control de robots, el control granular en computacion paralela/distribuída y las busquedas difusas o borrosas en bases de datos. ABSTRACT In this work we provide a theoretical basis (syntax and semantics) and a practical implementation of a framework for encoding the reasoning and the fuzzy representation of the world (as human beings understand it). The interest for this work comes from two sources: removing the existing complexity when doing it with a general purpose programming language (one developed without focusing in providing special constructions for representing fuzzy information) and providing a tool intelligent enough to answer, in a constructive way, expressive queries over conventional data. The framework, RFuzzy, allows to encode rules and queries in a syntax very close to the natural language used by human beings to express their thoughts, but it is more than that. It allows to encode very interesting concepts, as fuzzifications (functions to easily fuzzify crisp concepts), default values (used for providing results less adequate but still valid when the information needed to provide results is missing), similarity between attributes (used to search for individuals with a characteristic similar to the one we are looking for), synonyms or antonyms and it allows to extend the number of connectives and modifiers (even negation) we can use in the rules. The personalization of the definition of fuzzy concepts (very useful for dealing with the subjective character of fuzziness, in which a concept like tall depends on the height of the person performing the query) is another of the facilities included. Besides, RFuzzy implements the multi-adjoint semantics. The interest in them is that in addition to obtaining the grade of satisfaction of a consequent from a rule, its credibility and the grade of satisfaction of the antecedents we can determine from a set of data how much credibility we must assign to a rule to model the behaviour of the set of data. So, we can determine automatically the credibility of a rule for a particular situation. Although the theoretical contribution is interesting by itself, specially the inclusion of the negation modifier, the practical usage of it is equally important. Between the different uses given to the framework we highlight emotion recognition, robocup control, granularity control in parallel/distributed computing and flexible searches in databases.

Soundscape quality analysis by fuzzy logic: A field study in Cordoba, Argentina

This research studies urban soundscapes through the comparative analysis of twelve public open spaces in the city of Córdoba (Argentina), taken as case studies. The work aims to examine selection of indicators and assessment tools intended to characterize soundscape quality. The field study was carried out through surveys and acoustic and psychoacoustic indicators, that are used together to objectively describe the sound quality of urban spaces. The study shows that, while there is a relationship of these indicators with the sound quality of the spaces, this is not linear. Their relative importance or influence depends on the interrelations occurring between the parameters studied. A model analyzing and correlating the parameters with the sound quality, based on the postulates of fuzzy logic, was applied as a tool of analysis, and it was seen to achieve a very close approximation to the subjective or perceptual response of the inhabitants. This close match between the model results and the perceptual response of the users confirms the fuzzy model as an effective tool for the study, not only of soundscapes, but also for those situations in which objective parameters must be related to the perceptual response of users.

Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Structure-activity relationships derived by machine learning: the use of atoms and their bond connectivities to predict mutagenicity by inductive logic programming.

We present a general approach to forming structure-activity relationships (SARs). This approach is based on representing chemical structure by atoms and their bond connectivities in combination with the inductive logic programming (ILP) algorithm PROGOL. Existing SAR methods describe chemical structure by using attributes which are general properties of an object. It is not possible to map chemical structure directly to attribute-based descriptions, as such descriptions have no internal organization. A more natural and general way to describe chemical structure is to use a relational description, where the internal construction of the description maps that of the object described. Our atom and bond connectivities representation is a relational description. ILP algorithms can form SARs with relational descriptions. We have tested the relational approach by investigating the SARs of 230 aromatic and heteroaromatic nitro compounds. These compounds had been split previously into two subsets, 188 compounds that were amenable to regression and 42 that were not. For the 188 compounds, a SAR was found that was as accurate as the best statistical or neural network-generated SARs. The PROGOL SAR has the advantages that it did not need the use of any indicator variables handcrafted by an expert, and the generated rules were easily comprehensible. For the 42 compounds, PROGOL formed a SAR that was significantly (P < 0.025) more accurate than linear regression, quadratic regression, and back-propagation. This SAR is based on an automatically generated structural alert for mutagenicity.

