A confiabilidade de estruturas apresenta sólidos desenvolvimentos teóricos e crescentes aplicações práticas. Durante os últimos anos, avanços significativos foram obtidos em termos dos métodos de transformação (FORM, SORM), bem como em termos das técnicas de simulação de Monte Carlo. Métodos de transformação se mostraram eficientes para problemas de dimensões e não-linearidades moderadas. Já técnicas de simulação sempre permitiram a solução de problemas de grandes dimensões e fortemente não lineares, embora o custo computacional possa ser uma séria limitação. Com o avanço da capacidade de processamento dos computadores e com o desenvolvimento de técnicas de amostragem inteligente, a simulação de Monte Carlo passa a ser cada vez mais viável. Este trabalho tem por objetivo estudar e programar em computador técnicas de amostragem inteligente em simulação de Monte Carlo. O StRAnD é um programa de computador que já possui implementadas as técnicas de simulação de Monte Carlo Bruto e com Amostragem por Importância, ambas utilizando a Amostragem Simples na geração das variáveis básicas. Assim, são adicionadas, ao StRAnD, as técnicas de Amostragem Assintótica, Amostragem Melhorada e Simulação de Subconjuntos. Além disso, são programadas as técnicas de Amostragem por Hipercubo Latino e Amostragem por Variáveis Antitéticas. Nesta dissertação, são analisados seis problemas distintos, de forma que as vantagens e desvantagens de cada técnica sejam avaliadas, em termos da probabilidade de falha, do coeficiente de variação da probabilidade de falha, do erro relativo da probabilidade de falha e do tempo de processamento. / The structural reliability presents solid theoretical developments and increasing practical applications. During the past few years, significant advances were achieved in terms of transformation methods (FORM and SORM), as well as, in terms of Monte Carlo Simulation. Transformation methods are effective in problems with moderate dimensions and moderate nonlinearities. On the other hand, simulation techniques can be used to solve high-dimensional problems and highly nonlinear problems, although the computational cost could be a serious limitation. With the progress of computer processing capacity and with the development of intelligent sampling techniques, the Monte Carlo Simulation becomes increasingly feasible. This work aims to study and program intelligent sampling techniques in Monte Carlo simulation. The StRAnD (Structural Reliability Analysis and Design) software already has Crude Monte Carlo and Importance Sampling Monte Carlo, both using Simple Sampling as basic samples generator. Thus, the Asymptotic Sampling technique, the Enhanced Sampling technique and the Subset Simulation were added to the software. Moreover, the Latin Hypercube Sampling technique and the Antithetic Variates techniques were also added to the software. Six problems were evaluated in order to evaluate the advantages and disadvantages of each technique, in terms of probability of failure, coefficient of variation of the probability of failure, relative error and processing time.

Tradeoff studies are a common part of engineering practice. Designers conduct tradeoff studies in order to improve their understanding of how various design considerations relate to one another. Generally a tradeoff study involves a systematic multi-criteria evaluation of various alternatives for a particular system or subsystem. After evaluating these alternatives, designers eliminate those that perform poorly under the given criteria and explore more carefully those that remain. The capability to compose preexisting tradeoff studies is advantageous to the designers of engineered systems, such as aircraft, military equipment, and automobiles. Such systems are comprised of many subsystems for which prior tradeoff studies may exist. System designers conceivably could explore system-level tradeoffs more quickly by leveraging this knowledge. For example, automotive systems engineers could combine tradeoff studies from the engine and transmission subsystems quickly to produce a comprehensive tradeoff study for the power train. This level of knowledge reuse is in keeping with good systems engineering practice. However, existing procedures for generating tradeoff studies under uncertainty involve assumptions that preclude engineers from composing them in a mathematically rigorous way. In uncertain problems, designers can eliminate inferior alternatives using stochastic dominance, which compares the probability distributions defined in the design criteria space. Although this is well-founded mathematically, the procedure can be computationally expensive because it typically entails a sampling-based uncertainty propagation method for each alternative being considered. This thesis describes two novel extensions that permit engineers to compose preexisting subsystem-level tradeoff studies under uncertainty into mathematically valid system-level tradeoff studies and efficiently eliminate inferior alternatives through intelligent sampling. The approaches are based on three key ideas: the use of stochastic dominance methods to enable the tradeoff evaluation when the design criteria are uncertain, the use of parameterized efficient sets to enable reuse and composition of subsystem-level tradeoff studies, and the use of statistical tests in dominance testing to reduce the number of behavioral model evaluations. The approaches are demonstrated in the context of a tradeoff study for a motor vehicle.

