Subset simulation with adaptable intermediate failure probability for robust reliability analysis: an unsupervised learning-based approach

Subset simulation (SS) was known for its computational efficiency in estimating small failure probabilities as well as reducing emulation demands. The main idea behind SS lies in decomposing the original reliability problem into sub-reliability problems with more frequent probabilities. By taking advantage of Markov Chain Monte Carlo-based sampling technique (MCMC), this innovative strategy enables the computational feasibility for estimating small failure probability based on the prescribed number of simulations. However, SS still has several limitations that can potentially decrease its computational efficiency. It is mainly attributed to the fact that the estimated failure probability can be inconsistent due to insufficient samples in each subset. Moreover, SS requires empirical definition for MCMC proposal sampling to guarantee a good acceptance rate. However, the inherent shortcoming of MCMC brings the correlations among the samples in each subset, which can inevitably cause the biased estimate for failure probability. To address these limitations, a new method, called ULSS, that combines SS, importance sampling (IS), and DBSCAN algorithm is proposed to overcome these limitations. Specifically, the batch size of samples in each subset is adaptively increased until the prescribed threshold is satisfied, which facilitates the adjustment of intermediate failure probabilities. To enable the process of adaptive sampling, MCMC is substituted with IS to draw samples located in the effective sampling regions defined through DBSCAN. Computational performance of ULSS is demonstrated by investigating three examples with one for illustrative interpretation and the other two for engineered paradigm. Results indicate the computational consistency, unbias, and robustness of ULSS in terms of the statistical properties of the estimated failure probability.

Automated summary

Subset simulation (SS) is a computationally efficient method for estimating small failure probabilities and reducing emulation demands. ULSS is a new method that combines SS, importance sampling (IS), and DBSCAN algorithm to overcome the limitations of SS.