Reliability analysis with cross-entropy based adaptive Markov chain importance sampling and control variates

In reliability analysis, high dimensional problems pose challenges to many existing sampling methods. Cross-entropy based Gaussian mixture importance sampling has recently gained attention. However, it only performs well in problems with low to moderate dimensionality. Several efforts have been made to improve this method. This paper, suggests a method of improving the performance of cross-entropy based Gaussian mixture importance sampling, and compares its performance with the recent advancements. To enhance the efficiency for high dimensional problems, the paper proposes to employ Markov Chain Monte Carlo (MCMC) sampling. In this new approach, Markov chain samples gradually populate the failure domain in accordance with an optimal density function. In this process, a seed generation scheme ensures that the Markov chain truly covers the whole failure domain. Then, the parameters of the Gaussian mixture model are derived by modified closed-form formulas. The incorporation of MCMC and modification of the parameter updating rule make the method more robust against the dimensionality. Also, a control variates scheme further improves the performance. The performance of the proposed approach is compared with recently developed importance sampling algorithms. The results support the efficiency, robustness and accuracy of the proposed method.