Técnicas de simulação aplicadas à análise confiabilística: o desafio da obtenção de baixas probabilidades de falha

Abstract

The advances of safety analysis in Structural Engineering are increasingly improved by science, since its application is notorious in various branches of engineering, from the most conventional structures present in civil construction to the boldest structures in aerospace engineering. Among the requirements that a structure must follow, ensuring a good safety of the structure is essential in an engineer’s daily life, so that the mathematical characterization of limit states must ensure a limit between the failure domain and the safety domain of this structure. Thus, one can use the Structural Reliability Theory to analyze the safety requirements of a structure from the analysis of its design parameters in a probabilistic way. The uncertain ties related to these designs are incorporated into the model in an attemptto obtain amore accurate response to the predicted behavior of the structure and an estimate of its failure probability. Among the reliability analysis techniques, the FORM method (First Order Reliability Method) is widely used because it is a semi-analytical method capable of solving several problems with low computational cost, although it has limitations when applied to complex and non-linear problems. Thus, one can highlight the Monte Carlo Simulation method, a powerful technique capable of solving complex, large and non-linear problems. However, the associated high computational cost can be come a problem, especially in cases with low failure probabilities. To circumvent this, variance reduction techniques (called Intelligent Sampling) are proposed in the literature in order to obtain a good estimate for low failure probabilities with a computational cost that is not prohibitive. Therefore, this paper aims to explore some of these techniques and evaluate the potential of this estimation, highlighting Asymptotic Sampling and Enhanced Sampling. It seeks to explore bench mark problems from the literature where the solution tends to be complex and, in some cases, difficult to obtain via FORM, to highlight the need for simulation techniques. All the analyses are done with the Python programming language and the results obtained are compared in terms of the effectiveness of the convergence of the techniques and their accuracy with respect to the literature.