Benchmark of Structural Reliability Analysis Methods of Non-linear Structures

The present contribution presents a benchmark of a selection of techniques for assessing structural reliability for non-linear dynamical systems. The benchmark is conducted for an uncertain structural system with two localized nonlinearities, i) due to the friction between two structural elements and ii) due to the presence of a vibration control system. The reliability analysis techniques selected are divided into two groups. The first group of techniques are Monte Carlo Simulation based methods, namely, Crude Monte Carlo Simulation, the Monte Carlo Simulation Extrapolation Technique and Sub-set Simulation. The second group is composed of a surrogate method suitable for dynamical non-linear systems called the Probability Density Evolution Method. The efficiency of each reliability technique is assessed for different excitation models; deterministic, random non-Gaussian and random non-stationary; aiming to assess the applicability of the techniques for each type of excitation. Additionally, different levels of uncertainty associated with the parameters defining the dynamical system are considered; aiming to analyse the effect of this on the efficiency and applicability of each reliability analysis technique.