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Abstract

In this paper, Monte Carlo simulation algorithms that utilize selective sampling schemes combined with variance reduction techniques for structural reliability assessment are introduced. The results of the proposed algorithms are compared to the results of methods without selective sampling schemes. The selective sampling method considered herein is Latin hypercube sampling (LHS). The method provides a constrained sampling scheme instead of random sampling according to the direct Monte Carlo method. Based on the examples presented in this paper, Latin hypercube sampling results in stabilizing the estimation process of the probability of failure. This result is manifested in the regions of small numbers of simulation cycles, because the generated values for the random variables according to LHS cover more adequately their ranges than the ones generated by a random sampling process. In addition, the generated random values according to LHS are affected to a lesser extent by the choice of the seed in the random number generator for small numbers of simulation cycle, than in the case of random sampling. Latin hypercube sampling does not provide any reduction in the variance of the estimated probability of failure. In order to obtain the most accurate estimate of the probability of failure using conditional expectation variance reduction techniques with LHS, conditioning should be performed on the variables with the least variabilities.