Método para geração e otimização de funções de pertinência para previsão de séries temporais

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Ciência da Computação, Florianópolis, 2017.Sistemas fuzzy são utilizados para diversos tipos de aplicações cujos domínios são caracterizados por vagueza e imprecisão. Para que um sistema atue de forma apropriada, isto é, para que alcance os resultados almejados, é necessário definir a base de conhecimento adequadamente. Isso significa definir o conjunto de regras e as funções de pertinência condizentes com o problema. Em sua forma tradicional, um sistema fuzzy é projetado utilizando funções de pertinência tipo 1, cujo grau de pertinência atribuído a cada elemento do conjunto é um valor numérico. No entanto, uma abordagem alternativa também considerada apropriada emprega funções de pertinência tipo 2, cujo grau de pertinência é também fuzzy. A definição dessas funções de pertinência, contudo, é uma etapa complexa, sem metodologia ainda definida e dependente da aplicação, sendo muitas vezes estabelecida com o auxílio de especialistas, heuristicamente, ou por meio de sucessivas simulações ou algoritmos de busca e otimização. Nessa direção, esta pesquisa propõe um método híbrido para a geração de funções de pertinência otimizadas por um Algoritmo Genético (AG) que admite tanto funções tipo 1 quanto funções tipo 2 intervalares. O método permite detalhar o total de conjuntos empregados por variável do problema, assim como o tipo da função de pertinência de cada conjunto fuzzy. A avaliação do método proposto foi realizada em previsão de séries temporais e por meio da análise estatística dos resultados. Para fins de comparação, implementou-se também a otimização de funções de pertinência tipo 1 e tipo 2, exclusivamente. Os resultados do método proposto mostraram-se promissores, pois os erros médios obtidos são semelhantes aos dos melhores resultados obtidos por abordagens que empregam exclusivamente funções tipo 1 ou funções tipo 2. Além disso, a diminuição do total de conjuntos contribui para a interpretabilidade do modelo em termos de complexidade.Abstract : Fuzzy systems are used for various types of applications whose domains are characterized by vagueness and imprecision. For a system to act suitably, that is, to achieve the desired results, it is necessary to adequately define the knowledge base. This means defining the set of rules and the membership functions that are suitable to the problem. A fuzzy system is traditionally designed by using type-1 membership functions, for which the degree of membership attributed to each element of the set is a numeric value. Nevertheless, an optional approach also considered appropriate uses type-2 membership functions whose degree of membership is also fuzzy. The definition of these membership functions, however, is a complex step, for which there is still no defined methodology and which is dependent on the application. It is often established with the assistance of specialists, either heuristically or through a series of simulations or by using search and optimization algorithms. In this context, this study proposes a hybrid method for the generation of membership functions that are optimized for a Genetic Algorithm that admits both type-1 and interval type-2 membership functions. The method allows detailing the number of sets used per variable of the problem, as well as the type of membership function of each fuzzy set. The evaluation of the method proposed was conducted by predicting time series data and by conducting a statistical analysis of the results. For comparative purposes, the type-1 and type-2 membership functions were optimized, exclusively. The results of the proposed method revealed themselves to be promising, because the mean errors obtained are similar to the best results obtained through approaches that exclusively use type-1 or type-2 membership functions. Moreover, the decrease in the total number of sets contributes to the interpretability of the model in terms of complexity

A fuzzy expert system for automatic seismic signal classification

Automatic classification of seismic events is of great importance due to the large amount of data received continuously. Seismic analysts classify events by visual inspection and calculation of event signal characteristics. This process is subjective and demands hard work as well as a significant amount of time and considerable experience. A reliable automatic classification task considerably reduces the effort required and makes classification faster and more objective. The aim of this study is to develop a fuzzy rule based expert classification system that is able to imitate human reasoning and incorporate the analyst's knowledge of seismic event classification. The fundamental idea behind using this approach was motivated by the way in which human analysts classify seismic events based on a set of experiential rules. Additionally, this approach was chosen due to its interpretability and adjustability, as well as its ability to manage the complexity of real data. Relevant discriminant features are extracted from event signal. Using these features, the classification system was built based on the vote by multiple rule fuzzy reasoning method with three types of rules. Comparison of this method with the single winner classical fuzzy reasoning model was carried out. Classification results on real seismic data showed the robustness of the classifier and its capability to operate in on-line classification

Solución rápida y automática de parámetros hipocentrales para eventos sísmicos, mediante el empleo de técnicas de aprendizaje de máquina

La generación de alertas tempranas para sismos es de gran utilidad, en particular para la ciudad de Bogotá-Colombia, dada su importancia social y económica para el país. Con base en la información de la estación sismológica de El Rosal, la cual es una estación de banda ancha y tres componentes, localizada muy cerca de la ciudad, perteneciente al Servicio Geológico Colombiano (SGC) se desarrolló un modelo de regresión basado en máquinas de vectores de soporte (SVM), con un kernel polinomial normalizado, usando como datos de entrada algunas características de la porción inicial de la onda P empleadas en trabajos anteriores tales como la amplitud máxima, los coeficientes de regresión lineal de los mismos, los parámetros de ajuste logarítmico de la envolvente y los valores propios de la relación de las tres componentes del sismograma. El modelo fue entrenado y evaluado aplicando correlación cruzada, permitiendo llevar a cabo el cálculo de la magnitud y la localización de un evento sísmico con una longitud de señal de tan solo cinco segundos. Con el modelo propuesto se logró la determinación de la magnitud local con una precisión de 0.19 unidades de magnitud, la distancia epicentral con una precisión de alrededor de 11 kilómetros, la profundidad hipocentral con una precisión de aproximadamente 40 kilómetros y el azimut de llegada con una precisión de 45°. Las precisiones obtenidas en magnitud y distancia epicentral son mejores que las encontradas en trabajos anteriores, donde se emplean gran número de eventos para la determinación del modelo y en los demás parámetros hipocentrales son del mismo orden. Este trabajo de investigación realiza un aporte considerable en la generación de alertas tempranas para sismos, no solamente para el país sino para cualquier otro lugar donde se deseen implementar los modelos aquí propuestos y es un excelente punto de partida para investigaciones futuras.Abstract. Earthquake early warning alerts generation is very useful, especially for the city of Bogotá-Colombia, given the social and economic importance of this city for the country. Based on the information from the seismological station “El Rosal”, which is a broadband and three components station, located very near the city that belongs to the Servicio Geológico Colombiano (SGC) a Support Vector Machine Regression (SVMR) model was developed, using a Normalized Polynomial Kernel, using as input some characteristics of the initial portion of the P wave used in earlier works such as the maximum amplitude, the linear regression coefficients of such amplitudes, the logarithmic adjustment parameters of the envelope of the waveform and the eigenvalues of the relationship between the three seismogram components of each band. The model was trained and evaluated by applying a cross-correlation strategy, allowing to calculate the magnitude and location of a seismic event with only five seconds of signal. With the proposed model it was possible to estimate local magnitude with an accuracy of 0.19 units of magnitude, epicentral distance with an accuracy of about 11 km, the hipocentral depth with a precision of approximately 40 km and the arrival back-azimut with a precision of 45°. Accuracies obtained in magnitude and epicentral distance are better that those found in earlier works, where a large number of events were used for model determination, and the other hipocentral parameters precisions obtained here are of the same order. This research work makes a considerable contribution in the generation of seismic early warning alerts, not only for the country but for any other place where proposed models here can be applied and is a very good starting point for future research.Doctorad