In this paper the problem of calculating the failure probability of general nonlinear systems subject to random vibrations is considered. The proposed methodology is based on dividing the failure domain into a number of subregions. Each subregion is the intersection of a spherical ring and the failure domain and its probability is calculated with the help of a relatively small number of samples generated according to the conditional distributions of various subregions using a Markov Chain Monte Carlo (MCMC) slice-sampling-based algorithm proposed by the authors. This algorithm overcomes difficulties in choosing an appropriate proposal sampling density encountered by other popular MCMC algorithms, such as the Metropolis-Hastings algorithm. The method is found to be significantly more efficient than Monte Carlo simulations (MCS), especially for small failure probabilities. The robustness and efficiency of the method is demonstrated with a numerical example involving 3000 random variables.
展开▼
