Reliability Analysis Based on Efficient Simulation
In the practical engineering, to solve the small failure probabilities with correlated high-dimensional variables, the subset simulation (SS) is combined together with the Monte Carlo and importance sampling (IS) method. The samples from the probability density functions (PDF) of the importance sampling are used to construct the intermediate failure events, by which the small failure probabilities are turned into a Markov chain (MC), which is a continuous product made of a series large failure probability or conditional failure probability (CFP) which is easily answered, on which the structural reliability can be efficiently simulated by directly obtaining the samples with correlated ones. Finally, the 3 planet carriers of 3 grade planetary reducers in shield tunneling machine(STM) are as examples to check the algorithm above, the results show that the SS of the IS with correlated variables can highly simulate failure probability.
Hun Guo, Taiyong Wang, Zeyu Weng, Weidong Jin, Shaoze Yan, Xuda Qin, Guofeng Wang, Qingjian Liu and Zijing Wang
X. S. Gong and G. Q. Zhang, "Reliability Analysis Based on Efficient Simulation", Applied Mechanics and Materials, Vol. 141, pp. 594-600, 2012