A confiabilidade de estruturas apresenta sólidos desenvolvimentos teóricos e crescentes aplicações práticas. Durante os últimos anos, avanços significativos foram obtidos em termos dos métodos de transformação (FORM, SORM), bem como em termos das técnicas de simulação de Monte Carlo. Métodos de transformação se mostraram eficientes para problemas de dimensões e não-linearidades moderadas. Já técnicas de simulação sempre permitiram a solução de problemas de grandes dimensões e fortemente não lineares, embora o custo computacional possa ser uma séria limitação. Com o avanço da capacidade de processamento dos computadores e com o desenvolvimento de técnicas de amostragem inteligente, a simulação de Monte Carlo passa a ser cada vez mais viável. Este trabalho tem por objetivo estudar e programar em computador técnicas de amostragem inteligente em simulação de Monte Carlo. O StRAnD é um programa de computador que já possui implementadas as técnicas de simulação de Monte Carlo Bruto e com Amostragem por Importância, ambas utilizando a Amostragem Simples na geração das variáveis básicas. Assim, são adicionadas, ao StRAnD, as técnicas de Amostragem Assintótica, Amostragem Melhorada e Simulação de Subconjuntos. Além disso, são programadas as técnicas de Amostragem por Hipercubo Latino e Amostragem por Variáveis Antitéticas. Nesta dissertação, são analisados seis problemas distintos, de forma que as vantagens e desvantagens de cada técnica sejam avaliadas, em termos da probabilidade de falha, do coeficiente de variação da probabilidade de falha, do erro relativo da probabilidade de falha e do tempo de processamento. / The structural reliability presents solid theoretical developments and increasing practical applications. During the past few years, significant advances were achieved in terms of transformation methods (FORM and SORM), as well as, in terms of Monte Carlo Simulation. Transformation methods are effective in problems with moderate dimensions and moderate nonlinearities. On the other hand, simulation techniques can be used to solve high-dimensional problems and highly nonlinear problems, although the computational cost could be a serious limitation. With the progress of computer processing capacity and with the development of intelligent sampling techniques, the Monte Carlo Simulation becomes increasingly feasible. This work aims to study and program intelligent sampling techniques in Monte Carlo simulation. The StRAnD (Structural Reliability Analysis and Design) software already has Crude Monte Carlo and Importance Sampling Monte Carlo, both using Simple Sampling as basic samples generator. Thus, the Asymptotic Sampling technique, the Enhanced Sampling technique and the Subset Simulation were added to the software. Moreover, the Latin Hypercube Sampling technique and the Antithetic Variates techniques were also added to the software. Six problems were evaluated in order to evaluate the advantages and disadvantages of each technique, in terms of probability of failure, coefficient of variation of the probability of failure, relative error and processing time.

In this thesis several sampling methods for Statistical Learning with imbalanced data have been implemented and evaluated with a new metric, imbalanced accuracy. Several modifications and new algorithms have been proposed for intelligent sampling: Border links, Clean Border Undersampling, One-Sided Undersampling Modified, DBSCAN Undersampling, Class Adjusted Jittering, Hierarchical Cluster Based Oversampling, DBSCAN Oversampling, Fitted Distribution Oversampling, Random Linear Combinations Oversampling, Center Repulsion Oversampling. A set of requirements on a satisfactory performance metric for imbalanced learning have been formulated and a new metric for evaluating classification performance has been developed accordingly. The new metric is based on a combination of the worst class accuracy and geometric mean. In the testing framework nonparametric Friedman's test and post hoc Nemenyi’s test have been used to assess the performance of classifiers, sampling algorithms, combinations of classifiers and sampling algorithms on several data sets. A new approach of detecting algorithms with dominating and dominated performance has been proposed with a new way of visualizing the results in a network. From experiments on simulated and several real data sets we conclude that: i) different classifiers are not equally sensitive to sampling algorithms, ii) sampling algorithms have different performance within specific classifiers, iii) oversampling algorithms perform better than undersampling algorithms, iv) Random Oversampling and Random Undersampling outperform many well-known sampling algorithms, v) our proposed algorithms Hierarchical Cluster Based Oversampling, DBSCAN Oversampling with FDO, and Class Adjusted Jittering perform much better than other algorithms, vi) a few good combinations of a classifier and sampling algorithm may boost classification performance, while a few bad combinations may spoil the performance, but the majority of combinations are not significantly different in performance.