This paper reviews methods and strategies that have been developed recently for reliability analysis of complex and realistic structural systems using advanced non-linear Finite Element methods. The focus is on adaptive response surface techniques able to provide high quality local approximations in the region of the random variable space that contributes most to the probability of failure. In particular, polynomial regression models, artificial neural networks, Kriging models (or Gaussian process models) with adaptive capabilities, and their applications to the reliability analysis of ship structures and subsea pipelines are reviewed. The paper also addresses the role of the structural reliability methods to assess the safety levels of damaged ships and to code calibration, particularly to derive the target safety levels of the ship hull girder. The review presented in the paper is mainly focused on the contribution of the authors to the developments in this subject area.

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