Structural Reliability Sensitivity Analysis of Rare Events by Parallel Adaptive Bayesian Probabilistic Integration

Efficient estimation of small failure probabilities and their sensitivities to distribution parameters of input random variables is critical for decision making on engineered components or systems. Bayesian active learning reliability methods have gained considerable attention and exhibited more attractive features than most existing active learning algorithms; however, they focus exclusively on reliability analysis and neglect sensitivity. To address this problem, this study proposes a new method, termed parallel adaptive Bayesian probabilistic integration, for efficient reliability sensitivity analysis of rare failure events. The posterior reliability sensitivity is first defined based on the partial derivative of the posterior mean of failure probability with respect to the distribution parameters of random variables. The sequential variance-amplified importance sampling technique is then extended to estimate the posterior statistics of failure probability and the posterior reliability sensitivity. Later, a modified pseudo posterior variance contribution learning function is developed by considering the correlation between the candidate points and the existing observations. Finally, a parallel sampling strategy is designed to support parallel computing through combining the adaptive determination strategy of the sampling region and learning function-weighted K-means clustering algorithm. Numerical results demonstrate that the proposed method is able to accurately estimate small failure probabilities and their sensitivities with superior efficiency over several existing reliability sensitivity algorithms.