Simulation Methods For Structural Reliability And Probability Failure Analysis

Subset simulation and line sampling are two kinds of efficient simulation methods that are used for reliability analysis. The basic idea of subset simulation is to express the small failure probability as a product of a series of large conditional failure probabilities by introducing intermediate events. These large conditional failure probabilities can be estimated efficiently by Markov chain Monte Carlo (MCMC) techniques and consequently the efficiency of reliability analysis will be improved. The efficiency of subset simulation comes from the efficiency of MCMC when MCMC is adopted to simulate the conditional distribution. Line sampling, which computes the failure probability by one-dimensional interpolating along the important direction of the performance function and randomly sampling along the rest directions, can reduce the computational cost required and depends on the importance direction. At present, MCMC is frequently used to carry out pre-sampling process in the failure region and to search the design point and get the importance direction accordingly.Metropolis-Hastings (M-H) algorithm is one of the most commonly used methods among numerous MCMC techniques. Multiple-Try Metropolis (MTM), which is a generalized version of M-H algorithm, can populate the probability space sufficiently better and sample from a probability distribution more efficiently when compared with M-H. By incorporating MTM with subset simulation and line sampling, respectively, it is expected to improve the efficiency of the two simulation methods by means of improving the efficiency of MCMC sampler. Necessary theoretical derivation and several numerical examples are presented to evaluate the feasibility of the proposed scheme. Simulation results show that MTM can obtain the same convergence rate with M-H, and that both of MTM and M-H outperform the direct MC method significantly, demonstrating that MTM can be applied as an alternative of M-H.Structural probabilistic failure analysis based on importance sampling Markov chain simulation, i.e. utilizing the samples from those already obtained in importance sampling during reliability analysis, is discussed at the last chapter. Information such as the weak part and the most vulnerable component revealed by probabilistic failure analyzing, can be explored to guide the structural design. The proposed strategy, which just makes use of information given by importance sampling and requires very little computational effort, can reveal valuable information about structures and thus has a high performance price ratio.