Uma análise comparativa do desempenho dos métodos Kernel Smoother e Monte Carlo aplicados a problemas de confiabilidade estrutural

Abstract

A great problem on the structural design field are the uncertainties associated to random variables (RV) present on the project equations. Also, with assertive considerations and a strict quality control, the structures can be exposed to uncertainties from the load and others unexpected phenomena. In that context, the structural reliability is one important tool to measure safety through indicators, such as probability of failure (𝑃𝐹). Among the structural reliability methodologies, stand out the transformation methods, such as the First Order Reliability Method (FORM) and the simulation-based methods, such as Monte Carlo (MC), that estimate the 𝑃𝐹 by simulating observations of the involved RV’s. Alternatively, the surrogate-models, which describes a complex model by one analytical function, are evolving in this knowledge field. Kernel Smoother (KS) is a meta-model that isn’t much explored for structural reliability analysis. This work aims to stablish a comparison between different methods, (FOMR, MC and KS) evaluating the precision and computational timing of those methods as performance indicators. Aside from the crude MC, two variance-reduction techniques: Importance Sampling (IS) e Latin Hipercube Sampling (LHS), as a alternative to increase MC efficacy. With the proposed analysis, this work concludes that the MC was the method that demanded less time and computational efforts, however it showed inefficient on problems with relatively low 𝑃𝐹 magnitude. It presents, yet again, that the IS and the LHS methods showed themselves as being more precisely accurate when approximating lower 𝑃𝐹 with lower samples, although those were the methods that demanded more computational efforts and time.