Subset simulation method including fitness-based seed selection for reliability analysis

Probability estimation of rare events is a challenging task in the reliability theory. Subset simulation (SS) is a robust simulation technique that transforms a rare event into a sequence of multiple intermediate failure events with large probabilities and efficiently approximates the mentioned probability. Proper handling of a reliability problem by this method requires employing a suitable sampling approach to transmit samples toward the failure set. Markov Chain Monte Carlo (MCMC) is a suitable sampling approach that solves the SS transition phase using the failed sample of each simulation level as the seed of next samples. This paper is aimed to study the seed selection effect on the SS accuracy through several seed selection approaches inspired by the genetic algorithm and particle filter and using the main PDF of the variables to assign a mass function probability to each subset sample in the failure domain. Roulette wheel (I, II), tournament and proportional probability techniques are then employed to choose the weighed samples as seeds to be placed in the MCMC to transmit the samples. To examine the capability of each approach, reliabilities of some engineering problems were investigated and results showed that the proposed approaches could find proper failure sets better than the original SS method, especially in problems with several failure domains.