Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

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Geometric insight into the challenges of solving high-dimensional reliability problems (2008, methodology): “Spherical subset simulation method (S3) A new MCMC algorithm was proposed by Katafygiotis and Cheung [5].”
Reliability-based optimization of stochastic systems using line search (2009, background): “On the other hand, several tools for assessing structural reliability have lately experienced a substantial development providing solution to a number of complex problems [5,7,19–21,23,31,38].”
MCMC algorithms for Subset Simulation (2015, methodology): “…of random variables, a number of advanced simulation methods have been developed, including Subset Simulation (Au & Beck 2001), Spherical Subset Simulation (Katafygiotis & Cheung 2007), Line Sampling (Hohenbichler & Rackwitz 1988, Koutsourelakis et al. 2004) and Asymptotic Sampling (Bucher 2009).”
Uncertainty analysis of complex structural systems (2009, methodology): “The auxiliary domain method, proposed in [46, 47], can be used for cases where the failure domain can be covered approximately by an associated linear system.”