Department of Mechanical & Electrical Engineering, Changsha University, Changsha, Hunan, China.

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Abstract—In the practical engineering, to answer the small failure probabilities with correlated high- dimensional variables, the subset simulation (SS) is combined together with the Monte Carlo simulation and importance sampling (IS) method. The samples from the probability density functions of the importance sampling are used to construct the intermediate failure events, by which the small failure probabilities are turned into a hybrid Markov chain, which is a continuous product made of a series large failure probability or conditional failure probability that is easily answered, on which the structural reliability sensitivity can be efficiently simulated by directly obtaining the samples with correlated ones. Finally, the 3 planetary carriers of 3-stages planetary gear reducer in the earth-pressure-balance shield machine are as illustrative examples to check the algorithm above, the results show that the SS of the IS with correlated variables can highly simulate failure probability and its sensitivity.

Index Terms—Hybrid markov chain, reliability, reliability sensitivity, subset simulation, importance sampling, correlated variables.

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Cite: Ganqing Zhang, Yanghui Xiang, Lei Guo, Huixin Guo, Yonghong Nie, "Structural Reliability and Its Sensitivity Analysis by Hybrid Markov Chain with Correlated Variables," Journal of Software vol. 11, no. 5, pp. 481-493, 2016.