Desenvolvimento de estratégias de otimização contínua e discreta para problemas de fluxo de potência ótimo

O objetivo do presente trabalho é a investigação e o desenvolvimento de estratégias de otimização contínua e discreta para problemas de Fluxo de Potência Ótimo (FPO), onde existe a necessidade de se considerar as variáveis de controle associadas aos taps de transformadores em-fase e chaveamentos de bancos de capacitores e reatores shunt como variáveis discretas e existe a necessidade da limitação, e/ou até mesmo a minimização do número de ações de controle. Neste trabalho, o problema de FPO será abordado por meio de três estratégias. Na primeira proposta, o problema de FPO é modelado como um problema de Programação Não Linear com Variáveis Contínuas e Discretas (PNLCD) para a minimização de perdas ativas na transmissão; são propostas três abordagens utilizando funções de discretização para o tratamento das variáveis discretas. Na segunda proposta, considera-se que o problema de FPO, com os taps de transformadores discretos e bancos de capacitores e reatores shunts fixos, possui uma limitação no número de ações de controles; variáveis binárias associadas ao número de ações de controles são tratadas por uma função quadrática. Na terceira proposta, o problema de FPO é modelado como um problema de Otimização Multiobjetivo. O método da soma ponderada e o método ε-restrito são utilizados para modificar os problemas multiobjetivos propostos em problemas mono-objetivos. As variáveis binárias associadas às ações de controles são tratadas por duas funções, uma sigmoidal e uma polinomial. Para verificar a eficácia e a robustez dos modelos e algoritmos desenvolvidos serão realizados testes com os sistemas elétricos IEEE de 14, 30, 57, 118 e 300 barras. Todos os algoritmos e modelos foram implementados em General Algebraic Modeling System (GAMS) e os solvers CONOPT, IPOPT, KNITRO e DICOPT foram utilizados na resolução dos problemas. Os resultados obtidos confirmam que as estratégias de discretização são eficientes e as propostas de modelagem para variáveis binárias permitem encontrar soluções factíveis para os problemas envolvendo as ações de controles enquanto os solvers DICOPT e KNITRO utilizados para modelar variáveis binárias não encontram soluções.

Otimização não linear aplicada à operação de sistemas com múltiplos reservatórios para abastecimento de água.

O presente estudo considera a aplicação do modelo SISAGUA de simulação matemática e de otimização para a operação de sistemas de reservatórios integrados em sistemas complexos para o abastecimento de água. O SISAGUA utiliza a programação não linear inteira mista (PNLIM) com os objetivos de evitar ou minimizar racionamentos, equilibrar a distribuição dos armazenamentos em sistemas com múltiplos reservatórios e minimizar os custos de operação. A metodologia de otimização foi aplicada para o sistema produtor de água da Região Metropolitana de São Paulo (RMSP), que enfrenta a crise hídrica diante de um cenário de estiagem em 2013-2015, o pior na série histórica dos últimos 85 anos. Trata-se de uma região com 20,4 milhões de habitantes. O sistema é formado por oito sistemas produtores parcialmente integrados e operados pela Sabesp (Companhia de Saneamento do Estado de São Paulo). A RMSP é uma região com alta densidade demográfica, localizada na Bacia Hidrográfica do Alto Tietê e caracterizada pela baixa disponibilidade hídrica per capita. Foi abordada a possibilidade de considerar a evaporação durante as simulações, e a aplicação de uma regra de racionamento contínua nos reservatórios, que transforma a formulação do problema em programação não linear (PNL). A evaporação se mostrou pouco representativa em relação a vazão de atendimento à demanda, com cerca de 1% da vazão. Se por um lado uma vazão desta magnitude pode contribuir em um cenário crítico, por outro essa ordem de grandeza pode ser comparada às incertezas de medições ou previsões de afluências. O teste de sensibilidade das diferentes taxas de racionamento em função do volume armazenado permite analisar o tempo de resposta de cada sistema. A variação do tempo de recuperação, porém, não se mostrou muito significativo.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.