子集模拟中马尔可夫链蒙特卡罗采样算法的比较

The sampling efficiency and accuracy for the Markov Chain Monte Carlo ( MCMC ) methods in the subset simulation are evaluated in this work. The principles of the subset simulation for structural reliability and different MCMC algorithms of generating samples in the intermediate state are elaborated. Based on the construction of a steady-state Markov chain, a modified Metropolis-Hasting ( MMH ) with delayed rejection ( MMHDH) is proposed, in which the step of delayed rejection for the candidate sample is added over the current MMH to improve the sampling efficiency. The differences in the proposed flistrihution for MCMC methods based on random walk and diffusion equation are illustrated. Especially, the preconditioned Crank-Nicolson (pCN) algorithm and the conditional sampling (CS) algorithm with acceptance rates of candidate samples equal to 1 have been proved to be equivalent in the standard normal space. In addition，the method of evaluating the effective sample size is deduced，and the sampling efficiency is defined as the ratio of effective sample size to total sample size. Subsequently, to evaluate the influences of the proposed flistrihution and its parameters on the acceptance rate of candidate samples and the sampling efficiency, the samples are generated by the different algorithms and compared with the target distribution. The relative errors and variabilities for the failure probability calculated by different MCMC algorithms are studied to reveal the influences of sampling algorithms on the computing accuracy. The results indicate that the acceptance rate and the autocorrelation of candidate samples are influenced significantly by the proposed distribution and its parameters. For the complicated target distributions, the sampling efficiencies of the pCN and the CS algorithms are comparatively higher, and that of the MMHDR comes second. By using the CS algorithm and the MMHDR in the subset simulation, the higher accuracy and the lower variability for failure probabilities can he obtained. Also, the computing accuracy and the variability for failure probability ran be improved with the increase in the sample size of intermediate states.